Einstein, Science and Philosophy - by Friedel Weinert 2009 - Article review

This document contains article review "The Big Bang" by Friedel Weinert written in 2009
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Contents

Reflection

I. Problem-Situations

On September 26, 1905 Albert Einstein's paper 'On the Electrodynamics of Moving Bodies' appeared in the Annalen der Physik. It is generally agreed that it is one of the most important scientific papers ever written. But was it a revolutionary paper? Einstein generalizes the Galilean relativity principle to include electro-magnetic phenomena; he postulates the velocity of light in vacuum as an upper speed limit on all phenomena.
From a philosophical point of view can you do that.
More important is that he also declared the speed of light a constant.
Why not declare the speed of gravity as a constant?
He uses the Lorentz transformations for the calculation of spatial and temporal measurements in the transition from one reference frame to another.
Why do you need more than one reference frame. How is the speed of a (each) reference frame measured/calculated?
There is much to be said for the view that Einstein's Special theory of relativity completes classical physics, especially the work of James C. Maxwell. [Holton 2000] Einstein himself did not see his theory as a 'revolutionary act'. But Einstein's work did introduce a philosophical revolution in our fundamental notions. This means that general notions, like mass, energy, time, space, causation, determinism, which are used in human attempts to construct coherent schemes of nature, have undergone radical changes as a result of scientific discoveries, such as those associated with the Special and General theory of relativity (STR, GTR) and Quantum Mechanics (QM).
According to Max Born the revision of old concepts has to happen under the constraints of new experience. [Born 1949, 75] We can consider them as physico-philosophical notions because they are not tied to any particular physical theory and have often been the subject of philosophical reflection from the Greeks to the present day. Hans Reichenbach characterized Einstein as a philosopher by implication but also speaks of the 'philosophical consequences' of Einstein's work. [Reichenbach 1949, 310] (cf. [Howard 2004]) That is, Einstein was willing to consider the status of the physico-philosophical notions in the light of his scientific discoveries.
It may be more appropriate to characterize Einstein's philosophical innovations as consequences of his scientific work. Implications can be hidden in the logic of a situation. But Einstein and many other physicists of his generation were fully aware of the philosophical dimensions of their scientific work. I prefer therefore to speak of the philosophical consequences of Einstein's work. In order to appreciate what is meant by philosophical consequences, we should distinguish them from the deductive consequences of physical theories. A deductive consequence follows from the principles and internal logic of the theory. It is a deductive consequence of the premises of STR that reference frames do not share a universal time axis. A philosophical consequence of a physical theory concerns its conceptual features.

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Certain conceptual positions are compatible or incompatible with the theory but they are not directly testable and are subject to interpretations.
The concept of testable is a must.
For instance a notion of absolute time is incompatible with the theory of relativity.
This requires a definition of both: absolute time in STR and time in the theory of realtivity.
The problem of measuring time has nothing to do with neither theory. In fact in both theories the result should be the same using the same clock.
But physicists and philosophers have argued, alternatively, that the theory of relativity can be made compatible with a static or a dynamic view of time.
What is the definition of each?
The philosophical consequences of the theory of relativity extend far beyond the familiar reshaping of the notions of space and time. What made Einstein a great physicist was his ability to question unquestioned assumptions in the tradition of physical theorizing. What made him an even greater physicist was his ability to recognize the limits of his own work. This talent led him from the Special to the General theory of relativity and beyond to attempts to construct a unified field theory.
What made him a decent philosopher was his willingness to pursue the philosophical consequences of his physical discoveries, e.g., regarding the physico-philosophical notions.
First come the physical discoveries. That are the facts. Next are the philosophical considerations. The rules and methodes. Finally are the physical explanations.
Einstein followed the logic of the problem situation, which his physical discoveries had created, into the field of philosophy.
A problem situation indicates that at any time, t, in the history of science there exist perceived problems, which attract a number of tentative solutions [Popper 1963, 198–200]; for instance the great puzzle of the 17th century was to know why planets stay in their orbits around the sun;
You can call that the purpose science, specific of Newtonian mechanics and GTR. That means that the purpose of Newtonian mechanics is to explain why planets stay in orbit around the Sun and why stay the stars in orbit around in our Galaxy. The same with GTR.
some of these tentative solutions will be eliminated; for a certain period of time, t + t′, usually one theory survives and is regarded in the scientific community as the most adequate theory in the light of the available evidence.
If the available evidence is inconclusive with regard to competing theories, it may still be possible, as we shall see, to appeal to other constraints to achieve a distribution of credibility over the competitors.
These tentative solutions include philosophical presuppositions, which may change under the impact of scientific discoveries. For instance, classical physics presupposes a unique time axis for all reference frames; a presupposition, which became questionable with the emergence of the STR.
One of the first questions to answer in relation to the purpose of science is why do we need more than one reference frame.
To regard Einstein as a philosopher is to consider his position on a number of philosophical issues.
Einstein philosophizes within the constraints of science, in particular his science. His questions are familiar to every philosopher of science: How do theories relate to the external world?
A theory should be an explanation of an aspect of the external world.
What is the nature of reality?
The reality is a mutual agreed description of the same event by different observers. The purpose is that humans can repeat the same experiment.
What is the nature of time and space?
What is the status of scientific theories?
Scientific theories or explanations should be neutral.
What does quantum mechanics tell us about reality?
Quantum mechanics, the study of elementary particles, teaches us that an acurate description of the total universe at any instant is impossible.
Given the principle of relativity, what is to be regarded as the real?
The whole of the Universe at any instance, by definition is real and exists.

II. Facts and Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 102

As Einstein philosophizes within the ambit of the theory of relativity, he sets these philosophical questions within a concrete scientific problem situation. His answers derive their significance from this problem situation. The problem situation is the kinematics of reference frames, given the results of classical mechanics and electromagnetism.
The problem is that reference frames don't exist. A reference frame is a mathematical construct to visualise the position and movements of objects in 3D.
Historically, his first concern was the notion of time.
The most important problem with time is its definition. What do we mean with time?
It should be mentioned that the evolution of physical processes in the Universe don't depend on the concept time.
In order to visualise these movements we use clocks. The problem is that clocks have physical limitations.
The most practical solution of the notion time is to introduce the concept universal time, which definies a time base for the whole of the universe.
When the Special theory of relativity was generalized to the General theory, his second philosophical worry became the notion of space—or more precisely space-time, for Einstein had accepted Minkowski's four-dimensional representation of the relativity theory.
The concept of space-time is a type of geometrical construct, consisting of 3D space and as the fourth dimension a parameter defined as c*t. Space-time is not a physical construct.
But with hindsight we can reorder his philosophical concerns into a logically more coherent picture.
Einstein's fundamental philosophical position arises from the age-old puzzle of how a body of concepts is related to collection of facts.
It is the other way around. First you should have a collecting of facts. Secondly you should try to organize these facts in different groups, specific how certain facts or commmon observations belong to each other and influence each other.
More generally, how do abstract scientific theories relate to concrete empirical data? How do scientific theories represent empirical reality? Such questions of representation go beyond the immediate concern of scientists who could contend themselves with the solution of particular technical problems. However such questions lie in the nature of scientific theorizing, as the Greek astronomer Ptolemy already knew. Once a theoretical account, like geocentrism, is available the question arises: to which extent is it an accurate account of the real world? As we shall see, Einstein's solution to this question, with respect to the theory of relativity, can be cast in terms of scientific constraints. Einstein's philosophical worry derived from his dissatisfaction with Newtonian physics as a fundamental theory. When Einstein aired his worry, for instance in his Obituary of Ernst Mach (1916), he warned against the Kantian tendency to regard certain concepts as thought necessities.
Human thought is a difficult scientific concept.
Once certain concepts have been formed, often on the basis of experience, there is a danger that they will quickly take on an independent existence. People are tempted to regard them as necessary presuppositions, without which science cannot be done. For instance, for two thousand years astronomers regarded the circle as the only permissible orbit of planets. Concepts, however, just like theories, are always subject to revisions. Einstein complained that

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Concepts, which have proved useful in the ordering of things, easily acquire such a degree of authority over us that we forget their earthly origin. We take them as unchangeable givens. They come to bear the stamp of 'thought necessities', of the 'a priori given'. ([Einstein 1916, 102]; translated by the author)
What Einstein had in mind were the notions of space and time. Isaac Newton had regarded it as necessary to introduce the notions of absolute space and time into his mechanics in order to make sense of his laws of motion. Newton's laws of motion make reference to temporal and spatial notions: state of rest, rectilinear uniform motion.
Newton's laws make completely sense if you consider the Universe in its totality. As a whole.
It also makes sense to consider the Universe as one reference frame, linked to a Universal clock indicating Universal time. A Universal clock is not considered a physical clock.
A reference frame must be defined relative to which the movement of a body is 'uniform' or follows a 'straight' line.
In every combination reference-frame and Universal-Time there are points which identify the positions of all the objects considered.
There are known rotational inaccuracies in the movement of the earth around the sun. A straight line drawn on the surface of the earth is 'straight' for a surveyor on earth but 'curved' for an observer in space. Newton mistrusted physical regularities observed on earth because they may contain systematic distortions.
The three previous lines are not clear.
He required that the notions of space and time, for use in mechanics, must be freed from all reference to material motions.
The combination reference-frame and Universal-Time follows that approach.
Newton stipulated that spatial and temporal notions must be absolute—independent of physical events and universal—all observers, whatever their location or velocity in the universe, must agree on their temporal and spatial measurements.
All of that is completely acceptable.
Few classical physicists had questioned Newton's reasoning, with the notable exception of Gottfried W. Leibniz, Ernst Mach and James Maxwell. So these notions had become part and parcel of classical physics. They had congealed to philosophical presuppositions, to thought necessities, to unquestioned assumptions. The Special theory arrived at a different result. Temporal and spatial measurements became relativized to particular reference frames. This was a necessary consequence of embracing the principle of relativity and taking the velocity of light as a fundamental postulate of the theory. Through his own work Einstein witnessed how such fundamental physico-philosophical notions as time and space required conceptual revision.
All the concepts used must be clear to a large audience.
This made him forever suspicious about the sway that such notions could hold over people's minds.
All the concepts are unambiguous there is no issue.
Einstein aims at a careful balance between concepts and facts.
Although the fundamental notions—energy, event, mass, space, time—are logically speaking free inventions of the human mind, they must strike empirical roots. [Einstein 1920, 141] As Einstein's scientific theories unfolded, several philosophical consequences suggested themselves. This process can clearly be observed in the notion of time

