# Analysis of the article “On the Influence of Gravitation on the Propagation of Light” (Einstein, 1911)

“Accelerating Contraction of the Universe – the Reasonable Alternative“, ISBN-13‏: ‎ 979-8847420570.

Here is analyzed Einstein’s article “On the Influence of Gravitation on the Propagation of Light”, presenting the ambiguities and scientific inconsistencies on the basis of which Einstein deduced the formulas for the influence of gravity on the propagation of light. The analysis and astronomical observations prove that Einstein’s conclusions should not be supported by modern physics, which, however, unworthy refuses to discuss the problems in physics!

Chapter 5 of the monograph (and this website) contains 2 sections and 5 subsections:

5.1.1. The acceptance that the photons (quanta) have mass.

5.1.2. On the equivalence of inertial and gravitational masses.

5.1.3. On the gravitational force of the Sun at a distance “Earth’s orbit” and the gravitational force “on the surface of the Earth”.

5.1.4. On the proposed by Einstein formula about the dependence of the speed of light in vacuum on the gravitational potential.

5.1.5. On the validity of the deduced equations in the article “On the Influence of Gravitation on the Propagation of Light” as equations of theoretical physics.

5.2. Summary of the conclusions drawn in Einstein’s article on the propagation of electromagnetic radiation (of the light) in the gravitational field.

In the paper “On the Influence of Gravitation on the Propagation of Light” (Einstein, 1911), Einstein deduced a formula for how the frequency of each electromagnetic radiation changes depending on the gravitational potential (depending on the intensity of the gravitational field), which actually means that the frequency changes depending on the density of the medium of propagation (on the space contraction grade).

In this formula (3), according to Einstein, ν0  can be considered as the frequency of light emitted from the surface of the Sun, ν – is the frequency of received light on the Earth’s surface, с is the speed of light in vacuum, and Ф is the difference (negative) in the gravitational potentials between the surfaces of the Sun and the Earth, regarding the Sun gravitation.

It is this conclusion (this formula) from the applied reasoning in the article – that “every radiation (photon), when it leaves the surface of the Sun, overcoming its gravity, loses its energy” (which means that its frequency decreases) – contradicts the conclusions of the general theory of relativity!

According to the general theory of relativity, time in regions with stronger gravity flows more slowly – i.e. flows more slowly on the surface of the Sun compared to time on the surface of the Earth). This means that the duration of the base unit of time – the “second” on the surface of the Sun is longer. But this means that the frequency of any electromagnetic radiation on the surface of the Sun will be lower compared to that on the Earth’s surface (as well as the radiation corresponding to the transition between the two ultrafine levels of the ground state of the cesium-133 atom, which is the definition of “second” in the SI system). But this means that upon arrival at Earth, the electromagnetic radiation will be of a higher frequency than was on the Sun (the “second” will be shorter). But this is a shift to the blue side of the spectrum, not to the red side, which contradicts Einstein’s conclusion in the article!

5.1. Ambiguities and inconsistencies that led to the incorrectness of the formulas in the article “On the Influence of Gravitation on the Propagation of Light”

5.1.1. The acceptance that the photons (quanta) have mass

The whole logic of the presented influence of the gravitational field on the propagation of light, Einstein develops on the basis of the following thought experiment:

In a homogeneous gravitational field (acceleration of gravity γ) let there be a stationary system of co-ordinates K; orientated so that the lines of force of the gravitational field run in the negative direction of the z-axis. In a space free of gravitational fields let there be a second system of co-ordinates Kʹ, moving with uniform acceleration (γ) in the positive direction of its z-axis. To avoid unnecessary complications, let us for the present disregard the theory of relativity, and regard both systems from the customary point of view of kinematics, and the movements occurring in them from that of ordinary mechanics.

Two material systems of S1 and S2 located on the z-axis of K at a distance h from each other are considered, so that the gravitational potential at S2 is greater than that at S1 with γh. Each of the material systems is equipped with instruments measuring energy “which – brought to one location in the system z and there compared – are perfectly alike”.

Einstein analyzes the energy transfer process by considering a certain amount of energy emitted from S2 to S1.

“By our postulate of the equivalence of K and Kʹ we are able, in place of the system K in a homogeneous gravitational field, to set the gravitation-free system Kʹ, which moves with uniform acceleration in the direction of positive z, and by the z-axis of which the material systems S1 and S2 are rigidly connected.”

Einstein considers the process of transmission of energy by radiation from S2 to S1 from a third system K0, which is free of acceleration. At the moment when the radiation energy E2 is emitted from S2 toward S1, the velocity of Kʹ relative to K0 is accepted to be zero.

