On the meaning of Einsteins Relativity  Scientific review of and philosophical reflection  by Peter Kos 2014  Article review
This document contains article review "On the meaning of Einsteins Relativity  Scientific review of and philosophical reflection" by Peter Kos written in 2014
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Contents
Reflection
Abstract

These views misled him into an incorrect method and unrealistic theory with circular deﬁnitions, inconsistencies in the explanations and principles that contradict those developed from the empirical evidence.

The concept incorrect method and circular deﬁnitions are not discussed in the article



In particular, this study found that neither Einstein nor Poincare´ expressed sufﬁciently the “inertial frames of reference” (coordinate systems) in their respective relativity principles.


They expressed them in terms of the uniform movement of translation instead of absence of external forces.


Because of that they both overlooked that ﬁelds generated in one frame of reference cause forces at a distance in the other frames of reference turning them into noninertial ones.

This sentence is not clear. My understanding is objects (masses) influence other objects by means of forces, which can be described by means of fields. This is physics and has nothing to do with reference frames.






I. INTRODUCTION



“The chief attraction of the theory lies in its logical completeness.

IMO this should be physical completeness. All what can be demonstrated by experiments.






If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible.

To demonstrate that something is also requires experiments.
In the case of Newton, he was 'wrong' that the force of gravity acts instantaneous. Does that mean that all his conclusions are wrong? To call the conclusions not accurate is better.

Let no one suppose, however, that the mighty work of Newton can really be superseded by this or any other theory.
His great and lucid ideas will retain their unique significance for all time as the foundation of our whole modern conceptual structure in the sphere of natural philosophy."


Albert Einstein, “What Is the Theory of Relativity”


In his 1904 address to the Congress of Arts and Science, Henry Poincaré assessed the state of the mathematical physics and declared the second crises of this field.
He pointed out that the principles on which the physical theories are established are not always applicable.
Among others, he showed that the principle of relativity of classical physics is,not applicable in case of light and electromagnetism and that Lorentz’s attempt to preserve it with his transformation equations was possible only by “accumulating hypotheses."

More detailed information is required.

A year later, Albert Einstein published his article “On the Electrodynamics of Moving Bodies” that provided a new theory (later named the theory of special relativity) which is based on the principle of relativity and united classical mechanics with light and electromagnetism.

From a physical point of view mechanical processes and electric/magnetic processes (including light) are very different

Einstein’s theory is accepted as having initiated a conceptual revolution in theoretical physics in the 20th century.
It has been incorporated into other theories and has had a major impact on physics, astrophysics and cosmology.
It revolutionized our understanding of the physical world, changed fundamental concepts of space, time, light and energy and
altered our understanding of the kinematics and dynamics of physical systems.
It also required a change in the meaning of causality and determinism, two basic concepts on which the physical sciences are based.

The concepts causality and determinism require a clear definition of its physical meaning. What is and what is not.



The significance and impact of Einstein’s theory of special relativity is comparable only to that of the Copernican heliocentric system and Darwin’s evolution of species.

All these three fields of study are very difficult to compare.

Nevertheless, when Stephen Hawking assessed today’s state of theoretical physics in his 2002 lecture, “Gödel and the End of Physics,” he declared “The
theories we have so far are both inconsistent and incomplete."

For an article review select:
Article_Review_godelandtheendofphysics.htm



This raises a question: Was Einstein’s approach to developing his theory and his attempt to unite the classical physics with light and electromagnetism correct?
In spite of its widespread acceptance, Einstein’s theory introduced a number of new ideas that are counterintuitive with respect to our terrestrial experiences and Newtonian physics.
These new ideas required sweeping changes in the basic concepts and principles by which we understand Nature.
These changes stimulated not only physicists but also philosophers to subject Einstein’s theory to much greater philosophical scrutiny than any other scientific theory using only accepted ontological concepts.
Its ultimate acceptability became, in fact, an important concern for both physicists and philosophers.
Some influential philosopherssuch as Bertrand Russell and the founders of logical positivism were greatly impressed and influenced by it, making it an important paradigm for their philosophy of science, but others, such as Jules Henri Poincaré, Ernst Mach, Harald Nordenson, Henri Bergson, Aloys Wenzl, Alfred N. Whitehead, and Hilary Putnam, had trouble uniting parts of the theory with concepts and beliefs about Nature that they were unwilling to abandon.


At the center of the controversy between these two groups were the two main key ideas on which this theory is based: The invariance of the velocity of light (the second postulate) and the relativity of simultaneity.

Two of the most important physical concepts are gravity and the speed of gravity, which are important to study the behaviour of the objects in universe. This concept is much more important that the speed of light i.e. electromagnetic radiation.

Both ideas still baffle many people today.
The biggest problem attributed to the theory concerns the second postulate the invariance of velocity of light, which is not only counterintuitive with respect to our everyday experience, but has never been verified by direct measurement.
Although experiments which would verify this postulate have been for a long time within our technological capabilities, they have never actually been carried out.
Instead, proponents of the theory have tried to provide indirect proofs by measuring certain effects predicted by it or by the theory of general relativity.

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The effects predicted by Einstein’s theory of special relativity and by the theory of general relativity, which can be measured in our terrestrial conditions, are extremely small.
Review of some of these tests or measurements showed that these effects can be also explained by other than relativistic phenomena, by inadequate control over the measured phenomenon, by alternate theories, or by the fact that experiments were done in noninertial frames of reference.

The first step is to describe experiments and the results as detailed as possible. The second step is to understand the results. The third step is to compare the results with special theory of relativity.

There have been also reports of experiments that purportedly disprove the validity of Einstein’s theory.
Thus, there have not only been strong proponents of the theory, who accept the invariance of the light velocity and believe in it regardless of the fact that it has never been verified by an experiment but, also skeptics who disputed it.
With that, Einstein’s theory of special relativity became the most contested and challenged theory of modern theoretical physics.
The twentieth century brought tremendous progress, not only in physics but in other scientific and technological fields; the scope of which does not have a counterpart in the whole human history; and with that, our scientific and philosophical views of Nature are much broader and better defined than at Einstein’s times.
This gives us an opportunity to review in depth the concepts and principles on which Einstein’s relativity was based from today’s scientific and modern realistic philosophical perspective, and find out what philosophers and physicists of the past have missed or whether inconsistencies, contradictions and questions noted
in the past could be understood and explained today.
The author conducted an extensive philosophical and scientific review of Einstein’s writings not only to understand Einstein’s theory of special relativity and its meaning in light of today’s knowledge but also to uncover Einstein’s philosophical views and the thought processes which led to his relativity of simultaneity, two postulates and to theory of special relativity.
Although in the past, much work has been done to test the predictions implied by this theory, this review concentrated on its conceptual foundations: on the two postulates (principle of relativity and the invariance of velocity of light), the relativity of simultaneity and theory’s overall logical structure.
The purpose of this publication is to present only the most important findings. The full text with all details, findings, and full citation of quotes from Einstein’s writings will be published separately as a book.
Because one cannot fully separate science from philosophy and philosophy from science, especially when dealing with theory that required changes of the basic philosophical concepts of Nature, the scientific and philosophical findings are presented together as necessary for the purpose of explanation of different aspects of this theory.

Okay
II. THE PURPOSE OF THE THEORY OF SPECIAL RELATIVITY AND DEVELOPMENT OF ITS CONCEPTS

What were the problems or unanswered questions in physics which Einstein faced and wanted to solve? What was the purpose or intent of Einstein’s work? How was this theory developed? How did Einstein discover his postulates?

Interesting questions.
A. Three problems or questions in physics at the turn of the 20th century
1. The first one—Why the Michelson–Morley experiments failed to prove the existence of the luminiferous ether?

In the history of physics, there have been two hypotheses describing the nature of light: The emission theory, which assumes light to be a stream of emitted particles, and the
wave theory, in which light is imagined as propagation of waves through a luminiferous ether.

Both these hypotheses must be based on experiments. What I assume that these hypotheses are used to explain these experiments. The question is what are these experiments or observations.



Some properties of light, such as reflection and refraction, can be explained by either hypotheses, yet interference and diffraction were, at that time, easier to explain by the wave concept, and thus since the early 1800s, the wave concept of light became firmly established in physics.

This explains more or less the above question.
My understanding to demonstrate interference you need at least monochromatic light, which is light of the same frequency.
But that is not all, I also expect that many photons are involved to demonstrate interference. It is like demonstrating interference patterns using water; you need a large quantity of water.



After James Clerk Maxwellis to developed his theory of electromagnetism and showed that the equations of electricity and magnetism have solutions that consist of traveling waves whose velocity turned out to be close to that of velocity of light, light was considered the electromagnetic phenomenon.

That means you need an experiment to test the propagation speed of these waves is the same the speed of "photons"

When Heinrich Hertz demonstrated the existence of electromagnetic waves, Maxwell’s theory and his unification of the optical phenomena with the electromagnetism became widely accepted.

Okay

Different theories were then proposed to describe the mutual influence of matter and ether, and different experiments were conducted
to detect ether.

Why this path?

In 1892 Hendrik Lorentz proposed his theory, based on assumption of completely motionless ether which is not dragged by matter, which implies that velocity of propagation of light and electromagnetic phenomena is independent of its source.

The question is how this conclusion is reached. The standard practice should be to perform an experiment, in order to demonstrate, that the speed of light is independent of its source.
A different issue is what is the ether. To assume that the universe is not empty and is filled with something that cannot be observed is not by definition wrong. The universe is also filled with a gravitational field. In this context, concept vacuum requires a clear definition.

This Maxwell–Lorentz theory was the theory of physics when Einstein entered the field.
Einstein was a great admirer of Lorentz and believer of the Maxwell–Lorentz theory. Thus, his beliefs in the wave based optical and electromagnetic phenomena and in the independence of velocity of light from the motion of the source of light were not subject to questioning or doubt. Yet, attempts to detect the ether by various physicists culminated in Michelson’s and later by Michelson–Morley experiments, which failed to prove its existence, causing a great problem in theoretical physics. How to explain the failure to detect the luminiferous ether? Why these experiments are not consistent with the wavebased concept of light and electromagnetism?

Light is a state of the universe, a form of energyparticles which are emitted, for example, by the Sun. When these particles reach our eyes whe can see the source. This means when we look in the direction of the Sun, we can see the Sun. This implies that the universe is filled with these energyparticles.
We can also observe light in different colours. This underscores the hypothesis that the energyfrequency of the emitted energyparticles can be different.




2. The second one—Why the Maxwell–Lorentz equations are not invariant?

Besides this empirical problem with ether, Lorentz and Joseph Larmor realized that Maxwell–Lorentz’s equations were not invariant.

This requires more information to explain why the equations should be invariant.



That they do not have the same form when transferred from one inertial coordinate system into another; that they are not consistent with the Galilean relativity of mechanics.

Why do we need different inertial coordinate systems, to explain the physical reality?

In 1895, Lorentz attempted to explain the null results of Michelson’s experiments and to make his theory invariant by proposing that bodies moving through ether contract in the direction of motion.

This implies that a box with is square at rest becomes nonsquare when it moves through space.

George FitzGerald independently arrived at the same idea.
To achieve the invariance, they had to introduce a new time variable, which Lorentz called “local time,” which differed from the time of
the coordinate system associated with the ether.

This coordinate system associated with the ether is assumed to be at rest?
Difficult line of reasoning. The time on a clock using light lightsignals, decreases because the light path increases. Such a clock ticks slower.
It should be mentioned that the time on a clock is different than the time related to the age of the Universe.
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He used this term without giving any interpretation of its physical relevance.
Thus the second question was how to understand why the Maxwell–Lorentz equations are not invariant.

3. The third one—Why the principles and theories of physics are not always exact or applicable

At the turn of the 20th century, the empirical approach to science was well established, yet some of the principles were not always exact or applicable, causing a concern or
what Jules Henri Poincaré, one of the leading physicists and philosophers of science of that time, called “crises of mathematical physics”.
Among others, he showed that the principle of relativity is not applicable in case of light and electromagnetism and that Lorentz’s attempt to preserve it with his transformation equations was possible only by “accumulating hypotheses.”
While Lorentz and FitzGerald tried to make the Maxwell–Lorentz equations invariant by introducing new hypothesis, Einstein tried to make them
invariant with his new approach to science by introducing his two postulates and deriving his theory from them.

B. Genesis of the main concepts of the theory
of special relativity

Einstein started his original 1905 paper with a brief discussion of electromagnetic phenomena and then stated:
“Examples of similar kind, and the failure of attempts to detect a motion of the earth relative to the “light medium,” lead to the conjecture that notonly in mechanics, but in electrodynamics as well, the phenomena do not have any properties corresponding to the concept of absolute rest, but that in all coordinate systems in which the mechanical equations are valid, also the same electrodynamic and optical laws are valid, as has already been shown for quantities of the first order.
We shall raise this conjecture (whose content will be called “the principle of relativity” hereafter) to the status of a postulate and shall introduce, in addition, the postulate, only seemingly incompatible with the former one, that in empty space light is always propagated with a definite velocity V which is independent of the state of motion of the emitting body.
These two postulates suffice for arriving at a simple and consistent electrodynamics of moving bodies on the basis of Maxwell’s theory for bodies at rest.
The introduction of a “light ether” will prove superfluous, inasmuch as in accordance with the concept to be developed here, no “space at absolute rest” endowed with special properties will be introduced, nor will a velocity vector be assigned to a point of empty space at which electromagnetic processes are taking place.”


Neither this Einstein’s original 1905 paper nor typical textbooks or writings of others present more detail justification of his “conjecture” of the principle of relativity or the genesis of the concept of relativity of simultaneity and the second postulate , the three pillars of this theory.


The original paper presents only a brief discussion of a method and a definition of synchronization of clocks and its application that shows the relativity of simultaneity.


It does not provide a sufficiently detailed discussion of this method and its consequences, how Einstein got to it and why it is a good way to synchronize clocks, judge simultaneity and define time.


Similarly, the two postulates are only briefly introduced in the original paper without any detailed discussion and justification.
In the subsequent publications, Einstein clarified his concepts, and therefore these five references served as a starting point for the following detailed analysis.

1. Einstein’s approach to science



In his “Autobiographical Notes,” Einstein, at the age of 67, gave his recollection of the very beginnings of the theory of special relativity.
Here Einstein showed that after reviewing Planck’s work, he came to the realization “that neither mechanics nor thermodynamics could (except in limiting cases) claim exact validity."
He realized that our theories of physical processes are not always exactly valid and that caused desperation and loss of hope in the empirical approach and so he looked for a different one.
He “despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts” or empirical evidence and came to conviction that “only discovery of a universal formal principle could lead us to assured results."

My understanding is that the postulates 1 and 2 are Einstein's defintion of this 'universal formal principle' leading to the assured results.
2. First postulate



The intent or main purpose of this theory was to establish such a “universal formal principle” and Einstein’s first postulate (the principle of relativity) served that purpose.
This principle which expresses that “not only in mechanics, but in electrodynamics as well, the phenomena do not have any properties corresponding to the concept of absolute rest,
but that in all coordinate systems in which the mechanical equations are valid, also the same electrodynamic and optical laws are valid,” extends the Galilean relativity principle to include electrodynamic and optical phenomena.

How do you know that the mechanical equations are valid. This implies that they are not valid in all coordinate systems. I expect that in the following text this distinction will be explained.
3. The second postulate



Einstein believed that Maxwell–Lorentz equations of electrodynamics are correct, that they “revealed the true reality."
His second postulate, the invariance of light velocity, was deduced from presumed validity of the first postulate and Maxwell–Lorentz equations as he told us in his Kyoto address. Or the invariance of velocity of light is the requirement of the first postulate and the Maxwell–Lorentz equations.
The results of the Michelson–Morley experiments most likely also supported his intuition of the second postulate.

Also here a discussion about the MichelsonMorley is appropiate.
4. New problem which Einstein faced



The application of the new principle of relativity with the Maxwell–Lorentz equations resulted in the requirement of invariance of the light velocity (second postulate), and it would lead to the invariance of the Maxwell–Lorentz equations.

The problem is that the definition to claim that the speed of light is constant is physical difficult to accept. One problem is that in order to experimental verify this claim, the coordinate system used should be fixed in space.
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Thus, it would resolve one of the dilemmas that physicists faced at the beginning of the 20th century.
Unfortunately, “this invariance of light velocity conflicted with the law of the additivity of velocity well known in mechanics.

In general you cannot add velocities, because velocities requires a clocks, which all should be synchronised in one coordinate system.

Why on earth did these two contradict each other?” Einstein felt “I had come up against a serious difficulty.”
Thus, there was a new dilemma which Einstein faced, after establishing his two postulates.
The dilemma how to reconcile the invariance of light velocity, the second postulate, with the “law of the additivity of velocity,” with the Galilean transformation equations.
Then in his Kyoto address, Einstein mentioned a visit to a friend, telling him: “I have a problem that I cannot solve for the life of me.
Today, I’ve brought with me the battle to you.
I discussed various things with him.
Thereby, I felt inspired and was able to reach the enlightenment.
The next day, I visited him and said to him. Thanks a lot, I have completely interpreted my problem now."

5. The insight, the eureka intuition of this theory—Relativity of simultaneity





The insight or the Eureka intuition of this theory was Einstein’s realization that “time could not be defined absolutely, but is in an inseparable relationship with the signal
velocity."
“By means of revision of the concept of simultaneity in a shapeable form,”6
Einstein told us in this Ref. 6
that he thought that he resolved this problem, that his theory of special relativity reconciled the invariance of light velocity (second postulate) with the Galilean transformation equations, because it provides not only a more general principle of relativity than the Galilean relativity principle, but also a
more general transformation equations than the Galilean
ones.

6. Elimination of ether





The failure to detect luminiferous ether led Einstein to eliminating it and giving the physical properties of transmitting waves to space, to space which does not have any other
mechanical properties.
We can see that Einstein’s response to the problems in physics at the turn of the 20th century was different from the other physicists who tried to save the wavebased theory of
light and electromagnetism.
Einstein eliminated ether from his mind and gave the physical properties of transmitting waves to space.
Then he used his new approach to science by establishing a “universal formal principle” (first postulate)
and from that and Maxwell–Lorentz equations, attempted to
unite the optics and electromagnetism together with classical
mechanics and put the whole physics on a new basis.

III. THE FIRST POSTULATE—THE PRINCIPLE OF SPECIAL RELATIVITY AND EINSTEIN’S ONTOLOGICAL VIEWS
A. Einstein’s principle of special relativity





In his original paper, Einstein expresses his first postulate as follows:
“The laws governing the changes of the state of any physical system do not depend on which one of two coordinate systems in uniform translational motion relative to each other these changes of the state are referred to."

The use of the word "governing" is wrong. The subject is the evolution of physical processes. These processes can be studied from two different coordinate systems. My understanding is that the evolution is independent of these coordinate systems.

or in another translation:
“The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.”
It is important to notice that both of these translations
indicate also the meaning of the term “the laws” or “the laws
of Nature,” meaning which Einstein had in his mind.
“The
laws governing the change of the physical systems,” or “the
laws by which the states of physical systems undergo
change” are responsible for or govern changes of the physical systems.
If you check the German original, you will see
that the translation referenced10 is closer to the German original.
For our understanding of Einstein’s theory, it is important to know what Einstein understood by these terms.
It is
also important to notice that this postulate does not mention
“inertial” coordinate systems.
It refers to two coordinate systems in “uniform translational motion."

B. Einstein’s ontological views





Let us now go to Einstein’s understanding of the “laws of Nature."
In his numerous writings, letters and interviews, Einstein left many statements in which he expressed his scientific, philosophical, religious and spiritual views.
An extended search for his views is given in the Walter Isaacson’s book “Einstein, His Life and Universe."
The most revealing quotations from this book pertinent to understanding the meaning of Einstein’s first postulate and his view of
laws of Nature are as follows:

It should be mentioned that "Einstein’s first postulate" and the "laws of Nature" are two different subjects.

“We see the universe marvelously arranged and obeying certain laws but only dimly understand these laws.

The concepts "obeying certain laws" and "only dimly understand these laws." are in conflict with each other.