III. Philosophy of Being or Becoming? page 104

The Special theory of relativity leads to a relativization of time to particular reference frames. Observers, attached to different reference frames, which are in relative uniform motion with respect to each other, will measure the flow of time differently.
How can one observer, one point of observation, be linked to different reference frames?
In the present context the ancient philosophical question 'What is time?'—which famously puzzled Saint Augustine—reduces to the question 'What is physical time?' Physical time is simply what clocks in motion tell us.
In principle all clocks give a different (physical) time. All clocks are moving objects.
Einstein time is clock time.
When Einstein uses a physical clock than what he measures is also a physical time.
Clock time is to be understood in a broad sense. We use mechanical clocks to measure time intervals. Other regular processes—sound pulses, atomic oscillations—could be used for the same purpose. The problem is that such processes, too, are subject to relativization. Atomic oscillations yield to gravitational forces. The wavelengths of light and sound depend on the movement of the source, as evidenced in the Doppler Effect. In the world of special relativity there is only one signal, which escapes this restriction.
There does not exist a world of special relativity. You can have a collection of clocks and all these clocks can be manufactured differently.
Light retains the same velocity, c, in all directions and irrespective of whether it is emitted from a moving or stationary source.
You can make such a statement, but that does not mean that clocks working using lightsignals, moving in closed path, will all show the same time when they return.
These well-established facts led to a questioning of the traditional notion of absolute and universal time. Well-known physicists like A. Eddington [1920], K. Gödel [1949] and H. Weyl [1921] have claimed that the Special theory of relativity leads to a static view of time. The argument runs as follows: the Special theory shows that simultaneity cannot be absolute, as Newton assumed, since this presupposes a propagation of all causal influence at infinite speeds. But Einstein's light postulate shows that light propagates at finite velocity. It is a limit velocity so that no material process can travel as fast as light. This has drastic consequences. Observers in different reference frames, which travel at relative constant speed with respect to each other, will not agree on the simultaneous happening of some event, E. Einstein presented a well-known thought experiment: Let bolts of lightning strike the front and rear end of a moving train. Do they hit the ends of the train simultaneously or not? It is the motion of the observer, which determines the answer.
This discussion depends about a world view. Starting point should be, that at each instant the (universal) time in the whole of universe should be identical. That means that at each instant, all the events, that happening at that instant, are happening simultaneous. That also means that all these (simultaneous) events, happening anywhere in the universe, can not influence each other.
For stationary observers on the platform of a station, the events are simultaneous.
You can declare the whole of the flat surface of the the earth as one platform, you can also place observers, anywhere, at rest on this surface. How do you know that when there are two events that these two events are simultaneous or not?
For observers on the train they do not hit the opposite ends of the train simultaneously. The reason resides in the finite propagation of light. The train passengers rush toward the light signal from the front and run away from the rear signal. The same is true of the reading of clock times in different reference frames, which move with constant velocity with respect to each other. The observers will not agree on their respective clock times. Their clocks tick differently, depending on the state of motion.

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If there is no cosmic notion of time (as Newton assumed), to which all observers can appeal, time must pass at different rates for each observer, depending on the speed of the reference frame. Time cannot be an objective property of the universe. It depends on the perception of observers. The passage of time seems to be an illusion, as Eddington, Gödel and Weyl concluded. By contrast, the physical universe is static, a block universe. Einstein did at times adopt such a philosophy of being.
For us believing physicists, the distinction between past, present, and future is only an illusion, even if a stubborn one. (Quoted in [Hoffmann 1972, 257–8]) From a “happening” in three-dimensional space, physics becomes, as it were, an “existence” in the four-dimensional “world”. [Einstein 1920, Appendix II, 122; Appendix V, 150]
To understand the text it is important to have a clear understanding of the concepts: past, present, future, illusion existence and world.
My understanding is that the only thing that exists is the present, i.e. a now
Concepts like past and future exists in our mind, and are not real.
All what exists is a 3D world at present.
The argument infers the unreality of time from the results of the relativity theory: numerous reference frame are seen in constant motion with respect to each other; each reference frame carries clocks, rigid rods and perhaps an observer; the motion of the reference frames determines different clock times, which any resident observers will record; therefore the observers cannot agree on the simultaneity of two events and there is no absolute simultaneity as in Newton's mechanics; as observers cannot agree on the simultaneity of events across different reference frames, it seems that there are as many times as there are reference frames; the passage of time seems to be a human illusion in the sense that there is no objective, observer-independent Now.
My opinion is exactly the same; in general human observers cann't agree on anything, because every observer obsevers something different, even if they observe the same events. The question is how can different observers, which partly take observations of the same events, agree on predictions in the future.
But there are also numerous passages in Einstein's work, which express a more dynamic view of time. Rather than speaking of space-time, as Minkowski did, Einstein often prefers the expression, 'time-space'. [Einstein & Infeld 1938, 199–208] [Einstein 1922a, 29] And he points out that time and space do not have the same status in Minkowski's four-dimensional world.
The non-divisibility of the four-dimensional continuum of events does not at all (. . . ) involve the equivalence of the space co-ordinates with the time co-ordinate. [Einstein 1922a,30]
In his theory of space-time, Einstein aligns his thinking to the relationist position, espoused by Leibniz and Mach. According to the relational view, time and space are nothing but the order of actual and possible events. Space is the coexistence of such events and time is the order of succession of such coexisting events. In his deliberations of

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the General theory of relativity, Einstein leaves the reader in no doubt that he regards the total mass-energy distribution in the universe as the source of the space-time metric. 'The gravitational field determines the metrical laws of the space-time continuum.' [Einstein 1922a, 59; 1922b, 20–4] What could be said in favour of such a dynamic view? Consider first what would happen, if all references to observers were dropped. All observers can be replaced by clocks and rods.
That should be the practical solution. No observers should be used.
The clocks in different reference systems will be affected by the respective relative motions of the systems.
That the most important argument against the use of refence frames
No observer will conclude that there must be a mysterious transience of time—a moving Now, signalling the march of time from past to future. Without conscious observers, there is no need for the introduction of a tensed view of time, according to which objects change their temporal properties—their dates—by moving from past to present to future. The tensed view falls foul of McTaggart's objections and is incompatible with the findings of the Special theory of relativity. [Savitt 2000] In particular the tensed view of time requires a privileged Now, which cannot be squared with the principle of relativity. Does this leave us with a tenseless view of time, as McTaggart claimed, according to which there is only a static 'before-after' relation between events? Events are juxtaposed like beads on a string (B-series). The physical world just is, it is a block universe. The passing of time is a human illusion. There is an alternative between these extreme positions (of the tensed view versus the block universe). The tenseless view is mistaken in equating tenselessness with changelessness. [Grünbaum 1973, 325] [Smart 1963, 138-40] The physical occurrence of events does not exclude change. Change occurs in the transition between events, even if these events are ordered in four-dimensional Minkowski space-time.
Consider, for instance, the famous twin paradox. One of the two twins is a space traveller who returns to earth after a visit to a distant star only to find that his twin brother, who remained on earth, has aged more than he has.
One important issue in physical science is to use experiments, to describe the experiments, to show the results and finally to explain these results.
In this case I propose two experiments.
In the first experiment I propose a clock which moves in a closed curve from A to B and back to A.
In the second experiment I propose a clock which moves in a closed curve from A to C and back to A. Both experiments run in paralel.
The result will be that the number of counts of clock, following the longest path, will be the least. That will be the second experiment when A=B
This can be explained within the STR by a consideration of the effect of motion on the world lines of the two twins: the world line of the earth-bound twin turns out to be longer than the world line of the travelling twin [Lockwood 2005, 46–51] because the traveller's clock, including his biological clock, is subject to time dilation effects. If we were to take the heart beats of the twins as our clocks, these electromagnetic signals, which the twins exchange during the journey, will be subject to the relativistic Doppler Effect with the result that the number of signals the twins receive respectively will not be equal.
Why do they use such a complex explanation. Suppose we use a clock which uses a light signal. The point is that a clock, which does not move, has the higest ticking rate, because the light signal only moves up and down. When you compare this with a moving clock, the light signal not only moves up at down, but also moves forward. That means the (light) path between two ticks is longer, implying a lower ticking rate.
An important point is that, this experiment does not influence the (flow of the) universal time.
A physical change occurs. The relational view already emphasized that time was the order of succession of events.