“The radiation will arrive at S1 when the time h/c has elapsed (to a first approximation). But at this moment the velocity of S1 relative to K0 is γh/c=v. Therefore, by the ordinary theory of relativity, the radiation arriving at S1 does not possess the energy E2, but a greater energy E1, which is related to E2, to a first approximation, by the equation:

By our assumption exactly the same relation holds if the same process takes place in the system K, which is not accelerated, but is provided with a gravitational field.  In this case, we may replace γh by the potential Ф of the gravitation vector in S2, if the arbitrary constant of Ф in S1 is set to zero. We then have the equation:

Here we cannot agree with Einstein not only that he relies on the special (ordinary) theory of relativity, whose invalidity is indisputably proven in (Sharlanov, 2018) – see parts of the book on the site https://physics.bg/! We are bumping into the following obvious, definitely scientifically incorrect equations (4) and (5) that cannot be accepted. The reasons are:

•   We know that the energy E = Fh = mγh, where F is the applied force on a body with mass m; γ is the acceleration given to the body, and h is the movement of the body under the influence of the force F. The formula written in this way means that the emitted electromagnetic energy (the quanta) has a mass equal to one (m = 1). However, the quanta (photons) do not have mass! Therefore, formula (4) is completely unacceptable!

•   By definition, the gravitational potential at a given point is equal to the work (the energy expended) required to move an object with a unit of mass from the point to a fixed reference location.. I.e., the acceptance, that the emitted energy by means of electromagnetic radiation has a mass, means that formula (5) is also unacceptable!

What conclusions can all this incorrectness can lead to? In “§ 3. Time and the Velocity of Light in the Gravitational Field” of Einstein’s article we read:

If the radiation emitted in the uniformly accelerated system Kʹ in S2 toward S1 had the frequency ν2 relative to the clock at S2, then, relative to S1, at its arrival at S1 it no longer has the frequency ν2 relative to an identical clock at S1, but a greater frequency ν1, such that, to a first approximation:

This formula (6) shows that the frequency ν1 of electromagnetic radiation in the region with stronger gravity S1 will be higher than the frequency ν2 in the region with weaker gravity S2 (with the corresponding gravitational potential). However, experiments show that the atomic clocks tick faster high in the mountains. I.e. the frequency of emitted electromagnetic radiation increases in regions of lower gravitational field intensity. Furthermore, this formula (6) means that the frequency of each electromagnetic radiation decreases as it moves away from the surface of the celestial body, which is, in fact, contrary to the conclusions of the general theory of relativity. The contradiction is that the duration of the unit of time “second”, defined by means of the frequency (as defined in the SI system) on the surface of the Sun will be with a shorter duration than the “second” on the surface of the Earth – i.e., that the time on the surface of the Sun (where the intensity of the gravity is stronger than that on the Earth’s surface), and the time will flow faster than the time flows on the surface of the Earth. But according to general relativity, it is the exact opposite, and Einstein himself contradicted general relativity!

5.1.2. On the equivalence of inertial and gravitational masses

In §2 “On the Gravitation of Energy” in Einstein’s article we read:

“The theory of relativity shows that the inertial mass of a body increases with the energy it contains; if the increase of energy amounts to E, the increase in inertial mass is equal to E/c2, where c denotes the velocity of light. Now, is there an increase of gravitational mass corresponding to this increase of inertial mass?”

It is well known that the equation E = mc2 was proposed in 1904 by the Italian scientist Olinto de Pretto, studying radioactive decay. The equation refers to the correspondence between the energy released during decay and the difference in the masses of the elements involved before decay and those obtained after the decay. This formula is not deduced or discussed in Einstein’s article “On the Electrodynamics of Moving Bodies” (Einstein, 1905a), in which Einstein presents the special theory of relativity. Einstein has an attempt to deduce this notorious formula in the article “Does the Inertia of a Body Depend Upon Its Energy-Content?” (Einstein, 1905b), but with this derivation of the formula, most scientists do not agree…

In fact, the mass of a body is the content of the amount of substance in it. In other words, the mass of a body is determined by the amount (number) of molecules of the substance of which the body is composed, and by the atomic weights of the atoms in these molecules. Then, what does the increase in the inertial mass mean… does the number of molecules increase, or do the atomic weights of the atoms in these molecules change?

