**Abstract.**

This web page presents an analysis of the article ** “On the Electrodynamics of Moving Bodies”**, where Einstein presented

**The analysis is based on**

*the special theory of relativity.**classical mechanics and Galilean relativity, which are indisputably valid in our local time-spatial domain “on the Earth’s surface”.*Einstein’s conclusion that

**It is shown exactly where and how the erroneous claim “the speed of light is the same in all inertial frames of reference” is applied**. It is also proven here that*, is based only on this erroneous claim ‒ that*

**“we cannot attach any absolute signification to the concept of simultaneity”***“the measured speed of light is the same in all inertial reference systems”*. This claim, however, as evidenced by the analysis of the experiments (see sub-pages), has been experimentally proven to be false.

**The special theory of relativity** was published in the article *“On the Electrodynamics of Moving Bodies”*, in the scientific journal Annalen der Physik (Einstein, 1905а).

The current analysis of the article *“On the Electrodynamics of Moving Bodies” *** is based on the classical mechanics and Galilean relativity** that is in effect in our physical reality – the area of uniform and unchanging gravity

*“on the surface of Earth”*. This analysis is classical, and because it analyzes to what extent the hypothesis presented in the article corresponds to the physical reality.

**Remark: **In order a theory to have scientific value (this applies not only to physics),

Our time-spatial area “near the Earth’s surface” has the following three defining characteristics relevant to the topic discussed:

• the intensity of the gravitational field is approximately the same;

• it follows, from this, that the defined by us measurement units of length and of time do not change ‒ these are the primary constants that we have chosen;

• also that the speed of electromagnetic radiation (speed of light) in vacuum is constant, as well as all physical constants in a region with a uniform and constant intensity of the gravitational field.

As mentioned, the Earth is rotating around its axis in stationary space, and only the deformation (the “contraction” itself) of the space moves along with the Earth around the Sun, along with the Solar System in the Milky Way, and along with our Galaxy in the Universe.

**Start of the analysis:**

At the beginning of his article, Einstein refers to Maxwell’s Theory of Electrodynamics, and then gives an initial formulation of the two postulates on the basis of which the special theory of relativity is created.

The formulation of the first postulate, which Einstein calls the “principle of relativity” refers to natural laws – that the laws of electrodynamics and optics are valid in all inertial frames of reference, where the laws of mechanics are valid:

*“the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.”*

The second postulate, *which is only apparently irreconcilable with the former*, is formulated as follows:

*“that light is always propagated in empty space with a definite velocity c, which is independent of the state of motion of the emitting body.”*

By applying the “scientific method”, each scientist can analyze:

**Do these formulations correspond to our physical reality?**

**The first postulate** is formulated so generally that it cannot be accepted without detailed analysis!

First, on what basis is the dependence and the analogy between the laws of electrodynamics and optics with the equations of mechanics? On the basis of such an unreasonable assertion of analogy (between electromagnetic waves and mechanical waves), the second big blunder in physics of the 20th Century on *“the accelerating expansion of the Universe”* is due. The equations of mechanics refer to the motion of material bodies in the stationary space. For the equations describing the motion of material bodies in moving systems at different speeds in a stationary space, Galilean transformations are in effect. The Galilean principle of relativity states that the laws of motion (Newton’s laws of motion) are the same in all inertial frames of reference, and therefore:

*It is impossible to determine by any mechanical experiment, conducted in any inertial system, whether the given inertial system is at rest or moving uniformly and rectilinearly in the stationary space*.

This means that there is no dependence of the velocity of a body with mass ** m** on the direction of motion of the body in the inertial reference system (i.e. there is no anisotropy of the velocity)! However, if the system moves at a constant velocity, but not rectilinearly, it can be ascertained by a mechanical experiment (Foucault’s pendulum). So, it is not scientifically acceptable to claim “for all reference systems”, which means that it doesn’t matter if the reference systems are inertial or not. In other words, this assertion cannot be accepted without analysing in detail the results of the experiments and without discussing the differences. Many of the experiments, however, are explained by modern physics on the basis of the unrealistic results of the special relativity theory (see this page), which is an unacceptable

*.*

**logical circular reference****The second postulate**, which, according to Einstein’s words, **“ is only apparently irreconcilable with the former”**, is:

*“that light is always propagated in empty space with a definite velocity c, which is independent of the state of motion of the emitting body.”*

**Yes**, the light is propagated in the “empty space” (in vacuum) at a constant speed, but in regions with a uniform (the same) intensity of the gravitational field, like our local region “near the Earth’s surface”. However, the speed of light in vacuum is not the same in all regions of the Universe – **the speed of light in vacuum depends on the intensity of the gravitational field in the regions through which the light propagates**

*. The evidence for this was mentioned above.*

**Yes**, the speed of light *in vacuum* *is independent of the state of motion of the emitting body*, because the emitting becomes at the quantum level.

