This document contains comments about the subject "Special relativity" in arxiv. https://arxiv.org/find
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

The following articles are discussed:

Reflections:

### 2008 The Einstein formula: E0=mc^2 "Isn't the Lord laughing?

For a copy of this document by P.C. Peters and J. Mathews select: https://arxiv.org/abs/0808.0437
This document starts with the text:

### 1 Introduction

The formula E = mc2 is perhaps the most famous formula in the world.
Accepted.
And only a small minority of physicists — those who specialize in elementary particle physics — know that Einstein’s true formula is E0 = mc^2, where E0 is the energy contained in a body at rest, and that the mass of a body is independent of the velocity at which it travels.
See: General Reflection "Special Relativity" documents
A much easier equation is E = mc^2 + mv^2 meaning that m is the mass of the object independent of the velocity.

### 3. 1905 — annus mirabilis

Thus he derived in the formula for the transformation of the energy of light in the transition from one inertial reference frame to a different one that moves at a velocity v relative to the former:
E'/ E = {1 - (v/W ) * cos(phi)} / sqrt (1 - (v/W )^2) Here W is the velocity of light and phi is the angle between the direction of motion of light and that of the observer.
The problem is how is this speed v (relatif to the speed W = c) measured. The interesting part is that in Einsteins opinion the energy of light is not always the same.
There he considered ‘two amounts of light,’ with energy L/2 each, both emitted by a massive body at rest but traveling in opposite directions. In this paper, Einstein for the first time introduced the rest energy of a massive body, denoting it by E0 before emission and by E1 after. In view of the energy conservation law,
E0 - E1 = L.
The interesting part is here that Einstein discusses here the mass of light or photons.
The next mathematical step becomes:
E0 - E1 = L = m0*c^2 - m1*c^2 = dm * c^2
dm is the mass of the photons.
He then looked at the same process in a reference frame moving at a velocity v relative to the body, and obtained the following expression for the difference between kinetic energies of the body before and after the act of emission:
The question to ask is does it makes sense to study a frame moving at velocity c?
The energy and momentum of a free particle are uniquely defined in the theory by the relation E^2 - p^2*c^2 = m^2*c4; we return to it more than once in what follows.
This equation is very tricky.

### 4 Have I been led around by the nose?

Einstein wrote: “A consequence of the study on electrodynamics did cross my mind. Namely, the relativity principle, in association with Maxwell’s fundamental equations, requires that the mass be a direct measure of the energy contained in a body; light carries mass with it.
The problem is that "Energy" does not exists by it self. There exists no free energy. Energy is always linked to an object. Energy defines the state of an object, of matter.
• The mathematical relation in general is E=mv^2 with v being the speed of the object. This relation is used when different objects are considered and is part of Newton's Law or GR
• In some special cases E=mc^2 with c being the speed of light. This relation is used for radiation (photon's) also for chemical applications at rest. The objects considered are protons, neutrons, atoms and molecules.

### 5 1906 – 1910. Minkowski

#### 1906

For the cylinder not to move as a whole, he imposed the condition that light with an energy E has the mass E/V^2; he thereby reproduced Poincar´e’s result of 1900.

### 6. 1911 – 1915. On the road to General Relativity Theory

#### 1911

he discussed the propagation of light in a gravitational field, starting with the assumption that a photon with energy E has an inertial and a gravitational mass, both of which are equal to E/c^2, and he calculated that the angle of deflection of light by the Sun’s gravitational field would be 0.83 arc second — which is half the correct value that he would later derive (in 1915) using general relativity.
It is interesting that he started with the assumption that a photon has mass. The reality is when you use Newton's law you get the same value as 0.83 arc second when you consider a photon as a point-like particle with a very small mass or zero.
Not mentioned in the above text is how do you measure E.
Einstein mentioned uniting the law of conservation of mass with the law of conservation of energy: “However odd this result might seem, still, in a few special cases, one can unequivocally conclude from empirically known facts, and even without the theory of relativity, that the inertial mass increases with energy content.”
etc
But this would suggest that he believed that mass increases with increasing kinetic energy and therefore with increasing velocity.
The problem is that in principle you cannot discuss this issue in relation to Special Relativity because 'increasing velocities' involve accelerations which is the subject of General Relativity.

