Einstein's argument to extend the relativity of motion to accelerated motion (general relativity) is based on his equivalence principle, which states that gravitational and inertial forces are of a similar nature and often indistinguishable. In other words, the effects of gravity are equivalent to the effects of acceleration, and vice versa. For example, an observer in a freely falling elevator would feel weightless, as if there was no gravity, while an observer in a rocket accelerating at 9.8 m/s^2 would feel the same gravitational force as on Earth.

Einstein's equivalence principle implies that there is no absolute distinction between inertial and non-inertial frames of reference, and that gravity is not a force but a manifestation of the curvature of spacetime. Therefore, the laws of physics should be the same in all frames of reference, whether they are at rest or accelerating, as long as they are locally flat (i.e., small enough to neglect the curvature effects). This is the basis of general relativity, which is a generalization of special relativity that can account for gravity and accelerated motion.

However, Einstein's equivalence principle is not a proven fact, but a postulate that has been tested and confirmed by many experiments and observations. There may be situations where the equivalence principle breaks down or is violated, such as in quantum gravity or alternative theories of gravity. Therefore, Einstein's argument to extend the relativity of motion to accelerated motion (general relativity) is justified as long as the equivalence principle holds true.

Preston Guynn ,

Lyudmil Antonov ,

I appreciate the information on the equivalence principle, but surely the question is to do with the generalisation of the Relativity of Motion?

The equivalence principle is a separate issue, isn't it?

"You are correct that general relativity (GR) is a theory of gravity and not a generalization of special relativity (SR)."

I think this sums it up nicely.

Dear Professor Guynn,

"2) your mistaken interpretation of Einstein's exposition,"

What mistaken interpretation of Einstein's exposition?

I have no interpretation of Einstein's exposition. I was simply asking if : "Is Einstein's argument to extend the Relativity of Motion to accelerated motion (General Relativity) justified?"

And you answered :

"You are correct that general relativity (GR) is a theory of gravity and not a generalization of special relativity (SR)."

It looks to me that the "generalisation" of Special Relativity -- to relatively accelerated frames, was just a marketing campaign.

There is no such generalisation. In fact one is antipode of the other. One is symmetrical, the other is asymmetrical.

Preston Guynn ,

time dilation is a fact but the relativity of simultaneity no.

The equivalence of inertial frames is not applicable....

The Lorentz transformations (LT), hence 4D space-time, given in the equivalent Lorentz' form is the following,

(1) t'= tγ-1 - vx'/c2

(2) x' = γ(x-vt)

where the primed and unprimed are relevant to two inertial frames.

The time transform (1) is a direct outcome of mixing a time dilation (experimental evidence, twin effect) and light-time variation

vx'/c2 = x'/c *v/c (additional time taken by light in reaching a moving target).

In accelerators the light-time x'/c is negligible due to the small dimension x' .

The tested relations become the following

(1) t'= tγ-1

(2) x' = γ(x-vt)

• it is simple time dilation and length contraction in 3D space and time.
• No test of Lorentz Invariance is performed in accelerators .
• if x'/c is large enough, LT do not reduce to Galilean transformations.

The LT have inbuilt the equivalence of inertial frames and the constancy of the one-way speed of light (SOL).

Experimental evidence in Radar Doppler complies to a good approximation with the formula, derivable from the LT

f/f0 = (1+β)/(1-β) where β = v/c

where f0 is the frequency of the radar and v is the speed of the target in one dimension.

Δf/f0 = 2β/(1-β) which gives, being E0=hf0

ΔE/E0 = 2β/(1-β),

For an approaching target the frequency detected by the RADAR increases, so the energy in the inertial frame of the RADAR increases.

ΔE/E0 > 0.

Given two inertial frames (with mirrors) and transmitting light in the same way, by choosing one of the two, the net result would be that the energy measured in the frame at every bounce increases, but nothing else happens since the speed of the frames remains constant by definition of Inertial frame.

• This gives a perpetuum mobile of the first kind (something which Physics avoids like plague)

Since half-way it is simply ΔE/E0 = β/(1-β), there is not a real need to resort to a RADAR, the infringement occurs just by mere transmitting light from an inertial frame to another, some energy gets created.

This means that there is no experiment which can involve light and two inertial frames. The real objects cannot be inertial to comply with conservation laws, so the application of equivalence of inertial frames, putting them in relation in experiments is a theoretical limit not suitable for Physics.

The formula which gives the proper account for the conservation of energy and momentum (derived from it) is the following

f/f0 = (1+β)/(1-β+ 2hf0 /mc2)

hence for the RADAR

Δf/f0 = 2(β-hf0 /mc2)/(1-β+ 2hf0 /mc2)

in the RADAR inertial frame where m is the mass of the object, the object is not inertial and the light as experimentally verified recoils (energy and momentum).

For a simple Doppler, one emission and absorption only

ΔE/E0 = (β-hf0 /mc2)/(1-β+ 2hf0 /mc2)

in this case the mass m slows down while the energy of the detected light increases.

Conclusion: the LT involving light transmission (meaning always) cannot be applied in between inertial frames unless infringing conservation laws.

What Professor Quattrini means by

"The equivalence of inertial frames is not applicable...."

(correct me if I am wrong)

is that there is (ultimately) a mass relative to which everything moves.

However, I would argue, or at least suggest, that the Relativity of Motion might still hold as an approximation.

yes, Galilean relativity

Dear Professor Quattrini,

I'm with you some of the way, but how do you square "Galilean relativity" with Maxwell's equations-- such that the speed of light when emitted from a moving torch is always a fixed speed 'c' ?

Gary Stephens , In temporal light theory, light creates time and inertia, and as a result creates a gradient of time = gravitational field. The light field is an electromagnetic field and a gravitational field, so it is different from the energy of the electromagnetic field and the energy of the gravitational field. Therefore, relative time and relative rate of motion or the speed of light are covariant.

https://note.com/s_hyama/n/n36da9fb827df

Einstein's theory of relativity(SR and GR) employs the covariance of relative time and space, without distinction between this light and its application, the electromagnetic wave. But this is the convention that light is an electromagnetic wave. Which of these theories is correct depends on the observation of differences in relative velocities between systems.

Dear Professor Hamaji,

Thank you for your post.

Who is the originator of "temporal light theory"

What experimental results does "temporal light theory" predict, that are different from existing theories? ie. Special Relativity or General Relativity, or Newton's theory of gravity?

Are there any experimental results of "temporal light theory" that are accessible to experiment?

Gary Stephens , It originally started by replacing the unit dimension of absolute time γ = 1 with the equivalence principle of light momentum with relative rate factor γ = c/w = m₁/m₉.

https://academicjournals.org/article/article1384786430_Hamaji.pdf

Fly-by anomalies of unresolved problems are generated by observing the recession motion v₊ with the motion and the speed of light ratio (β = v₋/c = v₊/w), at the speed of light c on the ground.

4-3.Unresolved flyby anomaly

https://note.com/s_hyama/n/n36da9fb827df

Gravitational wave detection, which is a time-varying wave, detects changes in the speed of light through interference between light waves and gravitational waves. "It cannot be detected if the space changes."

The above indirectly indicates the covariance of time and relative velocity, and precise measurements are expected in outer space such as ESA's LISA.