However, Einstein does not claim or mention anywhere in the article *that the speed of light is the same for all inertial reference systems* (though, as we will see, he used it in his article). Perhaps, that’s why Einstein had never discussed the experiment performed in 1912 by the French physicist Georges Sagnac, because not only this experiment confirms the validity of Galilean relativity in a local time-spatial region. Furthermore, the following important difference is not taken into account – that, while the motion of the material bodies is in the stationary space, the electromagnetic waves are actually vibrations of the stationary space itself (in terms of wave theory), and their velocity of propagation is always the same in a time-spatial region with a uniform gravitational field intensity. So, while it is impossible, through some mechanical experiment carried out in an inertial frame of reference, to determine whether the given system is at rest or moving uniformly and rectilinear in the stationary space – by means of measuring the velocity of light in a moving inertial frame of reference, the task*“to determine the velocity of the inertial frame of reference in the ‘empty space’”* is elementary. We must elucidate that we are talking about the local stationary *“empty space”* in a region with a uniform gravitational field intensity – as the region *“near the surface of the Earth”*. This task has been demonstrated with the “Michelson-Gale-Pearson experiment”, but can also be demonstrated with experiments at different latitudes where the linear velocity of the Earth’s surface is different!. All these experiments will once again prove that ** “the speed of light is not the same for all inertial reference systems”**.

After all these clarifications, the reader can judge not only the extent to which the second postulate is compatible with the first postulate, but to what extent those postulates are valid!

=> Follows: examining of the first part “I. KINEMATICAL PART” and then – of the second part of the article “II. ELECTRODYNAMICAL PART”.

**15.1. ****Analysis of “I. KINEMATICAL PART. § 1. Definition of Simultaneity”**

Einstein starts exposing his logic by presenting a stationary coordinate system:

*“a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the “stationary system”.”*

Let us ask the aforementioned question (*see* the ** Remark** at the beginning of the analysis), concerning the scientific value of the article. Therefore, the question arises:

**What is the correspondence of the considered “stationary system” with our physical reality?**

The answer is:

• Yes, the equations of Newtonian mechanics are in force, (valid) in our physical reality.

• Obviously, the so-called “stationary system” is a frame of reference related to the stationary space itself (not related to the moving Earth’s surface). This is clear from *“synchronization criterion”*** ** for two clocks in the stationary system defined below.

• The “stationary system” in question has the defining characteristics of our physical reality: The measurement units are non-variable *(rigid standards of measurement)*. Einstein’s chosen unit of length is *“a rigid rod”* as a standard of measurement – (in the International System of Units (abbreviated as SI), we have chosen this to be the unit of length “*(in all respects resembling each other)* that measure the same time intervals – (in the SI system we have defined the unit of time “second” by means of the frequency of specific electromagnetic radiation).

Thus, the position of a material point at rest relative to this (actually stationary Descartes coordinate system), is defined “*by the employment of rigid standards of measurement and the methods of Euclidean geometry”*, and can be expressed in Cartesian co-ordinates. (Renatus Cartesius is the Latin name of René Descartes). In fact, the concept of *“space”* refers to the concept *“position of a stationary material point”*.

**However, if we talk about “motion”, the quantity “time” should also be included:**

*“If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time.”*

Einstein logically shows us that the concept of *“time*” is inextricably bound up with the concept of *“simultaneity”.* Indeed, when we talk about the “time-point” – we mean the simultaneity of at least two events: *“the moment of any certain event”*, and “*the certain position of the clock’s arrows”*.

That is why, regarding the definition of the term “time”. Einstein suggests that it be replaced with the “position of the arrows of the clock”:

*“It might appear possible to overcome all the difficulties attending the definition of “time” by substituting “the position of the small hand of my watch” for “time”.”*

But this is acceptable, Einstein continues, only if the observer is in the place where the clock is located. If the observer is distant from the clock, an additional time interval is required for the transmission of the information (the indication) of the remote clock to the observer. In the case under consideration, we must imagine an observer with a clock, positioned at the beginning (the origin) of the coordinate system, which determines the time of occurrence of events at different points of the system by receiving light signals from the point of occurrence of the relevant event. Einstein talks about the disadvantages of such coordination:

“But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience.”

**In fact, the disadvantage is** that the synchronization of clocks located in different locations requires a different correction *for the time of receiving the signals*.

Actually, Einstein considers a stationary system where the time is the same, and calls it *“the time of the stationary system”*. Of course, we have to accept some initial event to start measuring the time, and a point from which the time in all other points to be synchronized…

The definition of the *“synchronization criterion for two clocks”* in the considered stationary system follows in the article. For this purpose, Einstein examines two points (point A and point B) in the stationary coordinate system, where identical clocks are located: *“another clock (at B) in all respects resembling the one at A”* is positioned. As mentioned, the clocks in every respect *“resembling”* each other. It actually means that the two clocks measure the same time intervals equally (i.e. the duration of the “seconds” is the same for the two clocks). I.e., in the considered stationary coordinate system – the measurement unit of length and the unit of time are constant. Another condition is that the clocks in point A and point B are synchronized (the readings are the same), but with denotations *“A time”* and *“B time”* respectively.