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In the STR the relational notion of the 'order of successive events' becomes restricted to the light cone structure of Minkowski spacetime. The crucial notion of the finite propagation of light in STR limits the connectibility of reference frames to time-like connected events. It is interesting to note that several early commentators on the Special theory already proposed a dynamic interpretations of space-time, according to which worldliness propagate through space-time and acquire a history. [Cunningham 1915, § 60] [Schlick 1917, 181] [Reichenbach 1958, 183] The crucial point is that traditionally the STR only considers purely kinematic aspects of the propagation of worldlines and the relations between reference frames. But these kinematic relations have entropic aspects, as revealed in the asymmetric behaviour of electromagnetic radiation. It is these entropic aspects of worldliness, which give the relationist the purchase to consider a dynamic view of spacetime. This fits in well with a specific argument from entropy, which Einstein employed against Kurt Gödel's idealistic interpretation of the Special theory of relativity [Gödel 1949]. Einstein considers the question of the temporal direction of events. Imagine we send a signal from B to A through P. This is an irreversible process. On thermodynamic grounds he asserts that a time-like world line from B to A through P in a light cone takes the form of an arrow making B happen before P and A after P (see Figure I).
This piece of text is not clear.
This secures the 'one-sided (asymmetrical) character of time (. . . ), i.e., there exists no free choice for the direction of the arrow.' [Einstein 1949a, 687] This is true at least if points A, B and P are sufficiently close in cosmological terms. But the asymmetrical character of time is here based on a fundamental earlier-later or before-after relation between physical events without reference to an observer. There is an event, B, at which the signal is emitted. And there is a later event, A, at which the signal is received. This whole event is irreversible. There is an entropy gradient between the state of events at B and A. The assessment of this differential entropy between the two locations does not depend on a particular reference frame. According to a fundamental result of the Special theory of relativity the entropy of a system is frame-independent. [Einstein 1907, § 15] Thus all time-like connected frames will agree on the order of the succession of events, even if there is disagreement about the simultaneity of these events. It may be objected that this entropic theory of time could not form the basis for a general dynamic theory of time. As is well known the second law of thermodynamics is a statistical principle; there is an extremely low probability of a reversal of events in our observable space-time regions. Although it is unlikely in the lifetime of the universe, the second law permits a spontaneous reheating

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Figure I: Einstein's consideration of the (local) direction of time in response to Gödel's idealistic interpretation of the Special theory of relativity. A time-like world line exists between events A and B, which lies within, not outside, the light cone. of a glass of cold water by a rearrangement of the molecules. But the arrow of time is supposed to be one-directional. This objection need not worry the relationist in the present context, because the concern here is to establish the possibility of a dynamic interpretation of space-time not on a global but local scale. Locally, the entropy gradient points in the direction from B to A. All time-like connected observers agree. For the relationist this establishes, within local space-time regions, an order of the succession of events and thereby physical time for time-like related frames. Reichenbach expressed such a view in his hypothesis of the branch structure:
The paradox of the statistical direction (of time) was solved, in a continuation of Boltzmann's ideas, by the recognition of the sectional nature of time direction: a large isolated system can indeed define a time direction in a section of its whole temporal development, if this section is rich in branch systems governed by the laws of statistical isotropy. [Reichenbach 1956, 207] (cf. [Davies 1974, § 3.4])
Laws don't govern the behaviour of physical systems.
Although Einstein endorsed, from time to time, the unreality of time, his whole theory of time-space is relational.

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It points towards a philosophy of becoming since physical time is constituted by the asymmetric, invariant order of physical events in space-time. There are several statements in Einstein's work which suggest this relational reading of his space-time concept:
I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. [Einstein 1920, vi]

There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space. [Einstein 1922b, 21]

It is not the job of the philosopher to put Einstein's philosophical thinking into a straight-jacket. The philosopher must evaluate whether the philosophical consequences, which the physicist claims to follow from the physical discoveries, do indeed follow. (As we have seen prominent physicists like Eddington, Gödel and Weyl explicitly claimed that the block universe was a philosophical consequence of the STR, whilst Einstein wavered in his support for a static universe.)
This is a question of conceptual evaluation, not empirical testing. We have indicated that a dynamic interpretation of space-time is possible and compatible with the STR. It is possible if we consider the entropic aspects of space-time events and align the STR to relationist thinking. There are similar philosophical presuppositions and consequences at work in Einstein's views on quantum mechanics.

IV. Quantum Mechanics

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Above we characterized the philosophical consequences of scientific theories—they do not follow deductively but are nevertheless conceptual consequences of these theories. As such they are not 'justifiable by scientific methods.' [Frank 1949b, 355] Einstein revolutionized our philosophical notion of time by relativizing both time and simultaneity to particular inertial reference frames. He thereby uprooted a prior philosophical commitment to absolute time. Scientific revolutions or innovations often upset earlier philosophical presuppositions. Such presuppositions seem to be unavoidable in science. But in his discussions of quantum mechanics, for example, Einstein was guided by a traditional notion of causality.

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In his lifelong opposition to the Copenhagen interpretation of quantum mechanics he disregarded the lesson about thought necessities, which the theory of relativity had taught him. According to Einstein, quantum mechanics was incomplete because it only permitted statistical statements about ensembles of atoms.
The reality, through measurements, teaches us that it is impossible to define the positions of individual atoms accurate. The problem is when you try to measure one, you disturb its position and the ones in its surrounding.
Quantum mechanics was unable to make precise spatio-temporal predictions about the trajectories of individual atoms.
The same reasoning.
Heisenberg's indeterminacy principle, whose validity Einstein fully endorses, prevents deterministic spatio-temporal determinations of atomic trajectories.
Heisenberg's indeterminacy principle does not prevent this. The principle is a description is a description of the underlying process or cause, that causes this behavior.
The same behavior is also relevent that is impossible to calculate the positions of all objects in the universe exactly. That means in space and time.
The ability to make such predictions was for Einstein one of the fundamental requirements of science.
The fundamental requirements of science is to understand these physical processes in detail.
To make predictions is based on acurate measurements and involves mathematics. To make acurate predictions depents how acurate the measurements are. This is an issue for all types of sciences.
Only differential equations, he said, would satisfy the demand of the physicist for causality.
[Einstein 1927, 255] Note that Einstein associates the notion of causality with the availability of differential equations and therefore predictive determinism. It is a functional view of causality, because it reduces the causal relation between two parameters to a functional relation between the rate of change with respect to time of one parameter, say velocity, ν, and the application of a force, F. (See [Frank 1932] [Weinert 2004, ch. 5.1]) This demand for deterministic causality is a reflection of Laplacean determinism, which the quantum theory was hoping to overcome. When Einstein warns that a probabilistic view of quantum mechanics will lead to its incompleteness, on the grounds that it does not allow for precise space-time trajectories of atomic particles, he clings to one of the most venerable presuppositions of classical physics. In his criticism of Newtonian mechanics, Einstein bemoans the inability to jettison fundamental notions like absolute space and time. But in his view of quantum mechanics he himself relies on a presupposition inherited from classical physics, e.g. the belief in strict determinism.
It has often been debated whether Einstein's fundamental worry about quantum mechanics derived from fear of 'action-at-a-distance', rather than his belief in strict causality. (See [Howard 1993] [Fine, 1986] [Cushing & McMullin, 1989]) In quantum mechanics two particles, issued from a common source with particular spin alignments, may be so far separated in space-time that no known causal interaction can take place between them. Yet a measurement of the spin property of one particle will instantly change the spin direction of the other particle even over cosmic distances. Einstein found such 'action-at-a-distance' unpalatable. The Born interpretation offered him a way out of the dilemma. According to the Born rule, which Einstein embraced [Einstein 1940, 923-4], the square of the wave function, |Ψ|2, only delivers statistical statements about the probability of events, not the determination of actual events in space and time.