“My religiosity consists of a humble admiration of the infinitely superior spirit that reveals itself in the little that we can comprehend about the knowable world.
That deeply emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God."
“I believe in Spinoza’s God, who reveals himself in the lawful harmony of all that exists, but not in a God who concerns himself with the fate and the doings of mankind."
“What separates me from most socalled atheists is a feeling of utter humility toward the unattainable secrets of the harmony of the cosmos."

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“‘Do you believe,’ Einstein was once asked, ‘that humans are free agents?’ ‘No, I am a determinist,’ he replied. ‘Everything is determined, the beginning as well as the end, by forces over which we have no control .It is determined for the insect as well as for the star.
Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible player.’”

The information contents (or value) of this discussion is zero. The information contents of the periodic table, showing all the different chemical experiments is very high.

“‘Human beings in their thinking, feeling and acting are not free but are as causally bound as the stars in their motions,’ Einstein declared in a statement to a Spinoza Society in 1932."
“Scientific research is based on the idea that everything that takes place is determined by laws of nature, and this holds for the actions of people."

Scientific research is used to describe all processes in more detail. The more detail is known the beter we can predict the future.
Scientific research is partly based to study identical or almost identical processes. For example the behaviour of stars (the influence between stars) can be described by Newton's Law. Newton's Law does not govern the behaviour of stars.

“Scientists aim to uncover the immutable laws that govern reality, and in doing so they must reject the notion that divine will, or for that matter human will, plays a role that would violate this cosmic causality."

laws don't govern the reality. The evolution of every process, the reaction between, has nothing to do with any law.

“The cosmic religious feeling is the strongest and noblest motive for scientific research."

Religion has nothing to do with scientific research i.e. the endavour by humans to understand the reality in more detail.

From these quotes, as well as from other Einstein’s writing, we can conclude that he believed:
1. In “the presence of a superior reasoning power, which is
revealed in the incomprehensible universe."
2. “In the lawful harmony of all that exists.”
3. In causal determinism where “Everything is
determined…we all dance to a mysterious tune, intoned
in the distance by an invisible player.”
4. That the scientific aim is to “uncover the immutable
laws that govern reality.”
The repetition of the “laws or laws of Nature,” with the
meaning that the laws govern reality in Einstein’s writings is
an indisputable fact.

C. Poincaré’s relativity principle





Einstein was not the first physicist who proposed the
relativity principle.
Poincaré used the term “principle of relativity” in 1902 in his “Science and Hypothesis,”12 which
Einstein presumably studied, and formulated it in his address
to the International Congress of Arts and Science at St. Louis
in 1904,2 as follows:
“The principle of relativity, according to which the laws of physical phenomena should be the same,
whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not and could not have any means of discerning whether or not we are carried along in such a motion."
This principle is today considered to be the same as the Einstein’s principle of relativity.
Today’s scientists do not go back to the original papers to learn the true meaning in the authors’ minds and thus misrepresent the old ideas.
We need to go back to this address and see in which context Poincaré defined his relativity principle.
From reading this address, it is clear that the law of
physical phenomena defined by Poincaré has different meaning than the one presented by Einstein.
In this address, Poincaré is discussing the development of “mathematical
physics” (theoretical physics) and showed the difference
between the 18th century science “how the ancients understood law,” and the 19th century phenomenological
approach.
Poincaré wrote:
“I will explain myself; how did the ancients
understand law? It was for them an internal
harmony, static, so to say, and immutable; or it
was like a model that nature constrained herself to
imitate.
A law for us is not that at all; it is a
constant relation between the phenomenon of today and that of tomorrow; in a word, it is a differential equation.
Further, he wrote:
“These principles are results of experiments boldly
generalized; but they seem to derive from their
generality itself an eminent degree of certitude."
And later:
“So we have been led to regard them as
experimental verities”
It is without any doubt that for Poincaré, the “laws of
physical phenomena” was an expression of empirical experience “experimental verities” similarly to the Galilean relativity.
Thus Poincaré’s principle of relativity is a true extension
of the Galilean invariance principle of mechanics to all physical phenomena, while Einstein’s principle of relativity was
“how the ancients understood the law,” “It was like a model
that nature constrained herself to imitate."
Einstein most
likely did not get a chance to read Poincaré’s address, presented to the International Congress of Arts and Sciences at
St. Louis, and thus did not realize the difference in their
understanding of the “laws of Nature."
It is interesting to notice that Poincaré’s expression of
relativity principle also does not mention “inertial” frames of
reference or coordinate system that it only refers to “an
observer carried along in a uniform movement of
translation."

D. Inconsistencies in the explanation of the principle of special relativity





In his 1914 paper “On the Principle of Relativity,” Einstein provides more detailed explanation of his principle of
special relativity as follows:
“Even a cursory analysis of the processes we call motion already teaches us that we can perceive
only the relative motion of things with respect to one another.
We sit in a railway carriage and see
(on the adjacent track) another carriage pass by.
If we ignore the vibration of our carriage, we have no
immediate means by which to decide whether the two carriages are moving ‘in reality.’ We find only that the relative position of the carriages changes in time.

*****
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Even if we look at the telegraph poles alongside the track, nothing essential changes in this situation.
For when we usually refer to telegraph poles (and the surface of the earth) ‘at rest,’ and every object moving relative to them ‘in motion,’ we merely use a customary and handy expression without deeper meaning.
An observer in a ‘moving’ railway carriage will not come into conflict with his perceptions if he states that the carriage is at rest and the ground and telegraph poles are in motion.
Physicists have found over the course of time that this characteristic of motion, to appear purely relative, is not merely attributable to primitive perception, but rather, that one is justified to call any single thing ‘at rest’ among a multitude of things which are in relative (uniform) motion with respect to one another.
Let’s think again of a uniformly moving carriage on a straight track.
Let the windows be closed airtight, with no light coming in; wheels and tracks are absolutely smooth.
Inside the carriage is a physicist with all kinds of apparatus imaginable.
We do know that all experiments done by this physicist will come out exactly the same as if the carriage were not moving or, for that matter, if it were moving at a different velocity.
This statement is essentially what physicists call the ‘principle of relativity.’
One can phrase this principle in a general fashion as: ‘The laws of nature perceived by an observer are independent of his state of motion.’”
The description which Einstein used in this article is similar to what Galileo Galilei described in 1632 in his “Dialogue concerning the two chief world systems."
The idea which Galileo presented in his dialogue was to refute Aristotle’s argument that Earth must be standing still.
Galileo presented that the same physical processes carried out at the Earth and in the cabin of a ship moving uniformly at constant speed relative to Earth will come out the same, and thus we cannot make assertion that Earth is at rest and ship is in motion.
It showed that there is only relative motion, relative to the frame of reference we use.
This argument is supported by two other principles.
Principle of inertia and same causesame effect principle (see Fig. 1).
This figure compares the Einstein’s first postulate, based on “laws that govern physical changes,” the idealistic, incorrect ontological understanding of the world with Poincaré’s principle of relativity that is extending the Galilean relativity (Galilean Relativity principle and Galilean Invariance principle) derived from the empirical evidence; to the fieldbased processes.
Furthermore, this diagram also shows the inconsistencies or contradictions of each of these two principles of relativity as they are discussed in the following sections (each number indicates section where they are discussed in detail).
The idea described by Galileo Galilei and which Einstein referred to, using analogy of train, is called the Galilean relativity principle and should be understood as:
The results of the same mechanical physical experiments carried out the same way in two inertial physical systems moving with uniform velocity relative to each other will come out exactly the same.
Einstein’s first postulate does not refer to the fact that the same physical process, carried out the same ways in two inertial physical systems, will come out exactly the same.
His postulate does not refer to physical processes but to the laws of Nature.
He said one can “phrase” Galileo’s principle “in a general fashion” by saying “The laws of nature perceived by an observer are independent of his state of motion.”
In his “phrasing” the Galileo relativity principle “in a general fashion,” Einstein skipped one important step in his explanation.
Classical mechanics is based not only on the validity of the Galilean relativity principle, but also on a premise that the same physical process can be observed from and expressed or referred to in different inertial coordinate systems which are moving at a uniform translational movement (at constant speed) relative to the physical system
where the physical process takes place (in different inertial coordinate system).
Thus an integral part of the classical mechanics are the equations called Galilean transformation equations, which express the transformation of data measured and expressed in one inertial coordinate system into another such system.
Einstein called these Galilean transformation equations “laws of the additivity of velocity."
The
true physical parameters, depicting the physical changes,
are then those that have the same values when expressed in
different inertial coordinate systems; That are invariant
under Galilean transformation. Thus a part of the classical
physics, the most important part, is a set of parameters,
invariances, and their relations expressed by equations that
are invariant under Galilean transformation. Regardless of
what our inertial coordinate system which we use to express
our observations with may be, as long as it is in the uniform
movement relative to the actual physical system, we will get
the same values for these invariant parameters and the same
relations (equations) expressing the physical changes.
These ideas are expressed then in what some physicists
today also call the Galilean relativity principle of mechanics
but what needs to be called the Galilean invariance principle:
The invariant physical parameters and their
relations, expressed by equations which depict the
physical changes of mechanical processes “do not
depend on which one of two ‘inertial’ coordinate
systems in uniform translational motion relative to
each other these changes are referred to."
The principle which Einstein extended to all physical
processes was not therefore the Galilean relativity principle
that he described in his 1914 paper, “On the Principle of Relativity” but the Galilean invariance principle. When Einstein
phrased his principle “in general fashion” he:
(a) moved from Galilean relativity principle to the Galilean invariance principle, and
(b) took only the equations from the Galilean invariance
principle, which depict the empirical evidence, and

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FIG. 1. Comparison of Einstein’s and Poincaré’s principles of relativity.





gave them name “Laws of Nature” with meaning of
something what govern the real physical world.
In doing these two things, he changed the causality of
physical processes. The equations that depict physical
changes in classical physics became in Einsteinian principle
of special relativity the cause that “governs” those changes.
By “phrasing this principle in a general fashion” did not
mean that Einstein only extended the Galilean invariance
principle to the other than mechanical phenomena. It meant
that Einstein also replaced the results of the experiments, the
observable facts, the behavior of the real things expressed by
the invariances and their relations (equations), with the
“laws of Nature” and postulated entirely different principle.
By substituting the laws for the real things, he gave priority,
higher importance to “the laws of Nature” over and above
the real physical behavior and empirical evidence. By
“phrasing this principle in a general fashion” (whatever he
meant by this statement) Einstein changed the meaning from
that of the original Galilean invariance principle, and thus
his first postulate has nothing to do with the Galilean invariance and Galilean relativity principles, nor with the Poincaré’s relativity principle.
Some might say that the point just made amounts to
splitting hairs, but the change from describing the results of
experiments to describing the Laws of Nature that “govern”
such results is a change in ontology: the Laws (or principles)
of Nature are items of an entirely different category than the
phenomena, behavior or changes in the real things that we
can actually observe, and cannot be used or substituted one
for the other. This change in ontology is very important for
the proper understanding of Einstein’s theory.

E. Philosophical (category) mistake in the Einsteinian principle of relativity



Since the time of Plato and Aristotle, philosophers have been divided into two main groups in regard to ontology.
Idealists viewed the human mind (soul), with its ideas and
ideals that lead human actions, as a key to understanding of
the rest of the world.


They believed that just as human ideas cause human behavior, ideas of another kind cause all things and happenings in the Nature: they “govern” them.

Physical processes are not governed by something.

For some Idealists, these later ideas were even more real than the real things themselves. Because many Idealists held theistic world views, they thought such ideas as well as laws were imposed on the world by deities or the Judaeo–Christian God.
The other group of philosophers investigated natural objects on their own and stepbystep developed a realistic/ materialistic understanding of Nature.
They believed that for the causes we should look to the other natural things, not to supernatural things, deities or laws which govern Nature.

Physical processes are not governed by laws of Nature.

Modern science is the extension and continuation of this realistic/materialistic philosophical tradition and its successes are the result of that tradition.
The natural phenomena or changes of physical states are the result of interactions of different forms of matter and the
extent of the changes depends on properties and relations of the interacting forms.

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Most of the matter in the known universe is not conscious, and its behavior, its physical states and changes have nothing to do with human conscious intelligent behaviors and actions, directed by human consciousminds with its ideas and ideals.
Human ideas and ideals, their generation and application in human life, have a place insocial studies, but not in the natural science.
The term “laws of Nature” is a remnant of Plato’s anthropomorphism and
theism in the Western philosophy, which unfortunately survived all the way to our times and gives incorrect connotation to the ideas we have about Nature.
Nature does not need
any supernatural laws or principles that would govern individual parts of it in their existence, behavior and changes.
The use of the term “laws” or “laws of Nature” in natural science carries with that the connotation of something that governs or causes the physical changes in Nature and
thus gives inappropriate meaning to the concepts and theories that we generate to describe or to depict Nature.
Today we should not use this misleading term at all.
What we abstract, depict, or generalize from our observations and
experimentation are principles; principles that describe or depict the real things their behavior and changes.
The principles, concepts, and theories which we come up with are
only depictions of the matter in its various forms, interactions and changes.
Our theories are representations, abstract models of reality.

100% correct



The principles which we abstract or derive from our observations and experimentations, and our
theories with equations which quantify the relationships of the interacting objects and their properties and changes, are our attempts to depict it as close to the real things as possible, as true to its nature as we can.

That is correct.

Natural objects and
their behavior are primary.
Our theories are secondary;
they do not influence or govern the natural behaviors.
They
are not something real in Nature; some active agent in Nature which governs Nature in course of its existence and
changes.
They are abstractions in our heads which we generated to depict the Nature’s behavior, and if we understand correctly and in all details, what is going on, what
interacts, what causes the forces and how these forces
change different forms of matter, then our models represent
correctly the Nature.
Nature does not need any separate
agent or entities, ideas, laws of Nature to direct it.
For Einstein to write “the laws governing the changes” or “the laws by which the states of physical system undergo
change” and use it as a basic postulate of his theory; then use
it with this meaning to derive the second postulate and build
his theory of special relativity on it, meant to embrace
the idealistic/theistic misunderstanding of Nature.
With it,
Einstein gave primacy to theory as if it influenced the actual
behavior of Nature.
It elevated our theories, our abstractions
and our equations, to a higher, more important, level than
reality itself.
It assumed as Idealists do that there exists some
higher level of laws which govern the real world and which
we want to uncover.
By doing it, Einstein reversed the significance.
He put the wagon in front of the horse.
He turned
science upside down, or in another analogy, he took the
reflection in the mirror for the real thing and assumed that it
directed the real object in front of the mirror.
This rephrasing
of the Galilean relativity principle into the Einsteinian
relativity principle was based on a major philosophical misunderstanding and is the major flaw of the whole theory.
In his numerous writings, Einstein claimed to be an
empiricist influenced by the philosophical writings of Hume,
Kant, and Mach.
Whether consciously or subconsciously in using the term “law” or “law of Nature” to refer to something governing or causing the changes of physical system or being something prior to or superior to Nature and its behavior, Einstein embraced speculative metaphysical philosophical views in the idealist/theistic tradition.
Embracing this metaphysical view resulted in his embracing a metaphysical theory, giving superior importance and priority to his two postulates and to laws expressed by his equations, than to the actual physical behavior and to principles (including Galileo invariance principle) derived from the empirical experience of such behavior.
Thus Einstein, with his presumably empiricist views, turned out to be an Idealist.
Einstein got caught in a philosophical misunderstanding, a misunderstanding which was not of his own making, in the misunderstanding of many philosophers and scientists of the past that persists in minds of some people all the way to our time.
This misunderstanding misled him into the world of unrealistic abstractions and speculations that do not represent the realities of the real world.

F. Einstein’s and Poincaré’s relativity principles and the outside forces





There is still another very important aspect related to the Einstein’s and Poincaré’s relativity principles, which is not mentioned or addressed in depth in Einstein’s and Poincaré’s writings.
There is an assumption in the Galileo relativity principle, transformation equations, and invariants of classical physics which is frequently omitted in physics books.
This is the assumption that they are valid only for physical systems not affected by “outside” or “external” forces; they are valid only for the socalled inertial systems in which the principle (law) of inertia is valid.

That is an important limitation.

They are valid where the principle of inertia, one of the fundamental principles of classical physics and the Newton’s First Law of Motion, is valid.
To define the inertial coordinate system, in his expression of the first postulate, Einstein referred only to “uniform translational motion relative to each other” and Poincaré
referred to “a uniform movement of translation” in his principle of relativity.
In their expressions, they did not mention either the inertial systems or outside forces.
They might have thought that the uniform translational motion adequately defined the inertial system, but it does not.
The uniform translational movement is a necessary condition for the coordinate system to be inertial, but it is not a sufficient one.
The sufficient conditions for the inertial coordinate system are that it must be:
(a) nonrotational
(b) free from outside or external forces
It can be also stated that the requirement of the inertial coordinate system to be in the uniform translational movement can be met only when it is free from outside or external
forces.

In reality these conditions are never met
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In his book “The Meaning of Relativity,” Einstein explained his first postulate and alluded to inertial system.




Here he excluded the “jolting railway train,” the train subjected to outside forces but no mentioning of inertial system
in his “principle of special relativity."
At that time, physicists were captivated (interested NV) by Ernst Mach’s attack on the absolute rest in the universe and absolute coordinate system and
paid attention to uniform velocities rather than to the effects of fields on the frames of reference.

The problem is if you mention velocities you must use some sort of frame in order to measure positions.
Frames IMO have nothing to do with fields, nor the effects of fields.



In mechanics, we deal with direct interactions of objects, and the presence of one frame of reference does not affect the physical process taking place in the other frames of reference.

Reference frames or inertial coordination frames have nothing to do with the evolution of any physical proces.



Thus the same process taking place in two inertial frames of reference are going to yield the same results, and the results from one can be expressed in the other coordinate system using Galilean transformation equations.

Such a sentence highlights the concept to use only one coordination system.



In the case of fieldbased physical processes, the situation is quite different.
Electromagnetic and gravity fields cause forces at a distance.
One object affects other ones indirectly through the fields which it generates or influences.
Field affects not only the physical processes in the frame of reference where it is generated, but also in other frames of reference.
We need to pay attention, not only whether the same process is going to take place in the two frames of reference but also how field generated in one affects the other frames of reference; whether it will cause forces that will accelerate them and thus turn them into noninertial ones.

That is the general case.





If in the physical process, the electromagnetic or gravity fields are involved, the Poincaré’s and Einstein’s idea of extending the Galileo invariance principle to all other physical processes is not as simple as it appears at the first look.
The Galileanlike relativity principle and the Galileanlike invariance principle would not apply if the fields are generated outside of the physical system under study and if they cause forces at a distance in it or are involved for any reason.
In a simple case, were electromagnetic field is generated the same way in each of two inertial physical systems moving at constant speed relative to each other, without affecting each other, then the results observed in these two physical systems could be the same and so the equations which will quantify the changes, but not generally in all cases (see Fig. 2).
When the electromagnetic (or gravity) field is generated
in, or is influenced by, a different physical system, outside of
the one in which we carry out our physical experiment, outside of our frame of reference (coordinate system), then this
FIG. 2. Comparison of the effects of fields generated within the frames of reference with that caused by field generated outside.

Okay


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experiment as well as the frame of reference are influenced by forces caused from outside, and this frame of reference cannot be any longer in the uniform translational movement
and becomes noninertial, and the Galileanlike relativity and invariance principles cannot be valid.

This sentence demonstrates that before you know that the concept of inertial frames becomes unworkable. Solution: Be carefull; Don't use them.