Here is the thought experiment:

*“Let a ray of light start at the “A time” t*_{A}* from A towards B, let it at the “B time” t*_{B}* be reflected at B in the direction of A, and arrive again at A at the “A time” t́*_{А}*.”*

The given criterion, according to which two stationary clocks are synchronized in the stationary coordinate system under consideration (where the light is propagating in the space at a constant speed), is:

*“In accordance with the definition, the two clocks synchronize if *

, where **t**_{A}** **and * t΄_{A}* are the readings of the clock in point A, and

*is the reading of the clock in point B. The formula (44) shows that two remote stationary clocks in a stationary system are synchronized, when the readings of the clocks for the time intervals in both directions of the light’s travel are equal.*

**t**_{B}Einstein calls this formula (44) a *“criterion for the synchronization of two clocks*”. However, we must emphasize again that Einstein had accepted these clocks to be at rest in a stationary system. If we refer to the (see above Remark at the beginning of the analysis):

*The formula is true for our physical reality: on the **condition that the considered stationary system corresponds to the reference system related to the stationary space itself (where the speed of light is constant and where the Earth’s surface moves* *in relation to the stationary space).*

In other words, this formula as *“criterion for the synchronization of two clocks”*, is true when points A and B are stationary in relation to the “empty space”, where the speed of light is a constant. *However, the formula is not correct when A and B are fixed to the Earth’s surface that moves in the stationary space.* When the circumstances under consideration are not juxtaposed with the physical reality, a contradiction can be created – such as the equation (45):

*“In agreement with experience, we further assume the quantity *

*to be a universal constant – the velocity of light in empty space.”*

This equation is true because it involves the traveled path in both directions – and therefore, the resulting speed of light is average for both directions and will always be equal to *c* (as is in the “two-way light speed measurement” – the case of the Michelson-Morley experiment)! However, this equation is misleading because it is true not only for the reference system related to the stationary “empty space”, but it is also true for the frame of reference related to the moving Earth’s surface. In the physical reality, *(this time really in agreement with experience),* is that if the referenced system is related to the moving Earth’s surface (points A and B are fixed to the ground), and the point B is located east of point A, then:

As we analyzed the experiments “One-way measurement of the speed of light”, when the frame of reference is related to the Earth’s surface – the difference (46) in the different directions will depend on the linear velocity of the Earth’s surface of the corresponding latitude. However, the total sum of the light beam travel time in both directions will always be constant *(* **t΄**_{A}* – * **t**_{A}*) = const)*, (as in the case of the Michelson interferometers) – and the equation (45) will also be true for this frame of reference. **That is why this equation is misleading!**

**Summary of section § 1 of the article: ***It is a fact that the correspondence of the considered “stationary system” with our physical reality is not determined. This system was called “stationary”, **only** “to distinguish verbally this system of co-ordinates from others which will be introduced hereafter”. It creates conditions for contradiction, which is actually evolved in the next section.*

**15.2. Analysis of “I. KINEMATICAL PART. § 2. On the Relativity of Lengths and Times”**

At the beginning of this paragraph, Einstein defines the two postulates on which the special theory of relativity is based, in the following way:

“The following reflections are based on the principle of relativity and on the principle of the constancy of the velocity of light. These two principles we define as follows: ‒

*1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion. *

*2. Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray **be** emitted by a stationary or by a moving body. Hence:*

*, where time interval is to be taken in the sense of the definition in § 1.”*

We can compare this definition of the “speed of light postulate”, with the definition given at the beginning of the article:

*“that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”*

** In fact, living in the time-spatial area **

**“on the surface of the Earth”, let us summarize : **

*to what extent should the reader agree to these definitions of the postulates?*

• Indeed, in the inertial frames of reference: the physical laws are the same (because, in fact, the processes are carried out in the common, for all frames of reference, stationary space).

• Indeed, the speed of light is constant in “empty space / i.e. in vacuum” – i.e. in the frame of reference related to the stationary space.

• Indeed, it does not matter whether “the photons are emitted from a stationary or moving body” – their speed in vacuum is the same, because the photon emission happens on a quantum level.

• But nowhere does Einstein discuss the fact that *the measured speed of light depends on the motion of the observer in relation to the stationary system of the empty space* – that would mean that the measured speed of light depends on the motion of the observer’s frame of reference in the stationary space. Actually, it would mean that the statement *“the measured speed of light is the same for all inertial reference systems”* – is not true! Einstein does not postulate this statement directly, but as we shall see below, it is used to obtain the results of the special theory of relativity. The phrase *“for all frames of reference”* exists only in one place in the article, and it is:

*“the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.”*

But let us continue with this line of thought of Einstein – * with the examination of a stationary rigid (with a constant invariable length) rod*:

*“Let there be given a stationary rigid rod; and let its length be **l **as measured by a measuring-rod which is also stationary. We now imagine the axis of the rod lying along the axis of x of the stationary system of co-ordinates, and that a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod.”*

Concerning the length of the moving rod – the following two methods (operations) are specified, by which the length of the rod can be determined:

(**а**) The observer moves together with the given measuring-rod and the rod to be measured and measures the length of the rod directly by superposing the measuring-rod, in just the same way, as if all three were at rest. Measured in this way, the length of the rod AB, Einstein calls *“the length of the rod in the moving system” *and that –* “must be equal to the length l of the stationary rod”*.

**(b)** By means of stationary clocks set up in the stationary system and synchronizing *“in accordance with § 1”*, (*“criterion for the synchronization of two clocks”*) the observer ascertains at what points of the stationary system the two ends (A and B) of the rod to be measured are located at a certain time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length that may be designated *“the length of the rod”*.