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Einstein accepted the quantum theory as a heuristic device because the Born rule told him that it only delivered an incomplete description of reality.
It is physical impossible to give an accurate description of the reality at any instant of time, because what we observe has happened in the past. Our observations are based on the rule: the futher away the events happened we observe, the earlier they happened.
An incomplete description may not satisfy the 'causal' demand for differential equations.
The fact that all these events happened at different moments make it difficult to describe the reality by a differential equation.
This incompleteness charge gave him the freedom to believe that a complete description of atomic reality could be found.
That is strange. What this means that to describe the physical reality by means of mathematics is difficult.
Einstein yearned for a complete and direct description of reality.
Einstein should have accepted that an accurate description of the world is impossible.
[Einstein 1940, 924] By this he means a direct representation of the actual space-time events, rather than a probability distribution of possible outcomes of measurements.
All astronomical based measurements (observations) have an error range i.e. are problematistic.
Such a complete description of actual events in space-time will avoid non-local effects. For it will be subject to the 'strict laws for temporal dependence.' [Einstein 1940, 923] [Einstein 1948, 323] In physics the 'strict laws for temporal dependence' are typically expressed in differential equations.
Differential equations can be used for processes which are stable in nature. The most difficult are chaotic processes.
The incompleteness charge against QM gave him the freedom to believe that a complete description of reality would recover the differential equations, which described the temporal evolution of real physical systems in space-time. The Schrödinger equation is of course a differential equation, which spells out the time evolution of a quantum system. However, this does not satisfy Einstein, because the Schrödinger equation describes time evolution in an abstract Hilbert space. Einstein's insistence on a complete description of real events and his functional view of causality leads me to agree with Fine [Fine 1986, 97–103] that Einstein's concern with nonlocality was not primary. It was a consequence of a deeper concern with strict causality. Einstein actually maintains that a renunciation of the principle of locality would render empirically testable laws impossible. And locality is expressed in differential equations in real space-time. [Einstein 1927, 261] Since the discovery of Bell's inequalities in the 1960s much effort has gone into distinguishing various senses of 'locality.' If we speak, with Einstein, of the 'mutually independent existence of spatially distant things', we formulate a principle of spatial separability. (See [Einstein 1948] transl. in [Howard 1993, 238]) In view of the results of quantum mechanics, we must distinguish this principle of separability from the principle of locality. This principle has been formulated in a number of ways. Einstein locality means that no 'faster-than-light-signals' should be permitted to propagate between spatially separated quantum systems.
This issue requires a type of physical world view. This world view should indicate that objects can not influence each other simulataneous.
But locality can also mean that a spin measurement performed on one system, which is spatially separated from another system in the sense of satisfying Einstein locality, cannot influence the spin state of the other system. This type of locality Einstein calls the 'principle of local action'.

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However various types of entanglement have been observed between quantum systems, which display degrees of correlations of their spin properties even though they are spatially separated in the sense of Einstein locality.
This requires a clear definition of what entanglement is. Entanglement is not, that the act of measuring one particle in some sense changes the state of the other particle. It does not involve any action-at-a distance. The most common sense explanation is, that the correlation is establised as part of the reaction when the two particles were created.
Einstein's principle of local action is violated in quantum mechanics.
[Cushing & McMullin 1989] [Howard 2004, § 5] Schrödinger dubbed this now familiar type of correlation 'entanglement of our predictions or of our knowledge' concerning the quantum states of a photon pair.
My understanding is that each photon, of a photon pair, has a parameter which are each other opposite. That means they are correlated. This correlation has to be established by multiple (identical) experiments.
[Schrödinger 1935, 827] Recently, the programme of decoherence has identified environmental entanglement, i.e. the irreversible loss of interference terms to the environment in the creation of classical states. Quantum mechanics was Einstein's bête noire. His opposition never faltered. Today it is generally regarded as untenable. Quantum systems manifest degrees of entanglement over large distances.
The fact that the entanglement (correlations) can be measured over large distances implies that the particles are stable.
Einstein's 'spooky action-at-a distance' is a laboratory reality.
This requires an explanation.
We see in Einstein's work both the role of presuppositions (causality in QM) and the effect of scientific discoveries on fundamental notions (time, space, mass). Less well-known is that Einstein makes some significant contributions to our understanding of scientific theories. In particular his views harbour a possible solution to the vexing question of the representational power of scientific theories.
More detail is required of what the concepts representational power and theory mean. Why should a scientific theory have representational power?

V. The Representational Nature of Scientific Theories

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To Einstein, scientific constructs (laws, models, and theories) are free inventions of the human mind.
No they are not. The concepts: Laws, Models and Theories require a clear definition. The most important issue is to what extend mathematics can be used to understand physics i.e. the physical world and processes.
What is of specific importance is the difference between a law and a theory.
No amount of inductive generalizations can lead from empirical phenomena to the complicated equations of the theory of relativity. But science is not fiction. Science assumes the existence of an external world.
The act of understanding the world, in which we live, is supposed to be performed, in an organised, structured fashion.
The starting point can be a certain number of assumptions. Next come observations and experiments. Mathematics (quatifycation) comes as the last resort.
Scientific theories are statements about the external world. 'Physics is the attempt at the conceptual construction of a model of the real world, as well as its lawful structure.' (Quoted in [Fine 1986, 97], italics in original) Einstein therefore depicts scientific knowledge as a synthesis of reason and experience, which raises them question of the representational nature of scientific constructs.
A model is always a simplification of the real world. A model (physical, mechanical) shows the relation between different parts of the reality. It often shows how certain (biological) processes show a cyclic behaviour, from birth to maturation to deadth.
Einstein makes a famous distinction between constructive theories and principle theories. [Einstein 1919; Miller, 1998, 125] The role of a constructive theory is to propose models, which assign an underlying structure to the observable phenomena. The kinetic theory of gases models gas molecules as if they were billiard balls. Early atom models modelled atoms as if they were tiny planetary systems.

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The role of a principle theory is to propose fundamental principles: the laws of thermodynamics, the principles of relativity, of covariance and invariance, and the constancy of light.
All these principles first require a clear definition, based on experiments, other wise the consequences cannot be understood.
These principles constitute constraints on the construction of models and theories. They forbid the occurrence of physical events, like superluminary velocities or perpetual motion machines.
The prove that a perpetual motion machine does not exist, is to try to build one.
All scientific theories give rise to a philosophical question: how do scientific theories relate to the external world?
Philosophical question is much more: What is science? What is the purpose. How is science performed and what are the rules.
First you must observe the external world and try to find commonalities in features and attributes. Next you perform experiments.
A ground rule should be that you cannot performing science by means of thought experiments.
Ernst Mach's answer is cast in terms of phenomenalism; Duhem's answer in terms of holism; Poincaré's answer in terms of conventionalism.
All these concepts require a clear definition.
Einstein's answer was influenced by these authors but it was also particularly pragmatic, e.g., it was shaped by his work on relativity. Firstly, Einstein was primarily concerned with what he called principle theories, like the theory of relativity. Here the role of constraints comes to the fore. Einstein often declares the world of experience as the final arbiter of the validity of scientific theories.
Experience has nothing to do with science. You must write down what you know, such that it can be chalenged.
In Popperian fashion he regarded all scientific theories as falsifiable.
This requires a definition of falsifiable. All of science should be clearly defined. All of science should be clearly described. This should included the type of observations involved and the experiments used.
But empirical evidence, in the theory of relativity, is only one form of constraint.
What does that mean? What means empirical evidence?
According to Wikipedia: https://en.wikipedia.org/wiki/Empirical_research implies observations and experience.
Scientific theories present hypothetical 'pictures' of the external world. But Einstein was no naïve realist. A scientific theory constructs a coherent and logically rigid account of the available empirical data. Logical consistency was Einstein's second constraint on theories since he believed in the mathematical simplicity of nature. [Einstein 1933, 274] The coherence of a theory may always come under threat with new empirical discoveries. There is nothing final about the representation of a scientific theory of the external world. Theories are free inventions, yet they must retain roots in the empirical world.
Theories are supposed explanations and are (mainly) based on observations.
Does this mean that there is always a plethora of competing theoretical accounts, which nevertheless are compatible with the available evidence?
There can only be one physical explanation for the same identical observations. That means all the planets around the stars in our galaxy should have the same physical explanation.
The issue is that not all stars are identical. These differences require different explanations.
If this were the case scientific theories would face the serious problem of underdetermination. That is, there would always be a number of theories, which are able to explain the empirical evidence, although they fundamentally disagree about their theoretical structure. For instance the Copernican model of the solar system (1543) explains the same observational evidence as the Ptolemaic account although the Copernican model is based on the principle of heliocentrism, while the Ptolemaic account embraces the principle of geocentrism. In this situation Einstein recommends pragmatically to distinguish a logical from a practical point of view. From the logical point of view, Einstein grants that there are always numerous theoretical accounts, which could in principle account for the available evidence.
For there seems to be no limit to the number of competing constructions, which, at least in principle, could claim to give a coherent and simple account of the available phenomena.
The most common phenomena that can be observed in our solar system, is a large object surounded by smaller objects, which revolve around the larger object.
The explanation of this common behaviour (model) is the force of gravity.