The so-called “inertial mass” and “gravitational mass” are in fact the reaction of a body with a certain mass (amount of substance) to a corresponding type of force. According to Newton’s second law of motion, when a force is applied to a body of mass m, it receives an acceleration depending on its mass. If an object with a certain mass is subjected to any force equal to the Earth’s gravitational pull, the object will receive the same acceleration equal to the acceleration that it would have received if the force of gravity was applied to it.

Then, what’s the point of talking about any difference between inertial mass and gravitational mass?

In the preprint “The new SI – another proposal on the future revision of the International System of Units” (Sharlanov, G.V. (2014). DOI:10.13140/2.1.1897.1849, the issue of the so-called inertial mass and gravitational mass was discussed, and it was substantiated that the so-defined unit of force “newton” is a consequence of our choice of the unit of length “meter”. I.e., if we choose the unit of length “new meter” to be 9.80665 times larger than the currently accepted unit of length “meter”, and we re-use the same definition of the unit of force “newton”it will turn out that there will be no difference between the units of measurement “new newton” and “kilogram-force”.

All this actually means that the difference between the so-called gravitational mass and the inertial mass is artificial – this is only the reaction of a body with a certain mass (with a certain amount of substance) when applying forces with different names.

That is why, in “The new SI – another proposal on the future revision of the International System of Units”, a proper, intrinsic definition of the base unit of mass “kilogram” was proposed as a measure of the quantity of a substance by means of the  Avogadro’s number. Depending on the mass (the amount of substance contained in a body), the acceleration, or reaction of the body is determined by the forces applied to it (be it gravitational or other forces).

5.1.3. On the gravitational force of the Sun at a distance “of Earth’s orbit” and the gravitational force “on the surface of the Earth”

In principle, the gravitational potential at a point in a gravitational field (with respect to a body of mass M) is equal to the work (of energy expended) per unit mass (located at the point) that would be performed by the force of gravity created by the body with mass M to move the object from its location to a “zero” reference point (infinitely far from the body with mass M).

Therefore, at any not-infinite distance of the point, the gravitational potential relative to the body with mass M is negative. Thus, the gravitational potential of the Sun’s surface (relative to the center of the Sun), is more negative than the gravitational potential of the Earth’s orbit distance and is equal to zero at an infinite distance from the Sun. However, Einstein uses the Sun’s surface as a reference place, and according to the deduced formula (3), ν0 is the frequency of light emitted from the Sun’s surface, and this frequency changes to ν when it reaches the Earth’s surface. In fact, the applied logic for the gravitational potential relative to the Sun refers to the distance to the Earth’s orbit, not to the Earth’s surface, where the Earth’s gravity is dominant (all bodies on the Earth’s surface are attracted to the Earth rather than flying toward the Sun)! I.e., the gravitational potential of the Earth’s surface (the intensity of the gravitational field) is determined by the gravity of the Earth, not by the gravity of the Sun (at the distance of the Earth’s orbit)!

So, the erroneously derived frequency ν in the incorrect formula (3) is not even for the Earth’s surface, but for a point on the Earth’s orbit!

5.1.4. On the proposed by Einstein’s formula about the dependence of the speed of light in vacuum on the gravitational potential

According to the general theory of relativity, time flows more slowly in regions with stronger gravity – i.e. that the frequency of each electromagnetic radiation becomes lower in regions with stronger gravity (e.g. on the surface of the Sun compared to that of the Earth’s surface, ν0) – see “Analysis of the influence of gravitation in regions with stronger gravitation”.

Another consequence of the general theory of relativity is that the unit of length “meter” will be shorter in regions with stronger gravity (e.g. on the surface of the Sun compared to that of the Earth’s surface). Therefore, based on the definition of the unit of length “meter” in SI in 1960, the wavelength of each electromagnetic radiation should be smaller (less) in regions, where the intensity of the gravitational field is higher (regions with stronger gravity), i.e. 0<λ) – see “Analysis of the influence of gravitation in regions with stronger gravitation”.

From here, it indisputably follows that the local physical constant speed of light in vacuum in the region near the Sun (the region with stronger gravity than the region on the Earth’s surface), will be less than the speed of light in vacuum on the Earth’s surface (c0 = λ00 ) << (c = λ.ν). This fact was proved experimentally by Irwin Shapiro (Shapiro, 1964), and, as mentioned – confirmed very accurately later, using controlled transponders onboard the space probes “Mariner-6” and “Mariner-7”.

However, when analyzing the propagation of light in a gravitational field in his paper, Einstein did not take into account the fact that the wavelength (not just the frequency) of any electromagnetic radiation also depends on gravity!