As a relativistic philosophy, light has the aspect of time, but as a means, we separate time and light and use the trade-off between time and space. The contradiction is caused by the convention that light is an electromagnetic wave. Rather, light's field creates time and inertia, resulting in a time-gradient gravitational field. It must be separated from light waves and gravitational waves, which are energies.

from ChatGPT:

In the philosophical framework of relativity, light indeed has a temporal aspect. It utilizes the trade-off between time and space as a means of understanding. The contradiction arises from the convention of categorizing light solely as an electromagnetic wave. Instead, it is more accurate to consider that the field of light generates time and inertia, resulting in a gravitational field with a gradient in time.

In this context, it is necessary to distinguish light waves and gravitational waves as forms of energy from the underlying fields of light and gravity. By separating light waves and gravitational waves from the fields that give rise to them, we can better appreciate the role of light in generating time and the resulting gravitational effects.

Professor Hamaji,

I understand from the above that you alone are the orignator of "temporal light theory," which is fine.

Can you tell me what are the new experimental results, qualitative or quantitative, predicted by your theory?

Or can you tell me, what existing experimental results can be explained by your theory?

Gary Stephens , Basically, the hierarchical structure of the universe does not change even if absolute time is eliminated, so the hierarchy problem remains as an unsolved problem at full scale. In my theory, I would like to explain the hierarchy problem of the universe from the micro to the large scale. I don't have an experimental plan, so if you are interested in my theory, please help me.

The two frames are indeed asymmetrical (different) because one of them is accelerating and the other (the reference frame) is inertial (non-accelerating) or at rest. The force of inertia (equated to force of gravity by Einstein) is felt only in the accelerating frame. The reference frame is always inertial. One cannot take an accelerating frame as reference and say that an inertial frame is accelerating compared with this "reference".

For example, let's take two trains accelerating with the same acceleration in the same direction. If we compare one train with the other, none of the passengers in the trains should experience a force. But it is not so because the reference frame should be inertial (the platform) and not the train which is accelerating.

Dear Professor Antonov,

"One cannot take an accelerating frame as reference and say that an inertial frame is accelerating compared with this "reference". "

That's my understanding as well.

In the case above, Einstein confused the situation by pretending the force (equiv. gravitation field) was in the platform frame. When in actual fact the force (equiv. gravitation field) would only be in the train frame, -- the one that experienced the "jerk" as he put it.

If there is no equivalence between "relativity" accelerating frames,--- which there isn't, there is no extension of "Special Relativity" .

The "General Theory of Relativity" does not exist ----only a separate "theory of gravitation." ?

Gary Stephens

Your view above coincides with mine and also in so many physicists ("relativists") that it can be accepted as mainstream. For example, Vladimir Fock in his classic "The Theory of Space, Time and Gravitation" writes:

"When speaking of the relativity of a frame of reference or simply of relativity, one usually means that tliere exist identical physical processes in different frames of reference (for more detail see Sections 6 and 49*). According to the generalized Galilean principle of relativity identical processes are possible in all inertial frames of reference related by Lorentz transformations. On the other hand, Lorentz transformations characterize the uniformity of Galilean space-time. Thus the principle of relativity is directly related to uniformity. This also shows that the nomenclature introduced in Einstein's first papers, by which the theory of uniform Galilean space is named " Theory of Relativity " can to some extent be justified.

In the following we shall see that relativity in the sense defined above is related to uniformity in all those cases in which the space-time metric can be considered fixed. This can be done not only in the theory of Galilean space, where the metric is given once and for all, but also in the theory of Riemann and Einstein space, provided only the processes under discussion have no practical influence on the metric. In these cases relativity is uniquely related to uniformity: in uniform Galilean space it exists, in non-uniform Riemannian space it is absent. If, however, the discussion is to include processes which themselves essentially influence the metric (displacement of heavy masses) it will be shown at the end of the book (Section 93) that relativity can to a certain extent be retained, even in inhomogeneous space, albeit only in those cases in which the non-uniformity produced by heavy masses may be treated as a local perturbation in infinite Galilean space.

The preservation of a certain degree of relativity, even in non-uniform space, is due to the fact that in going over to a new frame of reference the previous gravitational field is replaced by a new one, which has the same form in the new frame as the old in the old frame. Thus, if a laboratory on the Earth is turned upside down, the processes in it will be disturbed (there is no relativity) but if the reversal is accompanied by a parallel transport of the laboratory to the antipodes, the course of all processes in it will be the same as in the beginning (relativity is maintained).

Thus, even in non-uniform space the still existing relativity is indirectly connected with uniformity, namely with the uniformity at infinity if one discusses relativity " in the large", and with local uniformity in a geodesic coordinate system if one is discussing relativity " in the infinitely small ". We have seen, however, that uniformity stands in an antagonistic relation to the degree of generality of the geometry; this is why relativity either does not exist at all in a non-uniform space with Riemannian geometry, or else it does exist, but does not go beyond the relativity of Galilean space. But there can be no question of a generalization of the concept of relativity in going over to nonuniform space.

However, when Einstein created his theory of gravitation, he put forward the term " general relativity " which confused everything. This term was adopted in the sense of " general covariance ", i.e. in the sense of the covariance of equations with respect to arbitrary transformations of coordinates accompanied by transformations of the metric tensor. But we have seen that this kind of covariance has nothing to do with the uniformity of space, while in one way or another relativity is connected with uniformity. This means that " general relativity " has nothing to do with " relativity as such ". At the same time the latter received the name " special " relativity, which purports to indicate that it is a special case of " general " relativity.

To show what misunderstandings resulted we shall consider some examples. As will be shown in Chapter IV, the theory of uniform Galilean space can be formulated not only in a way covariant with respect to Lorentz transformations, but also in a generally covariant manner. In the language of " general" and " special " relativity it would be extremely difficult to express this simple idea, and we shall not attempt to do so, for we would have to say that " special" relativity includes " general " relativity or something of that kind.

Remembering that even in Newtonian mechanics one deals with the generally covariant Lagrange equations of the second kind, one would also have to say that Newtonian mechanics contain in itself " general " relativity. It has become a convention, since Einstein, to use the term " general " relativity or " the general principle of relativity " in the sense of " theory of gravitation ". Einstein's fundamental paper on the theory of gravitation (1916) is already entitled " Foundations of the General Theory of Relativity ". This confuses the issue still further because the words " general " and "relativity " are not used with their proper meaning. In the theory of gravitation, space is assumed non-uniform whereas relativity relates to uniformity so that it appears that in the general theory of relativity there is no relativity.

Enough has been said to make clear that the use of the terms " general relativity ", " general theory of relativity " or " general principle of relativity " should not be admitted. This usage is inconvenient because it not only leads to misunderstanding, but also reflects an incorrect understanding of the theory itself. However paradoxical this may seem, Einstein, himself the author of the theory, showed such a lack of understanding when he named his theory and when in his discussions he stressed the word " general relativity ", not seeing that in the new theory he had created, the notion of relativity was not among the concepts subjected to generalization. In the present book we do not use the term "'general relativity ". Following established practice, we call the theory of Galilean space the Theory of Relativity, but without the adjective " special ". We call the theory of Einstein space the Theory of Gravitation, not the " general theory of relativity ", because the latter name is nonsensical."

This is the strongest rejection of the term "General relativity" that I have seen.

BTW, by "jerk" we understand the third time derivative of the coordinates, that is, the acceleration of acceleration.

Lyudmil Antonov , Since energy and momentum are not absolute quantities, it is impossible to generalize without generalizing with the quantity observed by the observer whose progress of time is delayed.