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This is due to the fact that theories are the result of human ingenuity. Yet in practice, the number of available theories is always limited. Einstein did not believe that many competing representations of the empirical world could be sustained. He goes even further: he believes that there is one correct theory. The structure of the external world has the power to eliminate many rival accounts. The surviving theory displays such a degree of rigidity that any modification in it will lead to its falsehood. 'Rigidity here means that the theory is either true or false but not modifiable.' [Einstein 1950b, 350; 1936] (cf. [Hentschel 1992], [Scheibe 1992] and [Weinberg 1993]) Einstein illustrates the lack of underdetermination, from the practical perspective of the working physicist, by the analogy of solving a crossword puzzle. Although we are free to insert any word into the columns and rows of a word puzzle, this freedom is very restricted. Only one word will 'fit', only one word will solve 'the puzzle in all its forms.' [Einstein 1936, § 1] The structure of the external world practically determines the form of the theoretical system. [Einstein 1918b; 1933] Going beyond Einstein it will also be useful to split the space of possible theories or models into alternative and rival accounts. Alternative accounts, like the Schrödinger and Heisenberg pictures in quantum mechanics are mathematically equivalent; covariant formulations of physical laws in the General theory of relativity are form-invariant.
This requires a discussion what the problem scope of GTR is.
They pose no problem in terms of underdetermination. Rival accounts like Lorentz's and Einstein's models of the kinematics of reference systems are based on incompatible theoretical principles.
Why?
Lorentz's account of time dilation and length contraction postulates an absolute rest frame, whilst Einstein's motivation was to abandon all need for absolute reference frames.
I would say that Lorentz's account is based on one reference frame, whilst Einstein's account is based on many. The first seems the most logical.
Rival accounts therefore pose a problem from the point of view of underdetermination. In the practice of science, however, there is little underdetermination. How can this be explained? If we look at Einstein's philosophical writings about physics, we notice his insistence on constraints such as unification and the logical simplicity of a theory; he also holds that evidence is the final arbiter of a theory's fate.
Einstein locality, logical simplicity and unification are methodological constraints, since they are principles of the methods of science.
They each require a clear definition.
Compatibility with available and new evidence is an empirical constraint. In the present context the methodological constraints are of lesser importance than some of the other constraints, which are associated with the theory of relativity. Looking at Einstein's way of doing physics, we notice his employment of a number of theoretical constraints, since they derive more

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particularly from the theories of relativity. In particular, as we shall see, the light postulate, relativity principles, covariance and invariance principles. We can characterize constraints as restrictive conditions of an empirical or theoretical kind, which descriptive and explanatory accounts must satisfy to count as viable candidates for the scientific description and explanation of the natural world. With respect to the theory of relativity, Einstein holds that the interplay of specific constraints—like covariance, invariance, relativity—creates a fit of the theory or model with the evidence extracted from the external world. Any modification, he holds, would destroy the coherence of the theory of relativity. [Einstein 1918b; 1919; 1933] This provides a clue to a solution of the puzzle of how theories manage to represent the world. A theory 'represents' a section of the empirical world, if it satisfies a certain number of constraints. The representation is illustrated in terms of fit, as in the analogy of the crossword puzzle. But 'fit' should be understood in terms of satisfaction of constraints. [Weinert 2006] The representation is not an image, nor need it be perfect or absolute.
In order that thinking might not degenerate into 'metaphysics', or into empty talk it is only necessary that enough propositions of the conceptual system be firmly enough connected with sensory experiences and that the conceptual system, in view of its task of ordering and surveying sense-experience, should show as much unity and parsimony as possible. [Einstein 1944, 289]

We have thus assigned to pure reason and experience their places in a theoretical system of physics. The structure of the systems is the work of reason; the empirical contents and their mutual relations must find their representation in the conclusions of the theory. In the possibility of such a representation lies the sole value and justification of the whole system, and especially of the concepts and fundamental principles which underlie it. [Einstein 1933, 272]

As it changes with the changing nature of constraints, fit comes in degrees. In the simplest case, a model represents the topologic structure of a system; e.g. a heliocentric scale model of the solar system represents the spatial arrangement of the planets around the sun. The models used in the theory of relativity are more sophisticated structural models, which combine a topologic with an algebraic structure. The algebraic structure of the model expresses the mathematical relations between the components of the model.

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Consider, for instance, Einstein's thought experiment, which involves two discs whose circumference and diameter are to be measured. [Einstein 1920, 80; 1922a, 58–9] Let the discs be arranged in such a manner that disc B rotates uniformly about a common axis with disc A. This is its topologic aspect. But the main interest lies in the algebraic structure, e.g., how the parameters on the two discs will be measured. To carry out the measurements, measuring rods are placed along the radius and tangentially to the edge of the disc. A does not rotate so that the ratio of circumference to diameter is equal to π. From the point of view of A the ratio C/D on B will be greater than π. Due to length contraction of the tangential rods the circumference will appear greater on B than on A. Now place two similar clocks on B, one at the centre, C1 and one at the periphery, C2. Judged from A, C2 will go slower than C1. We may assume that no faulty instruments are involved. These respective measurements are objective. Observers on the respective discs will regard their respective measurements as accurate. Mathematically, the thought experiment stresses the effect of motion on the measurement of the parameters. Note that the algebraic structure implied by Euclidean geometry fails and must be replaced by a structure provided by Riemannian geometry. Let the empirical facts, methodological principles and theoretical postulates constitute a constraint space. The theory of relativity satisfies a number of empirical and theoretical constraints, which improve its fit to the external world. The empirical facts comprise Einstein famous predictions: the red shift of light as a function of gravitational field strengths and the bending of light rays in the vicinity of strong gravitational fields. He also explains the perihelion advance of Mercury and other planets. In the theory of relativity the most important theoretical constraints are the following:

5.1 The postulation of the constancy of the speed of light page 116

It had been known since Roemer's first determination of the speed of light in 1675 that light propagates at a finite velocity of approximately 300.000 km/s. Einstein turned this value into a theoretical postulate such that the speed of light becomes the limit velocity, which no material particle can reach. In the language of the Minkowski representation of space-time this means that from any event, E, light signals converge from the past and diverge into the future at a constant speed, forming past and future cones. All inertial observers will see the angle of convergence

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and divergence inclined at 45◦ to the vertical. The light cones do not tilt. And all observers measure the same velocity for c, irrespective of the direction and their state of motion with respect to the light source.

5.2 Principles of Relativity page 117

Einstein began his 1905 paper on the Special theory of relativity by a consideration of standard attempts to explain Faraday's induction current. He complained that according to the then current view an asymmetry of explanation for an observationally indistinguishable phenomenon occurred. If the coil is in motion with respect to the magnet at rest (in the ether), the charges in the coil experience a magnetic force, which pushes the electrons around the coil, inducing a current. If the magnet is in motion with respect to a coil at rest, the magnetic force is no longer the cause of the current, for no magnetic force applies to charges at rest. The magnet now produces an electric field in the coil, resulting in the current.
To avoid this asymmetry of explanation—an asymmetry not present in the phenomena—Einstein postulated the physical equivalence of reference frames.
To avoid any postulate you should try to stick to physical explanation.
The physical situation is that you have a magnet and electric coil surrounding the magnet.
In its general form the principle of relativity states that all coordinate systems, which represent physical systems in (uniform or non-uniform) motion with respect to each other, must be equivalent from the physical point of view.
The question is why is the principle of relativity required?
A more specific question is: Why do you need more than one coordinate system?
In other words, the laws which govern the changes that happen to physical systems in motion with respect to each other are independent of the particular coordinate system, to which these changes are referred.
Laws don't govern the behaviour of physical systems. They are descriptions.
In order to explain physical phenomena only one coordinate system should be used.
So it is not admissible that an induced current is explained differently, depending on whether the magnet or the coil is in motion.

5.3 Invariance and Symmetries page 117

We can understand reference frames (in the STR) as idealized physical systems whose space-time coordinates are given by rigid rods and idealized clocks. They are subject to various symmetry operations, like rotation or translation in space and time. The Special theory obeys the Lorentz-transformations, because the Galilean transformations fail as we approach the speed of light. The Galilean transformations, for instance, result in different values for the speed of light, if we change from a stationary to a moving reference frame. The Lorentz-transformations deal with space-time transformations of a global kind; that is, they are constant throughout the space-time region. They form a symmetry group.

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(The General theory requires a larger symmetry group.) Symmetry constraints emphasize physical aspects: the symmetry operations return some values of parameters as invariant (like the space-time interval) and leave others as variant (like the clock readings in different reference frames, in constant motion with respect to each other). Symmetries result from transformations that leave all relevant structure intact. We are familiar with such symmetry transformations in daily life. We easily change the clock as we travel between different time zones. But the tennis games we play at home and abroad are the same as far as the physical parameters are concerned.

5.4 Covariance page 118

Covariance is prima facie a mathematical constraint. The modern use is quite different from the way Einstein uses the notion of covariance. Einstein associates covariance with the transformation rules of the theory of relativity. He imposes on the laws of physics the condition that they must be covariant a) with respect to the Lorentz transformations (in the Special theory of relativity) [Einstein 1949c, 8; 1950, 346] and b) to general transformations of the coordinate systems (in the General theory). [Einstein 1920, 54–63; 1950, 347] The theory of relativity will only permit laws of physics, which will remain covariant with respect to these coordinate transformations. [Einstein 1930, 145–6] This means that the laws must retain their form ('Gestalt') 'for coordinate systems of any kind of states of motion.' [Einstein 1940, 922] They must be formulated in such a manner that their expressions are equivalent in coordinate systems of any state of motion. [Einstein 1916; 1920, 42–3, 153; 1922a, 8–9; 1940, 922; 1949a, 69] A change from coordinate system, K, to coordinate system, K′ , by permissible transformations, must not change the form of the physical laws. This leads to the characterization of covariance as form invariance. [Weinert 2007a] Einstein often illustrates covariance with respect to the space-time interval ds2. [Einstein 1922a,28] In Minkowski space-time, the space-time interval ds2 is expressed as an invariant expression in what remains essentially a quasi-Euclidean space:
ds^2 = Sum over (ν=1 to 3)  (∆xν )^2 − c^2∆t^2 = 0
If the expression satisfies covariance it must remain form-invariant under the substitution of a different coordinate system, i.e., ds2 = 0 = ds′2 :