Thus, the Einstein’s and Poincaré’s attempts to unify classical mechanics with electromagnetism by some simple general principle, like the ones they proposed, is precluded for the physical processes which include fields generated outside of it, or whose fields are influenced by outside objects.
Similarly, such a principle could not be valid when light or radiation are involved and generated outside of the frame of reference in which we
study the physical phenomena.
Thus Poincare’s and Einstein’s attempts to extend the Galilean relativity and invariance principles of mechanical processes to the physical processes dealing with fields, with fields which generate forces at a distance are not possible.
Thus both Einstein as well as Poincare did not define sufficiently the inertial systems in their relativity principles and thus they did not notice that their definitions overgeneralized the Galilean invariance principle into the region where forces at a distance turn the physical systems (frames of references) into noninertial ones.
This is the second most important finding about the Einstein’s first postulate.
Einstein did not see that his generalization, his extension of the Galilean invariance principle of mechanics to gravity and electromagnetic phenomena, was not correct.
He did not see that his postulate included noninertial systems and thus is inconsistent with the principle of inertia.
He took it and Maxwell–Lorentz equations and deduced from that his second postulate, the invariance of light.

You can 'not use' mathematics to conclude that the speed of light is constant. You must use realistic experiments.

The requirement of the second postulate that the velocity of light is independent of whether it is emitted by a body at rest or a body in motion is thus incorrect.
Light generated by a body in motion relative to the frame of reference would turn this frame of reference into noninertial one and thus
would be outside of the validity of the first postulate.

Physical experiments don't change reference frames. Starting point should be that inertial frames are noninertial.

Thus, Einstein’s theory starts with the principle that overgeneralized into a region where it cannot be valid.
The use of this principle then led Einstein to an incorrect inference of the second postulate and that to inference of relativity of simultaneity, all three incorrect.
It led to the theory that provides the transformation equations for the case where the principle of relativity is not applicable.
Thus these equations, similarly to Lorentz’s transformation equations, are only a mathematical transformation of Galilean transformation equations to satisfy the invariance of light velocity, and do not express any real conditions in the real world.
Thus, one simple oversight at the bottom of this theory made it possible but also incorrect.

G. Comparison of the invariants of classical mechanics with the Einstein’s invariance





By embracing the incorrect idealistic/theistic metaphysical view and expressing his relativity principle in terms of laws that govern Nature, Einstein not only elevated his humanmade model above Nature, he also relegated reality and our observations to the dependent role.
With that he also relegated
Galileo relativity principle with Galilean transformation equations and Galileo invariance principle to a secondary, lower or
dependent role.
The Galileo relativity principle, which Einstein expressed as “the experiments done by the physicists will come out exactly the same as if the carriage were not moving or for that matter, if it were moving at a different velocity”
became only a first approximation in the Einstein theory and
not an exact principle.
With that the Galileo transformation
equations and invariances of classical mechanics became also
only a first approximation, valid for small values of the relative
velocities of the coordinate systems.
The creation of this elevated, primary, or higher level of the laws that govern real things allowed Einstein to deduce his second postulate, the postulate of constancy of velocity
of light from his incorrect relativity principle and from equations (Maxwell–Lorentz) instead of from observations of
the real behavior.
Thus this second postulate, which itself contradicts the Galilean transformation equations, was also
elevated on the higher level above the empirical evidence and above the Galilean relativity principle and transformation equations.
This new invariant now trumps all the other
ones which classical physics developed and relegated them
into secondary, dependent role.
Thus in Einstein’s theory, one physical process, the propagation of light, gain a superior significance over and above all other ones.
Only that one will have the same value in all coordinate systems.
This one is on the higher level of
laws and is thus same in all equations regardless in which
coordinates they are expressed and the reality has to adjust to
it.
All the other physical processes do not have the invariants
anymore; only the light velocity is the one.

H. Contradiction between the Einstein’s theory and Galilean relativity principle





In his 1914 paper (quoted above), Einstein described the basis of his relativity principle in the same terms as Galileo did; in terms of results of experiments.

That is the correct way.



“We do know that all experiments done by this physicist will come out exactly the same as if the carriage were not moving or, for
that matter, if it were moving at a different velocity."

That is the question. Many accidents re a function of speed.

What Einstein was saying is that for the same experiment conducted in two inertial physical systems (coordinate systems) moving at the different uniform velocities, the results of the experiments “will come out exactly the same."
The concept of inertial physical systems is not important.
The question is if the result of two almost identical experiments (except their speeds) are identical

The importance of this claim is limited. The isue is to what extend the results of two almost identical performed experiments, except in speed, will be the same. My understanding that the tiking rate of the clocks, assuming they twice meet each other, can be different.

Clocks—be it a water clock, grandfather’s pendulum clock, a modern digital watch or scientific atomic clocks— are all based on periodicity of a physical process in a physical system.




Thus running of identical clocks, identical physical process in both inertial coordinate systems, moving at constant speed relative to each other “will come out exactly the same."

Yes that is true, but not important. What is important when this is not the case.
How is the constant speed of each clock, measured?
My understanding is that the light path of the fastest moving clock, between ticks, is longer than the lightpath of the slower moving clock, making the slower moving clock run faster. The result is that in order to understand the behaviour of mechanical processes moving clocks should not be used?



That is what Einstein said and it is what is expressed by Galilean relativity principle.




Then, Einstein “phrase in a general fashion” this principle into his Einsteinian principle of special relativity by changing the meaning from results of experiments to “laws of Nature which govern” and goes on, developed his theory of special relativity, which concludes that the time is different in each of these coordinate systems and thus the clocks which measure time are not running at the same rate as he assumed at the beginning by extending the Galilean invariance principle.

It should be mentioned that "laws of Nature" don't govern physical experiments.
Page 422





He developed a theory which contradicts the Galilean relativity principle; principle upon which the Galilean invariance principle is based and which was presumably only extended in Einstein’s theory.
The principle which tells us that all mechanical processes are going to run exactly the same way in two inertial physical systems, yet according to the theory of special relativity, they are not running the same way.

You need an experiment to explain this. That is very important



Only the velocity of light will be the same in all inertial physical systems, but all others will not.
Einstein created a contradiction.
The contradiction caused by phrasing his principle in terms of laws or laws of Nature which shifted the meaning and significance from facts about the real world to abstract principles and equations, which are supposed to depict or represent the real world.

There is nothing wrong to describe certain mechanical processes by means of mathematics. This allows us to predict the future. The issue is that these predictions are not 100% accurate, often caused because the model used is not an accurate description of the reality.
IV. THE SECOND POSTULATE AND EINSTEIN’S EPISTEMOLOGICAL VIEWS
A. The expression of the second postulate





In his 1905 paper, Einstein expressed his second postulate as follows:
“Each ray of light moves in the coordinate system ‘at rest’ with the definite velocity c independent of whether this ray of light is emitted by a body at rest or a body in motion.

This requires a definition what means 'at rest' and what 'in motion'

Here,
Light path
Velocity = 
Time interval
where ‘time interval’ should be understood in the sense of the definition in §1.”
The definition in §1 is the definition of simultaneity which is presented in Section V E .
In this definition of simultaneity, Einstein introduces his method of clock synchronization using light signal traveling from point A to point B; where it is reflected by a mirror; and returns back to point A.

This definition is based on the concept of a system at rest.



In this method, Einstein established “by definition that the ‘time’ needed for the light to travel from A to B is equal to the ‘time’ it needs to travel from B to A.”
Furthermore, he is “taking into account the principle of constancy of the velocity of light” for both coordinate systems.

As mentioned this definition is based on a system at rest. The problem is that it is very difficult to establish that a body is at rest
You can also rewrite this as such: Most probably if you send a light signal (in a straight line) from a point A on Earth towards the Moon and back to point A than the length of the two light signals is not the same.
B. Interdependence of the second postulate and the relativity of simultaneity





We can see from this definition of the second postulate that it is tied up to the definition of simultaneity and with that to the method of synchronization of clocks by light signal.
The analysis of Einstein’s synchronization method and relativity of simultaneity in Section VI will show that the concept of relativity of simultaneity requires the validity of
the second postulate.
That only if the second postulate could be correct, then the relativity of simultaneity would be correct.
Thus we can see that the second postulate, the light invariance as defined by Einstein, depends on validity of the relativity of simultaneity and its requirements, which can be valid only if the second postulate is valid.
We can see that this definition of the second postulate requires the validity of the second postulate in the first place.
In this definition the second postulate depends on its own validity, the second postulate is derived from itself, creating circular argument or circular logic.
We can further see that the second postulate and the relativity of simultaneity are mutually dependent.
That one can only be valid if the other one is valid.
That one of them cannot be used as an argument for validity of the other one.

C. Origin and validity of the second postulate





As shown in Section II B, Einstein’s original 1905 paper started with the assumption of his two postulates and only mentioned some examples which lead him to the first postulate.
From his 1922 Kyoto address,5 we learned that Einstein deduced the second postulate from presumed validity of the first one and the hypothesis that the Maxwell–Lorentz equations revealed the true reality.
Thus the second postulate did not originate from any experiment but was deduced from the first one, from the first postulate which was shown in previous section that it is not correct.
If we will try to replace Einstein’s incorrect “highlevel” metaphysical relativity principle with Poincaré’s, empiricalbased relativity principle, we cannot deduce the second postulate from it either.
As shown in the Section III F and depicted in Fig. 1, Poincaré’s principle of relativity, similarly as Einstein’s principle, overgeneralized the Galilean invariance principle into the region where forces at a distance turn the physical systems into noninertial ones.


Poincaré’s principle could be valid only for light and fields generated in the same frame of reference in which we study them.
Thus this
principle cannot lead to the second postulate which defines
invariance of light velocity for light generated outside of the
frame of reference, outside of its own validity.

D. Was there any empirical base for the second postulate?





There was no mentioning of any direct experimental evidence of the second postulate in Einstein’s 1905 paper.
Only in his later writings, Einstein mentioned experiments related to the second postulate.
In Einstein’s book “The Evolution of Physics” from 1938, after introducing his two postulates, Einstein made a general statement: “There are many experiments to confirm these two statements” (his postulates), “and not a single one to contradict either of them."
Yet, he did not give any examples.
Did he mean the Michelson–Morley experiments or something else? We do not know.
The Michelson–Morley experiments were performed with the light source in the same coordinate system where its effects were measured.
The light source was at rest in the physical system where its performance was measured.
Thus these experiments do not indicate anything about the behavior of light which would be generated in the physical system moving relative to the one
where these experiments were conducted.

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A few pages ahead of this statement, Einstein discussed
the case in which light would move with constant velocity
relative to its source and presented conclusions he derived
for this case.
Then he just stated: “But there is no indication as to the truth of these
conclusions.
On the contrary, they are contradicted by all observations made with the intention of
proving them.
There is not the slightest doubt as to the clarity of this verdict, although it is obtained
through rather indirect experiments in view of the great technical difficulties caused by the enormous
value of the velocity of light.
The velocity of light is always the same in all CS independent of whether or not the emitting source moves, or how it moves.
We shall not go into detailed description of the many experiments from which this important conclusion can be drawn.
We can, however, use some very simple arguments which, though they do not prove that the velocity of light is independent of the motion of the source, nevertheless make this fact convincing and understandable.”
Einstein is telling us: “The truth of these conclusions
that light would move with constant velocity relative to its
source are contradicted by all observations made with the
intention of providing them."
Then “We shall not go into
detailed description of the many experiments from which
this important conclusion will be drawn. We can, however,
use some very simple arguments which, though they do not
prove that the velocity of light is independent of the motion
of the source, nevertheless make this fact convincing and
understandable."
No real facts, no empirical proof of the
second postulate, only a lot of talk to reassure himself about
validity of this postulate.
In his 1922 book The Meaning of Relativity,13 Einstein
mentioned two other observations which supported his
ideas of the second postulate and validity of Maxwell–
Lorentz equations: “No other theory has satisfactorily
explained the facts of aberration, the propagation of light
in moving bodies (Fizeau), and phenomena observed in
double stars (De Sitter)."
Neither the Fizeau experiments
with the propagation of light in water, nor observation of
double stars are direct experimental verification of the second postulate.

E. Einstein’s epistemological views





Section III presented Einstein’s ontological (the nature and relations of being) views.
It is
also necessary to find out the epistemological (the theory of knowledge) views which
guided him during development of his theory.
Even though Einstein claimed the influences of empiricists like Hume and Mach, his writings show some oscillation between
empiricisms and rationalist/idealistic tendencies.
In Section II B, we have presented a statement from Einstein’s “Autobiographical Notes,” where he indicated his desperation with empirical approach and the need to find different way to science by “discovering of universal formal principle."
Let us see how Einstein thought we can discover such principle.
Probably the most extensive text on Einstein’s epistemological views is in his Herbert Spencer lecture delivered at Oxford in 1933.
In this lecture, almost three decades after developing his theory, mature physicist Einstein is looking
back, reflecting on his theoretical pursuits and is telling us that:
(1) “We are concerned with the eternal antithesis between the two inseparable components of our knowledge, the
empirical and the rational.”
(2) “We reverence ancient Greece”… “Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable—I refer to Euclid’s geometry.”
(3) “The structure of the (theoretical) system is the work of reason; the empirical contents and their mutual relations must find their representation in the conclusion of the theory.”
(4) “the fundamentals of the scientific theory has purely
fictitious character.”
(5) “the fundamental principles are free inventions of the human intellect” and not based on the empirical knowledge.
(6) “every attempt at a logical deduction of the basic concepts and postulates of mechanics from elementary experiences is doomed to failure.”
(7) “If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way?”
(8) “that nature is the realization of the simplest conceivable mathematical ideas.”
(9) He was “convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of the natural phenomena.”
In this lecture, Einstein reveals his true epistemological view.
He does not refer to the empirical tradition in science and to empiricists who influenced him in his early years.
He does not pretend that his relativity theory reflects the empirical evidence or is extension of Galileo invariance principle.
He actually criticized empirical tradition.
He criticized Newton and other natural philosophers “possessed with the idea that the fundamental concepts and postulates of physics were not in the logical sense free inventions of the human mind but could be deduced from experience by abstraction” and then tells us that “A clear
recognition of the erroneousness of this notion really only came with the general theory of relativity,” telling us indirectly that his two postulates of the theory of special relativity are his free inventions.
That these two postulates are the two simplest universal principles and “Nature is realization of them."
His epistemological view goes together with his idealistic/theistic metaphysical view of Nature governed by some supernatural laws of Nature.

Nature is not governed by any law
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With his views, Einstein turns
the clock back to times before English empiricists, Kant, and
modern positivism.
With that, Einstein brought theoretical physics into the realm of fictitious mathematical models.


German idealism and rationalism were too strongly
implanted in German culture, science and philosophy, which
formed young Einstein’s mind, that they eventually took
over Einstein’s mind and redirected him from basing and
deriving the principles from empirical and experimental evidence, back to idealism and rationalism and to inventing
some simple fundamental or universal principles; principles
from which all will be derived.
By the time of this lecture,
the influence of empiricism was completely gone as it is also
shown in Einstein’s letter to a friend, Cornelius Lanczos (on
January 24, 1938), see Ref. 16 (p. 259) where Einstein
wrote:
“Coming from skeptical empiricism of somewhat
the kind of Mach’s, I was made, by the problem of
gravitation, into a believing rationalist, that is, one
who seeks the only trustworthy source of truth in
mathematical simplicity.
The logically simple does
not, of course, have to be physically true; but the
physically true is logically simple, that is, it has
unity at the foundation."

F. Einstein’s two levels of natural principles





To understand Einstein and his higher level of laws of
Nature which govern nature, and the lower level of principles which are arrived at from observations of the real world,
we need to understand that it was very common character in
German thought, very prevalent at the time of Einstein’s
education.
This character is eloquently described by Arthur
O. Lovejoy in his “The Reason, The Understanding, and
Time”17 Lecture 1.
“Characteristic of nearly all the more typical and
influential of the philosophic systems which
introduced a new temper into German and
eventually into European thought between 1795
and 1830 was a fashion of distinguishing two
radically different modes of knowing, a “lower”
and a “higher,” of which the former was said to
constitute the method of science, the later that of
philosophy.
This fashion appeared in several
somewhat differing forms.
But in all its forms it was marked by a depreciation of what was called
“the ordinary logic” and also of senseperception as means of becoming acquainted with “reality”—
with the true nature of things; and its representatives all proclaimed that there is in man another
cognitive “faculty,” a different way of knowing, unrecognized by most earlier modern philosophy,
through which he can gain a veritable and certain
access to Being as it actually is."
In this lecture, Lovejoy showed how this new fashion
started from Johann Georg Hamann and Friedrich Heinrich
Jacobi, and how it influenced others like Johann Gottlieb
Fichte, Friedrich Schelling, Friedrich Schlegel all the way to
Georg Wilhelm Friedrich Hegel and Henri Bergson.
He also
showed that even Kant’s philosophy shares some of these
aspects.
These philosophers saw the reason as a superior
kind of apprehension to which the understanding is unable
to rise.
The reason gained by “intellectual intuition” or
“intuitional reason” producing postulates while the understanding, gained from senses, presents merely a world of
appearances and provides only lower level of knowledge.
Many philosophers of that era were still religious people,
and so for them, to think about the higher level of knowing,
the metaphysical level, was the normal way of thinking.
Western philosophy of 17–20th centuries was in a transition
from philosophies influenced by Judaeo–Christian beliefs to
philosophies based on study of realities of the world, based
on empiricism and science.
In this period, the abstractions
and imaginary things and imaginary happenings which people generate and which allow them to understand the world
were not yet recognized for what they are.
That they are only
representations of the world and are not some supernatural
agents or higher order laws of Nature, agents involved in the
real world.
It is inconceivable to think that the young Einstein would
not be exposed to and influenced by this kind of philosophical thinking because those of us who were brought up in the
continental Europe more than a half a century after Einstein,
we were still exposed to them.
Einstein’s ontological views
presented in Section III B showed clearly the strong influence of religion on his thinking.
His opinions were a mixture
of religious and scientific ideas where the “ultimately superior spirit,” “presence of a superior reasoning power,” and
the “immutable laws that govern reality” were among his
strong beliefs.
In Section III A, the beginning of Einstein’s original
1905 paper was presented in which he discusses his
“conjecture that not only in mechanics, but in electrodynamics as well, the phenomena do not have any properties corresponding to the concept of absolute rest” and then declares
“We shall raise this conjecture to the status of postulate."
Einstein still had the higher and lower mode of knowing in
his mind, and thus he created for us a theory which had the
higher level of his two postulates and which had relegated
the Galileo invariance principle, principle derived from empirical evidence, into the lower dependent level.
Thus, Einstein created for us scientific metaphysics.
By generating this higher level of laws of Nature, which
govern the world, he was not bound anymore to the reality
and the need to derive principles from empirical and experimental evidence.
He freed himself from reality and from the
need to analyze it in detail using principles derived from it,
and proceeded development of understanding of Nature from
postulating some “universal formal principles” (his two postulates) similarly to the way Euclid developed geometry
based on his axioms.
Einstein did not understand that geometry; be it Euclidian or NonEuclidian; is an arbitrary system
of abstract imaginary objects.
That the basic elements like
points, lines or planes, were abstracted from the reality and
based on them and their definitions, the whole system of
abstract geometrical objects was then developed; system

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which provided a model for understanding of the spatial relationships of real objects.
This model helps us to calculate the
volume of real objects, but cannot tell us what these objects
are, how they were created and why the elements which
compose them hold together, what forces keeps them together.
For that we need to go back to Nature and study the
physical nature of the microworld, the physical nature of
crystals, atoms, and subatomic particles.
These questions
cannot be answered by geometry or from Einstein’s two
postulates.

G. Einstein and logical positivists





The problem of logical positivists and many philosophers of science who followed them is that they thought that
Einstein generated his theory as an empiricist.
In his early
writings, Einstein mentioned the influence on empiricism on
his thinking, but as evidenced from the genesis of his theory,
and from his 1933 Herbert Spencer lecture, he switched back
to idealism and rational way of deducing his theory from
some higher level postulates which govern the world.
While
logical positivists grounded science in observations, they did
not analyze Einstein’s thinking to realize that none of his
two postulates or relativity of simultaneity came from, or is
supported by, empirical evidence.
They did not notice Einstein’s idealistic understanding
of the term “Law of Nature” in his first postulate, as discussed in Section III, and that the second postulate with relativity of simultaneity were then only deduced from it.
By the time Einstein revealed the views which guided him
in developing his theories, logical positivists already associated
him with empirical tradition, accepted and promoted his theories and did not notice his complete reversal back to idealism
and rationalism which made his theory possible.
Before we will go to the third pillar of this theory, the
Einstein’s concept of relativity of simultaneity and his definition of time, let us see how the question of time looks from
our today’s philosophical perspective.