By analogy with the deduced formula (3) for the change of frequency, Einstein proposes a formula (without derivation of the formula) for the change of the speed of light in vacuum depending on the gravitational potential:

Formula (7) is proposed by analogy with formula (3). From this formula follows that when leaving the gravitational field of the Sun (toward the regions with weaker gravity), the speed of light in vacuum will decrease. This means that the speed of light in vacuum will be higher in regions of stronger gravity – i.e. will increase when passing through a region of stronger gravity (near the Sun), which is contrary to the slowing down effect of time detected by Irwin Shapiro…  (i.e. i.e. the experiment does not register time haste, but time delay!)

As a result of the incorrectness of the deduced formulas, the calculated aberration turned out to be about 2 times smaller than that experimentally established in the experiments in 1919 by the British expeditions to Sobral and Principe. Of course, Einstein corrected his calculations, but his correction (fitting) was based on the special theory of relativity, for which the full evidence of its invalidity (including the so-called “fundamental tests of the special theory of relativity”) is presented in the monograph “The Special Theory of Relativity – the Biggest Blunder in Physics of the 20th Century(Sharlanov, 2018).

The proof of the invalidity of Einstein’s conclusions, as a consequence of the formulas (3) and (6), is:

that if the photon loses energy when overcoming the star’s gravity (as Einstein “proves”), then the photon will lose a different amount of energy depending on the mass of the star!

– i. e. the “redshift” will be different and the spectral series of the emission spectrum of the hydrogen atom – will be shifted depending on the mass of the star!

However, there is no such dependence… and no astronomer has observed it! Therefore, Einstein’s claim in this article that:

“Thus according to our view the spectral lines of sunlight, as compared with the corresponding spectral lines of terrestrial light sources, must be somewhat displaced toward the red”

… there is no reason to be supported by modern physics!

5.1.5. On the validity of the deduced equations in the article as equations of theoretical physics

There is a very important omission…

In order for an equation of theoretical physics to be valid, the units of measurement used must be constants in the considered scope of validity of the equation. Everyone can see the “simple example” illustrating why an “equation” of theoretical physics is actually a meaningless equation if the measurement units used therein are not constants. In the discussed case, the gravity on the surface of the Sun is much greater than the gravity on the surface of the Earth. Therefore, the base units of time and of length will be significantly different in the two locations. Therefore, it is logical to ask the question of whether the deduced equations in Einstein’s article are valid as equations at all. In this sense, let us consider the emitted electromagnetic radiation at the corresponding transition between the two hyperfine levels of the cesium-133 atom (used in defining the unit of time “second” in the SI system). It is more than obvious that if the frequency on the Sun’s surface is “n times” lower than the frequency of the same electromagnetic radiation on the Earth’s surface, then the duration of the unit of time “second” will be with “n times” longer on the surface of the Sun than the duration of the “second” defined in the same way on the surface of the Earth.

However, if we measure the frequency of this radiation with the corresponding unit of time, defined at the same corresponding locations – then the resulting numerical value will be the same both on the surface of the Sun and on the surface of the Earth, because the unit of time is defined with the synchronously changed frequency used in the definition!!!

This is actually a demonstration of the existing principle of uncertainty in the macro-world!

However, Einstein does not specify where the units of time and of length, used in the formulas in the article, are defined. Actually, he uses the units of measurement defined on the surface of the Earth as if they were the same as those on the surface of the sun!!! In fact, equation (3) would illustrate the change in frequency (i.e. the change of the unit of time “second”) from the surface of the Sun to a point in Earth’s orbit. Therefore, however, it will not be an exact equation of theoretical physics, because the units of measurement in the scope of the equations are not constants!

5.2. Summary of the conclusions drawn in Einstein’s article on the propagation of the electromagnetic radiation (of the light) in a gravitational field

In “On the Influence of Gravity on the Propagation of Light” (Einstein, 1911), Einstein deduced a dependence of the propagation of light on the intensity of the gravitational field using the gravitational potential between two material systems located in a gravitational field, accepting that quanta (photons) have mass…, … which is not true!

The consequence of this, as well as the other aforementioned scientific inconsistencies, is that the derived formulas (and the conclusions drawn) contradict both the otherwise ingenious idea of general relativity that time and space change according to the force of gravity, and that these formulas are not confirmed by the observations of astronomers. For example, if the photon loses energy when overcoming the star’s gravity (as Einstein “proves”), then the photon will lose a different amount of energy depending on the mass of the star – i. e. the “redshift” will be different and the spectral series of the emission spectrum of the hydrogen atom will be differently shifted depending on the mass of the star! But there is no such dependence… and no astronomer has observed it!