Here we must emphasize that the used measurement unit of length “measuring-rod” is the same for the stationary and for the moving system. The clocks used in the moving reference system are synchronized with stationary clocks and measure the same time intervals – therefore, the same measurement unit of time is used. According to Einstein, the measured length of the rod in the moving system (by method (a)), will differ from the measured length of the rod in the stationary system (by *method ( b)*):

*“The length to be discovered by the operation (b) we will call “the length of the (moving) rod in the stationary system.” This we shall determine on the basis of our two principles, and we shall find that it differs from l.”*

It is not true, obviously, but let us first answer the question again:

**What is the correspondence of the experiment under consideration with our physical reality?**

In our real time-spatial region*“near the surface of the Earth”:*

• the analogue of the considered “stationary system” is the *Earth-centered inertial coordinate system* (the ECI frame of reference), which is the considered stationary in relation to the surrounding space – *a frame of reference related to the stationary space itself;*

• the analogue of the moving frame of reference, *“the moving rigid rod”*, is a rod (oriented and moving in a “West-East”) – firmly fixed on the moving Earth’s surface in the stationary space.

• In this real (our) region, the units for measuring the length and time are constant, the time flows in the same way, and the speed of light is constant in the stationary *“*empty space*”* (vacuum) – i.e. in the “ECI coordinate system”.

Let us proceed with the description of the measurement of the length of the rod using method (b):

*“We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to **say**, that their indications correspond at any instant to the “time of the stationary system” at the places where they happen to be. These clocks are **therefore** “synchronous in the stationary system.”We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks.”*

Let us analyze how Einstein presented the case under consideration:

• We have synchronized clocks in the “stationary system” – i.e. their readings are the same.

Let us remember that we have established that the *“synchronization criterion”* (see equation (44)), is valid for a system connected to the stationary empty space, where the speed of light is constant in all directions.

• The readings of the clocks in the “moving system” (the clocks at both ends A and B of the rod), correspond **at every moment** to the readings of clocks in the corresponding location in the “stationary system”, along which the rod passes. However, these clocks in the stationary system are synchronized, which means that the clocks in the “moving system” are synchronized too!

*It means, in fact, that Einstein assumed a**s an initial condition of the thought experiment** that both in the “stationary system” and in the frame of reference “moving system” **the clocks are synchronized** – i.e. the clocks’ readings are the same and the time goes in the same way**!*

In other words, it is set as an initial condition that at any time, the readings for the time of the two clocks in the moving system (the rod), and at each point of the stationary system through which the clocks pass, are the same.

**This Einstein once again explicitly emphasized in a footnote: **

*“Time” here denotes “time of the stationary system” and also “position of hands of the moving clock situated at the place under discussion.”*

As we will see, the adopted initial condition for the synchronicity of all clocks, therefore, turns out to be false, due to the unannounced direct acceptance that *“the speed of light is the same for both the systems considered”!*

**The subject of the experiment.**

Let at time * t_{A}* (which is actually the time in both the stationary system and the moving system), a light beam is emitted from A, then is reflected in B at a time

*, and reaches again A at a time*

**t**_{B}*. For observers located in the moving system, Einstein asserts:*

**t΄**_{A}*“Taking into consideration the principle of the constancy of the velocity of light we find that *

, *and*

*where **r*_{AB}* denotes the length of the moving rod – measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.”*

In these equations, ** c** is the speed of light in the “empty space” (the common space for the stationary reference system and for the reference system of the moving rod), and

**is the speed of the rod (the relative speed between the two inertial frames of reference).**

*v*Let us go back to the definition of the principle of the constancy of the speed of light, where the following is written – see (47):

i.e. :

Therefore, if for observers in the moving system the lengths of the path of the light beam in both directions are the same and equal to the length of the rod *r _{AB}*

*(“light path” = r*, but the time intervals

_{AB})**and**

*(t*_{B}– t_{A})

*(*

**t΄**_{A}**are different – it follows that the speed of the light in the moving system in one direction is**

*– t*_{B})*(c-v)*, and in the other direction is

*(c+v)*. It means that for the observers in the moving system, the speed of the light for the two directions

**is different from**Furthermore, the observers in the moving system have no reason to think that their watches are not synchronized… In fact, it’s analogous to the experiments “One-way measurement of the speed of light”!

*c!***But that is the essence of the matter:**

Obviously, here is **the key place in the special theory of relativity**! The claim that “the speed of light is the same in all inertial frames of reference” is applied here.

I.e., for the condition **“the speed of light is the same for all inertial systems”** to be valid, it must be accepted that the clocks are not synchronized.

However, according to the initial condition of the thought experiment ‒ they are synchronized. **This is obviously an unacceptable contradiction!**

Actually, the real fact that is not accepted by modern physics (although this is experimentally proven nowadays), is that *“the speed of light is different for both directions in the moving reference system”*.