V. TIME, TEMPORAL TERMS, AND EINSTEIN’S SPACE
A. What is time?





“I know what time is,” said Augustine, “but if
someone asks me, I cannot tell him."
Things have
not changed very much since then.
The ordinary
man (or woman) thinks he knows what time is but
cannot say.
The learned man, physicist or
philosopher, is not so sure he knows but is ready to
write volumes on the subject of his speculation and
ignorance."
18 p. 1.
Time is one of the most elusive things which defied analysis and definition.
The difficulty of defining time can be
traced throughout the whole history of philosophy resulting
in a great variety of opinions.
There has been number of
books; for example;19–21 which present in detail these opinions and their justifications.
The review of these books
revealed that the understanding of time by various philosophers and scientists who took on this challenge in the past
and justifications of their views reflect the diversity of their
ontological and later also of their epistemological views.
To
understand time, we will first look at two specific philosophical advances in the 20th century.

1. Continuation of being





There were three philosophers whose ontological views
influenced our view of time.
Alfred N. Whitehead, who, in
his “Science and the Modern World,”22 brought to our attention that Nature needs to be understood from viewpoint of a
process, being in the ongoing process rather than from the
view of individual events.
Henri Bergson, in his “Creative
Evolution,”23 and Martin Heidegger, in “Being and Time,”24
addressed human life as a continuous process rather than a
sequence of events.
They pointed towards the fact that things
of nature as well as life of living creatures are a dynamic
way of being, dynamic ongoing way of being.
All three together point out to the need to view and understand not only
the form of things and life, the form of beings and sequences,
but also the way real things exist, or live, to the ongoing
process of existing or living.
Even so they did not express it
explicitly, they pointed out towards continuation of being.
This was different from the prevalent understanding of time
in science at the beginning of the 20th century, which was
the view introduced by Leibnitz who understood time as a
sequence of events, stepwise progression of events and attention to simultaneity of events.
That view was also shared by
Einstein.

2. Abstractions





The true understanding of time and temporal terms
comes also with a second advance, with the modern understanding of human mind and its relationship with the outside
world.
It comes from understanding of mind as a representation, reflection, of the world in the human brain.
In the brain,
we cannot have the world so that we could run it there and
play with it.
The world is too big to fit into it.
In our brain,
we can have only representations of it.
We have there visual
images and other senseimpressions, abstractions, feelings,
symbols (words and gestures) and models of the real things
of the world.
In our brain, we have not only these representations of real things and happenings which we experienced in
the real world but also those we imagined, the imaginary
things and happenings.
As we experience and are conscious of individual
objects or the whole groups of them and their behaviors, we
generate names, categories of things, and happenings.
We
notice different aspects, different characteristics of things
and happenings, and abstract these characteristics, separate
them from the things themselves, and give them also names.
We talk about length, shape, softness, color, as if they would
be something separate from the things themselves.
We are
also conscious of continuities and discontinuities, beginnings, duration and endings, and describe real things by these
abstractions.
We needed to make this step to understand abstractions,
what they are and where they came from, in order to understand time and temporal terms.
Time is not a real thing;
object or process of change of real things.
You cannot take

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time into your hands.
The facts we can observe or detect and are conscious of are that real things exist and continue to exist.
That they continue in place where they are, continue in movement, or in change, in process of transforming themselves into different forms, different objects; that they continue and change.
Time and temporal terms are abstractions that we generated to characterize, to represent, continuation or continuance of real things in the world; continuation of existence of inanimate matter, objects, and life of living creatures.
Time represents continuation in whatever form matter is with
whatever changes and transformations it undergoes; continuance manifested in permanence as well as in change, sequences or processes of transformation.
We feel the continuation of being when something is happening, when things are changing.
If there would be no motion, no change in the
world and if the whole history of world’s existence would be
the same as at the instant we observed it, then we would not
have a feeling of time, we would not need it; even so the
world would still continue to exist.
Yes, time is an abstraction and that is why since the time of Augustine, we know that we “cannot tell” even though we “know what time is."
We could not see it, or take it in our hands, but we knew “what time is."
It is an abstraction, something about real things, real world, but not a real thing itself.
It is something that characterizes the real things, characterizes their continuous presence.
It is the abstraction that characterizes the continuation of real things, continuation of their presence, their existence, continuation of being.

B. Measure of time and scientific time





All measurements are comparisons, comparisons of the measured with a measure.
Comparison of two real things.
The measure, the real thing, is a standard that people selected and established as the measure.
All other things are then compared, related to this measure.
As people learned to quantify and measure different properties of real things, they also divided time, the continuation of being, into segments, increments, or duration and call it time periods or time intervals.

It is not possible to divide time. Time is always related to an event. You can only divide a duration.



Because time characterizes the continuation of real things, people used real things and their changes to segment this ongoing continuation into time intervals or time periods.
The fact that we use changes of real things to segment this continuation of being into the time periods does not change anything on the fact that time and time periods are abstractions (human constructs) which only represent real world.
Duration of the time intervals or time periods is chosen by selecting certain specific object(s) in the real world which exhibit(s) periodic or cyclic behavior or a physical or chemical process of real things which can be easily repeated and has an easily observable or detectable beginning and end.
This selection of the specific real thing with its specific behavior as a measure of time is arbitrary.
Once people selected it as a standard, they compared and calibrated all other clocks, watches and instruments by it and used it in their everyday life as well as in science and called it by different names: mathematical, scientific, or even geometric time.

The most proper way to call the time established with a clock is clock time. A different way is to call it clock count.

Thus, scientific time is time with a measure which was arbitrarily selected.
It is a more complex human construct.
It is the abstraction to which we attached a quantitative measure, measure which we selected by convention.
We generated this human construct and projected it on the world as if it would be part of it so that we can record how it changes in that ongoing continuous existence.
The real world does not have and does not need any quantitative measure to run the way it runs.

To understand the real world in all its details does not require a clock. What is important if you want to compare events, all the clocks used should be identical, all the clocks should be synchronized and the distances between each should be fixed.

This quantitative measure is only for us to keep track of the world and our affairs.
Since each physical process has its causes as well as interferences from other processes, each clock has deviations from the uniformity of its operation.

The previous comment prevents this.

Whether the rotation of Earth, “the natural clock” or “humanmade instrument” each is subject to conditions in which it operates.

To prevent such problems all clocks use in the solar should be linked to the center of the solar system.

Rotation of the earth can be altered upon the impact of a large meteorite, and we have evidence that such events happened in the past.
“Clepsydrae,” one of the first clocks, depends on the flow of water through an orifice, and as such, depends on water viscosity which is highly dependent upon temperature.
Thus at summer high temperatures, this clock ran faster than at winter low temperatures.
Similarly all other time pieces utilize different phenomena and depend on uniformity of conditions for uniformity of their operation, uniformity of time intervals.
The pendulum clock depends on gravity and temperature.
Temperature increases the length of pendulum, but people found the way to compensate for it.
Yet at higher elevation, it still goes slower and needs to be recalibrated.
Atomic clock depends also on gravity, and if operated in place with different gravity, it will not give the same reading.
The accuracy of each clock differs and depends on the use or purpose for which people developed it.
Different clocks with different accuracy have been used throughout history, yet their dependence on the conditions under which they operate does not change anything on the fact that they represent arbitrarily selected period of time, period of continuation of being specified under certain conditions; for the standard
conditions.

What should be emphasized is the that evolution of the universe has nothing to do with the behaviour of clocks.

In practice, the operation of clocks is also influenced by the frames of reference they are attached to because these frames of reference are not truly inertial and thus clocks are affected by accelerations of these frames of reference.

The operation of clocks have nothing to do with the reference frames. They are influenced by physical processes.

Thus, identical clocks placed on the earth at different latitudes will have small difference in readings caused by small differences in acceleration as the earth rotates and moves around the sun.

That is physical correct.

Similarly the small difference between the readings of two atomic clocks, one on the earth and the other on board
of the airplane or in the satellite flying around the earth, is, due to the fact that their frames of reference, these clocks are
connected to, are not truly inertial; each subjected to different accelerations due to their movement as well as due to the
difference in gravity.

That is correct.


C. Time, coordinate system, and frame of reference





In science, people use various socalled coordinate systems.
Coordinate system is a “scaffolding”; an independent imaginary system of coordinates with invariant measures; which allows us to build our understanding, theories and
models of Nature, similar to scaffolding around a building that allows its construction.

That is correct description. In reality we need such a scaffolding to describe the total universe. The benefit such a structure defines us to establish all events that happen simultaneous.


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This imaginary coördinate system can be “attached” to a particular physical object and called frame of reference or can be imagined to be free in space.

That is not very practical. In reality you should use one coordinate system.

For any practical purposes, it needs to be attached to an object so that it can be clearly defined and related to other objects.
More importantly still, it has to be attached to a physical object because otherwise we could not put there any observers and/or instruments to provide measurements and we could not carry out any physical experiments so that we could compare their results with those performed in or on another physical object; in another coordinate system, in another frame of reference.

It does not make sense to link a coordinate system to a comet.

Coordinate system allows to relate various forms of matter in space to it in order to relate them mutually.
The spatial coordinate system is an imaginary spatial grid of lines and planes which allow people to locate real things relative to this grid with planes.
By combining this spatial coordinate system with time measurement, allowed them to keep track of real things in space, with time; to keep track of continuation of their existence.
Both spatial grid with its scale as well as time measure were determined by arbitrarily selected measures, by convention.
Both defined by, as well as measured by matter, by selected real objects and processes.
Thusm the coordinate systems; be it rectilinear Euclidian three dimensional or nonEuclidian curved grid; and the measures of time and length are our human inventions, human imaginary grids with scales to allow us to locate and track the progression of location of objects and their transformations with time.

All these different types of coordinate system are not very practical.

They are imaginary things that do not have real existence outside of our minds and our written, graphical or algorithmic, mathematical forms, which we use to represent world in our minds.

Our mind has nothing to do with this.
The grid is not something physical but it requires a clear definition such that we can establish the position of the stars and planets at any instant. Establish to mean in the past, at present and in the future.

Space is a “stage” in which matter performs its phenomena.

Space in this coordinate system is not something that exists. It is our human experience that there are distances between the objects in all directions.

The spatial coordinate system is an artificial imaginary grid.
Time scale allows recording of the progression of the location, processes, states or forms in which matter exists and changes in the space.

The time used in this coordinate system is based on identical clocks linked to fixed points in the grid.

Some of you might argue that time is in our equations which we use in physics, and thus it is something real in the world and not only a human abstraction.

What is true that time is not something that exists, it is part of our human experience stored in our brain. It has nothing to do with mathematics or equations.

What is real is the fact of continuation of existence, and we characterize it by selecting a measure of this continuation, selecting arbitrarily periodicity of one natural process and thus, we generate human construct which only represent the real world and its happenings.

This sentence is too romantic.

This measure together with the spatial coordinate system provides a background or grid against which the presence of matter, real objects, are observed, recorded, and
mutually related.

The importance of a coordinate system and clock is that we can monitor the position of the objects in due time.

Background that allows us to keep track of matter so that we can relate the individual objects with each other.

To establish that certain objects are related to each other has been improved by more acurate observations methodes, specific the invention of a telescope.

It allows us to define other parameters as velocity or acceleration.

the defintion of velocity and acceleration belongs to mathematics.

It allows us to develop kinematics so that we can study the mutual relationships and interactions of the real matter, real objects in space.
The coordinate system is only a “scaffolding” which allows the structure of mutual relationships of matter to be erected.
The structure which allows us to find what forms interacts, their relationships, forces and changes.

The most important physical concept are forces, which are the origin that objects interact which each other. There are different forces involved to describe different physical interactions.

Which allow us to find invariances which reflect the mutual relations and interactions of matter, not relations to the background, to the grid, to the “scaffolding."
Invariances give us equations which represent or express real causality, real interactions, which do not depend on the position in the space and time, but which give
us relative measures, measures of the interacting forms of matter relative to each other.

The concept invariance has no physical meaning. Equations are descriptions in mathematical notation that descripe the positions of differnt objects.

You might say, but in the equations which reflect invariances we still have the dimension of time and length, as well as other measures like mass, force and so on.
Yes, we have but for expressing the resultant changes so that we can predict the future changes and relate them to our measures of
length and progress of continuation, the time; to scale we use in our life, to scale we selected and understand.
To express the true character and nature of thing in universe unaffected by our humanmade measures, the true invariants, we developed socalled dimensionless analysis that provides dimensionless quantities or numbers without associated physical dimensions.
These dimensionless numbers are products of ratios of quantities with dimensions, but in these ratios the dimensions of the individual items cancel out.
There are about a hundred such numbers in science, each allowing us to express facts about real world without being affected by the arbitrarily selected human measures.
We use these numbers to judge whether we have the same conditions or causes in two circumstances and so whether we can expect the same phenomena and effects to take place.

D. Newton’s definition of time

Throughout the history, there was one man who came close enough to today’s understanding of time.
He was Isaac Barrow, Newton’s teacher, and his predecessor in the Lucasian chair at the Cambridge University.
Barrow influenced Newton’s view of time so that he used time correctly, yet Newton’s definition was not clear and caused a lot of criticism and confusion.

My understanding is that Newton only used two concepts of time: Real time or astronomical time and clock time.
For our understanding and in mathematics both are the same.
My feeling is that Newton knew that the accuracy of not all clocks is the same.

In his “Absolute Time,” which was a part of his lectures on geometry, Barrow writes:
“Time, (to speak abstractedly) is the continuance of any Thing in its own Being.
But some Things continue longer in their Beings than others; those were when these were not, and are when these are
not; they enter’d first into Being, and cease to be after these; nor is there any Person but perceives, that some Things enter into Being, and cease to be at the same Time; keeping an equal Pace, as it were, from the beginning to the end of their Duration.
Time absolutely therefore is Quantity, as admitting in some Manner the chief Affections of Quantity, Equality, Inequality, and Proportion; nor do I believe there is any One but allows that those Things existed equal Times, which rose and perished together; and that those Things had unequal Durations, when the one was in Being
before the other had existence, and continue in its
Being, after the other had ceased to be.
But a longer and shorter Time is common in every Body’s Mouth; and there is no Man but seems to understand the Meaning of these Words.

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Common Sense, therefore allows Time to partake of Quantity, as the Measure of the Continuance of Things in their Being."
Barrow understood clearly that term “time” represents continuation of being, that “Time, (to speak abstractedly) is the continuance of any Thing in its own Being,” and for the purpose of mathematics or science, time is the measure of “the continuance of any Thing in its own Being."
Most likely, because he presented his view in the lectures on geometry, it might not be known to philosophers so it did not become a part of their discussions and disputes about time.
Barrow’s treatise on time was brought up in the 20th century by Whitrow21 and Milicˇ Capek, 19,20 who presented Barrow’s definition without clear understanding that time is an abstraction, human construct and not something real in the real world.
This indicates that even in our times the significance of Barrow’s view was not recognized and clearly understood.
Barrow, nevertheless, influenced Newton, who did not acknowledge the abstract character of time and that it characterizes continuation of being of the real things in space
and who expressed it as follows: “Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year."
Newton expressed the continuation of being in the first part as “absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration."
He does not express the “own nature” of time, that it is an abstraction, but he expresses the most important aspect that it “flows equably without relation to anything external,” that for time to be of use for mathematics, it needs to be uniform without regard to what is happening in the world.
Thus, Newton’s definition is telling that mathematical time is something that is independent of the real world and which is uniform.
He did not express it as an abstraction, yet his definition of mathematical time was sufficiently correct for his theoretical work to provide correct quantification of the
physical phenomena; to have a uniform measure of the continuance of the world.
He also presented that this time is also called by another name, “duration;” the term which has been used with this meaning before him and is used all the way to our time.
In the second part of his definition, Newton expressed that instead of true time (duration), we commonly use “relative, apparent, and common time,” which “is some sensible and external (whether accurate or unequable) measure of duration."
Here, he expressed the fact that the measure of time is external to the true time, external to the abstraction of time, whether it is “accurate or unequable,” whether it is
accurately measured or equal or unequal, it is still different from the true time.
Also here Newton is correct in distinguishing that our determination of the time measure is external to our abstraction, because we measure time periods by real things which are external to the abstraction of time.
Thus even though Newton’s understanding and definition of time was not as clear as Barrow’s, its meaning gave him sufficient understanding to establish mathematical (scientific) time as something external to the world, something which is uniform measure and thus can provide an objective, uniform evaluation of the happenings in the world.
Newton’s definition, in contrast to Barrow’s, was well known.
On one hand, it made an impression on empiricist John Locke; on the other hand, Newton’s definition was criticized by mathematician and rationalist Leibniz, and
many others.
Leibniz rejected the idea that moments of absolute time exist in their own right.
Instead, he thought of them as classes of events related by the concept of simultaneity and defined time as the order of succession of phenomena.
While Newton’s definition of time stressed the continuous character of time periods, Leibniz stressed the sequence or the order of events related by concept of simultaneity.
Various terms of Newton’s definition of time, especially his use of adjective “absolute,” has been debated by some philosophers all the way up our time.
It was debated by those who did not have a clear understanding of the “nature of the time,” that it is an abstraction and that in science, we need to have an objective “external” measure so that we can compare all the happenings to the same “common” measure; and the adjective “absolute” expresses just that.

HELP4
E. Einstein’s view of time

In his 1922 book “The Meaning of Relativity,”13 Einstein revealed his view of time: “The object of all science, whether natural science or psychology, is to coordinate our experiences and to bring them into a logical system.
How are our customary ideas of space and time related to the character of our experiences? The experiences of an individual appear to us arranged in a series of events; in this series the single events which we remember appear to be ordered according to the criteria of “earlier” and “later,” which cannot be analyzed further.
There exists, therefore, for the individual, an Itime, or subjective time.
This in itself is not measurable.
I can, indeed, associate numbers with the events, in such a way that a greater number is associated with the later event than with an earlier one; but the nature of this association may be quite arbitrary.
This association I can define by means of a clock by comparing the order of events furnished by the clock with the order of the given series of events.
We understand by a clock something which provides a series of events which can be counted, and which has other properties of which we shall speak later."

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From this statement, we can see that Einstein’s views of time came from using time for logical ordering of events and not for a purpose of quantification of the continuation of
existence of physical world.
Einstein’s view of time was influenced by mathematician/rationalist Leibniz, not by empiricist Locke, whose understanding was similar to Newton’s.

F. Reality versus its models

It was not only Einstein who did not see that scientific time, time with measure, is a human construct and not something real what participate in or what influences the physical
processes.
That he did not see that our theories are only models made out of abstractions and imaginary things by which we try to depict the physical world, that he did not distinguish clearly what is real and what are abstractions and imaginary things; and changed the abstraction of time to suit his purpose.
His contemporaries, his role models Lorentz and Mach, were not exactly clear on these matters either.
It was actually the problem that always plagued philosophers all the way to Einstein’s contemporaries like Bertrand Russell, Ludwig Wittgenstein, and logical positivists; philosophers who centered their philosophies around logic and rational thinking.
They did not realize that logic is also only a humanmade system of abstractions, which does not need to reflect the “logic” of real world.
Only after Go¨del’s Incompleteness Theorem in 1931, logicians and philosophers realized the limits of logic and deductive thinking, and the need for oneonone correspondence between the real things and abstractions which we use to represent them.
That their theories, models, or logical systems can be consistent
but they cannot tell us whether they represent the real world
or not.
That abstractions, which science and philosophy use,
have to be grounded more closely in the facts and observations of the real things if we want them to reflect the truth
about the world in which we live.
The basic principles (or
axioms) of a theory must be based on and reflect correctly
the nature of the studied real world, and must reflect the empirical evidence.
Einstein generated a model, which to him and his followers looked consistent, yet as this study found, it was
inconsistent with many things we know about the real world
from our empirical experiences.
Einstein based his theory on
his metaphysical first postulate from which he deduced his
second postulate, which then contradicted the empirically
based Galileo relativity principle and transformation equations.
Then he got his Eureka, with which he modified the
abstraction of time for the moving coordinate system and got
what he wanted; that the Maxwell–Lorentz equations would
be invariant to transformation between coordinate systems.
Yet, each coordinate system would have to have different
measures for distance and time to achieve such invariance.