Shinsuke Hamaji

I don't understand your arguments. You seem to support the non-relevance of the term "general relativity" but the introduction of Lagrangian and Hamiltonian in the discussion is unclear. For the Lagrangian, it is known that it is the linchpin of the whole Gravitation theory, Einstein equation being a consequence of its application. For the Hamiltonian, which physically is the total energy of the system, it cannot be introduced in the general theory without some special models like 3+1 decomposition. This is connected with the inability to apply the energy-momentum conservation principle for arbitrary coordinate frame in the Einstein theory (the energy-momentum for the gravitational field is a pseudotensor, not a tensor).

Lyudmil Antonov , Please let me ask you a specific question.

Would it be necessary to use ⓨkg of fuel to uniformly accelerate and decelerate at 1G inside a ⓧkg spacecraft and go to the nearest star (4.2 light years away)?

Q1: When using fuel with 100% energy efficiency.

Q2: When using fuel with an energy efficiency of 10%.

Shinsuke Hamaji

The question is as unclear as the rest. How about this answer: If I use with 100% efficiency, I will use y kg of fuel, and if I use with 10% efficiency, I will use z kg of fuel.

Lyudmil Antonov , I thought that your reasoning is physically meaningless unless you can measure it, so I asked you a question.

Oh, I see. I was slow to get the joke :)

No, your assessment of GR is correct, but I wanted to specifically discuss the assessment of energy and momentum, but you are not a physicist.

Dear Professor Antonov,

I'd be quite interested to know your thoughts on the below.

https://www.researchgate.net/post/Is_there_a_misspeak_in_Einsteins_train_and_embankment_thought_experiment_as_described_by_Einstein_in_the_1952_edition_of_his_book

At first sight it would seem Einstein is correct to say the rays arrive at the man on the moving carriage at M' "one after the other".

But then you ask : What if I am "stationary" on the moving carriage (due to the relativity of motion) and must then conclude the rays arrive at M' simultaneously.

Next you say : Well if the rays arrive at M' on the moving carriage simultaneously, then they must arrive to the man on the embankment at M, "one after the other" -- but then you can use the same argument as before, and say : I am "stationary" with the man on the embankment (due to the relativity of motion,) and the rays arrive at M, simultaneously.

But I'm putting thoughts into your head. Please feel free to comment if you so wish.

Dear Gary Stephens

Einstein's train and embankment thought experiment is a way of illustrating the relativity of simultaneity, one of the consequences of special relativity. The experiment involves a train moving at a constant speed along a straight track, and two lightning bolts striking the track at two points A and B, equidistant from the middle point M of the track. An observer on the embankment (the ground) sees the lightning flashes simultaneously, as the light rays from A and B meet at M. However, an observer on the train (moving with velocity v) sees the lightning flash at B earlier than the one at A, as the light ray from B reaches him before the one from A.

Einstein described this experiment in his popular book "Relativity: The Special and General Theory", which was first published in 1916 and later revised in 1952. The 1952 edition is available online here: https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf

The relevant section is Chapter IX: The Relativity of Simultaneity, which starts on page 23 of the PDF file. There you can find Einstein's original words and diagrams explaining the experiment.

As for your doubts, I think they stem from some of Einstein's assumptions and arguments that are given in different places of the book. Let me try to clarify them:

- You said in the linked post that Einstein's definition of simultaneity seems indisputable for the embankment reference but not for the train reference, unless we assume the invariance of the speed of light. However, Einstein explicitly states that he assumes the constancy of the speed of light in all inertial frames of reference in Chapter VII: On the Idea of Time in Physics, which precedes Chapter IX. He says: "We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A." This is equivalent to saying that the speed of light is the same in both directions, regardless of the motion of A and B. This assumption is one of the postulates of special relativity, and it is not derived from classical mechanics or any other theory. It is based on experimental evidence (such as the Michelson-Morley experiment) and logical consistency.

- You also said that "M ′ moves towards the right" only within the embankment reference, and not within the train reference. This is true, but Einstein is not choosing any particular reference here. He is simply describing what happens from different perspectives. He says: "If we are assuming invariance of speed of light then " M ′ moves towards the right" only within the embankment reference." This is not a contradiction, but a consequence of relativity. Different observers may disagree on whether an object is moving or stationary, depending on their own state of motion. This does not mean that one observer is right and the other is wrong; they are both right in their own frames of reference.

- You also asked why Einstein said that "the observer will see" instead of "the observer will know". I think this is just a matter of wording, and not a significant difference. Einstein could have said "the observer will infer" or "the observer will conclude" instead of "the observer will see", and his argument would still be valid. He is not implying that the observer has direct visual access to the events A and B; he is assuming that the observer can measure or deduce when and where they occurred based on the arrival times and positions of the light rays. This is a common practice in physics, where we often use terms like "observe", "see", or "detect" to mean "measure", "infer", or "calculate".

- In the present post you said that Einstein is correct to say that the rays arrive at the man on the moving carriage at M' "one after the other". This is true, but only from the perspective of the observer on the embankment, who sees the train moving and measures the speed of light to be constant in all directions. From this perspective, the observer on the train is closer to point B than to point A when the lightning strikes, so he will receive the light ray from B before the one from A. This is what Einstein means by "the observer will see".

- You then asked what if you are "stationary" on the moving carriage and must then conclude that the rays arrive at M' simultaneously. This is also true, but only from the perspective of the observer on the train, who sees the embankment moving and measures the speed of light to be constant in all directions. From this perspective, the observer on the train is at equal distance from points A and B when the lightning strikes, so he will receive the light rays from A and B at the same time. This is what Einstein means by "the observer will infer".

- You then said that if the rays arrive at M' on the moving carriage simultaneously, then they must arrive to the man on the embankment at M, "one after the other". This is false, because you are mixing up two different perspectives and applying them to one situation. You cannot use both perspectives at once; you have to choose one and stick with it. If you choose the perspective of the observer on the train, then you have to accept that he sees both flashes simultaneously and that he sees the embankment moving. If you choose the perspective of the observer on the embankment, then you have to accept that he sees one flash before another and that he sees the train moving. You cannot switch perspectives in mid-sentence and expect to get a consistent result.

Dear Professor Antonov,

Where did I say "M ′ moves towards the right" -- in any sentence anywhere? I don't recall saying that. Can you copy and paste the full sentence? Thanks.

Dear Professor Antonov,

You are misquoting me. When you said "You then said that if the rays arrive at M' on the moving carriage simultaneously, then they must arrive to the man on the embankment at M, "one after the other. This is false..."

I know it is false. It was for the purpose of illustration.

The rays arrive both at M' and M simultaneously. You seemed to have picked up on some of my illustrations of what does not happen, and then declared "this is false" -- which means I cannot illustrate what does not happen without being misquoted.

Dear Professor Antonov,

"You said in the linked post that Einstein's definition of simultaneity seems indisputable for the embankment reference but not for the train reference, unless we assume the invariance of the speed of light."

Where did I ever say anything of the sort? Where did I use the words "seems indisputable" where did I mention "the invariance of the speed of light" ?

Dear Gary Stephens

Sorry that I misquoted you. I didn't mean to disparage you or anything of the sort. The problem is that I got confused by the post that you linked https://www.researchgate.net/post/Is_there_a_misspeak_in_Einsteins_train_and_embankment_thought_experiment_as_described_by_Einstein_in_the_1952_edition_of_his_book and the hundreds of opinions therein.