**Instead**, it is assumed that the speed of light is always equal to the

*“speed of light in vacuum”*The fact that in the moving frame of reference the speed in one direction is

**с**.*(c+v)*and in the opposite direction is

*(c-v)*, is attributed to the clocks … and, contrary to the factual initial accepting (that they are synchronized) – it is concluded that they are not synchronized…

**:**

*“Observers moving with the moving rod would thus find that the two clocks were not synchronous.”*

… and that is why they show that:

The consequence of this unfounded *“lack of synchronization”* – is the wrong
conclusion about the absurd lack of simultaneousness of events, that there is *no simultaneity of events*:

*“So, we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.”*

… i.e., there is no
simultaneity of events (because the reason for this is the assumption that
the speed of light in both directions in the moving frame of reference must be
the same), i.e*. *that* “the
speed of light to be the same in all inertial frames of reference”!!!*

As a consequence of this conclusion, it is normal to ask the following questions:

*“If there is no simultaneity of events (for example, “start of any event” and the corresponding event “movement of the clock’s hands”), is it possible to determine a “time interval” (like the unit of time“second”)?”*

*Everyone knows that every equation of theoretical physics exists on the basis of the most primal physical constants – the measurement units ***which ***we define!*

**Therefore, all the equations, where the physical magnitude “time” takes part (including the equations on the basis of which is concluded that there is no simultaneity of events) … **

**…are they equations at all?**

**In fact, this is an absurd logical circular reference!**

But if we go back to reality, in the reference system related to the moving Earth’s surface (as we have seen in* chapter 4)* – *the measured speed of the electromagnetic signals* in the direction of movement of the ground “from West to East” is *(c-v)*, and in the direction “from East to West” is *(c+v)* ! This fact nowadays is experimentally established using synchronized GPS satellite clocks.

*In fact, equations (48) and (49) can be called “criterion for synchronization of two clocks, moving in the stationary space with a fixed spacing between them”.*

*Obviously, if (v = 0), then we have the formula (44) – i.e. **“the criterion for the synchronization of two clocks”*, **which are stationary in the “stationary system”**.

In fact, it can be concluded ‒ to what extent in the logical consistency, presented in the article, concerning the *“lack of synchronization of the clocks in the moving frame of reference”* there is no contradiction…?

**Analysis of the “simultaneity of events” for the two reference systems in the thought experiment**

It can very easily be proved, on the basis of the physical reality, that the simultaneity of the events is present. Here is the reality:

The events in the thought experiment are three:

**“Event 1”:** “The light beam starts from point
А”,

**“Event 2”:** “The light beam is reflected in point
B”,

**“Event 3”:** “The reflected beam arrives back at
point A”.

Let us accept as an initial moment the event, when *“a uniform motion is imparted to the rod”*, which is *“Event 1”* (the light beam starts from point A).

——**The proof that there is ****“simultaneity of events”**** for the two systems of reference is:**

that* the t**ime** intervals between the aforementioned three events are respectively equal for both the reference systems.*

——

**• The time intervals between the three events in the moving frame of reference.**

As we have seen, the time intervals for the observers *in the moving reference system* are (illustrated by) the equations (48) and (49), as shown:

and

, where according to Einstein’s thought experiment mentioned above:

*“Let a ray of light start at the “A time” t_{A} from A towards B, let it at the “B time” t_{B} be reflected at B in the direction of A, and arrive again at A at the time t́_{А}.”*

, and the length of the moving rod is ** r_{AB}**.

**• The time intervals between the three events in the stationary frame of reference.**

For an observer *in the stationary frame of reference*, points A and B (the beginning and the end of the rod) move at the speed ** v** of the rod, the speed of the light beam in the stationary system is

**, but the distance traveled by the light beams differs in both directions. If point A of the rod is closer to the origin of the coordinate system, and the rod moves along the**

*c***towards an increase of**

*x-axis*

*x**,*then the light beam which starts from point A will pass a longer distance

**, when it reaches point B. This is because, during the travel of the light beam toward point B, point B has moved away with**

*(r*_{AB + }Δ_{AB})**. Conversely, the reflected light beam from point B back to point A will pass a shorter path**

*Δ*_{AB}**than**

*(r*_{AB}– Δ_{BA})**(the length of the rod), because, during the travel of the light beam, point A approaches point B with**

*r*_{AB}**. Therefore, in the stationary reference system, the measured time intervals between the events are respectively:**

*Δ*_{BA}, and

, where * ∆_{AB}* is the distance that point B passes during the time interval

*at the speed of the rod*

**(****t**

_{B }**– t**_{A}**)**^{st}*;*

**v**and** *** ∆_{BA}* is the distance that point A passes during the time interval

*at the speed of the rod*

**(t’**_{A}**– t**_{B}**)**^{st}

**v****.**

**The proof follows:**

*Let us examine, in the two frames of reference, the time intervals between the two events***“Event 1”**and**“Event 2”**– i.e., whether**(****t**_{B}**– t**_{A}**) = (****t**_{B }**– t**_{A}**)**^{st}:

Since, *in the stationary frame of reference*, * ∆_{AB}* in equation (52) is the distance by which point B has moved away during the travel of the light beam from point A to point B, so, if we replace

*with*

**∆**_{AB}*, we get:*

**(v(****t**

_{B }**– t**_{A}**)**^{st}**)**, and, as follows from equation (54),

Therefore we see, that the time interval * (t_{B} – t_{A})^{st}* in

*the stationary frame of reference,*is the same time interval

*as in the equation (48) for*

**(t**,_{B}– t_{A})*the moving frame of reference*!

**Therefore**, the time intervals between the two events “Event 1” and “Event 2” are the same for the two frames of reference.