G. Einstein’s space

Einstein’s understanding of space was mentioned in his
book “The Meaning of Relativity”13 where he presented it
the following way:

“For the concept of space the following seems
essential.
We can form new bodies by bringing
bodies B, C, … up to body A; we say that we
continue body A.
We can continue body A in such
a way that it comes into contact with any other
body, X.
The ensemble of all continuations of
body A we can designate as the “space of the body
A."
Then it is true that all bodies are in the “space
of the (arbitrarily chosen) body A."
In this sense
we cannot speak of space in the abstract, but only
in the “space belonging to a body A."
The earth’s
crust plays such a dominant role in our daily life in
judging the relative positions of bodies that it has
led to an abstract conception of space which
certainly cannot be defended.
In order to free
ourselves from this fatal error we shall speak only
of “bodies of reference,” or “space of reference."
From this description, we can see that Einstein did not
see the space as a vacuum or a common emptiness for all the
matter to exist and move in it.
He saw it as “space of the
body” or as “space belonging to a body."
Thus he spoke of
“bodies of reference” and “space of reference,” space which
belongs to the body of reference.
He did not see space separately from matter, from physical bodies, but as a continuation or extension of them.
Reference systems or coordinate
systems are human constructs; they do not have their own
space.
They can have it only as imaginary things in our
mind.
In Section II B, we saw that Einstein eliminated ether,
the medium which transmits waves, and gave the physical
property of transmitting wave to space.
He eliminated the
physical entity, the ether, and retained its property of transmitting waves in space.
He gave it to each space of reference, to space which belongs to the body of reference.
Thus
for Einstein, space did have material base, its body of reference and the material property of transmitting waves.
The
physical property, the abstraction, the human construct
which characterizes the behavior of physical medium, is separated from its material base and is given to space, to space
which belongs to the body of reference.
Wave became an
immaterial property of space which belongs to body of reference, and each space of reference had to have the same
velocity of wave propagation.
In Section II A, we saw that Einstein believed unconditionally in the wavebased nature of light and electromagnetism, and with that, in the fact that velocity of propagation of
these phenomena is independent of its source.
Now we can
see that he gave this wave propagation with its constant
velocity of propagation to each space which belongs to each
body of reference and thus got his second postulate.
Again as with time, distance and coordinate systems,
Einstein did not recognize the difference between the real
things, real world on one side and abstractions and imaginary
things which we create on the other side.
He separated the
characteristic of matter to transmit waves and gave it to
space, to emptiness free of any matter.
In his mind, Einstein
intermingled abstraction into a real world into the real
emptiness free of any matter and any material properties.

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He connected space to the body of reference and extended
material properties into the space.
He did not see that there
must be some intervening matter which causes the fields.
In Section VII, after analyzing the resulting equations,
we will see that the Einsteinian space or space–time continuum would not only transmit waves but it would also provide
time dilation, length contraction and limit movement below
velocity of light.
At the top of it, his space–time continuum
would be unisotropic, providing asymmetry in the moving
coordinate system so that things in positive direction will be
younger and those in the negative direction would be older;
reversing the younger for older and vice versa if we change
movement from positive to negative direction.
Einstein got lost in the wilderness of human constructs,
abstractions, and imaginary things which we create to represent world in our minds.
He projected them back on the real
world and got these absurd results.
These bizarre properties
of Einsteinian space, Einsteinian space–time continuum,
which belongs to the body of reference, goes along with his
idealistic/theistic ontological views of universe governed by
some higher level laws and with his rationalistic method of
deducing his theory from them.
It is a problem of all idealistic philosophers and scientists as well as religious people
that they project our human constructs which we imagined
back on the world as if they would be there and participated
there, instead of taking them for what they are, that they are
only our attempts to represent the world in our minds.
No
surprise that the use of this theory as a basis of other ones
generated today’s theoretical physics and astrophysics which
look more like science fiction than science.

VI. EINSTEIN’S CONCEPT OF RELATIVITY OF SIMULTANEITY

In his 1917 book Relativity, the Special and the General Theory,
Einstein gave the most extensive description of his method by means of which to decide whether two events are
simultaneous, and a thought experiment that explained and presumably led him to the relativity of simultaneity and a
new concept of time.
The thought experiment that explains why “time could not be defined absolutely but is in the inseparable relationship with the signal velocity."

A. Definition and method of simultaneity

in the 1917 book
In this book,7 Chapter VIII, Einstein wrote:

“Lightning has struck the rails on our railway
embankment at two places A and B far distant
from each other
I make the additional assertion
that these two lightning flashes occurred
simultaneously… …
Supposing that as a result of
ingenious considerations, an able meteorologist
were to discover that the lightning must always
strike the places A and B simultaneously, than we
should be faced with the task of testing whether or
not this theoretical result is in accordance with
reality
We encounter the same difficulty with all
physical statements in which the conception
“simultaneous” plays a part.
The concept does not
exist for the physicist until he has the possibility of
discovering whether or not it is fulfilled in an
actual case
We thus require a definition of
simultaneity such that this definition supplies us
with the method by means of which, in the
present case, he can decide by experiment whether
or not both the lightning strokes occurred
simultaneously."
Here, we can see that Einstein intended to provide a definition of simultaneity that will allow us to decide, by experiment, which events are simultaneous and which are not, and that judgment of simultaneity will be based on empirical evidence obtained from such experiment.
Then he proposed a definition and a method for determination of simultaneity:

“By measuring along the rails, the connecting line A—B should be measured up and an observer placed at the midpoint M of the distance A—B.
This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90
degrees) which allows him visually to observe both places A and B at the same time
If the observer perceives the two flashes of lightning at
the same time, then they are simultaneous… definition would certainly be right, if only I knew
that the light by means of which the observer at M perceives the lightning flashes travels along the
length A—M with the same velocity as along the
length B—M."
After some questioning of this method, Einstein followed:

“I maintain my previous definition nevertheless, because in reality it assumes absolutely nothing about light
There is only one demand to be made of the definition of simultaneity, namely that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled.
That my definition satisfies this demand is indisputable
That light requires the same time to traverse the path A—M as for the path B—M is in reality neither a supposition nor a hypothesis about the physical nature of light but a stipulation which I can make of my own free will in order to arrive at the definition of simultaneity."

In the above text no definition of simultaneity is shown. i.e. that two events happened simultaneous.

We can see that Einstein avoided the question of nature of light and characterized it for his purpose only by the requirement “that light requires the same time to traverse the
path A—M as for the path B—M."
In Chapter IX, the thought experiment, which explained the relativity of simultaneity, is then presented:

“Up to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.
We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1.

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People travelling in this train will with advantage use the train as a rigid referencebody (coordinate system); they regard all events in reference to the train.
Then every event which takes place along the line also takes place at a particular point of the train.
Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.
As a natural consequence, however, the following question arises:
Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative."
The question is if two events are simultaneous. If they are relative to the train or to the embankment




We need to interrupt this explanation and make a few important comments.
In defining his method for judging the simultaneity of events, Einstein stated: “it assumes absolutely nothing about light”… “that light requires the same time to traverse the path AM as for the path BM is in reality neither a supposition nor hypothesis about the physical nature of light but a stipulation which I can make of my own free will in order to arrive at the definition of simultaneity."
Yes, it is not telling us anything about the nature of light but it assumes certain behavior of light; behavior that it will traverse the path AM and BM in the same time period.
That the same distances in the embankment coordinate system will be traversed in the same time period.
Then in the description of his train thought experiment, he stated: “also the definition of simultaneity can be given relative to the train in exactly the same way as with respect
to the embankment."
This sentence is not clear enough.
Did he mean that this definition can be given relative to the train in the exactly the same way using different signals generated by sources at the ends of the train (in the moving
coordinate system) or using the same signals which were generated in the stationary (embankment) coordinate system? From the further description, it is clear that Einstein
meant that also for the train the same stipulation is valid, namely that the same light signal used for the stationary coordinate system will traverse the path from both ends of
the train to the middle of it in the same time period.
Einstein did not ask the question of the source of light because he assumed validity of the second postulate. He assumed that light will travel in both coordinate systems with the
same velocity c “independent of whether this ray of light is emitted by a body at rest or a body in motion,” regardless of whether it was generated in the embankment or on
the train.
By doing so, Einstein did not make any supposition or hypothesis about the physical nature of light but he did assume validity of the second postulate.
The requirement of his method was his stipulation which he made of his “own free will in order to arrive at the definition of simultaneity."
And in it, he assumed the validity of the second postulate.
Thus this method, which was supposed to explain and provide empirical evidence or the feeling of something real, was based on the hypothesis of validity of the second postulate
and not at any experimental evidence. This method, together with assumption of second postulate, only pretended to have anything to do with any empirical evidence of the train
experiment. It was only a thought experiment which assumed validity of the second postulate from the beginning.
Now we can return to Einstein’s explanation. When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the midpoint M of the length A! B of the embankment.
But the events A and B also correspond to positions A and B on the train. Let M’ be the midpoint of the distance A ! B on the travelling train. Just when the flashes (as judged from
the embankment) of lightning occur, this point M’ naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M’ in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B
would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.
Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.
Observers who take the railway train as their referencebody must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.
We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of
simultaneity).
Every referencebody (coordinate system) has its own particular time; unless we are
told the referencebody to which the statement of
time refers, there is no meaning in a statement of
the time of an event.
Now before the advent of the theory of relativity it
had always tacitly been assumed in physics that
the statement of time had an absolute significance,
i.e. that it is independent of the state of motion of
the body of reference.
But we have just seen that
this assumption is incompatible with the most natural definition of simultaneity.
Because Einstein used the light flashes generated in the embankment coordinate system, they could not arrive into the middle of the train simultaneously.
Because Einstein assumed the validity of the second postulate, according to which the light would have to travel also with the same velocity in the moving coordinate system, he concluded that these events were not simultaneous for the observer on the train because “every referencebody (coordinate system) has its own particular time."

Such a final conclusion is not very practical.
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B. Graphical depiction and analysis of Einstein’s
thought experiment

One important shortcoming of Einstein’s writings is that
he presented his verbal and mathematical thinking without
sufficient documentation of the visual thinking behind his
verbal descriptions.
That left us to imagine the visual form of
his thought experiments and their explanations.
There is no
way that one can understand and describe verbally and mathematically the visual aspects of space and time without sufficient visual images (pictures) and graphs (temporal images).
Therefore, there is a need to recreate Einstein’s thought
experiment and convert his verbal thinking into pictures and
graphs.
A picture is still worth a thousand words.
Classical mechanics assumed that light propagates with
infinite speed or too fast to measure, and thus the time interval
for light to travel from an event to an observer, or within the
coordinate system was not recognized as an issue and simultaneity of events did not raise any conceptual difficulty.
This situation has changed when Einstein proposed his definition of simultaneity and the method that will allow us to decide by
experiment which events are simultaneous.

That is not simple.



Now any observer of an event at distance needs to take into account a time delay
due to light travel, the time period of light travel, and with
that, the question of simultaneity of events at different places
became more complicated then Einstein led us believe from
his description of his thought experiment.
Figure 3 shows graphical depiction of this thought
experiment.
It shows a progression of the light flashes during
this experiment in the embankment coordinate system (x, y,
z, t). At time t0, the light flash from point A propagates in
both directions and its position on coordinate x at different
time t is depicted by lines a and b.
Similarly, the propagation
of light flash from point B is depicted by the lines c and d.
Einstein’s method and definition of simultaneity “assumes
absolutely nothing about light… about the physical nature of
light” but it “requires the same time to traverse the path AM
as the path BM."
It assumes the same velocity of light traveling from A to M as for the traveling from B to M.
An observer located at point A experiences the light flash
from point A immediately as it is generated; it is at time t0
,
and the light flash from the point B at time t1.
This light
signal from point A did not need to travel any distance and
so there was no time delay.
On the other hand, light from
point B had to travel the whole distance between point B
and A.
If the observer at the point A would rely only on the
observation of these two flashes of light, he would have erroneously concluded that these two events were not simultaneous.
He would think that point A flashed first and point B
later after time interval Dt ¼ t1 t0. Even though these two
events were simultaneous, the light signal from the point B
was delayed by Dt time interval giving him apparent time
not the real time of the event.
Unless he will get information
on the distance of A from B and the velocity of propagation
of light from B to A, he could not calculate this delay and
could not judge correctly the occurrence of the event at
point B.
Similarly, the observer at point B would arrive at an
erroneous conclusion that these two events were not simultaneous if he relayed only on the observation of the light
flashes as they arrive to him.
This observer would conclude
that point B flashed first and point A later after the same time
interval Dt.
In this case, observer at point B would have to
correct the apparent time of the event at point A to get its
true time.
An observer at a general point X, outside of interval A
and B, could not either observe these two flashes simultaneously.
He would record that flash at point A happened at time
tA and that at point B at time tB, Dt interval later.
Now let us go to Einstein’s observer who happened to be
in the middle at point M and uses Einstein’s method.
He
would see the flashes at the same time, tM and could judge
these two events to occur simultaneously.
This middle position satisfies Einstein’s “stipulation” to arrive at a definition
of simultaneity.
The distance traveled by light from point A
to M equals the distance from point B to M, and if the light
propagates with the same velocity along both paths then the
flashes will arrive at the same time and will indicate simultaneity of the two events.
Yet, these two flashes of light will
arrive also delayed, at time tM.
Because delays of both light flashes were the same, these apparent times coincide and give him a correct opinion on the simultaneity of these two events.
Yet, his judgment was based on the coincidence of apparent times of these two events being the same; not on knowledge of the true times of these events.
Thus this empirical method is based on appearance to a particular observer.
In his considerations, Einstein did not make a distinction
FIG. 3. Progression of light flashes in the embankment coordinate system.
between the simultaneity of events and the simultaneity of arrival of the messengers (light flashes) to a particular observer.

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In his method, Einstein depended only upon simultaneity of arrival of the light signals.
At the top of Fig. 3, there is a graph of the time difference between arrivals of light signal from point A and B as a function of the location of observer in the coordinate x.
We can see that there is only one place, point M where the observer could see these two flashes of light arriving at the same time, delayed for the same time interval, and giving
the same apparent time of both events.
It is a place where line b intersects line c.
Our observer at point M would be the only one who could judge the simultaneity of these events correctly using Einstein’s method, yet he would still judge it
by appearance with the time delay.
The moment he would
step out of the point M into the right or left and attempted to
do the same, he would have learned that this method does
not provide a good answer anymore, and so is not usable
outside of point M.
The moment the velocities of light signals from A and B would not be the same, the time delays
would be different, and he would not be able to use this
method either.
Figure 4 now shows the same progression of light flashes
as Fig. 3 with addition of the train progression; all in the
embankment coordinate system.
The location of the train at
time t0 is shown by the strong solid line between points A
and B.
The progression of the train at different times
is depicted by line f–trajectory of the front of the train, line
e–trajectory of the train end, and line m–trajectory of the
middle of the train M0
.
The velocity of train in this example
is one half of the velocity of light.
This progression of the light flashes and the train shown
here in detail is what Einstein described as follows:
Let M0 be the midpoint of the distance A–B on the
traveling train.
Just when the flashes (as judged
from the embankment) of lightning occur, this
point M0 naturally coincides with the point M, but
it moves towards the right in the diagram with the
velocity v of the train.
If an observer sitting in the
position M0
in the train did not possess this
velocity, then he would remain permanently at
M, and the light rays emitted by the flashes
of lightning A and B would reach him
simultaneously, i.e. they would meet just where he
is situated.
Now in reality (considered with
reference to the railway embankment) he is
hastening toward the beam of light coming from
B, whilst he is riding on ahead of the beam of light
coming from A.
Hence the observer will see the
beam of light emitted from B earlier than he will
see that emitted from A.
Observers who take the
railway train as their reference body must
therefore come to the conclusion that the lightning
flash B took place earlier than the lightning
flash A.
This is a point where Einstein made an erroneous conclusion.
The trajectory of point M0
(line m) intersects the trajectory of the light flash from point B (line c) at time t M0
c
and the trajectory of the flash coming from point A (line b) at
time t M0b.
As Einstein correctly imagined the observer at
point, M0
“will see the beam of light emitted from B earlier
than he would see that emitted from A."
Of course, because
he stepped out from the only point where Einstein’s method
gave the correct answer.
FIG. 4. Progression of light flashes and the train in the embankment coordinate system.

HELP5
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The flash from point B meets the observer situated at the middle of the train, point M', just when he is at point D of embankment.
The distance traveled from point B to a point D where the light signal meets the observer M' was much shorter than the distance traveled by light from the point A to meet the observer M' ; just when he
was at point B of embankment.
This observer cannot apply the Einstein’s method using the light signals generated by sources in the stationary coordinate system to judge simultaneity in the moving system.
He was at the midpoint M between the two events at the time when they happened, but then he moved out of it and the actual distance the light signals had to travel to reach him were not the same, giving him
different time delays and the incorrect notion that these events were not simultaneous.
The actual distance the light from point A had to travel to reach the observer at point M' was twice as long as the distance to travel to the observer at point M of the embankment.
The distance the light flash from point B had to travel to meet the observer at M' (between point B and D) was only two thirds of that between B and M.
Thus this observer at point M' cannot apply the Einstein’s “most natural” method to judge simultaneity
using the light signals generated in the stationary coordinate system.
Such an application of this method would mislead him.
If the observer at middle point M0 would acquire more
information from other observers on the train, he would be
able to analyze and plot it as we have done and correct the
apparent times by time delays, and thus would be able to
arrive at the correct conclusion: The conclusion that these
two events, even though they did not appear so to him, were
simultaneous and happened at time t0.
And so would Einstein
if he would have analyzed his thought experiment and his
empirical method in detail.
What did we learn from this analysis?

(a) Einstein’s empirical method to judge simultaneity of
events based on simultaneity of arrival of light signals
generated by these events gives a correct opinion only
in points of space which are equidistant from these
events at the time of arrival of the light signals and if
the speed of propagation of these two signals in that
coordinate system is the same.
Its application by the
observer in the middle of embankment gave Einstein
correct answer.
(b) The application of this method by a moving observer,
the observer in the middle of the train (point M0) using
the light signals generated in the stationary system,
gives an incorrect, misleading conclusion that even though the two events at point A and B were simultaneous that they were not.
What matters is not that point
M0 was equidistant at the time of events but where
the point M0 was at the time of light signals arrival.
Observer in the moving coordinate system would have to use light signals generated by sources at rest in his coordinate system to be able to judge simultaneity of distant events at point A and B.
Einstein did not analyze in detail his thought experiment and thus did not see that the observer in the middle of the train cannot use this method with the signal generated in the embankment system.
He applied this method using the light signals generated in the embankment system.
He relayed only on the appearance, on the apparent times, and on arrival of the light signals to one particular observer at point M0 of
train and, based on it, he made the false conclusion that these events were not simultaneous in the moving coordinate system.
While this method gave Einstein the correct opinion on simultaneity of events in the embankment coordinate system, where the observer was stationary relative to and equidistant from these two events, it gave a false opinion to the observer in the moving train with moving coordinate system because he was not equidistant from these two events at the time of signals arrival.
The application of this method, using light signals generated by sources which were not at rest in his coordinate system, was incorrect.
This incorrect application of this method in his thought experiment gave Einstein a false opinion and mislead him to
declaring relativity of simultaneity, allowed him to abandon the absolute time, and redefine time and distance.
As he wrote
at the end of the description of his train thought experiment:
“We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).
Every referencebody (coordinate system) has its own particular time; unless we are told the reference body to which the statement of time refers, there is no meaning in a statement of time of an event."
Einstein used the same light flashes generated in the stationary physical system (coordinate system) to judge the simultaneity in the moving physical system (moving coordinate system).
Since these two flashes did not arrive into the center of the train simultaneously, he concluded that the measure of time (and distance) must be different in the moving physical system than in the stationary one.
Einstein did not understand that coordinate systems are just human imaginary constructs and the measures of time and lengths are set by convention.
Putting it into the mathematical terms, Einstein changed the independent variables of time and lengths into dependent ones and thought that it will solve the problem which he created by hypothesizing his first and second postulates.
The lack of distinction of the real and apparent times, times delays due to light signal travel, difference between simultaneity of events and simultaneity of arrival of light signal caused Einstein to weave into his thinking, his moving coordinate system, his theory and equations the apparent times and times delays due to the light signal travel instead
of the real times.
It caused him to include into his consideration the messenger, the light and the time delays from the
events to the observer, which is demonstrated in his statement (presented above) in the Kyoto lecture: “My interpretation was really about the concept of time.
Namely, time
could not be defined absolutely, but is in an inseparable relationship with the signal velocity."
Yes, the apparent time has
“an inseparable relationship with the signal velocity,” but
not the real time of the event.