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ds2 = (Sum over v=1 to 3) (∆xν)^2 − c^2∆t^2 = 0 = ds′2 (Sum over ν=1 to 3) (∆x′ν)^2 − c^2∆t′^2 =
(2) The equation for the space-time interval, ds, remains form-invariant if K is substituted by another quasi-Euclidean inertial frame, K′, as indicated by the coordinates ∆x′ν.
For Einstein a fit must exist between the theory of relativity and the material world. We explicated fit in terms of the satisfaction of constraints, associated with the theory of relativity. If their amount and their interconnections can be increased, then many scientific theories will fail to satisfy the constraints. It will usually leave us with only one plausible survivor. For instance, after the development of the Special theory, Einstein increased the constraints on an admissible relativity theory. Inertial reference frames should not be privileged over non-inertial frames. This extension of the relativity principle and the demand of covariance lead to the General theory of relativity. This theory was able to explain the perihelion advance of Mercury, where Newtonian mechanics had failed.
Newtonian mechanics is based on the assumption that gravition (the force of gravity) acts instantaneous. In reality this is not true.
It would be exaggerated to claim that there is such a tight fit between the theory and the world, that there is a one-to-one mapping of the theoretical with the empirical elements. Einstein, in fact, rejected naïve realism. [Einstein 1944, 280–1] Due to the need for approximations and idealizations there will always be theoretical structure, for which there is no direct empirical evidence. For instance, the evidence does not tell us whether space-time exists, devoid of all matter. But Einstein holds that one theory always satisfies the constraints better than its rivals. It does not follow from this argument that the survivor—let us say the theory of relativity—will be true. It does follow that the process of elimination will leave us with the most adequate theoretical account presently available. New experimental or observational evidence may force us to abandon this survivor. The desire for unification and logical simplicity may persuade us to develop alternative theoretical accounts. Einstein's attempt to extend the principle of relativity from its restriction in the Special theory to inertial reference frames to non-inertial reference frame in the General theory is a case in point. Although Einstein does claim that there is one correct theory, he cannot mean this in an absolute sense. His insistence on the eternal revisability of scientific theories, including constraints, speaks against this interpretation. What he must mean is that there is always one theory, at any one point, which best fits the available evidence. This one theory copes best with all the constraints, which logic and evidence erect;

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but there is nothing final about such a theory; it will always remain falsifiable.

VI. What is Einstein's philosophical allegiance? page 120

He has been appropriated by neo-Kantians, realists, positivists and holists alike. Each camp can claim textual evidence for its preferred interpretation [Frank 1949] [Holton 1965; 1973] [Howard, 1990; 1993; 2004]. In a number of papers, Don Howard has promoted the view that Einstein agreed with Duhem's underdetermination thesis, and generally adopted a holist view of theory confirmation, e.g. only a theory as a whole body of statements faces the verdict of experimental evidence. [Howard 1990; 1993] This view implies the denial of crucial experiments, and a certain latitude of choice of conceptual elements with respect to the empirical evidence. It is akin to conventionalist ideas associated with Poincaré. According to this interpretation there exist logically incompatible theories, which nevertheless are equally compatible with the evidence. The question is whether Einstein's way of doing physics is compatible with this strong holist interpretation. If we look at the development of the theory of relativity, we notice that there are several problems with this holist interpretation. Einstein's insistence that at any one point in the history of science only one rival theory is the most adequate theory (alone capable of satisfying all the constraints) suggests that confirmation holism does not necessarily imply the existence of equally good competitors, e.g. observationally indistinguishable but ontologically divergent theories. In particular, Einstein's work on relativity shows that other than empirical constraints are at hand to distribute credibility unevenly over the space of possible theories. Einstein actually employs these constraints, as we have seen, to argue in favour of the relativity theory. In his discussion of the rotating disc thought experiment, Einstein explicitly avoids saving Euclidean geometry 'come what may', although this is a conventionalist stratagem. We should also note that neither Duhem nor Quine were the complete holists they are made out to be. Discussions of holism usually highlight the radical underdetermination of an entire theory by empirical evidence. [Howard 1993] It is often overlooked that both Duhem and Quine accepted the coherence of scientific theories as a constraint, as much as Einstein did. According to this aspect, theories are structured conceptual systems, which entertain many mathematical and conceptual

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interrelations between them. This aspect makes the deducibility of empirical laws from more fundamental laws possible. Duhem, for instance, appeals to an analogy of science with an organism,
in which one part cannot be made to function except when the parts that are most remote from it are called into play, some more than others, but all to some degree. [Duhem 1954,187–8] [Weinert 1995]
The coherence aspect corresponds to Einstein's insistence on the rigidity of scientific theories, for which he uses the analogy of the crossword puzzle (Section V). This rigidity shows that changes in one part of the theory will affect other parts of the theory, so that the 'latitude of choice' is more restricted than holism is ready to admit.
Any physical theory, any theory that describes the evolution of the universe shoud start with
The presence of constraints and the concern for 'fit' point in the direction of a stronger form of realism. Einstein is fond of the view that theoretical constructions are not inductive generalizations from experience but free inventions of the human mind. Nevertheless there must be a 'fit' between the theoretical expressions and the external world. This fit is achieved in the theory of relativity, we suggested, through the introduction of constraints. The increase in constraints—extension of the relativity principle to non-inertial motion, the introduction of the principle of equivalence and the form-invariance of laws (covariance principle)—takes Einstein from the STR to the GTR. If there is indeed a 'fit' between what the theory says and what the material world presents, the question of realism returns. Consider, for instance, Einstein's view of Poincaré's conventionalism about geometry. Einstein reflected on the status of geometry in the light of the GTR. [Einstein 1921; 1922b] He distinguishes an axiomatic and a practical geometry. He agrees with Poincaré that the laws of axiomatic geometry are based on conventional choices, say in favour of Euclidean geometry and its axioms. But Einstein sees an important difference between an axiomatic and a practical geometry: the former makes no reference to the world of experience, whilst the latter does.
The question whether the practical geometry of the universe is Euclidean or not, has a clear meaning, and its answer can only be furnished by experience. [Einstein 1922b, 23]
According to Einstein this view of geometry was an essential prerequisite for the development of the GTR.

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The question whether the structure of [the four-dimensional] continuum [of space-time] is Euclidian, or in accordance with Riemann's general scheme, or otherwise, is, according to the view which is here being advocated, properly speaking a physical question which must be answered by experience, and not a question of mere convention to be selected on practical grounds. [Einstein 1922b, 39]
What counterbalances the strong holist interpretation of Einstein's views is Einstein's repeated insistence that out of many rival theories there is one with the most adequate fit and that practical geometry allows fewer conventional elements than Poincaré is ready to concede. From the point of view of Einstein's problem situation, his philosophical attitude was characterized during his lifetime as a form of critical realism. Einstein certainly approved of this way, in which Lenzen and Northrop characterized his epistemological position (See [Lenzen 1949] [Northrop 1949] [Einstein 1949b, 683]). It simply regards scientific theories as hypothetical constructs, free inventions of the human mind. But there is also an external world, irrespective of human awareness. To be scientific, theories are required to represent reality. They represent reality by satisfying both empirical and theoretical constraints.
More information is required what is meant.
A theory is not a mirror image of the world. It is a mathematical representation, which provides coherence of the empirical data and shows their interconnections.
This requires a philosophical discussion of this is allowed.
Theories are hypothetical, approximate constructions, which in a process of fitting and refitting, deliver a coherent picture of the external world. In human efforts to understand the world, experience and reason go hand in hand. In modern terms, Einstein's relativity theory may be characterized as leading to a form of structural realism. [Weinert 2007b] The relativity theories are principle theories, which employ general coordinate systems to explain the behaviour of physical systems in uniform or accelerated motion with respect to each other. Such coordinate systems are well-suited to represent physical systems, since they can be regarded as structural models of the target systems. Physical systems typically display structures, consisting of relata and relations. As the models of the relativity theories are able to represent both the topologic and algebraic aspects inherent in physical systems, they can be said to represent the structure of physical systems. Einstein declares that 'the concepts of physics refer to a real external world, i.e., ideas are posited of things that claim a 'real existence' independent of the perceiving subject (bodies, fields etc.)' [Einstein 1948, 321, transl. Howard, 1993, 238] These representational claims cover both the relata (fields, material particles, reference frames) and the relations (the mathematical relations between the relata).

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Given that scientific theories manage to represent aspects of the external world, what picture of reality does the relativity theory espouse?

VII. What is Reality? page 123

The structural realist makes the assumption that there is a structured external material world.
What means structural or structured?
Theories which 'fit' a domain of this external world present us with a view of physical reality.
Any 'theory' about the Universe should start with the proposition that there exists a (physical) reality.
Such views have changed with the progression of physical theories. There was a time when physicists liked to think of the world as a massive clockwork. Particles populated the universe. Only their primary qualities mattered. They were at rest or in constant regular motion. Einstein suspected that this classical picture was mistaken. It required Newton's absolute space and time and action at a distance. For Einstein, physicists like Heinrich Hertz, Michael Faraday and James Maxwell made significant steps in the revision of the physical worldview when they introduced fields as fundamental physical entities. Einstein regarded the theory of relativity as a field theory, which dispenses with action at a distance. But Einstein was never able to overcome the fundamental dualism in the physical worldview between particles and fields. This may be the reason why we find in Einstein's work two concepts of physical reality.
There exists only one physical reality.
In his relativistic thinking about the nature of reality, Einstein becameone of the first physicists to realize the significance of symmetries and invariance in science as a new criterion of what the physicist should regard as objective and physically real.