*Let us now examine the time intervals between the two events***“Event 2”**and**“Event 3”**in the two frames of reference – i.e., whether**(t’**_{A}**–****t**_{B}**) = (t’**_{A}**–****t**_{B}**)**^{st}:

** For the stationary reference system**, in equation (53),

*∆*in equation (53), is the distance by which point A has come closer to point B during the travel of the light beam from point B to point A. Therefore, if we replace

_{BA}*∆*in the equation (53) with

_{BA}*(v(t’*, we again receive that the time interval

_{A}-t_{B})^{st})*(t’*, is the same time interval

_{A}-t_{B})^{st}in the stationary frame of reference*(t’*equal to

_{A}-t_{B})*r*for

_{AB}/(c+v)*the moving frame of reference*(see equation (49))

In other words, the time interval, between *“Event 2”* and *“Event 3”* in both frames of reference, turns out to be the same.

**Therefore, the simultaneity of the events for the two frames of reference is undeniably proven!**

**Summary for section § 2 of the article:** Einstein’s conclusion that “we cannot attach any absolute signification to the concept of simultaneity” is based on the erroneous statement that **“the measured speed of light is the same in all inertial reference systems”**. This statement has been proven to be inconsistent with physical reality – not only nowadays through modern technologies, but since the time of the **“Sagnac experiment” (1913) **and the **“Michelson-Gale-Pearson experiment” (1925)**.

THE FALSE CONCLUSION that there is no simultaneity of events, however, serves as the basis of the next fallacy step of the theory … i.e., the delusion deepens in the next section of Einstein’s article.

**15.3. Analysis of “I. KINEMATICAL PART. § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former”**

**In the previous section,** Einstein examines *a stationary coordinate system *and a moving rod *(moving reference system)* along the *x-axis*. It should be recalled that in both systems it was accepted that “the time” is the same. It was analyzed how the wrong conclusion was made that in the common space **“two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.”**.

**In this section,** the “thought experiment” is a modification of the experiment that was considered in the previous section – two coordinate systems are considered in the space that Einstein calls *“stationary space”*. One of the coordinate systems is called “stationary” and is denoted “K” system, and the other system is called the “moving” coordinate system and is denoted “k” system. Each coordinate system is Cartesian, with three rigid material lines (axes), perpendicular to each other and intersecting at one point (the origin of each coordinate system). The co-ordinates and time symbols in the two systems are different. The spatial coordinates and the time in the stationary system **“K”** are denoted with * [(x, y, z); t]*, in the moving system

**“k”**–

*.*

**[(ξ, η, ς); τ]**The* axes* * x and ξ *of the two systems coincide, and the movement of the

**“k”**system is at a constant speed of

**v****in the direction of an increase of**

*of the stationary system. The axis*

**x***and*

**η**

**ς****of the moving system are respectively parallel to the axes**

*y*and

*of the stationary system and remain parallel when the system moves.*

**z****The aim is** to derive the desired relationship (transformation) of the spatial coordinates and the time between them (which turns out to be the Lorentz transformation), but based on the assertion that *“the speed of light is the same for all inertial frames of reference”*.

**Concerning the description of the accepted measurement units of length and time:**

As an initial condition of the thought experiment, it is assumed that the accepted measurement unit of length is a *“rigid measuring-rod”*, and the accepted unit of time is measured by the same clocks – *“in all respects alike”*. Thus, as we read, the units of measurement are the same in both systems:

*“Let each system be provided with a rigid measuring-rod and a number of clocks, and let the two measuring-rods, and likewise all the clocks of the two systems, be in all respects alike.”*

From the presented initial conditions for the units of measurement, it is obvious that they are defined when the moving system “k” is at rest – because the final result of the special theory of relativity is that the units of both time and length (in the direction of the movement) change when one inertial system moves relative to the other.

**In
Galilean transformations** the units of time and
length do not change – there is only a transformation (recalculation) of the
spatial coordinates. Time goes in the same way – the clock readings for both
systems are the same. Therefore, Galilean transformations are consistent with
our physical reality. An observer, located at the origin of the stationary
system, can determine the local moment of occurrence of an event at a particular
point in the moving system. For this purpose, he has to adjust his clock, with
the time interval for which he receives the information about that event.

**About the applied scheme of the thought experiment in this paragraph of the article.**

The applied scheme of the thought experiment is the same as in the previous paragraph of the article. At the starting position it is:

• The measurement units in both reference systems are the same and are defined when the moving system is at rest.

• The same measuring units determine the spatial coordinates and moments in time of the events –** ****[(x, y, z); t]**** **and * [(ξ, η, ς); τ]*, respectively to the two frames of reference.