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Thus, “the gist most directly related to the development
of” Einstein’s thought and to the theory of special relativity,
the concept of time; concept that “time could not be defined
absolutely but is in an inseparable relationship with the signal velocity”; was based on a misunderstanding of the time
delays, simultaneity of events and appearance of simultaneity to a particular observer situated in the coordinate system.
Thus, we can see that the thought experiment with the
incorrectly applied method for judging simultaneity in the
moving coordinate system led Einstein to the mistaken interpretation of simultaneity of events and to the relativity of simultaneity.

C. Einstein’s inconsistency in application of his own
definition of simultaneity

In the description of the train experiment, Einstein
clearly stated “Also the definition of simultaneity can be
given relative to the train in exactly the same way as with
respect to the embankment."
He viewed this method with
assumption of the validity of the second postulate, validity of
the invariance of the light velocity.
In his mind, from his
viewpoint, the use of the light generated in the stationary
coordinate system in this method was appropriate and satisfied his criteria.
The observer at midpoint M0 of train was the
same distance from point A0 and B0 and according to the second postulate both flashes of light in the moving coordinate
system should also have the same velocity as in the embankment and thus should have arrived at the same time.
“Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.
Observers who take the railway train as their reference body must therefore come to conclusion that the lightning flash B took place earlier than the lightning flash A."
If the definition of simultaneity would be really given relative to train in exactly the same way as with respect to the embankment, then Einstein would have originated light
flashes at the beginning and the end of the moving train.
Then the light flashes would travel with the same speed relative to train coordinate system.
The observer in the middle of the train would then see them to arrive simultaneously while to the observer at the midpoint M of embankment, they would not appear simultaneous.
But these flashes of light would travel differently than the ones generated in the
embankment system.
They would be different set of light flashes as shown in Fig. 5. In this figure, the progression of
the light flashes generated in the train system, solid lines, are compared with the progression of the light flashes generated in the embankment, light lines.
Thus in his thought experiment, Einstein did not follow his own definition of simultaneity and thus he developed incorrect notion of relativity of simultaneity.
He did have a right method but applied it incorrectly to judge simultaneity in the train coordinate system.
The Michelson–Morley experiment showed that light travels with the same velocity in all directions away from the light source.
It did not indicate anything about light traveling in the coordinate system moving relative to the source of the light.
That was the addition which Einstein did.
The Michelson–Morley experiment did not indicate that light generated by a source at rest would also travel with the same speed in the moving coordinate system, moving with velocity v relative to the source.
That assertion came only in the Einstein’s hypothetical second postulate derived from the requirement of the first postulate and the Maxwell–Lorentz equations.
FIG. 5. Progression of light flashes generated at the train.

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As we have seen, Einstein did not consider both cases.
He did not give the definition of simultaneity relative to the train exactly the same way as with respect to embankment, and thus, he ignored the fact that from Michelson–Morley
experiment, we can conclude that there are two possible sets of light flashes for this method.
Once Michelson–Morley experiment failed to detect the difference in velocity in different direction, required by the ether based theories, the wavebased theories were out and the only thing we learned from this experiment is that light propagates with the same velocity in all directions away from its source.

D. Concept of relativity of simultaneity does not
satisfy the Einstein’s own criteria of validity

In the description of the definition and method of simultaneity in his 1917 book presented above, Einstein states:

“The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case.
We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment, whether or not both the lightning strokes occurred simultaneously."

What is important is a clear definition of what simultaneous means.
One defintion of simultaneous could be: Two events are simultaneous if they happen at the same time.
However this creates a new problem: what means time.
You can also state this different: What is the time of an event.
This requires the introduction of the concept: the age of the universe.



This analysis showed that this definition and method of simultaneity does provide means by which to “decide by experiment whether or not both the lightning strokes occurred simultaneously,” but Einstein applied it incorrectly for the moving coordinate system.

"To decide by experiment" is a tricky concept.
What you need a method is to decide the moment and or the time when the lightning strikes.

It further showed that Einstein deduced the relativity of simultaneity from his incorrect application of this method and from the hypothetical second postulate.
Thus, the concept of relativity of simultaneity was not derived by experiment but by deductive thinking in Einstein’s “Thought Experiments.”
Thus, the concept of relativity of simultaneity does not meet Einstein’s own criteria of validity and so it “does not exist."

E. Definition and analysis of the simultaneity as presented in Einstein’s 1905 paper

The actual definition and the method of simultaneity that Einstein used in his original 1905 paper are slightly different from those discussed in his 1917 book and analyzed above.
While in the 1917 book he used the empirical method based on two events and two light flashes, in his original paper he used a method based only on one light flash (signal) traveling from an event at point A to a mirror at point B and back to point A.
He used this method to demonstrate the relativity of simultaneity as well as to synchronize clock at point B with the one at point A.

There are two physical issues to study:
1. How to synchronize two clocks
2. How to demonstrate if two events are simultaneous.
The second issue can only be solved if the first one is solved.



We need to analyze this second thought experiment and approach to relativity of simultaneity to show that it suffers the same shortcomings.
Also, because this second approach served for the development of the equations of this theory, the understanding of it and its shortcomings will help us to understand the meaning of these equations and the logical structure of the whole theory.
This method of synchronization of clocks is now presented in Fig. 6, depicted similarly to the previous train thought experiment.
There is an observer with a clock at point A whose clock indicates time at this point, “Atime” as well as an observer at point B with clock indicating time at point B “Btime”; “a clock of exactly the same constitution as that at A.”
In this method of synchronization, we have only one light flash, at point A at the “Atime” tA which propagates to point B.
It reaches point B at the “Btime” tB, observed by the observer at this point and read from his clock.
After the light flash reflects, it travels back to point A and arrives there at “Atime” t'A, as observed by the observer at point A on his clock.

My understanding is that this type of synchronisation require clocks which are already synchronized. This does not seam the correct way.

This Einstein’s method of synchronization of clocks requires the same as the train thought experiment, namely that light travels the same distance with the same velocity in
both directions and thus the time period for travel from point A to point B is the same as that from point B to point A; even though Einstein does not mention it.




Instead he established
“by definition that the ‘time’ needed for the light to travel
from A to B is equal to the ‘time’ it needs to travel from B to
A."
It assumes that velocity of light c equals twice distance
from A to B divided by the total time period for signal travel
t
0
AtA. The two clocks in the stationary coordinate system (at
point A and B) are then synchronized if the “Btime” reading
tB minus “Atime” reading tA equals “Atime” reading t
0
A
minus “Btime” reading tB.
Figure 7 presents a progression of this thought experiment of synchronization of clocks in moving rod, coordinate
system, depicted in the stationary coordinate system, similarly to the train thought experiment.
It uses the same light
flash which was used to synchronize the clocks of the stationary coordinate system and depicted in Fig. 6. There is “a
rigid rod at rest; its length, measured by a measuring rod that
is also at rest, shall be l.
We now imagine that the axis of the
rod is placed along the Xaxis of the coordinate system at
rest, and that the rod is then set in uniform parallel translational motion (velocity v) along the Xaxis in the direction of
increasing x."
3
The rod is depicted by a strong solid line
between its endpoints A and B at time tA, and its progression
FIG. 6. Method of clocks synchronization in the stationary coordinate system.

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at different times is depicted by lines e and f.
Line e shows the progression of the endpoint A and line f progression of
the endpoint B in time.
The velocity of this; now moving rod; is again assumed to be one half of the velocity of light.
At the time tA, the points A and B of the moving rod were in position A* and B* of the stationary coordinate system.
“Further, we imagine that the two ends (A and B) of the rod are equipped with clocks that are synchronous with the clocks of the system at rest, i.e., whose readings always correspond to the ‘time of the system at rest’ at the locations they happen to occupy; hence, these clocks are ‘synchronous in the system at rest.
We further imagine that each clock has an observer comoving with it, and that these observers apply to the two clocks the criterion for synchronism formulated in Section I. Suppose a ray of light starts out from A at time tA, is reflected from B at tB, and arrives back at A at time t
0
A
.”3
At the time tA, the point A of moving rod is at the point A*
and point B at the point B* of the stationary coordinate system.
Because Fig. 7 is a depiction in the stationary coordinate system, the light travels with constant velocity c in the
stationary coordinate system.
Again, Einstein was not clear
on the source of the light in this thought experiment.
From
his calculations of tBtA and t0 AtB, above, it is clear that he
meant velocity of light in the stationary system is c.
The ray of light is depicted by lines a and b.
Line a for travel of light from point A to point B and line b for the return to the point A.
The location of the moving rod in the stationary coordinate system at the time of reflection of the ray of light at point B is depicted by the solid line at the time tB and its location at the return of the light to point A at the time t
0
A
is depicted by the solid line at time t
0
A
. Because
the clocks at point A and B were synchronized with the
clocks of the stationary system, they will show the time tB at
the time light will reflect at point B and time t
0
A
at the time of
arrival of light to point A.
We can now compare the synchronization of clocks by
observers at the stationary coordinate system (Fig. 6) with
the synchronization of the clocks by observers, at moving
coordinate system (Fig. 7). This comparison shows that
when Einstein imagined synchronization of the clocks in the
stationary coordinate system (Fig. 6), the light reflected at
point B of stationary system and returned along the same
length back to point A at time t
0
A
. This satisfies his requirement that time period for light travel from A to B equals the
time period for the light travel between B and A.
In case of moving rod (Fig. 7), the same light flash has to travel further
to reach point B of the moving rod than to point B* of the
stationary coordinate.
For comparison, the screened line in
Fig. 7 shows the progression of the light flash which is generated in the moving coordinate system.
We can see the same error, which we saw in the train thought experiment.
Namely, that when the same clock synchronization method is applied for the moving observer and moving coordinate system, using the light flash generated in the stationary coordinate system, it requires the light signals to travel different distances and thus requires different time periods for light to travel.
When the flash of light arrives to the point B* of stationary coordinate system, where the point
B of the moving rod was at the time tA, the rod and its endpoint B are already gone and thus the light has to travel further along the stationary coordinate system before it can
catch up with point B, just at time when point B is at the
level of point D* of stationary system.
In this particulate case where velocity v equals 1/2 of the velocity of light c, the light flash arrives at point B of moving rod just when it is passing point D* of stationary coordinate system; which is at
twice the distance between A* and B*.
Similarly, as in the train thought experiment, this clock synchronization method using the light signal generated in the stationary coordinate system is not applicable for the moving coordinate system.
This method requires that light travels the same distance with the same velocity in both directions and thus the time period for travel from point A to point B is the same as from point B to point A.
Using his second postulate, Einstein established “by definition that the
‘time’ required by light to travel from A to B equals the
‘time’ it requires to travel from B to A."
Yet the application
for the moving rod required light to travel twice the length
than between A* and B* before it reached the end of the
moving rod B; and thus it took it twice the time period before
it reached the end of the rod B.
Similarly the length traveled
by light on the way back was only 2/3 of distance between
A* and B*, and so the time period for the return trip of the
light signal was shorter.
Thus these two time periods of
light travel could not be the same.
Or, looking at it from the
moving coordinate system Fig. 8 (Galileo transformation
FIG. 7. Synchronization of clocks in the moving rod depicted in the embankment coordinate system.

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equations), the distance the light traveled between point A
and B and between B* and A* was the same but not the velocity of the light.
That was c v in direction from A to B
and c þ v in the opposite direction.
In both cases, Einstein
violates rules of his own method.
Using the same flash of light traveling with the velocity c in the stationary system
gives two different velocities for the same light flash depicted
in the moving coordinate system; velocities c v and c þ v.
In the train thought experiment, we saw that we cannot rely only on the arrival of light flashes.
That to judge simultaneity by an observer in the moving coordinate system, we need all information about the light travel; the actual distance and velocity to calculate time delays.
Similarly, in this clock synchronization experiment the time period for travel
from A to B and from B to A cannot be the same because the
light flash traveled different distance on the first leg of its
journey from A to B than on the return from B to A.
To
declare “by definition” that these two time periods have to
be the same and then to declare relativity of simultaneity
because they were not the same due to travelling different
distances does not make any sense, at least in the real world.
In the world of fiction, one can make any assumptions he
desires.
Yet, then he is not developing a theory, which
depicts realities of the world, but creates an imaginary fictitious world which has nothing to do with the world in which
we live.

VII. EINSTEIN’S TRANSFORMATION EQUATIONS


A. Einstein’s problem and the idea of relative time

Let us go back to Fig. 7. In this figure, we have seen that
light signal generated in the stationary system had to travel
longer distance on the first leg of its journey from point A to
point B, distance DL1 than distance DL2 on the second leg of
its journey from point B back to point A.
Similarly, the
time period Dt1 for travel from point A to point B was much
longer than the time period Dt2 for travel from point B back
to point A.
We can also look at the Fig. 8 where this clock
synchronization experiment is depicted in the moving coordinate system using Galilean coordinates.
Here, the same
light flash is traveling the same distance DL on the first leg
of its journey from A to B as on its second leg from B to A,
but with different velocity.
With velocity c – v for the first
leg and c þ v for the second leg; according to the law of the
additivity, the Galilean transformation equations.
Einstein assumed, according to the second postulate, that the light flash generated in the stationary coordinate system will travel with the same velocity in the moving coordinate
system as in the stationary one, and that it is due to the length contraction and time dilation in this moving system.
One can
declare that length DL1 of the first leg of light journey (in
Fig. 7) equals some lower value DL
0
1
and adjusts time period
Dt1
to some value Dt
0
1
to achieve the same numerical value c
for the moving coordinate system.
Alternatively one can
declare DL2 of the second leg of light journey to equal some
higher value DL
0
2
, and again adjust time period Dt2
to some
value Dt
0
2
to get the same numerical value c, but not for both
legs of the light journey at the same time.
Or in other words,
in terms of velocities and Galilean transformation equations
(see also Fig. 8); one can declare velocity of light in moving
coordinate system c
0 ¼ v – c or c
0 ¼ v þ c and achieve that
the velocity of light in the moving coordinate system c
0
equals c and satisfy it by changing scale of length and time
in the moving coordinate system but not for both cases (for
both legs of the light’s trip) at the same time.
We can achieve
it for the light travel from point A to point B, but that does
not give us then the same c
0 value for travel from point B to
A. Or vice versa, we can please this requirement for travel
from point B to point A, which then does not give us the
same value of c
0
for the travel from point A to B.
Regardless,
how you will try to squeeze or stretch the time and lengths
scales of the moving coordinate system, you cannot make
the resultant velocity of light in the moving coordinate system same for these two light beams traveling in the opposite
directions.
While the scale of time needs to be stretched for
light traveling in one direction, it needs to be squeezed for
the light traveling in the opposite direction.
To satisfy the second postulate, Einstein would have to
provide different sets of measures for his moving coordinate
system; one for the light traveling in the positive direction,
and the other one for the traveling in the negative direction.
We can imagine that if the rod AB, in Fig. 7, would be
moving faster, the time period Dt1 would increase and if the
velocity would be equal to the velocity of light, then the light
flash could never reach the point B and Dt1 would be infinity,
see Fig. 9. As value v exceeds the c value, the distance
between point B and the light flash increases and the light
flash will never reach the mirror at the point B, see depiction
by screened line at Fig. 9.
Thus the use of the Einstein’s
incorrectly applied method of synchronization of clocks is
limited to the range of values v lower than c.
It is not that
FIG. 8. Synchronization of clocks in the moving rod depicted in the moving coordinate system.

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there cannot be any object moving faster than the speed ofmlight.
It is the Einstein’s incorrectly applied method of synchronization of clocks which is not usable for range of values v higher than c.
The method which first of all is not applicable for moving coordinate system using the light signal generated in the stationary coordinate system; as shown in
Section VI; when applied anyway then its use is limited to
values v lower than c.
This realistic depiction of Einstein’s problem shows that Einstein’s idea that “every referencebody (coordinate system) has its own particular time” does not lead to the resolution of his problem.
This is the problem which Einstein told us that he was facing and “solved completely at the first time."
This was the problem which is at the heart of this theory, the problem which is presumably solved by this theory.
It will be interesting to see how Einstein’s equations achieved that.

B. Analysis of the transformation equations of the theory of special relativity

The derivation of Einstein’s transformation equations
was presented in the 1905 paper in the “§3 Theory of transformation of coordinates and time from a system at rest to a
system in uniform translational motion relative to it."
Einstein is again using a signal of light generated in the
stationary coordinate system as it is projected into the moving coordinate system using Galileo transformation (Fig. 8)
and is trying to find the values of length and time which
would satisfy the requirements of his second postulate.
He assumes that time and distance measures are variable quantities and is trying to find a mathematical transformation equation for length and time measures which would satisfy the Galileo transformation equations as well as the requirement of his second postulate, the Eq. (1) for case of his incorrectly applied method of clock synchronization presented in Fig. 7.
He defines the time at point B of the moving coordinate system, when the light flash generated in the stationary system
reached point B, as average of values of tA and t
0
A
.
In his 1905 paper,3
Einstein wrote:
“Suppose that at time s0 a light ray is sent from the
origin of the system k along the Xaxis to x
0
and is
reflected from there at time s1 toward the origin,
where it arrives at time s2; we then must have
1
2
ðs0 þ s2Þ ¼ s1 (1)
or, if we write out the arguments of the function s
and apply the principle of the constancy of the
velocity of light in the system at rest,
1
2
sð Þ 0; 0; 0; t þ s 0; 0; 0; t þ
x
0
c v
þ
x
0
c þ v
¼ s x
0
; 0; 0; t þ
x
0
c v
(2)
From this we get, if x
0
is chosen infinitesimally
small,
1
2
1
c v
þ
1
c þ v
@s
@t
¼
@s
@x
0
þ
1
c v
@s
@t
(3)
Or
@s
@x
0
þ
v
c
2 v
2
@s
@t
¼ 0: (4)
It should be noted that, instead of the coordinate
origin, we could have chosen any other point as the
starting point of the light ray, and the equation just
derived therefore holds for all values of x
0
, y, z.”
Note: Similarly to previous quotes, the symbol V
for velocity of light used by Einstein in his 1905
paper was replaced by c.
Then Einstein goes on with his mathematical development and ends up with following transformation equations for
the length and time which would satisfy his requirements:
FIG. 9. Synchronization of clocks in the moving rod coordinate system for
v ¼ c (solid lines) and v > c (screened lines).

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Since Einstein did not analyze his thought experiment of synchronization of clocks in detail, as we did, he did not see that his problem, the problem which he created himself by postulating the second principle, would require that the moving coordinate system would have to have two different measures, one for each direction of light travel.


Therefore, he did not look for it.
He also did not analyze the case that the moving coordinate system is moving in the opposite direction (for minus v) or even for case that the clocks synchronization would be carried out starting at point B (instead of point A) reflecting light flash at point A and returning to
point B.