The starting point is the principle of relativity. In the STR it states that all reference systems, which represent physical systems in motion with respect to each other, must be equivalent from the physical point of view. But we have already observed that in the transition from one reference system to another some properties change. The classic examples are temporal and spatial measurements, as well as mass determinations. From the phenomenon of time dilation and the relativity of simultaneity some physicists concluded that time cannot be a physical property of the universe.

Time in general is not a physical property. Time is property what people experience, what people remember. As such for people there exist a past and a future, but these concepts are not part of the reality.
Time dilation is a property of clocks which move at different speeds.
Some transitions to other reference systems do not, however, affect the physical properties. The classic example is the velocity of light in vacuum. The Special theory of relativity postulates that the value of 'c' will be the same in all time-like connected reference systems, which move at constant speed with respect to each other.
How do you know that two reference systems move at a constant speed respect to each other?
IMO that is impossible by means of experiment.
Some physical properties are immune to changes in reference systems, while others are not.

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The velocity of light is the same in all directions and irrespective of whether it is emitted from a moving or stationary source. But the wavelengths of light depend on the movement of the source (Doppler Effect). Symmetry principles, like the geometric symmetries of the STR, show the invariant aspects of the equations, which apply to Minkowski space-time. While in classical physics, many properties, like time, mass, space, energy were regarded as 'absolute', in the Special theory of relativity, many properties became relational. Relational means that they cannot be considered in abstraction from the coordinate values in particular reference frames. So the question arises, 'What is real?' For it seems that if two observers disagree about the length of an object or the simultaneous occurrence of an event, they cannot both be right.
It can never be such that measurements of the length of objects, which are physical the same, can disagree.
An object, so it appears to us, cannot have two different lengths at the same time.
That is correct.

But we need to take into consideration the lessons of relativity.

The answer to the question of reality is embedded in the mathematics of the Special theory of relativity.

Mathematics can not be used to understand the physical evolution of processes.
Minkowski's four-dimensional interpretation of space-time provided Einstein with a new criterion for the physically real.
Space-time is a mathematical construct.
Physics, he says, deals with 'events' in space and time. [Einstein 1949c]
Correct
Temporal and spatial measurements varied from reference frame to reference frame.
That makes it very different to compare the results of the same events in different reference frames. This highlights the tricky use of reference frames (plural)
They could not be physically real. But the space-time interval, ds, remained invariant for every observer.
You need a description how ds is calcalculated.
It was therefore to be regarded as real. In general, what a scientific theory tells us to regard as 'real' is what remains invariant in transitions between different reference frames. These transitions are governed by transformation groups.
The physical concept 'what is real' has nothing to do with mathematics or the mathematical concept invariant and is not governed by transformation groups.
In the STR the Lorentz transformations take us from one reference system to another.
They state how the spatial and temporal coordinates of one reference systems translate into another. As we change between various reference systems, say, from stationary to constantly moving systems, the laws of physics express invariant properties of physical systems, like the space-time interval of equation (1). Einstein at first considered inertial systems and later accelerated systems.
The laws of physics must retain their form (remain covariant) under the substitution of coordinate systems through all transformations.
This requires a clear definition of what a law of physics is.
The problem is all systems are accelerated systems. Each planet defines an accelerated reference frame. Also each comet
[Norton 1989; 1993] What remains invariant is to be regarded as the physically real.
How is it possible to declare someting physically real by means of mathematics. I would say at least by observations.
More specifically Einstein advanced his 'point-coincidence argument'. Einstein explicitly claims that the laws of physics are statements about space-time coincidences. In fact only such statements can 'claim physical existence'. [Einstein 1918a, 241; 1920, 95] [Norton 1992, 298]

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As a material point moves through space-time its reference frame is marked by a large number of co-ordinate values x1, x2, x3, x4. This is true of any material point in motion. It is only where the space-time coordinates of the frames intersect that they 'have a particular system of coordinate values x1, x2, x3, x4 in common'.
[Einstein 1916a, 86; 1920, 95] In terms of observers, attached to different reference systems, it is at such points of encounters that they can agree on the temporal and spatial measurements. Many physicists concluded as a philosophical consequence of the relativity theory that only the invariant can be the physically real. [Eddington 1920] [Weyl 1921] [Born 1953] [Dirac 1958] [Wigner 1967, Part I] [Planck 1975]

However, as Born pointed out frame-dependent properties may also lay claim to reality. [Born 1953] [Weinert 2004, ch. 2.8] Clock and meter readings in particular reference frames are not perceptual illusions of observers. These measurements have perspectival reality since they are relational. They are relational in the sense that they must be derived from the coordinate values of particular reference frames. Born compared the perspectival realities to projections, which are defined in a number of 'equivalent systems of reference'.
In every physical theory there is a rule which connects projections of the same object on different systems of reference, called a law of transformation, and all these transformations have the property of forming a group, i.e. the sequence of two consecutive transformations is a transformation of the same kind. Invariants are quantities having the same value for any system of reference, hence they are independent of the transformations. [Born 1953, 144]
The Lorentz transformations show, Born adds, that quantities
like distances in rigid systems, time intervals shown by clocks in different positions, masses of bodies, are now found to be projections, components of invariant quantities not directly accessible. [Born 1953, 144]
This leads to a modified view of physical reality, which is still compatible with the Minkowski presentation of the theory of relativity. It admits both frame-dependent and frame-independent realities. The invariant is not the only reality but it is the focus of physics. What now becomes of the criterion that only the invariant is to be regarded as real?

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It derives from the fact that physics is not interested in perspectival realities. Physics is interested in the underlying structures, which relate the different perspectives. Relativistic physics is interested in the structure of space-time. This structure can be described mathematically, as Minkowski has done. It will tell us that the space-time interval, ds, is invariant across the reference systems.
That is not simpel to understand. Why systems?
The particular perspectives then result from attaching clocks and rods to the world lines, which crisscross space-time. Once the symmetries tell us what remains invariant across reference frames, it is not difficult to derive the perspectival aspects, which attach to different reference frames, as a function of velocity. The theory of relativity led Einstein to an invariance view of reality.
This requires a clear definition of what invariance means.
But his opposition to the Copenhagen interpretation of QM led him to a more classical separability view of reality: spatially separated system, A and B, which obey Einstein locality, possess physical properties, which are not immediately affected by external influences on either of the systems. [Einstein 1948]

VIII. Philosophy and Science page 126

Philosophical consequences do not flow from scientific theories with logical compulsion. Nevertheless, certain kinds of philosophical positions are more akin to scientific findings than others. For instance, a belief in Newton's absolute space and time and the invariance of mass has become incompatible with the findings of STR.
This requires a more detailed discussion of both Newton's mechanics and STR.
My understanding that you cann't compare both.
An adherence to Euclidean geometry has become incompatible with the GTR. Einstein's belief in deterministic causality and the principle of local action has become questionable in the light of QM. He once accused philosophers of dragging concepts into the den of the a priori.

Philosophers had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori. [Einstein 1922a, 2, italics in original]
Sometimes, however, the very foundations of science become shaky. This happened twice in Einstein's lifetime: relativity and quantum theory.

Both concepts are very difficult to compare. GTR has to do with the movement of the masse's. STR with electrical, magnetical processes and with light. Quantum theory with elementary particles: Molecules, atoms and smaller.
Then the physicist himself is forced to become a philosopher through a 'critical contemplation of the theoretical foundations'. The philosopherscientist is a familiar figure in the history of science (Newton, Leibniz,

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Darwin, Bohr, Born, Duhem, Planck, Poincaré). Max Born gave expression to the role of the philosopher-scientist when he wrote that
History has shown that science has played a leading part in the development of human thought. [Born 1949, 75]
Or is it more the other way around?

This philosophical turn of scientists is due to a basic epistemological situation in the sciences, of which Einstein was very aware: the need to map symbolic systems (theories, models, equations) onto an independently existing reality.

Science starts by accepting that there exists a reality, which we want to understand, in detail, in its physical details.
The most important concept to be used is a physical model.
This mapping has to satisfy criteria of 'fit'. If the scientific discoveries are sufficiently profound, conceptual consequences become unavoidable because they touch on our most profound physicophilosophical notions (determinism, nature, time etc.).
Before they can be used these concepts has to be clearly defined.
A need arises to rethink these fundamental notions; Einstein and other philosopher-scientists did not shirk from this task. A philosopher-scientist is someone who in Einstein's words considers the career of 'certain fundamental concepts' within the problem situation, in which they arise. The problem situation may be the kinematics of reference systems or the evolutionary theory. The physico-philosophical concepts need to be reassessed in the light of scientific discoveries, because they acted as unquestioned assumptions prior to the new discovery. In Einstein's case these were concepts like mass, space and time, the nature of physical reality and of scientific theories.
All these concepts require a clear definition.
In such reassessments the scientist turns to more conceptual issues, which are no longer deductive consequences of the theory. As Einstein realized, when the foundations of science become problematic, the man of science becomes a philosopher. [Einstein 1936, § 1] The philosophical legacy of Einstein's scientific work is immense. It ranges from metaphysics to the philosophy of physics. The theory of relativity demonstrates clearly how difficult the relationship between facts and concepts has become. We cannot simply cling to the concepts, irrespective of what experiment and observation tell us. This was Einstein's charge against Newton and Lorentz. Ironically it also reflects his own difficulties with quantum mechanics, since he relies on notions like determinism and separability. Nor can we simply inductively generalize from the facts, neglecting the concepts. Therefore Einstein believed in the importance of theoretical thinking and the power of constraints. As Einstein realized himself, science makes philosophical presuppositions. The scientist needs philosophical ideas, simply because amongst the experimental and mathematical tools in the toolbox of the scientist there are conceptual tools, like the fundamental notions. Philosophical presuppositionscan both guide and misguide the scientist. When the philosophical presuppositions change as a result of scientific discoveries, science does not dictate to philosophy the answers.