But let us follow the thought experiment:

*“If we place (x΄ = x – vt), it is clear that a point at rest in the system “k” must have a system of values *

**[x΄, y, z]***, independent of time.”*

As а resting point for the system **“K”** has coordinates * (ξ, η, ς)*, then the aforementioned values

*are actually the applied Galilean transformations between the two systems –*

**(x΄=x-vt; y; z)***.*

**(ξ=x-vt; η=y; ς=z**)To find the relationship (transformation) between the spatial coordinates

and the time of the two systems, Einstein presents the time τ in the moving system as a function of the spatial coordinates and time in the stationary system * (x΄, y, z; t)*:

*“From the origin of system k let*

*a ray be emitted at the time*

**τ**

_{0}

*along the*

**X**-axis to**x’**, and at the time**τ**

_{1}

*be reflected thence to the origin of the coordinates, arriving there at the time*

**τ**

_{2};

*we then must have:*

*or, by inserting the arguments of the function τ and applying the principle of the constancy of the velocity of light in the stationary system:*

However, equation (57) is a consequence of equation (44):** (*** t_{B }– t_{A }= t́_{A} – t_{B})*, which is true, but for the case where the reference system is “stationary” in relation to the empty space (where the light propagates at a constant speed). But in this case, the observer is in the “moving system”. The difference with equation (44) is only in the denotation – the time is written with

**.**

*τ**Here we must emphasize that equation (57) would be true, if the speed of light is the same in both directions in the moving system – in fact, if “the speed of light is the same in all inertial frames of reference”.*

Einstein defines the speed of light postulate: *“that light is always propagated in empty space with a definite velocity c”*. It is true in our time-spatial domain (our reality), where the intensity of the gravitational field is the same. However, the claim *“the speed of light is the same in all inertial reference systems”* means something completely different. In fact, the conditions under which this statement is true in the presented “thought experiment” are not consistent:

• on the one hand, the “empty space” itself must be stationary for *“the stationary system ( K)”,* and

• on the other hand, the “empty space” should
move along with *“the moving system (k)”*
– (i.e. the “empty space” is not to be stationary)!

It is not anything else except *a logical contradiction*

**…**

*The physical reality, however, is the following:**the stationary system “ K*” is stationary in the

*“stationary space”*, and the

*moving system “*moves in relation to the

**k**”*stationary system “*

**K**”*(i.e. in the stationary space)*, in the direction of increase of the

*, and therefore:*

**x**-axis, because ** in the moving reference system:**
the interval of time necessary for the light beam to travel the distance in the
direction of movement of the reference system (in the case is (

*τ*), is greater than the necessary time interval

_{1 }– τ_{0}*(τ*for the light beam to pass the same distance back in the opposite direction of the movement of the moving reference system.

_{2 }– τ_{1})As we have seen in the previous section – according to equations (48) and (49) for the moving system:

This is the same, but written with the new denotation of time for the moving system (**k**):

, which is:

, which means that equation (57) **does not correspond to physical reality**, as well as the claim that *“the speed of light is the same in all inertial reference systems”*.

Thus, on the basis of equations (57) and (58), which are inconsistent with the physical reality, the Lorentz transformations are derived. The Lorentz transformations themselves are not incorrect – they have their mathematical value. The Lorenz transformations show how the time and spatial coordinates between two inertial frames (moving relatively to each other) must be transformed, *so that the measured value for the speed of light in the two frames to be the same*.

**In fact, the Lorentz transformations give a solution to the following mathematical task:**

*“How should the units of length and of time **be changing in a moving system (depending on its velocity) relative to the units in the stationary system, so that the result obtained (the numeric value) when measuring the speed of light in both frames of reference to be the same.”*

There are other solutions to this task besides the Lorentz transformations. One such solution is given in *chapter 20* of the book. Although these solutions have a mathematical value, they cannot be applied in our physical reality to transform the coordinates between two inertial reference systems moving at constant speed relative to each other, because they are based on a non-existent claim in the physical reality that *“the speed of light is the same in all inertial frames of reference”!*

*Consequently**, inconsistency with physical reality also applies to all the results of the special theory of relativity because they are the consequence of, and result from the consecutive incorrect steps outlined here.*

As Einstein, himself stated that if it is proved that a step in the logical structure of the theory is not true, then the whole theory of relativity is not correct. That is exactly what Einstein said when he explained the theory of relativity to the readers of the * “London Times”*:

*“The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; **to modify it without destroying the whole structure seems to be impossible.**”*

**… so, with this statement, Einstein himself actually declares the invalidity of the special theory of relativity.**

Other statements by Einstein may also be mentioned that state the invalidity of the theory of relativity. Such a statement was published in * “My theory and Miller’s experiments”* (Einstein, 1926), after the widely discussed publication by Dayton Miller

*(Miller, 1926):*

**“Significance of Ether- Experiments of 1925 at Mount Wilson”***“If the results of the Miller experiments were to be confirmed, then relativity theory could not be maintained, since the experiments would then prove that, relative to the coordinate systems of the appropriate **state of motion (the Earth)**, the velocity of light in a vacuum would depend upon the direction of motion. With this, the principle of the constancy of the velocity of light, which forms one of the two foundation pillars on which the theory is based, would be refuted.” *(Einstein, 1926).

In this statement, however, Einstein changes the focus! The speed of light *in a vacuum* is the same, but the measured speed of light in a moving system is not the same! This actually means that *the* *measured speed of light is not the same for all reference systems*!