#### 1913-1914

Paper gave an expression for the energy – momentum 4-vector and the relation E0/c^2 = m which would appear again only in 1921. We note that m was referred to in as rest mass (Ruhemasse), which seems to imply that the mass of a body at rest is not the same as when the body moves.
This is the subject of GR. In our nomenclature the equation is: E0/c^2 = m0

### 7. 1917. Cosmological constant

The available data indicate that ordinary matter contains only 4% of the energy of the Universe, that about 24% is contained in the particles of the so-called dark matter whose nature is as yet unknown, and about 70% of the entire energy of the Universe is usually referred to as dark energy and attributed to Einstein’s cosmological constant Lambda
It is interesting to know how you can demonstrate that of the total energy content of the universe, 4% is related to baryonic matter, 24% to non-baryonic matter en 70% to dark energy, while the two last components are invisible.
It should also be mentioned that in order to explain Galaxy Rotation curves no dark energy is involved.

### 8 1918 – 1920. Noether

#### 1918

At the end of this paragraph we read;
Soon after that Einstein sent for publication a paper [77] on the conservation of energy in general relativity, which presented a statement that the energy of a closed system plays the role of both inertial and gravitational mass.
The law conservation of energy also applies to Newton's Law.

#### 1919

Among other things, Einstein wrote:
“The most important upshot of the special theory of relativity concerned the inertial masses of corporeal systems. It turned out that the inertia of a system necessarily depends on its energy-content, and this led straight to the notion that inert mass is simply latent energy. The principle of the conservation of mass lost its independence and became fused with that of the conservation of energy.
The definition of the individual mass of each object, within a collection of objects, is a problem in Special Relativity in case one reference system is used. Only one can be at rest. In reality none object is at rest, they are all influenced by each other as described by Newton's Law or GR,

### 11 1938 – 1948. Atomic bomb

#### 1945

He [Einstein] concluded that the amount of energy, E, equivalent to a mass, m, was given by the equation E=mc^2
This law is only true for particles which move with the speed of light.
The major issue is how to calculate the mass of such a particle.

### General Reflection about "Special Relativity"

Special Relatavity depends very much about the three concepts: t0, l0 and m0.
These concepts are all related to an object (resp an obeserver) at rest.
• t0 defines a clock at rest in a coordinate system.
• l0 defines the length of an object at rest in a coordinate system
• m0 defines the mass of an object at rest
At the same time Special Relativity also uses the other concepts: t, l and m. Those three concepts are the same as the concepts at rest, except that the object is moving with a velocity v. The parameter that links each of the three concepts is the parameter gamma.

One problem with the parameter m0 (m at rest) is, how do you calculate each m0 when different objects are involved.

A whole different problem is how do you measure the mass of an object at rest versus the mass of that same object travelling through space?

### Reflection document 1: 2008 The Einstein formula: E0=mc^2 "Isn't the Lord laughing?

The general message of the article is that the mass m in the equation E0 = mC^2 is not a function of the speed v. As such the mass m is a constant. That conclusion is not so strange because the issue is, also expressed in General Reflection about "Special Relativity" how do you measure m, when different objects are considered.
The problem is when you observe the trajectories of different objects, the speed of each changes continuous. What makes this issue so tricky that you cannot calculate masses in de context of SR when accelerations are involved. This belongs to the context of Newton's mechanics or GR.
The only way you can say anyting about m0 for different objects, is when they all are at rest here on earth, by weighing them. In that situation no different speeds are involved.

In some way there are two completely different areas of research:

• one is to study the chemical bonds and energies involved in chemical reactions in a laboratory. In this case the reactions involved change the masses of the molecules or atoms studied. Specific for these reactions the total energy is constant.
• A whole different field is astronomy where the masses studied are constant, except when collisions are involved. Within that field there is no issue of a rest mass or rest energy. There are only masses and energies.

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Created: 5 November 2016

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