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But it constrains the philosophical consequences, which follow. The philosophical consequences include such questions as to which extent the Special theory is compatible with objective becoming or static being. Then there was the question of determinism in the interpretations of quantum mechanics, and the question of causal relations between entangled quantum systems. There is the issue of the representational nature of theories, more precisely the question of fit, which we interpreted as the requirement for the satisfaction of certain constraints. Finally, the philosophical notion of physical reality must be in harmony with the scientific findings. The 'point-coincidence argument' therefore led physicists to the invariance criterion of physical reality but Einstein's notion of 'local action' (no-action-at-a-distance) has not found the approval of quantum physicists. Einstein's work has shown that there is a genuine interaction between science and philosophy. Every true theorist is a 'tamed metaphysicist'. [Einstein 1936 17; 1950b, 342] We have seen how Einstein's physical problem situation lead to philosophical consequences.
A consideration of Einstein's career as a physicist-philosopher illustrates Reichenbach's observation that the 'evolution of philosophicalc ideas is guided by the evolution of physical theories'. [Reichenbach 1949,301]
The phylosophicalc considerations come first

Index

absolute time page 101, page 103, page 104, page 109, page 123 page 126
action at a distance & action-at-a-distance page 112, 123
empirical page 102 , page 103 , page 109 , page 111 , page 121 , page 122 ,
Entanglement page 112, 121
Equivalenc page 105, page 117, 121
faster than light signals & faster-than-light-signals page 112
indeterminacy principle page 110
principle of local action page 111 , page 112 , page 126
Locality page 114 , page 126
Logical simplicity page 114
Lorentz transformations page 100, 118
methods of science page 114
Newtonian mechanics page 102, page 110, page 119
Now page 105, page 107, Ref 1
physical system page 108, page 111, page 117, page 122, page 123, Ref 1
Special theory of relativity page 104, page 106, page 107
uncertainty principle page 110
unification page 114

Reflection 1 - The philosphy of Science

The phylosophy of Science start with a question: What do we want. What do we want to understand.
To answer that question requires the definition of the concept understanding
In fact all the concepts used require a clear definition
To answer the first question what we want to understand is: Why do planets revolve around the Sun. Why do they move in a flat plane. Why are there clusters of stars. Why do the stars in our Galaxy revolve around a center. Why most probably is there a Black Hole in the center. Why is there an Universe.
All these questions are physical questions. If you want to understand something you should study the details. That means if you want to understand the Universe, you start with the details. The starting point is to do observations and to perform experiments.
There are different ways to perform observations: By using our eyes, by using a microscope and by using a telescope.
However physical observations have its limits, mainly what you see has happened in the present. What we want to know is the "REALITY" or the present position of all star, what we observe is the "reality" or the positions of all the stars in the past.
What we want is to know is the REALITY as a sequence of instances in order to establish how the stars move in the Universe. As such you can establish how the two stars move in a binary system. The next step is how do you explain such a system.
To do that you should study a even simpler system: Two objects of the same size a certain distance apart. We all know what happens: an apple falls from a tree. The quivalence is that the two objects will move towards each other and collide. The physical explanation is that each object causes an attractive force on the other object and because the size and composition of both objects will move to wards each other and collide. That force is called the force of gravity.
Now we go back to our binary system. In order to explain that you need two forces 1) the force of gravity and 2) an initial force which pushes each object, in the same plane and in a direction perpendicular to the line which connects the two objects. The direction of each should be opposite of each other.

From these simple observations we can learn much more.

  1. To understand the physical movement of the stars no mathematics is required. Mathematics is required if you want to predict the future positions of the stars or the positions of the planets around the Sun. That is possible because considering a period of 1 million years in the past and in the present our Solar system is stable. Considering the solar system of a much larger scale that is not possible. However in order to understand the physics involved no methematics is required.
  2. To understand the physical movement of the stars only one reference frame is required. GTR discusses many reference frames, but to consider that each observer is linked to its own reference frame seems an overkill. As such each star in a binary system has its own reference frame, which does not seem practical, because the position of both objects is symmetrical.
  3. To understand the movement of objects does not require the concept of light. Stars emit light, but the amount is small and don't influence the movement of the stars. Light (the speed of light) is an issue for electical or magnetic processes, however, there influence on the movement of stars is also minimal. A different case is when a star explodes, as during a super nova, but they are rare.
    A different case is when you want to predict the future position of a star. In that case light is necessary. The problem is that light is a different physical phenomena compared to gravity and should be treated seperately. All in all light is not required to understand the physical movement of the objects.
    Light is more a problem for objects which are invisible. These objects can be very small or very large. The reason is, all these invisible objects, influence the behaviour of the visible objects and vice versa.
  4. To understand the movement of stars no clocks are required. This is different if you want to predict the future positions of the stars which requires to measure the position of the objects involved at regular intervals.
    The problem is that a clock is a physical object, which behaves based how it is constructed. For example, a moving clock which uses light signals, ticks slower as a clock at rest. The solution is that all clock used should be synchronized with a point at rest.
  5. As already mentioned previous, what we want to know is the present position of all the stars in the universe. To say it differently: the position at present, Now. This implies that what we want to know, are simultaneous positions. By definition all the events throughout the universe that are happening at present, or Now, are happening simulataneous.
    The problem is, that is not what we observe. Suppose we observe an explosion on the Moon and at that same moment an accident close by, both events don't happen simultaneous. That is the problem: how do we know the universal time of both events.
  6. Thought experiments.

Reflection 2 - Understanding the physical universe - Mathematics.

What we want is to understand the physical processes evolving in the physical universe. What does that mean.? IMO to understand these processes is by performing experiments as much as possible. What you cannot do is to use existing laws. These laws are in fact descriptions of experiments. As such you cannot claim that laws govern physical phenomena.
It is also important is that the universe a hugh chemical melting pot is, in which chemical reactions take place. When you consider preparing soup than the basic ingredient is water and a small part is vegetables and meat. When you compare that with the universe the main part is empty and gas. At the other side the universe consists of objects, of mass from very small to large. It are these objects which all influence each other and which make the universe at large distance in all directions and at large time scale, dynamic. What this means is that the whole of the universe, in its totality, is constantly changing. Many of these changes are streams of material.

When we study STR and GTR the emphasis is on light and the speed of light. The problem is that almost all processes in the universe don't depend on light, or any thing that is vissible. When you study Newton mechanics you will see that the speed of light is not an issue. In the case of Newton's mechanics the reason why the planets move around the is Sun is explained by introducing the force of gravity, which proposes that all forms of matter (objects) atract each other. However there is one complication and that is when you consider a system which consists of two rotating objects that the force of gravity, originating in from object 1, which attracts object 2 at present, does not originate from the present position of object 1, but from a position in the past of object 1. How far in the past depents about the distance between the two objects and the speed of gravity.
In Newton's time this issue was not considered, because it was considered that the force of gravity, originating in object 1, which attract object 2 at present, originates from the present position of object 1. That means the force of gravity acts instantaneous and the speed of gravity is infinity. That means there are no gravity waves. By introducing the speed of gravity, gravity waves appear more pronounced.

When you study any simulation using Newton Mechanics starting point are differential equations, which are implemented as difference equations.
See: https://en.wikipedia.org/wiki/Differential_equation and https://en.wikipedia.org/wiki/Recurrence_relation#difference_equation

Reflection 3 - Length contraction - Length expansion

Consider an arrow, which passes in front of you, horizontal, from left to right.
Consider the end of the arrow touches your nose (don't try it), moving away from you. What do you observe?
At that moment you will see the end of the arrow and you will also observe the front of the arrow, but you will not see the front of the arrow (light coming from the front of the arrow) at the present position but from an earlier position, closer by. That means the length of the arrow seems to be contracted.
Consider the front of the arrow touches your nose (don't try it), moving towards you. What do you observe?
At that moment you will see the front of the arrow and you will also observe the end of the arrow, but you will not see the end of the arrow (light coming from the end of the arrow) at the present position but from a earlier position, further away. That means the length of the arrow seems to be expanded.
From a physical point of view the length of the arrow cannot be both contracted and expanded, implying that the vissible observations, don't agree with the reality.

There is nothing wrong, to calculate the center of gravity on both sides, using the same methodology. The result is assymetric. The center of gravity, from an arrow moving away from you, compared from the center of gravity, from an arrow moving towards you, will be different. In the above example, instead of the speed of light, the speed of gravity should be used.

Reflection 4 - page 106 - 11/4/2024

This page shows IMO why GTR is a very difficult theory, to be used in practice.

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Created: 1 April 2024

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