I.e., according to this statement by Einstein, too *“the relativity theory could not be maintained” …* *because, as we have seen in * the “Analyses of the famous experiments related to the speed of light examination” :

*It has been experimentally demonstrated that in the coordinate system (in the frame of reference), related to the moving Earth’s surface, the measured speed of light depends on the direction of its propagation ( although the speed of light is constant in a vacuum).*

**15.4. Analysis of “II. ELECTYROMAGNETIC PART”**

This part of the analyzed paper contains sections: “§ 6. Transformation of the Maxwell-Hertz Equations for Empty Space”; “§7. Theory of Doppler’s Principle and of Aberration”; “§8. Transformation of the Energy of Light Rays”; “§9. Transformation of the Maxwell-Hertz Equations when Convection-Currents Are Taken into Account”; “§10. Dynamics of the Slowly Accelerated Electron”. The reasoning and all the conclusions in these sections are based on the erroneous results of Part I of the article, which in turn were obtained on the basis of the allegation that the speed of light is the same in all inertial frames of reference. Not in vain in the article “Does the Inertia of a Body Depend upon its Energy Content?”, where the mass-energy equivalence formula *E=mc ^{2}* is derived, Einstein refers to the postulate of the constancy of the speed of light, as well as, and on the results, he deduced

*(inter alia,*as he says

*)*in section

*§ 8. Transformation of the Energy of Light Rays*of the currently viewed article.

It is known that the famous equation ** E=mc^{2}** was previously proposed by

**Olinto De Pretto**, an Italian industrialist and scientist. He suggested that the radioactive decay of uranium and thorium was an example of mass transforming into energy.

However, this equation is generally attributed to Albert Einstein. It is well-known that Einstein’s first paper on * E=mc^{2} * as published in the

*Annalen der Physik*in 1905, is problematic in that it suffers from the error of circular reasoning (circular reference).

This shortcoming of the paper was pointed out by many scientists and writers including Max Planck, Herbert Ives, Max Jammer, and also biographers of Einstein including Gerald Holton and Arthur I. Miller. The list of authoritative figures associated with objections to Einstein’s 1905 paper started with Max Planck, the father of quantum theory. His criticism of Einstein’s 1905 work was included in an important 1907 paper, which some consider to contain the first generally valid and correct derivation of * E=mc^{2}*.

We also have to mention the fact that neither the article * “On the Electrodynamics of Moving Bodies”* (Einstein, 1905a

*“*(Einstein, 1905b), contain the words

**Does the Inertia of a Body Depend Upon Its Energy-Content?”***“gravitational mass”*or

*“*inertia mass”. However, at the beginning of section

*“§ 2. On the gravitation of Energy”*of the article

*(Einstein, 1911), we read:*

**“On the Influence of Gravitation on the Propagation of Light”***“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/c*^{2}*, where **c** denotes the velocity of light.” *(Einstein, 1911).

In fact, the difference in mass ascertained in the radioactive decay of uranium and thorium is at the base of the mass-energy equivalence formula * E=mc^{2}* proposed by

**Olinto De Pretto**for the transformation of the “mass-energy” transformation. Actually, this is the energy that would be released at radioactive decay in a time-spatial area where the speed of light in

*c*(speed corresponding to the intensity of the gravitational field inside this time-spatial domain). Therefore, the released energy will be different in regions with different intensities of the gravitational field. The difference in mass of the atoms before the radioactive decay and the mass of the atoms after the decay is equal to the energy released at the radioactive decay, according to the formula E=Δm.c2. That is why, the law of conservation of mass is not valid when considering the masses of atoms actively involved in nuclear reactors, particle accelerators, and in thermonuclear reactions in the Sun and the stars. However, this has nothing to do with the movement of the inertial reference systems that the special theory of relativity considers – the

*“longitudinal mass”*and the

*“transverse mass”*which in physical reality cannot exist.

**If there is a dependence of the mass (for example the mass of our planet) on the planet’s speed, then the Earth must have simultaneously different mass as its relative speed is different in relation to all other celestial bodies in the Universe… (another absurd)!!!**

**16. Conclusion on the Special Theory of Relativity **

The experimental and logical evidence that are presented in this site reveals the essence of the special theory of relativity that:

**The special theory of relativity turns out to be only one hypothesis that can exist only in the field of mathematics.** It is based on the claim that “the speed of light is the same in all inertial frames of reference”, which is not true – it is experimentally proven to be inconsistent with physical reality!

**That is why it is a delusion in the field of physics.**

**The main reasons for this delusion are:**

• The “Michelson-Morley experiment”, rather, *the inappropriate conceptual design of the construction of Michelson’s interferometer* **is actually the primary cause for the delusion** that **“the speed of light is the sa****m*** e for all inertial frames of reference”*, which is the core of the special theory of relativity.

• Sometimes a persuasion that has survived for many years is surrounded by the halo of absolute truth. However, with the development of new technologies, scientists see undoubtedly that the existing physical reality is different. The “one-way light speed measurement” experiments, performed using GPS, are an example of this. The existing “paradoxes” proved to be actually an attempt at an incorrect explanation of the physical reality.

*As incredible as it may sound, the Michelson-Morley experiment (albeit mistakenly constructed interferometer), and the special theory of relativity (although it does not correspond to the physical reality) – **have played a positive role in the progress of physics!** Although they are wrong steps, they played a role as a springboard for the giant leap for mankind – t**o be broken the perception of the absoluteness of the time and space**!*

Here is the place to pay tribute to the genius of Albert Einstein. Although the special relativity theory does not correspond to physical reality, although the field equations of Einstein in General relativity are not correct from the point of view of physics:

**The general theory of relativity is a genius’s brilliant idea that violates our perception of the absoluteness of time and space!**

_