If he would have done that, he would have realized
that by expressing the same for travel from B to A or for negative value of v the Eqs. (2) and (3) would have c þ v
(instead of c – v) in the denominator of the right hand terms.
The resulting Eq. (5) for the s would then have plus instead
of minus in front of the second term indicating different values than those he developed.
Because in his view of time, he concentrated on the
instants (simultaneity of events) and not on the time periods
or rate of change; Einstein did not look at the scale of time in
detail.
We can see the scale of time and length better if we
express the resulting Einstein’s Eqs. (5) and (6) for s and n
as the total differentials.
From these expressions, you can clearly see that the
expression for time period Ds provides two different values,
depending whether Dx is positive (for light travel from A to
B) or negative (for travel from B to A).
Similarly if the moving coordinate system is moving in the opposite direction,
the v changes the minus sign in the second terms into plus
and thus provide different value of Ds, than for movement in
positive direction.
Mathematical equations, if properly set up, take care of
the signs (negative values) and derivation of Einstein transformation equations also took care of them.
Because Einstein
did not expect to find two different time measures for s in
the moving coordinate system, he did not look for them.
Thus he overlooked that the results of his effort, the transformation equations which he developed, indicate that to
accommodate his assumption of the second postulate would
require different time measures for his moving coordinate
system depending on the direction of the movement.
Whether movement is in positive or negative direction;
whether v is positive or negative.
Figure 10 now presents the values of s as a function of
position in the moving coordinate system (k system) for the
example presented in Fig. 5. It also shows dials of clocks, at
different places of the moving coordinate system which indicate the required s values and compares them with time values at the stationary one (K system).
The circumference of
these clocks is divided into four onesecond intervals.
At time t ¼ 0 in the stationary coordinate system K, all
the clocks along this system are synchronous and show t ¼ 0.
At the same instant, the value of s at the beginning of the
moving coordinate system k is also zero; s0 ¼ 0, but each
place of the moving coordinate system would have to have
different value of s.
Places in the positive direction would
have to have value of s behind the time at the beginning of
the moving coordinate system and those which are in the
negative direction would have to have value of s ahead of it.
Thus in the moving coordinate system the values of s according to Einstein’s Eq. (5) would be different along the n axis
and thus the clocks according to this theory would have to be
asynchronous in the moving coordinate system.
Einstein, who was so particular about clocks synchronization, ended up with the clocks which would have to be
asynchronous in the moving coordinate system.
Einstein,
who used his method of synchronization of clocks as a basis
of development of his equations, ends up with clocks which
would have to be asynchronous.
What an irony that the
method of synchronization gave him a solution which would
have to have asynchronously arranged clocks to measure
time.
Of course, because as was shown in Section VI E, this
method, the way Einstein applied it (using the light signal
generated in the stationary coordinate for synchronization of
clocks in the moving coordinate) is not applicable.
Thus, the
incorrect application of his method of synchronization of
clocks together with his second postulate provided the solution which is inconsistent with the original purpose; the purpose to synchronize the clocks.
In the development of his transformation equations, Einstein states “First of all, it is clear that these equations must
be linear because of properties of homogeneity that we attribute to space and time."
3
This assumption means that no
region of space is different from any other and with that that
there are no preferred directions in space.
Then he obtained
the transformation equations which would require time to be
asynchronous and so directionally different in the moving
coordinate system.
This equation is inconsistent with his
assumption of homogeneity of space and time.
FIG. 10. Values of T in the moving coordinate system as a function of
position at time zero, for v ¼ 1=2 c.

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Every point in his moving coordinate system would have to have different time.
In Section VII A and in Fig. 7, we saw that during synchronization of clocks in the moving coordinate system using the light generated in the stationary one, the light flash from A to B traveled longer distance and required longer time period than for travel from B to A.
From that, we saw that there is no way to get the same time measure in the moving coordinate system to satisfy the light travel in both directions.
Now we see how this condition can be satisfied.
By providing asynchronously set clocks “asynchronous time” along the moving coordinate system.
This “asynchronous time” would mean that all things in the positive direction would be “younger” and those in the negative direction would be “older."
Further away from the beginning of the moving coordinate system, older or younger, they would be.
And if you would be the observer traveling in such a moving coordinate system and you would move in positive direction, you would become younger than when you would move in the opposite direction, when you would become older.
This long story is also clearly demonstrated if you express x from the Eq. (6) and substitute it into the Eq. (5), you will get s ¼ t
and so you can see that the value of s in the moving coordinate system is a function of t and n; s ¼ f(t; n). That values of s depends on the position n in the moving coordinate system.
That there is not one value of s for all the points along the n axes but each point n in moving coordinate system has its own value of s; its own “time.”
Einstein overlooked all of this.
He addressed the clocks or the s values only at the origin of the moving coordinate system, and thus he did not realize the asynchrony of time in the moving coordinate system.
It is not that clocks would run slower because they move in the uniform movement, with speed v relative to the stationary coordinate system.
It is a requirement of the Einstein’s transformation equations to satisfy the incorrectly applied method of synchronization and second postulate that the time measures would have to be different for the moving coordinate system than for the stationary one.
If clocks which are moving with constant velocity relative to the stationary coordinate would be running slower than those of the stationary system, it would violate or contradict Galileo principle and causality.
For same causes, we would have different effects, different rate of clocks, and thus the whole concept of determinism would have to be changed.
Einstein’s interpretation, of course, does not have any meaning because if we now assume that the moving coordinate system is the stationary one and we express the same, we get the same equations, Eqs. (5), (6) and (7), only the sign minus in front of the second term of equation, Eqs. (5) and (6) will be plus.
Then Einstein’s interpretation will tell us that now the clock in the moving coordinate (formerly stationary one) is running slower than in the other system.
It is an absurdity and the inconsistency in the Einstein’s interpretation of his transformation equations.

C. Application of the Einstein’s equations for
light travel

Einstein developed his transformation equations for the light signals generated in the stationary system and thus the
application of his equations for these light signals provides velocity c.
For the case we presented (v ¼ 1/2c and unit of the length equals 300,000 km) and for both signals running from A to B as well as from B to A of Fig. 7, we will get the
c value equal one.
Different situation is if we looked at the light signals generated in the moving coordinate system.
Let us now look what will happen if the observer travels with the moving coordinate system will decide to use Einstein’s method of clock synchronization and will generate light signals himself.
This is the case which we depicted in the Fig. 7, screened line.
If the distance of the point A and B in the moving coordinate system is 1 unit, then the beam a will reach point B after Dt ¼ 1 s. while it travelled distance
instead of one.
In derivation of his equations, Einstein imposed the condition of the second postulate for the case of light generated in the stationary coordinate system.
Now that we looked at the light flashes generated in the moving coordinate system, the same condition is not satisfied and so the resulting equations cannot provide the velocities equal one.
Thus the results of Einstein’s theory contradict the second postulate when applied for light generated in the moving coordinatesystem.

VIII. WHY THE PRINCIPLES AND THEORIES OF PHYSICS ARE NOT ALWAYS APPLICABLE OR CORRECT

As presented in Section II B, it was the third problem in physics which Poincaré called in 1904 “crises of mathematical physics."
2 In the Autobiographical Notes,8 discussed also in Section II B, we saw that the very beginning of the theory of special relativity came from Einstein’s realization “that
neither mechanics nor thermodynamics could (except in limiting cases) claim exact validity."
That our theories of physical processes are not always exactly valid.
That led Einstein to abandoning the empirical approach to science and led him to his approach, based on the postulating of some universal formal principles and then to deduction of the physical behavior from them.

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From today’s philosophical perspective, we can understand better the reasons why the principles and theories of physics are not always applicable or correct.

A. Ontological reasons

Since the time of Greek philosophers, the Western thoughts were under the influence of atomists and reductionism.
These philosophical ideas came from realization that the real things can be reduced or broken down into smaller ones, into its parts.
This eventually led to understanding of the real things as a hierarchy of things; the hierarchy from the largest to the smaller and still smaller ones, where “atoms” were assumed to be the ultimate building blocks.
With that, philosophers thought that the understanding of the real things can be derived from the understanding of its parts.
On the other side, the Eastern philosophers stressed the unity of things; they stressed the whole and not its parts.
The Western and Eastern tendencies were finally joined in the modern ontological views generally called “systems theory."
This theory views the real things as composed from its parts where the properties and behavior of the whole system are not given only by the properties of its parts, but are also a
result of the structure of the system; structure that is the result of relations, interactions and internal forces of the parts.
Thus each higher system has some new “systemic,” also called by some “emergent,” properties and behaviors specific to it.
With that, the principles that we derived and that describe the physical changes of certain kind of systems does not have to have the universal validity for all other ones, especially for the lower levels of systems.
From this today’s ontological view, the Poincaré’s concern or “crises of mathematical physics”, the concern that the principles and theories of physics are not always applicable, does not look like a crisis anymore, but rather as a result of the insufficient ontological understanding of the world at that time.
With that, the Einstein’s attempt to unify light and electromagnetic phenomena with mechanics, to unify quite different types of physical systems, does not look justifiable
anymore.

A. Ontological reasons

B. Epistemological reason
There are different kinds of theories which have different meaning and provide different degree of accuracy.
1. Phenomenological models
Due to the limited empirical data (caused by limits of our senses and instruments) and due to limited understanding of the nature of studied things and their behavior, scientists of the 19th century have been satisfied with approximate, semiempirical or phenomenological models.
Such models have a great value in practical life because they can predict behavior of studied systems even though they are not able to explain in detail the process itself.
These models are not based on understanding of the causes of the process; they are not based on the understanding of the physical nature of the studied physical objects and their behaviors (processes); they are based on appearance
or observable phenomena.
Today, we have different kinds of phenomenological physical theories; theories applicable for nonliving part of the Nature, for our physical processes.
1. Correlational theories
Many of the early theories identified only one or a few
parameters which are changing with the studied phenomenon and showed the correlation between these parameters and the outcome of the phenomena.
The theory of expanding universe is one of them.
There is only a correlation (not functional relationship) between the red shift of light and the distance of the stars that emitted it.
2. Limited phenomenological (“blackbox”) models
Many physical theories, especially at the early stages,are theories which are not based on understanding of the physical nature of matter which is involved in the physical process, which are not based on the true understanding of causes and effects, and are relating observable “outside” parameters.
Which are comparing this outward manifestation without understanding “inside” of the physical system.
These theories are expressing the limited number of easily observable parameters and depend on empirically measured constants.
For example, the Boyle’s Law shows pV ¼ constant, at constant temperature.
Another example are the theories of Quantum physics.
3. The full phenomenological (“blackbox”) models
These theories express the full set of the observable outward parameters or observable behavior.
An example is the Gas Law which includes now not only relationship of pressure (p) and volume of gas (V) but also effect of temperature (T) pV ¼ nRT (14) or Newton’s Law of Gravitation.
Newton’s gravitational theory describes only the gravity force between two bodies and the trajectory of their movement.
Newton refused to hypothesize on the causes of the gravity forces on the nature of the gravity field.
He went one step further towards constructive model by defining gravity force and then derived the movement of planets around the sun from that, even though he did not have a physical model of actual interactions which cause these forces.
These theories also require empirically measured constants and can predict behavior with a great accuracy, yet they do not tell us the actual nature of the physical process, or can give us incorrect results if applied for conditions outside of the range of experiences which served as the experimental basis of such a theory.
For example, the Gas Law gives incorrect results at extremely high pressures when molecules are too close together.

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2. Constructive theories
Constructive theories are based on understanding of the “inside of the physical systems and their processes."
They are based on understanding of “things in themselves,” nature or essence of the studied phenomena; understanding of the forms of matter involved, their interactions, and the effects they produce.
There are theories which are based on understanding or on a hypothesis of the “inside of the physical system” which exhibits the studied phenomena.
We do not have too many
of these theories outside of mechanics because of our limited abilities to detect, measure and understand the inside of the objects and matter on the atomic and subatomic levels.
Therefore, most of these theories are based on “assumed,” “simplified,” “idealized” nature of the phenomena.
Examples of such theory are the kinetic theory of gases; which depends on assumption of properties of gas molecules and their behavior; wave theories of light and electromagnetism which depends on assumption of the ether, or the LeSage’s theory of gravitation; which depends on assumption of the nature of the gravity causing particles, and their interactions with matter.
These theories depend upon our hypothesis of the nature of the matter involved in the process, on the nature of the matter which we do not detect by our human senses or by our instruments, and which depend on some indirect measurements, observations or our hypothesis.
As our science and technology allowed us to invent better instruments, we made great progress in the 20th century allowing us to understand the nature of the physical systems on atomic and subatomic level better than ever, giving us a chance to develop better, more “close to reality,” constructive theories in the future.
To generate constructive model, one has to start with an ontological view of the real world and from that to generate physical model of the matter which is involved, and what kind of interactions take place in the studied physical system that cause forces and the changes.
Only then one can generate mathematical model, the equations which quantify the interactions of the physical model.
The main difference between phenomenological models and constructive theories is that phenomenological models are only reflecting relations among different measured parameters.
They are not based on understanding of the physical nature of the things which exhibit the phenomena; they do not need the detailed physical model of interactions and causal chains of events.
In case of Einstein’s theory of special relativity, we saw that he attempted to formulate the constructive theory yet he had an outdated idealistic ontological view of causality; view that there are some ideas, some intelligence, behind the behavior of nature.
Thus he constructed his theory on his two ideas, his two postulates that didn’t come from any empirical experience.
3. Complex processes
In Nature, there are many physical processes going on,
at the same time, making it very difficult to separate or isolate each individual process from the other ones, so that we
can study it by itself.
In laboratory conditions, we always
attempt to eliminate the interferences caused by other than
studied processes, yet for more complex processes, we cannot separate the individual processes because they take place
simultaneously, or even support each other.
To understand Nature and its behavior then requires
studying the systems where more than one physical process
is taking place at the same time, when each process is also
affected by other ones, or is modified by interferences from
other forms of matter and their processes, creating quite a
complex behaviors.
Atmospheric weather system being probably the most familiar complex of physical processes, which
are in effect together, with different intensity at different
times at different places.
The quantum physics is another
example.
The mathematical models of the behavior of
Nature where many processes are in effect at the same time,
are then extremely complex, or only probabilistic, and their
accuracy depends not only on the accuracy of the theories or
each involved process but also on our abilities to measure, in
situ, the necessary values for our models.

C. Assumption of the inertial frames of reference

In our models, we make assumptions.
One of them the inertial frame of reference or inertial coordinate system that requires the absence of the external forces.

There does not exist any place in the universe with is without any force.

Because of the omnipresence of gravitational field, the true inertial systems do not exist in the real world; inertial systems are only human imaginary idealized condition.

It is true that there are no inertial systems.
It is even also true, that it does not make sense to speak of inertial systems in plural.
Only one reference frame should be considered.

All real frames of reference are only quasiinertial systems that depart from the
ideal one into a different degree, causing that our experimental results do not always need to be accurate to a high
degree.

D. Back to Einstein’s theory of special relativity

Most of these reasons why the principles and the theories
of physics are not always applicable or correct presented
above were not understood at Einstein’s and Poincaré’s time.
Einstein’s realization that our theories of physical processes are not exactly valid was a correct one.
It caused him desperation and loss of hope in the empirical approach and so he was looking for a different way to science.
He did not realize that the problem is that we develop theories without having the full set of facts and measurements.
That our theories are based on limited inputs and on hypotheses which are frequently incorrect, and thus provide incomplete or even incorrect models or approximations of the physical processes.
He gave up on empiricism because he could not understand well why the existing theories are not exact and switched back to idealism and rationalism.
Einstein used the Maxwell–Lorentz equations as the base of his theory because he believed in their correctness “that they revealed the true reality."
The Maxwell–Lorentz theory is based on assumption of propagation of waves through ether; ether which was never detected.
Thus, Einstein’s theory was based on hypothetical Maxwell–Lorentz theory whose base (assumption of ether) was never proved but rather disproved by the Michelson–Morley experiments.
Thus, the Einstein’s effort to build a constructive theory

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was based on his incorrect first postulate and on Maxwell–Lorentz theory which itself is based on the hypothesis of ether; ether which was never detected but rather
disproved.
In Section II B, we saw that the results of Michelson–
Morley experiments led Einstein to elimination of ether.
For him, ether became “enfant terrible” and thus he gave
the physical properties of transmitting waves to space.
Space became a medium for propagation of waves.
He took
out the material medium of ether and replaced it with immaterial Einsteinian space–time continuum.
He replaced the
physical medium with his imaginary abstract space–time
continuum (for more, see Section V G). For Einstein, the idealist, with his metaphysical laws of nature which govern
reality, it was not strange to come up with imaginary
abstract space–time continuum if it is required by his laws of
Nature which govern, if it is required by his first and second
postulates.

E. Why Poincaré did not accept Einstein’s theory of special relativity

There is an obvious question why Poincaré, who was the
first to propose the extension of the Galilean relativity to
other than mechanical processes, did not accept Einstein’s
theory of special relativity.
Was he aware of Einstein’s
incorrect understanding of the “Laws of Nature” or was there
another reason?
In his “The Measure of Time,”27 Henri Poincaré discusses various aspects of time, simultaneity and time measurement. In Section XII, where he discusses simultaneity,
his second conclusion reads:

“(2) It is difficult to separate the qualitative problem of simultaneity from the quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether account must be taken of a velocity of transmission, as that of light, because such a velocity could not be measured without measuring a time."


Velocity requires definition of lengths and time interval.
Thus velocity, velocity of light cannot be definition of time interval.
It would be putting a wagon in front of a horse.
It is another circular logic in Einstein’s concept of this theory.
This was probably the simple reason why Poincaré; the conventionalist; rejected Einstein’s theory, theory based onm defining measurement of time by velocity of light, velocity
which “could not be measured without measuring a time."

Poincare was correct. In fact what you must do is to explain in detail how the speed of light is measured. If this requires a clock and this clock uses light you have a problem.
IX. SUMMARY OF FINDINGS


A. Why review or question Einstein’s relativity?

Einstein’s theory of special relativity is accepted as having initiated a conceptual revolution in theoretical physics,
astrophysics and cosmology, and thereby revolutionizing our understanding of the physical world.
The ideas on which the theory is based, particularly invariance of the velocity of light and relativity of simultaneity, are nevertheless counterintuitive in relation to our everyday experiences and in respect to the Newtonian physics.
Although this theory has been widely accepted for nearly a century, there have been physicists and philosophers who expressed reservations about it.
Some contended that it contains inconsistencies and even outright contradictions; some provided experimental discrepancies between the results of their experiments and predictions of the theory, making it the most contested theory of modern physics.
In his 2002 lecture “Gödel and the End of Physics,” Stephen Hawking assessed today’s state of theoretical physics and declared “The theories we have so far are both
inconsistent and incomplete."
Because one of the main pillars of the present theoretical physics is the Einstein’s theory of special relativity, it is important to raise question: Was Einstein’s approach to developing his theory and his attempt to unite the classical physics with light and electromagnetism by his theory of special relativity correct?
Because our philosophical and scientific views have advanced significantly since the time Einstein published his theory, it is appropriate to reassess some of the reservations raised in the past and to evaluate its overall acceptability
from today’s perspective.

B. Scientific review and philosophical reflection
on the theory

Because this author has experienced as well as learned from the history of science that philosophical ideas as well as scientific thinking guide scientists in their quests for new
theories, he has conducted an extensive review of both these elements in Einstein’s theory and in his writings.
Although in the past, much work has been done to test the predictions implied by this theory, this review concentrated on its conceptual foundations: on the two postulates (principle of relativity and the invariance of velocity of light), the relativity of simultaneity and theory’s overall logical structure.
The review revealed that explanations and justifications of the theory actually contain contradictions, circular definitions and inconsistencies in its explanations, which means
that its internal logic undermines it.
The review also revealed that the philosophical ideas involved in Einstein’s thinking contain no insights that positively advance our philosophical understanding but rather represent outdated, incorrect philosophical views.

C. The purpose of the theory

Einstein’s theory was a response to three problems or questions in the theoretical physics at the turn of the 20th
century:
(1) Why the Michelson–Morley experiments failed to
prove existence of luminiferous ether?
(2) Why the Maxwell–Lorentz equations are not invariant
under the Galilean transformation?
(3) Why the principles and theories of physics are not
always applicable or correct?
At that time, neither science nor philosophy was developed further enough to provide answers to these questions. While Lorentz and FitzGerald tried to make the

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Maxwell–Lorentz equations invariant by introducing new hypotheses, Einstein tried to make them invariant with his new approach to science.
He established a “universal formal principle” (his first postulate or relativity principle) that was supposed to extend the Galilean relativity of mechanics to optical and electromagnetic phenomena, and from that and Maxwell–Lorentz equations deduced his second postulate (the invariance of light velocity) and other principles of his theory.