Thinking more broadly, my opinion is that misunderstanding arises because Einstein tries to convey in words the Lorenz transformations giving examples that sometimes complicate matters instead of simplifying them. The lightning example is one of those. It tries to explain simultaneity and why it cannot exists in different reference frames (another misconception, "reference" in this case does not mean that one frame refers to another) but the reader is confused by two kinds of light signals: one coming from the lightning itself and another coming from the points where the lightning bolts strike. For me, it is much simpler to write the Lorenz transformations

$$\begin{align} t' &= \gamma \left( t  - \frac{vx}{c^2} \right)  \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end{align}$$

where $(t, x, y, z)$ and $(t′, x′, y′, z′)$ are the coordinates of an event in two frames with the origins coinciding at $t=t'=0$, where the primed frame is seen from the unprimed frame as moving with speed $v$ along the $x$-axis, where $c$ is the speed of light, and $\gamma = \left ( \sqrt{1 - \frac{v^2}{c^2}}\right )^{-1}$ is the Lorentz factor.

The inverse Lorenz tranformations, from stationary to moving frame, are

$$\begin{align}   t &= \gamma \left( t' + \frac{v x'}{c^2} \right)  \\   x &= \gamma \left( x' + v t' \right)\\   y &= y' \\   z &= z', \end{align}$$

From these transformations, the following counterintuitive phenomena are derived:

Relativity of simultaneity

Two events occur along the $x$ axis simultaneously ($\Delta t = 0$ in the stationary frame (the platform), but separated by a nonzero displacement $\Delta x$ (the two lightning bolts that fall on different points A and B along the track).  Then in the moving frame (the train), we find that $\Delta t' = \gamma \frac{-v\,\Delta x}{c^2}$, so the events are no longer simultaneous according to the observer moving in the train, that is, the bolts happen in one point earlier than the other.

Time dilation

Let a clock be at rest on the platform. If a time interval is measured at the same point on the platform, so that $\Delta x = 0$, then the transformations give this interval in the train by $\Delta t′ = \gamma \Delta t$. Conversely, suppose there is a clock at rest in the train. If an interval is measured at the same point in the train, so that $\Delta x′ = 0$, then the transformations give this interval on the platform by $\Delta t = \gamma \Delta t'$. Either way, each observer measures the time interval between ticks of a moving clock to be longer by a factor $\gamma$ than the time interval between ticks of his own clock.

Length contraction

There is a rod at rest on the platform aligned along the x axis, with length $\Delta x$.  On the train, the rod moves with velocity $-v$, so its length must be measured by taking two simultaneous ($\Delta t′ = 0$) measurements at opposite ends.  Under these conditions, the inverse Lorentz transform shows that $\Delta x = \gamma \Delta x′$. If the rod is on the train moving with velocity $v$, an observer on the platform measures $\Delta x' = \gamma \Delta x$. So each observer measures the distance between the end points of a moving rod to be shorter by a factor $\gamma$ than the end points of an identical rod at rest in his own frame. Length contraction affects any geometric quantity related to lengths, so from the perspective of a moving observer, areas and volumes will also appear to shrink along the direction of motion.

We see that math helps us to infer much more from this example without misquoting and misunderstanding.

The explanation can be further simplified and approximated as follows:

The platform observer is midway between points A and B. Because light has a constant speed c, the signals from A and B will come to him at the same time.

The train moves from A to B. The speed of the train is v. The signal from A comes with speed c-v (because A moves relative to train with speed -v), and the signal from B comes with speed c+v. At the moment when the train observer is at almost the same point as the platform observer (midway between A and B), the signal from B will come first and from A will come second for him, because the signal from B moves faster. The formulas are somewhat more complicated because times and lengths are different for the two observers.

Dear Professor Antonov,

"The signal from A comes with speed c-v"

How is the light signal travelling.... not at light speed?

I thought Maxwell equs. say light always travels at speed "c", for all observers, in what ever frame?

Are you proposing a modification of Maxwell's equs. ?

Gary Stephens

"How is the light signal travelling.... not at light speed?"

Exactly.

Einstein postulates, following Maxwell and Lorenz, that the speed of light is the constant $c$ in all inertial frames and there can be no such things as light travelling with speeds c+v or c-v. But in order for this to be true, times and lengths should be transformed according to the Lorenz transformations. The person on the platform and the person in the train will see simultaneously the events occurring in A and B at different times and at different places ("relativity of simultaneity").

Dear Professor Antonov,

"The train moves from A to B. The speed of the train is v. The signal from A comes with speed c-v (because A moves relative to train with speed -v), and the signal from B comes with speed c+v. At the moment when the train observer is at almost the same point as the platform observer (midway between A and B), the signal from B will come first and from A will come second for him, because the signal from B moves faster."

And then

"there can be no such things as light travelling with speeds c+v or c-v"

Are you saying, apropos your first quote, that -for him (the observer on the train)- the signal from B will arrive first and the signal from A will arrive second, is now not valid? in view of your second statement?

Or do you stick with your first analysis-- ie. the top quote above, and say the light-rays hit the man at M' on the moving carriage one after the other?

I'm not sure what your view is?

I've included the original Einstein train-embankment thought experiment attached. Here you notice, there is no mention of space or time warping. No mention of Lorentz transformations.

The answer is obvious: if we stick with the constant speed of light, it is necessary for times and lengths in different inertial frames to be different in relation to each other (relativity). This difference depends on their relative speeds.

Einstein does not include Lorenz transformations because he aims this book towards the general public: no math, only everyday examples. He does not mention space and time warping because the subject of the chapter is the relativity of simultaneity. I am sure that in other chapter of the book he gives an example for space and time warping but at the moment I am too busy to look for it.

As for the observer in the train, when he reaches a point midway between A and B the light signals will reach him simultaneously but his when and his midpoint will be different from the person on the platform.

Dear Professor Antonov,

"Einstein does not include Lorenz transformations because he aims this book towards the general public: no math,"

Lorentz transformations are included later in the book &c.

But I'm still unclear on your view. Are you saying the light-rays will always reach the man at M' on the moving train simultaneously? irrespective of the speed of the train?

The light rays will reach the man on train simulaneously only if he is exactly in the midway between A and B. Otherwise, say if he is closer to A, the light rays from A will reach him first because the distance is smaller and the light speed is constant. This is irrespective of the speed of the train.

Dear Professor Antonov,

Thank you for your definite answer!

So we can say you are in direct opposition with Einstein.

Einstein, according to you, is in error, in his most famous thought experiment. Perhaps the most famous thought experiment of all time.

He clearly says -- above, "hence the observer will see [receive] the beam of light emitted from B earlier than he will see [receive] that emitted from A"

Einstein then concludes from this, (in the subsequent sentence,) that the light must have been emitted from B earlier than it was emitted from A.

You are saying, no, Einstein is wrong, and the rays will reach the man at M' (in the middle of the carriage) simultaneously, and this is irrespective of the speed of the train?

Sorry, I now read the Einstein example completely and it is different than I thought, more complicated and confusing. The points A and B are on the ends of a very long train and are moving with the train. This changes the situation. The rays from A and B for the person on the embankment come from two different sources: source A is moving towards the person on the embankment and source B is moving away from him. If the speed of light is constant and its source is moving, there is no rule that prevents adding the speed of light to that of the speed of its source. Therefore for the person on the embankment the speed is c (for the light) + v (for the source A) and c (for the light) - v (for the source B). So the combined speeds (light and source) are bigger for A and less for B for the person on the embankment. For the light rays to reach the person on the embankment simultaneously the lightning must strike B before A because the combined speed from B is less than that for A. The person on the embankment thinks that lightning has struck simultaneously A and B because the rays from these points come to him simultaneously. This does not mean, however, that the speed of light is c+v or c-v. It means that the speed of source is added or subtracted from the speed of light; the latter is always c. The person on the train moves together with A and B (these are on the ends of the moving train) and for him these sources are not moving. Light from A and from B come to him with the same speed c because both sources are not moving with respect to the person in the train. So from his point of view, the person on the train sees lightning striking first the point B.

Einstein explains this differently entirely from the view of the person in the train. He says that the person in the train sees lightning strike B first because in reality he is hastening towards the beam of light coming from B whilst he is riding on ahead of the beam of light coming from A. This gives the false impression that light speeds from A and B are different but this is not so. In fact, the person in the train just receives light with speed c from two sources A and B which do not move with respect to him. He is not riding any beam and does not hurry towards B.

Dear Professor Antonov,

You seem to be changing your view with every post. Now you are back to saying the light speed observed in one frame (the embankment) is c + v , ie.

"Therefore for the person on the embankment the speed is c (for the light) + v (for the source A)"

"speed" meaning speed of a light ray-- what other speed can it mean in this sentence?-- it can't be speed of the source-- you already said that was v.

So in this sentence, you are saying the "speed" of the light-ray is c and the "speed" of the light-ray is c + v.

So the light-ray has two speeds?

-----

"The rays from A and B for the person on the embankment come from two different sources"

Can you clarify what this sentence means? Do you mean there are two sets of rays ; one set located on the embankment, one set located on the train?

Or do you simply mean the left hand light-ray is different from the right hand light-ray?

-----

Have you changed your view, or do you stick with your post before last, and say, whatever the speed of the train, the light-rays will arrive at M' (in the middle of the moving carriage) -simultaneously.- ?

Please read carefully, I didn't say that the speed of light is c+v. What I said is that the speed of light is c and the speed of source A is v (towards) and speed of source B is -v (away) regarding the person on the embankment.

This may sound the same as if light gains the speed of the source but this is not so. The reality is that the moving source and the non-moving detector have different times, i.e. their times are not synchronised. That's why I prefer formulas instead of word examples which are as confusing as this one. All such situations are easily explained with Lorenz transformations as I explained in one of the previous posts.

Dear Professor Antonov,

Beg pardon, I did not mean to misinterpret you.

So, what is the conclusion? Do the rays reach the man at M' on the moving carriage -one after the other-, or -simultaneously-?

Sorry to be so definite about this.

Dear Professor Antonov,

Shall we just say your answer to this question is "indefinite".

You are probably realising now, this question is far from trivial, and in fact very difficult to answer.

It does, at first sight, seem trivial, and "easily explained" -- but that is a mirage.

The conclusion is that in the train the man sees rays from B first, on embankment the man sees rays from A and B simultaneously. But this is not explained satisfactorily with words, neither by myself nor by Einstein.

======================================================

I got another, much more interesting problem which has no definite solution. Let's say that we got a ship travelling with the speed of light. We travel from Earth to Proxima and back. The distance is 4.3 light years, so our trip lasts 8.6 years. The question is how many years will pass on Earth during our trip.

To answer this question, we need to use the concept of time dilation, which is the difference in the elapsed time as measured by two clocks in different inertial frames of reference. According to the theory of relativity, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's frame of reference. The formula for calculating time dilation is given by:

$$\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{v^2}{c^2}}}$$

where:

- $\Delta t$ is the time observed in the other reference frame

- $\Delta t_0$ is the proper time or the time observed in the rest frame

- $v$ is the relative velocity between the two frames

- $c$ is the speed of light in vacuum

In this case, we can assume that the ship travels at a constant speed of light ($v=c$) and that Proxima Centauri is 4.3 light-years away from Earth. Therefore, the proper time for the round trip is $\Delta t_0 = 2 \times 4.3 = 8.6$ years. However, for an observer on Earth, the elapsed time will be longer due to time dilation. Plugging in the values into the formula, we get:

$$\Delta t = \frac{8.6}{\sqrt{1-\frac{c^2}{c^2}}}$$

$$\Delta t = \frac{8.6}{\sqrt{1-1}}$$

$$\Delta t = \frac{8.6}{0}$$

This result means that the elapsed time for an observer on Earth is infinite, or undefined. In other words, it would take forever for the ship to return from Proxima Centauri if it travels at the speed of light. This is one of the reasons why nothing can travel faster than light, because it would violate causality and create paradoxes.

However, if the ship travels less than the speed of light, say 90% of light speed, then causality is restored and we get a definite answer.

If the speed is 90% of the speed of light ($v=0.9c$), for the ship's crew, the proper time would be 8.6/0.9 = 9.6 years. Then we can use the same formula to calculate the elapsed time for an observer on Earth:

$$\Delta t = \frac{9.6}{\sqrt{1-\frac{(0.9c)^2}{c^2}}}$$

$$\Delta t = \frac{9.6}{\sqrt{1-0.81}}$$

$$\Delta t = \frac{9.6}{\sqrt{0.19}}$$

$$\Delta t \approx 21.9 \text{ years}$$

So, if the ship travels at 90% of the speed of light, it would take about 21.9 years for it to return from Proxima Centauri as measured by an observer on Earth.

In the same way, if the ship travels with 99% the speed of light, 61.3 years will pass on Earth.

99.99% -- 193.7 years, etc.

Dear Professor Antonov,

"The conclusion is that in the train the man sees rays from B first, on embankment the man sees rays from A and B simultaneously. But this is not explained satisfactorily with words, neither by myself nor by Einstein."

------------------------------------------

The above is the wrong answer.

This can be seen at once, by saying the carriage is "stationary," and the embankment is moving to the left relative to the carriage.

This is the meaning of the "Relativity of Motion" for uniformly moving systems. Everything is perfectly symmetrical.

Since the light rays are emitted simultaneously at each end of the carriage, these rays will have to arrive simultaneously at M', on the now "stationary" carriage.

The same is true in the other case, in which we are "stationary" with the man on the embankment, in which case the rays will have to arrive to the man at M simultaneously, also.

So the right answer is that the rays arrive at M or M' simultaneously in both cases.

The event at M or M' is -absolute-, and not relative for both observers.

Dear Professor Antonov,

In response to your question on the Clock paradox, if you would permit me to advert to here:

https://www.researchgate.net/post/Who_can_tell_me_why_Dingles_and_Barters_objection_to_Special_Relativity_is_in_error

This also looks to be of interest-- although I haven't yet read it :

Article Popper’s response to Dingle on special relativity and the pr...

ChatGPT より:

光速の 90% で移動する場合、v = 0.9c。

まず、ロケット時間で経過年数を計算してみましょう。飛行距離は 8.6 光年であるため、ロケット時間での経過年数は t' = 8.6 / 0.9 ≈ 9.56 年となります。

次に、地球時間での経過年数を計算してみましょう。時間膨張係数は、√(1 - v^2/c^2) = √(1 - 0.9^2) ≈ 0.436 で求められます。したがって、地球時間での経過年数は、τ = t'√(1 - v^2/c^2) ≈ 9.56 × 0.436 ≈ 4.17 年となります。

したがって、正確に計算すると、地球時間では約 4.17 年が経過し、ロケット時間では約 9.56 年が経過することになります。あなたが正しく指摘したように、地球時間とロケット時間の間には経過年数に違いがあります。先ほどの間違いについて改めてお詫び申し上げます。

Even if GR is not a legitimate acceleration theory, in the absence of a better theory, we would still argue that GR is a valid theory. In any case, it's useless for someone who can't even calculate SR to say such a thing.