D. First postulate

The problem of this theory started even before Einstein formulated it.
It started when Poincaré proposed his relativity principle, the principle that Einstein adopted, reformulated into his first postulate and used as a basis of his theory.
The problem of this postulate as well as with Poincaré’s relativity principle is that they are not applicable for the fieldbased physical processes when fields are generated outside of the frame of reference with which we associate our coordinate system.
Both Einstein as well as Poincaré did not express sufficiently the relevant inertial systems.
They both concentrated on the relative movement and expressed inertial systems in their respective principles of relativity in terms of “uniform translational motion” instead of “absence of external forces."
This was sufficient for the classical physics, but is not for the physics dealing with fields.
Both of them overlooked the fact that in order to be in the uniform translational motion, the frame of reference needs to be free from outside forces.
They overlooked that fields generated in one frame of reference cause forces at a distance in the other frames of reference, turning them into noninertial ones.


Therefore, their relativity principles cannot be valid for the fieldbased physical processes when fields are generated outside of the frame of reference with which we associate our coordinate system.
Thus, Einstein’s theory starts with the principle that overgeneralized into a region where it cannot be valid.
The use of this principle for the conditions where it cannot be valid then led Einstein to an incorrect inference of the second postulate and that to inference of relativity of simultaneity, all three incorrect.
It led to the theory that provides the transformation equations for the case where the principle of relativity is not applicable.
Thus these equations, similarly to Lorentz’s transformation equations, are only a mathematical transformation of Galilean transformation equations to satisfy the invariance of light velocity, and do not express any real conditions in the real world.
Thus, one simple oversight at the bottom of this theory made it possible but also incorrect.
Another problem with Einstein’s first postulate is that it is based on the outdated, idealistic, unacceptable ontological view of the term “laws of Nature” and thus it has nothing to
do with the Poincaré’s relativity principle or with Galilean relativity.
Although by a means of this postulate, Einstein intended to extend the Galilean relativity principle to include other than mechanical processes (similarly to Poincaré’s intent with his relativity principle), he actually converted an empirically derived principle into idealistic “laws that govern the physical changes” which is empirically unsupported.
This allowed him to base his theory on his two postulates that are more general, on a higher level, and relegate the principles derived from empirical experience to lower, dependent level, having only approximate validity.
Thus this Einstein’s new approach to science was the result of his incorrect idealistic ontological view of laws of Nature.
Today’s ontology based on the system’s theory provides much better understanding of complex systems than that at Einstein’s time and provides explanation why the principles
and theories do not need to be always applicable or correct.
With that, it undermines Einstein’s intention and approach to unify light and electromagnetic phenomena with mechanics by some simple “universal formal principle,” by his first
postulate.

E. Second postulate

The second postulate, concerning the invariance of light velocity, does not have any experimental basis; it was deduced from the first postulate and the Maxwell–Lorentz equations.
The validity of this second postulate depends on unsupported, incorrect assumption that the relativity principle is valid also for fields generated outside of the frame of
reference with which we associate our coordinate system.
In the two steps by which Einstein established his two postulates, he left empiricism and returned to rationalism, thereby developing a theory based on two hypothetical postulates
that have no evidential basis in the physical behavior of the real world.
He recognized that his second postulate contradicts the Galilean transformation equations, but he mistakenly thought that he resolved this problem by means of “Eureka intuition: the relativity of simultaneity."

F. Time, temporal measure, and coordinate systems

As a part of this study, the history of the philosophical and scientific views of time, simultaneity, and temporal measurement were reviewed.
The review found that throughout
the whole history of philosophy, all the way to our time, there has been a lot of confusion in understanding of the term “time."
Therefore, it was necessary to explain and define time and time measure from our present realistic philosophical perspective; using the 20th century philosophical
views.
The comparison of this definition with Newton’s understanding of time shows that Newton understood and used time correctly, yet in his definition, he used the term “absolute” which gave his definition an unwanted connotation which others have criticized.
Einstein’s view of time was influenced by Leibnitz and other rationalists, who used time primarily for logical ordering of events, emphasized the importance of simultaneity,
missing the facts (a) that time is an abstraction, a human construct, that depicts world’s continuation in its existence, and (b) the temporal measure is also a human construct established by convention.
The insufficient understanding of time by rationalists allowed Einstein to propose his empirical methods to judge the distant simultaneity, synchronize clocks, and define time.
At Einstein’s time, people did not clearly distinguish the real things from the abstractions and the imaginary things.

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They did not see that the frame of reference has to be a real thing, an object, where we can carry out physical experiments and/or made our observations of other objects in
space; that the coordinate system is an imaginary grid with an abstraction of length measured by a real thing (rod for example) and the abstraction of time, measured by a real thing by a clock.
Einstein took the imaginary thing, the coordinate system with the abstractions of length and time and with their measures, that are supposed to form an independent system of measures with invariant parameters that are used for keeping track of matter in the space, and turned these independent abstractions of length and time into dependent parameters.
He postulated one invariant, the speed of light, and turned the independent variables of length and time into the dependent ones to serve his purpose of unification of light and electromagnetism with mechanics.
The velocity, another abstraction that depends on the definition on the length and time, is now in the Einstein’s theory defining its own basis; defining the measure of length and time.
This is a circular logic in Einstein’s thinking that Poincare detected and pointed out.
It was, most likely, the main reason why he never accepted Einstein’s theory.

G. Relativity of simultaneity
"Relativity of simultaneity" can only be explained if there also "Absolute simultaneity" exists. IMO it only makes sense to claim that there are events which happened simultaneous and others with are not. The same with clocks: You can decide that certain clocks run simultaneous and others not. These clocks move in respect to the first.

Einstein intended to provide empirical methods by means of which the distant simultaneity can be decided and the synchronization of clocks can be carried out.
When he envisioned these things in his socalled “thought experiments” for the moving coordinate system, he deduced the results from the supposed invariance of light velocity instead of analyzing them with principles supported by empirical evidence.
He did not present any detail analysis of his two methods and his thought experiments and thus he did not realize their complexity.
The analysis of these thought experiments presented here revealed that Einstein, in his mind, used wrong light signals for judging simultaneity in the moving coordinate systems and thus, applied incorrectly his own empirical methods.
With that, he misled himself to the relativity of simultaneity.

H. Einstein’s transformation equations

To develop his transformation equations, Einstein defined time in the moving coordinate system using his incorrectly applied method of synchronization of clocks together with his second postulate and Galileo transformation equations.
Mathematics plays a significant role in science because it allows quantitative analysis of the concepts that represent the studied phenomena of the real world.
Einstein arrived to the transformation equations by providing mathematical analysis of incorrectly applied concept of empirical method for synchronization of clocks for condition of incorrect concept of the invariance of velocity of light.
Thus these equations cannot represent any real conditions in the real world.
It was his incorrectly applied method of synchronization of clocks that limited the range of velocities to v lower than c and thus limited his transformation equations to velocities
below the velocity of light c.
Einstein interpreted this result as meaning that no particle or object can move faster than the speed of light.
The analysis offered here shows that to satisfy Einstein’s transformation equations, one would need to use a different measure (scale) of time as well as length for the moving coordinate system.
One would need to use clocks that run slower and a shorter measuring rod.
This theory would also require asynchronously arranged clocks in the moving coordinate system.
These clocks would need to be arranged differently in this moving coordinate system if it moves in the positive than in the negative direction, requiring an unisotropic space and time, thereby contradicting the whole effort and the purpose of this theory as well as the purpose of the method of synchronization of clocks used as a basis for development of these equations.

I. Einstein’s method

While empiricism and scientific method, based on the empirical evidence from experiments and measurements followed by quantitative analysis and development of equations for each individual physical process, was well established at the turn of the 20th century, the problems that physicists faced at that time caused Einstein to lose hope in this approach.
His reductionistic view, that the whole can be explained only from the parts, and the idealistic ontological view, that objects of nature are directed by or follow some
simple “laws of Nature,” led him to reversing the scientific method and return to rationalism.
Einstein postulated a “universal formal principle,” his first postulate, and from that and the Maxwell–Lorentz equations, deduced the other principles (the second postulate and relativity of simultaneity).
Using these three principles, he then modified the Galilean transformation equations and derived other consequences how nature should behave based on his postulates.
These consequences should be then verified by experiment, and that is what many physicists tried to do.
Later in his writings, he called his method “the principle theory” and claimed that it consists of a set of individual wellconfirmed empirical
generalizations; the definition that is far from the way he generated his theory of special relativity.
This Einstein’s attempt to unify light and electromagnetism with mechanics, based on some simple postulates, started a dangerous direction and misunderstanding in the theoretical physics of the 20th century; direction towards the theory of everything where equations of different physical
phenomena are combined and the nature of the world is then deduced from them.

X. CONCLUSIONS AND RECOMMENDATION

The findings of this study show that, at the turn of the
20th century, scientific and philosophical views were not
sufficiently developed to understand the problems that physicists faced and that Einstein tried to solve with his theory.
Regardless of how brilliant a scientist Einstein was, he was
guided by insufficient or incorrect philosophical views prevalent at that time; views that unfortunately persist in minds
of many even today.
Einstein postulated the principle of relativity that cannot
be valid for the fieldbased processes when field is generated outside of the frame of reference.

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The use of this principle for such conditions in combination with the incorrect idealistic, ontological view of the term “laws of Nature” and insufficient rationalistic understanding of time misled Einstein into an incorrect method of developing his theory and to incorrect inferences of the other principles and concepts of his theory.
It led to this unrealistic theory with circular definitions, inconsistencies in its explanations and principles that contradict those derived from empirical evidence.
Thus, the foundations of Einstein’s theory of special relativity, his two postulates (principle of relativity and the invariance of velocity of light) as well as the relativity of simultaneity cannot be any longer justified.
With that, Einstein’s attempt to unify light and electromagnetism with mechanics, his concept of light, time and space, and his theory of special relativity with its other consequences, cannot correctly represent realities of the physical world.
To accept Einstein’s theory today, one would have to accept the second postulate, the invariance of light velocity, which has never been verified directly by experiment, and ignore all the scientific, philosophical and logical problems presented in this study.
This study provides different explanation and meaning of Einstein’s theory of special relativity besides the one presently accepted by mainstream physicists and educational
institutions, causing a new problem in physics, problem of two diametrically different understanding of Einstein’s relativity and with it, two different views of the physical world.
There might be skeptics who will not want to accept authority of the philosophical insights and advances used in this analysis.
Fortunately, there is an empirical way to validate or disprove Einstein’s theory by verification or refutation of Einstein’s second postulate.
It is unfortunate that in the past so much effort has been done to test various predictions of this theory and no physicist saw it important to conduct experiments to demonstrate the basis on which this theory was established.
To test the invariance of light velocity is within today’s technological capabilities, and so it should be one of the most important tests that empirical physicists could conduct.
Such a test will have the major significance for today’s physics as the Michelson–Morley experiment had for the physics at the end of the 19th century.
Without the experimental verification or refutation of the second postulate, there is now even greater doubt about validity of this theory and the modern theoretical physics,
which has been built upon it.
Only reality and the results of experimental verification or disproval of the second postulate can be the final judge of this theory.

ACKNOWLEDGMENTS

This study would not be possible without the support of the author’s wife, Karin.
The author wishes to thank Bruce Aune, Bertram Bandman, Morton Inger, Piotr Decowski, and
Hy Edelstain for review, critique and valuable suggestions; to Jeannette Tibbetts for word processing; to Linda Byrne for graphical work; and to Philippe Lagier for the French
translation of the Abstract.











Index
Reflection 1  Physics versus Mathematics
The understanding of the details of the building blocks of the universe (objects) at present and the evolution of the universe (in time) is physics
To quantify the present universe and to predict the state of the universe in the future, is mathematics.
The most important and also difficult issues is to define the present state, that means the positions of all large and small objects including the elementary particles. All these measurements, representing the same moment, define simultaneous events.
The next step is to do the same for different moments. Using this data allows the calculation of a speed and acceleration of individual particles.
Understanding the universe in general does not require a reference frame. Quantifying the same requires a reference frame. Calculating a speed requires at least one clock (showing astronomical time), fixed to the reference frame.
Reflection 2  Basic Defintions
If you want to understand physics, that means the physical processes that are happening in the Universe you should start with some basic defintions, with we all understand and agree upon.
The first one is, that we assume that there exists only one universe. This universe is not static, but dynamic. This means that the universe in its totality, is constantly changing.
The second one is that there 'exist' a present, you can also call this now and that everything (of interest) that is changing now we call events. All these events, happening now, are considered as simultaneous events.
IMO the only way to decide that events are happening simultaneous, is that the universe is filled with a 3D grid of identical clocks, equally spaced in 3D, and all synchronized from one source. This can be done using mirrors, as such that the length of the light path from the source to each clock is the same.
An other important concept is that the universe is not empty but filled with objects or bodies or matter. For example: elementary particles, planets, stars, and black holes. As a side comment it is interesting to remark that most elementary particles are invisible, planets are invisible, stars are visible because they emit light (photons) and black holes are invisible.
This brings us to an other concept and that are humans. They are also objects, they have a brain and eyes. With these eyes they can observe the physical reality, specific the physical objects that emit light i.e., the stars. However the light emitted by the stars can also be reflected by the invisible objects in their surroundings. As such we can observe the planets in the solar system and the surface of the planet we inhabit.
There is one more important concept that we should not forget and that is time. Time is a typical human concept, and that comes because we humans have eyes and a brain. With our eyes we can observe the present and that information we can store as pictures in our brain. What is more we can compare these pictures, and than we realize that we can arrange these pictures in the past, the present and the future.
With these concepts we can do more. As mentioned between all the events that have happened in the universe, there exist a certain group of events that have happened simultaneous. The problem is that if we observe and listen what is happening around is, it is very difficult to decide which of these events happened simultaneous. When you consider light, without going to all details, it is possible that you can observe two light signals simultaneous, while the events that caused these, did not happen simultaneous. It is also possible that you observe two light not simultaneous, while the cause happened simultaneous. Why is this important: because two events that happened simultaneous (a certain distance apart) can not influence each other.
One very interresting sport is hammer throw. "It consists of a metal ball attached by a steel wire to a grip." of See: https://en.wikipedia.org/wiki/Hammer_throw.
What makes hamer throw interesting is that you can compare physically hamer throwing with the movent of the Earth around the Sun. That means the Sun is the athlete in the center and the metal ball is the Earth. What is missing is the steel wire. How ever there is one more important concept and that are forces (energy). It is the athlete, by turning around his axis, who transfers part of his energy into the metal ball.
When the athlete lets go the grip, the metal ball will continue from that point in a straight line.
In the Sun Earth configuration the steel wire is the equivalent of the force of gravity between the Sun and the Earth and between the Earth and the Sun. From a mathematical point you must know the position of both the Sun and the Earth at simultaneous events.
At a larger scale to predict the future of the Milky Way you must know the positions of the stars at simultaneous events.
Reflection 3  Additional Basic Defintions
One of the concepts not discussed is specific that the speed of light is constant. In casu the speed of photons. The point is that if you want to calculate the future of universe the speed of light is not important. What is important is the distribution of all forms of matter that influence each other, by means of the force of gravity and the speed of this force. In that context it does not make sense to make a difference between black holes, stars in general, planets and gas clouds. All of these are as important to understand the galaxy rotation curve.
What is not mentioned in the above discussion of different reference frames, specific the concept of inertial reference frames. Part of the problem is that in the Universe there are no objects which move at a constant speed in a straight line. Anyway suppose that there in the Universe different objects, with different constant speeds, moving in different directions. How are these objects detected? and how are these speeds measured? IMO only from one reference frame.
A different concept not mentioned are thought experiments. IMO you cannot understand physics without performing real experiments (and without any book). In that sense is does not make sense to speak about the speed of light in a vacuum, while nowhere in the universe there exist a vacuum. The problem is that when you use a concept like a vacuum, you must first define what a vacuum is.
Reflection 4  Experiment to understand the behavior of different lightflashes
The experiment assumes that each observer has an identical clock synchronized at t0.
Consider a point A (observer A) at rest. This point will emit a light signal at t0 in all directions.
Consider a point B (observer B) at a (fixed) distance l from A. The light signal will reach point B at t1. The speed of light c is = l/(t1t0)
Now consider a moving observer C who passes point A at t0 and also emits a light signal.
The question is: will an observer at point B observe the two light signals simultaneous. My expectation is that the answer is yes, and if that is the case, this demonstrates the proposition that the speed of light from a source at rest or moving is the same (in all directions).
Now consider a mirror at point B, perpendicular to the line AB. This mirror will reflect both signals towards A. When there is also a mirror at point A, you have created a clock.
In the above both observer A and observer B are at rest. Observer C is moving. Now take a different view and consider observer C at rest and A moving.
In that case the result will be the same.
Now consider that both A and C are moving. That means there exists a different observer D who is at rest.
First consider point A (observer A). This point will emit a light signal at t0 at point A, in all directions, as a sphere with point A at its center. Observer A will not stay at point A.
For observer C the situation is almost the same as for observer A. Observer C will not stay at point A, but move away with a different speed.
The situation for observer D will be different. He will stay at the center of the sphere arount point A.
But there is one more issue to solve. As indicated above all observers are also equipped with a clock. Suppose observers A and C both move away from point A in a straight line to a point B and return back to point A, what does that mean? My understanding is that the observer who returns the first, which has the higest speed (in the frame at rest), that his clock runs the slowest and has the lowest clock time.
After the experiment is finished and all the observers are back to point A the clock time of observer D will be the highest.
The conclusion of this experiment is, that the "sphere of each light flash" (all the points of each sphere) emanating from a source at any instant are all simultaneous events in 3D, with source at the center. It does not matter if the source is at rest or is moving.
Reflection 5  Special Relativity
Starting point of science to define what are simultaneous events. Simultaneous events have the physical condition that they don't influence each other. All what we observe influences us and is generated by non simultaneous events, to be more specific: they happened earlier.
All events that are happening now, in the total universe, are simultaneous events. IMO the only way to detect simultaneous events, is when you build in the universe a virtual 3D grid, which a virtual clocks at each grid point. You can also describe that, as if only one reference frame is used. The first action is to synchronise all the clocks. After all the clocks are synchronised any observer at each clock, will observe the same time from the clocks at the same distance from his clock.
When there is an event in the universe, the time of the event is the time on the clock nearest to the event. When the the time of the event of two events are the same the events are defined as simultaneous. The position of the nearest clock also defines the position of the event.
What is important in this description that no moving clocks are used.
When two reference frames are used, each with a virtual grid and virtual clocks, and each frame is synchronised from a clock which are both simultaneous at a certain place and moment in time than the clocks in each frame are synchronised. However that does not automatically mean that all the clocks are synchronised.
 In case all the clocks are synchronised this means that the distance between one clock in one frame with all the clocks of the other frame stays the same.
 Suppose that this is not the case in the x direction. In that case one set of clocks is considered at rest and the clocks are identified as r1, r2 and r3. All at equal distances. The other clocks are moving and identified as m1, m2, m3 etc. All the clocks are initialized (count = 0) when rn meets mn. That meets when r1=m1, r2=m2 etc.
The next important moment will be when r1 meets m2. Comparing clock counts you will see that r1 has 10 counts and m2 has 8 count. That means r1 counts faster. At that same moment also r2 meets m3 and r3 meets m4. De clock counts of all the clocks at rest will be 10 and of all the moving clocks 8.
The next important moment will be when r1 meets m3. Comparing clock counts you will see that r1 has 20 counts and m3 has 16 count.
If the experiment studied meets the above criteria the moving frame is identified and can be removed. If the number of m2 is higher than r1 than r1 is part of the moving frame.
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Created: 22 oktober 2023
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