"The above is the wrong answer."

The answer is not wrong, only counterintuitive. I explained it above with formulas but I see I have to explain it in more detail.

Let's first look at point M (enbankment). Time from A is $t_A$ and time from B is $t_B$. The interval between the times is $t_A - t_B = \Delta t = 0$ (for M). Now let's see M' (train). Time in A is $t_A'$ and time in B is $t_B'$. According to the Lorenz transformation $t_A' = \gamma \left (t_A - \frac{v x_A}{c^2} \right )$ and $t_B' = \gamma \left (t_B - \frac{v x_B}{c^2} \right )$. The time interval between A and B in M' is $t_A' - t_B' = \Delta t'$. Now we substitute $t_A'$ and $t_B'$ by the Lorenz formulas.

$$t_A' - t_B' = \Delta t' = \gamma \left (t_A - \frac{v x_A}{c^2} \right ) - \left( \gamma \left (t_B - \frac{v x_B}{c^2} \right ) \right = \gamma \left ( t_A - t_B - \frac{v \left ( x_B-x_A \right) }{c^2} \right ) = \gamma \left ( \Delta t - \frac{v \Delta x }{c^2} \right )$$.

But $\Delta t = 0$ and $\Delta x$ is the length of the train $L$ as seen by M. So we obtain for $\Delta t'$ the following:

$$\Delta t' = -\gamma \frac{v L}{c^2}$$

The length $L$ is positive, and the velocity $v$ we accept as also positive (from A to B). The $\gamma$ (Lorenz factor) and c are also positive. So the time interval $\Delta t'$ is negative (minus). Because $\Delta t' = t_A' - t_B'$ is negative, this means that $t_B' > t_A'$ which said in words is: for the train observer time the signal came from B is greater than time the signal came from A. So, effectively, the lightning struck B first for M'.

Gary Stephens

When trying to explain it without the Lorenz transformations but only with everyday common sense, the intuition fails at the following:

What if the light source is moving with velocity $v$ for an observer at rest: is $v$ added to the speed of light to become $v+c$? And reversely: if the observer is moving towards the source with velocity $v$: is $v$ subtracted from $c$ to become $c-v$. The right answer is counterintuitive: the speed of light in both cases does not change, nothing is added or subtracted, and it remains the same $c$ in both cases.

You ask: why so, all speeds are added or subtracted, why nothing can be added or subtracted from the speed of light. The short answer is: because the speed of light is constant everywhere, meaning that it stays constant whether the source or observer are moving or not. This is usually not satisfactory because intuition cannot accept it.

To accept it, you need the long answer which is a great part of the SR: Lorenz transformation, Minkowski metric, four-vectors and the rest.

On top of this, other phenomena happen with moving sources and observers such as the Doppler effect which require additional explanations connecting this to electromagnetic field theory, etc.

In fact, if looking more closely in the Doppler effect, we'll see speed of light added or subtracted from the speed of source there, namely:

According to the special theory of relativity, the speed of light emitted by a source with speed v is the same as the speed of light in vacuum, which is a universal constant denoted by c. This means that the speed of light does not depend on the motion of the source or the observer, and it has the same value in all inertial frames of reference.

The speed of light in vacuum is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour). This value is independent of the speed v of the source that emits the light.

However, the frequency and wavelength of the light emitted by a source with speed v may change depending on the relative motion of the source and the observer. This is known as the Doppler effect, which causes a shift in the observed frequency and wavelength of the light. If the source and the observer are moving towards each other, the observed frequency increases and the wavelength decreases. If they are moving away from each other, the observed frequency decreases and the wavelength increases.

The Doppler effect for light can be calculated using the following formula:

$$f' = f \sqrt{\frac{c + v_o}{c - v_s}}$$

where $f'$ is the observed frequency, $f$ is the emitted frequency, $c$ is the speed of light in vacuum, $v_o$ is the velocity of the observer relative to the medium (positive if moving towards the source), and $v_s$ is the velocity of the source relative to the medium (positive if moving away from the observer).

The wavelength of light can be obtained from its frequency using the following relation:

$$\lambda = \frac{c}{f}$$

where $\lambda$ is the wavelength and $c$ and $f$ are as defined above.

For example, if observer is moving toward a still source with speed v, we'll have the ratio $\frac{c + v}{c}$ which changes the frequency by the above formula.

So, the constancy of light speed is not so much a question in mechanics / dynamics as in electrodynamics (dynamics of moving electromagnetic sources). That's why field theory is closely connected with SR.

Dear Professor Antonov,

I see you have completely ignored my points, and written down a load of goggledegook. As you well know Einstein did not use Lorentz tranformation arguments in the "Relativity of Simultaneity" (train-embankment) chapter.

If you will take the time to look at this presentation, I think you will find it illuminating.

Special Relativity: Train/Lightning Paradox and Simultaneity

https://www.youtube.com/watch?v=bRxfxhJBm4g

Dear Gary Stephens

I am sorry if you consider the stringent mathematical proof of the questions that you asked a load of goggledegook (gobbledegook?). I am also sorry that I lost my time to help you in your confusion and my efforts were in vain.

I remain hopeful that someone else who understands physics a little and can read simple mathematical formulas can find these definite answers and explanations to the Einstein's confusing examples helpful and does not stumble in sophistics.

Shinsuke Hamaji

Your ChatGPT is sadly mistaken. It should divide the earth time by the Lorenz factor instead of multiplying it (inverse Lorenz transformation) -- 9.56 / 0.436 = 21.9 years on Earth. Tell ChatGPT to check its calculations.

If you don't have the courage to bend your knees, physics is impossible, so give up.

Dear Professor Antonov,

Thanks for your comments. I do appreciate you taking the time.

"Einstein's confusing examples"

Well that is true. When Einstein lists the the supposed results of Special Relativity, in a Nature article, the first on the list is : "The Relativity of Simultaneity". But what exactly does this mean?

If we go by the example in the train-embankment experiment, to my mind, it would mean two different realities at M' on the moving train. One in which the light rays arrived simultaneously (we are "stationary" with the moving carriage) and one in which the rays arrive one after the other (we are "stationary" with the embankment)-- which is a nonsense.

So Einstein's "Relativity of Simultaneity" makes no sense at all.

Dear Gary Stephens

I thought of a very simple explanation (without formulae). Let M and M' be at one place when lightning strikes B. The light from B takes some time t to reach M. But at this time M' moves at a distance x toward B. So light from B has smaller distance to travel and reaches M' before it reaches M. The same thinking about A concludes that light from A reaches M before it reaches M'. So if light from A and B reaches M simultaneously these events are not simultaneous for M'.

"If we go by the example in the train-embankment experiment, to my mind, it would mean two different realities at M' on the moving train. One in which the light rays arrived simultaneously (we are "stationary" with the moving carriage) and one in which the rays arrive one after the other (we are "stationary" with the embankment)-- which is a nonsense."

Here you put these two realities as experienced by M' but they are not. One reality is experienced by M' (not simultaneous) and the other is experienced by M (simultaneous). The key is that sources A and B are not moving (stationary) for M' and are moving for M. For M they are moving so that A moves toward him and B moves away from him. From the point of view of M', M receives light from B later than him and light from A earlier than him. This is because when light from A and B reach M simultaneously, M' is shifted a distance x towards B.

All the time light moves with the same speed c. What changes are times and distances for M and M'.

I recommend the following video:

https://youtu.be/vOSIGViCT-s

in which an Indian guy explains the Einstein thought experiment first with plain words and pictures and then with Lorenz transformations in exactly the same formulae as mine above. He has many other videos on special relativity and all are presented in easy to understand pedagogical manner.

Dear Professor Antonov,

Thanks for your simple explanation and video-- I will have a look at that.

"It means that two events which are simultaneous with respect to an observer is not necessarily simultaneous for some other observer in a different inertial frame of reference. For some other observer, one event could happen before or after. This js the relativity of simultaneity."

That is quite an astonishing statement-- "For some other observer, one event could happen before or after,"

for the reasons outlined above by A. A. Robb.

So, it is not just me that has questioned this "Relativity of Simultaneity" Cf. above.

Dear Professor Antonov,

"The light from B takes some time t to reach M. But at this time M' moves at a distance x toward B. So light from B has smaller distance to travel and reaches M' before it reaches M."

That's right, but what actually happens, -- what actually -must- happen, is the light from B -dawdles- on its way toward M' and the light from A -hastens- on its way to M'.

In the moving carriage the optical lengths are actually different. This again was noticed by A. A. Robb. Cf. above.

All the questioning stems from the inability to understand the consequences of the constancy of light speed which are counterintuitive mildly said such as the relativity of reference frames. The above author says this directly

"... this view of Einstein's appeared too difficult to grasp or analyse, and to this group the writer must confess to belong."

However, nowadays SR is a standard text in school textbooks, and this view is not only Einstein's, it is old and non-controversial truth established with many experimental proofs.

"That's right, but what actually happens, -- what actually -must- happen, is the light from B -dawdles- on its way toward M' and the light from A -hastens- on its way to M'."

Light speed remains constant for M and M', what effectively happens is that from M' perspective time of M runs slower and distance outside is shortened. Always remember that light speed remains constant for both frames and what changes are times and distances (time dilation and length contraction, see video lectures https://youtu.be/mMXa0OwFzWQ (length contraction) and https://youtu.be/wIS-LvdsAzg (time dilation)).

About realities and why they are different in the moving train and on the embankment. For M' trees, houses, stones, etc. are moving while for M those stand still. On the contrary, seats, lamps, windows, and everything in and on the train for M' stands still while for M the train and everything in it is moving. This goes for everything in the two frames with only one exception and this is light. Light has a constant speed c for both M and M'. SR is all about explaining this physically and mathematically.

Dear Professor Antonov,

Which of the following statements is false.

1. In the train-embankment scheme, Einstein has the flashes of light (the lightning strikes) occurring either end of the -moving- carriage simultaneously.

2. If we were on the carriage, with the man, light flashes (lightning strikes) would occur simultaneously at each end.

3. In any room or carriage, if light is emitted simultaneously from each end, it must always arrive to the middle of that room or carriage simultaneously.

4. The man is standing in the middle of the room or carriage.

Ergo : It is -ludicrous- to say the light -does not- arrive at the middle of the carriage simultaneously.

1 and 2 are false.

Dear Professor Antonov,

What part of the below statement is false?

1. In the train-embankment scheme, Einstein has the flashes of light (the lightning strikes) occurring either end of the -moving- carriage simultaneously.

Can you highlight the portion Einstein's text which proves the above is not an accurate statement of what Einstein said,--- the initial setup with the lightning strikes, with a quote?

This part is false:

the lightning strikes occurring either end of the -moving- carriage simultaneously (for the man in the carriage).

I don't have time to rummage for the exact text but as far as I remember, Einstein said that strikes occur for the man in the carriage not simultaneously (B first)

Ok, I took the time to find it:

page 26. "Hence the observer [in the train] will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A"

Dear Professor Antonov,

Ah but you have not found anything wrong with :

1. In the train-embankment scheme, Einstein has the flashes of light (the lightning strikes) occurring either end of the -moving- carriage simultaneously.

after your rummaging around. Instead you have quoted the inference, or the conclusion of Einstein, which comes later on. It is not the initial setup, as described by Einstein.

You have ignored the initial setup-- what Einstein said about the lightning strikes, because there was no discrepancy between what I described, and what Einstein said.

That is why there is the word "conclusion" in your quote.

So instead of quoting the initial setup-- about the lightning strikes, you have quoted the "conclusion," because, what I described in 1. is exactly what Einstein said.

Dear Professor Antonov,

Unless you can quote from the initial setup-- where Einstein describes the lightning strikes hitting both the train -and- the embankment, then it must be the case that was I described in 1.) was entirely accurate.

You said:

"1. In the train-embankment scheme, Einstein has the flashes of light (the lightning strikes) occurring either end of the -moving- carriage simultaneously."

But you missed that Einstein says that they are simultaneous for the man on the embankment.

So you missed the whole point.

Dear Professor Antonov,

Eureka! Yes so now you admit that 1. is accurate in what it says, but, as you rightly point out, I have only described -half- of what Einstein indited.

I missed out "Einstein says that they are simultaneous for the man on the embankment." Correct.

But since 1. is entirely accurate as it stands, then it follows that 2. must be true.

You have already admitted that 3 and 4 have to be true.

It follows that my supposition that the man on the train at M' -has to- receive the rays simultaneously is proved.

Dear Professor Antonov,

And the situation on the Einstein train carriage, is exactly equivalent to the Dingle - Michelson Morley experiment (above).

Again-- the rays arrive back to the lamp "simultaneously" notwithstanding any "motion" of the equipment.

If the Michelson Morley equipment were put on a train, again the rays would arrive back at the lamp "simultaneously".

The train-embankment scheme, and the Michelson Morley scheme are illustrating the -same- phenomenon.

It follows that my supposition that the man on the train at M' -has to- receive the rays simultaneously is proved.

There, you go again into a vicious circle.

Fact is: man on embankment (M) sees lightnings A and B simultaneously and man in carriage (M') sees them non-simultaneously (first B and then A).

Therefore, your 2. is dead wrong, and 1. is wrong if it pertains to man in carriage (M') or to both men (M and M'), and is true if it pertains only to the man on the embankment (M).

What you are saying above is actually: "Man on the train (M') sees light from B come before light from A so he concludes that lightning struck first B. But in fact, he is confused, we have to tell him not to believe his eyes but believe us because we know the ultimate truth that lightning strikes A and B simultaneously."

Dear Professor Antonov,

Regarding your ere post :

---------------------------------------

"1. In the train-embankment scheme, Einstein has the flashes of light (the lightning strikes) occurring either end of the -moving- carriage simultaneously."

But you missed that Einstein says that they are simultaneous for the man on the embankment.

---------------------------------------

So now you are saying something different.

You are saying that the lightning strikes, as described by Einstein, were not simultaneous at either ends of the carriage in the initial setup?

If that were the case, what would be the point of discussing the experience of the man on the train at M' later on? as it has already been stated, -at the outset- that the lightning strikes at either ends of the carriage are one after each other?

You are saying that what Einstein wished to be proved, was, a priori, stated before any argumentation took place?

Einstein did not strive to prove it, in this book, he has proven it rigorously before (using Lorentz transformations) in his famous paper "On the electrodynamics of moving bodies" that laid the basis of SR. The book that you quote is written for the general public (I say it a second time) and it has no rigorous proofs because these require math (goggledegook in your terminology). As an explanation, Einstein only mentions (page 26):

"Now in reality (considered with reference to the railway enbankment) he [the man on the train M'] is hastening towards the beam of light coming from B whilst he is riding on ahead of the beam of light coming from A. Hence the observer [in the train] will see the beam of light emitted from B earlier than he will see that emitted from A".

Shortly said, the man on train really sees B earlier than A because he is hastening towards B. Einstein thinks that this is enough for the general reader to explain the whole situation. Obviously, this is not enough for some readers. Again, I recommend the above video that explains the situation in detail and patiently, using pictures. This is something that I am not able to do at the moment.

"If that were the case, what would be the point of discussing the experience of the man on the train at M' later on? as it has already been stated, -at the outset- that the lightning strikes at either ends of the carriage are one after each other?"

The point of discussing the experience of the man on the train M' is that his experience is different from M (the man on the embankment). This is the whole point of this chapter and, in fact, the basis of SR (a very solid basis, I should add).

"You are saying that the lightning strikes, as described by Einstein, were not simultaneous at either ends of the carriage in the initial setup?"

I did not say such thing. This is too inaccurate and indeterminate. The only definite statement is that lightning struck at both ends of the train. It was never said that these strikes were simultaneous (or not) generally (for both observers).

Dear Professor Antonov,

---------------------------------------------------------------------------------------------

"You are saying that the lightning strikes, as described by Einstein, were not simultaneous at either ends of the carriage in the initial setup?"

I did not say such thing. This is too inaccurate and indeterminate. The only definite statement is that lightning struck at both ends of the train. It was never said that these strikes were simultaneous (or not) generally (for both observers).

---------------------------------------------------------------------------------------------

So the lightning strikes are not simultaneous for the embankment observer?

Everything is "indeterminate" ?

Nothing can be said to be true in the initial setup?

So what's the point of the initial setup?

If everything is "indeterminate" in the initial setup, I can simply say : "the lightning strikes were simultaneous at either end of the carriage". And by virtue of you saying this is "indefinite" you rather accept I can say that, and if you accept I can say that, then 2, 3, and 4 follow as true.

If everything is "indeterminate" in the initial setup, I can simply say : "the lightning strikes were simultaneous at either end of the carriage". And by virtue of you saying this is "indefinite" you rather accept I can say that, and if you accept I can say that, then 2, 3, and 4 follow as true.

No, I do not accept that you can say that and I explained why in the previous messages. I just want to ask: do you really not understand or you are trying to frustrate me?

Dear Professor Antonov,

Beg pardon, I'm not trying to frustrate you. All I am doing is pointing out what I believe to be a genuine error in the Einstein train-embankment scheme, as described by Einstein.

Simply put, I don't believe, as Einstein says : " there is no meaning in the statement of the time of an event".

I believe this to be false, -- to my mind A. A. Robb is right in his careful analysis of Special Relativity (starting before 1904 after attending a lecture by Larmor). And he was right to call his treatise "The Absolute Relations of Time and Space".

There is an Absolute tapestry of events, in the manner of Newton, and the simultaneous arrival of the rays to M or M' is one of these Absolute events.

Dear Professor Antonov,

But I understand mine (and Robb's) is not a mainstream view. The consensus is with you.

I'm glad we are in agreement with the notion that General Relativity is not actually an extension of Special Relativity-- but rather only a stand-alone theory of gravity. And you knew this long before me, it seems, from your very interesting quote by V Fock.

Looking at the beginning and the question itself, now I understand where your refusal to accept the obvious, proven, and accepted common knowledge of SR stems from. You are a proponent of A. A. Robb's theory for absolute space-time. Sorry but his system was no-goer from the start and is now only of historic interest.

The problem for his theory is that he converts everything that is subject to physics to geometry. Consequently, no physical experiment can prove of disprove any of his 21 postulates (postulates are statements that are taken for granted). You see, Euclid made his geometry on 5 postulates (axioms), and SR has only 2 postulates. And then there come the strange definitions. I have tried to read his magnum opus "The absolute relations of time and space" but it was too much for my common sense starting with stretched-rubber coordinates and finishing by representing the speed of light as the conjugate of unit inertia segmant related to unit separation segment. The relativity of simultaneity is a direct clash of Robb's theory with reality, and this absolutist theory undergoes a fatal catastrophy.

There are many experimental evidences that contradict Robb's theory and support special relativity (SR). Here are some examples:

- One of the main predictions of Robb's theory is that there is an absolute simultaneity that is independent of any observer or frame of reference. This means that two events that are simultaneous in one frame of reference must be simultaneous in all frames of reference. However, this prediction is contradicted by the experiments that test the relativistic effects of time dilation and length contraction, such as the Ives-Stilwell experiment, the Kennedy-Thorndike experiment, the Hafele-Keating experiment, and many others. For starters, you may see this video https://youtu.be/b-cdKCYX5ZA. These experiments show that the time and length measurements of moving observers depend on their relative velocity, and that there is no absolute simultaneity, but only a relative simultaneity that depends on the frame of reference. This is in agreement with SR, which postulates that the speed of light is constant in all frames of reference, and that the Lorentz transformations describe the relations between different observers.

- Another prediction of Robb's theory is that there is an absolute relation of before and after that is independent of any observer or frame of reference. This means that if one event causes another event in one frame of reference, it must cause it in all frames of reference. However, this prediction is contradicted by the experiments that test the relativistic effects of causality and simultaneity, such as the EPR paradox, the Bell test experiments, the Aspect experiment, and many others. These experiments show that there are quantum phenomena that violate the classical notions of causality and locality, and that there are situations where two events can be causally connected in one frame of reference, but not in another. This is in agreement with SR, which postulates that causality is preserved by the light cone structure of spacetime, and that no signal can travel faster than light.

- A third prediction of Robb's theory is that there is an absolute relation of space and time that is independent of any observer or frame of reference. This means that space and time are separate and independent entities, and that there is no mixing or curvature of space and time. However, this prediction is contradicted by the experiments that test the relativistic effects of gravity and cosmology, such as the gravitational redshift, the gravitational lensing, the Shapiro delay, the gravitational waves, and many others. These experiments show that space and time are not separate and independent entities, but are aspects of a unified entity called spacetime, and that spacetime can be mixed and curved by mass-energy and momentum. This is in agreement with general relativity (GR), which extends SR to include gravity and cosmology, and which postulates that spacetime tells matter how to move, and matter tells spacetime how to curve.

On the positive side, Robb showed a deep understanding of the mathematical aspects of relativity and offered some original insights into the nature of time and space. He also anticipated some developments in four-dimensional geometry and tensor analysis that became important later in physics and mathematics.

Robb made an interesting but flawed attempt to present an alternative theory of time and space based on relativity. It has some historical value as a witness of the early debates and controversies on relativity, but it does not have much scientific or philosophical relevance today.

Lyudmil Antonov ,

you are mixing the relativity of simultaneity with the relativity of time.

The simultaneity can be absolute but time can remain relative...

Stefano Quattrini

If I simultaneously see a dust storm on Mars and light from a distant galaxy forming 300 000 years after the Big Bang through the JWST, are these events absolutely simultaneous?

Lyudmil Antonov ,

if you use light there is retardation, that does not mean necessarily that the simultaneity is not absolute. It only means that with light you have that peculiar retardation effect due to its limited speed.