# The Physical Meaning of the Relatvity of Simultaneity

• peteb
In summary, the conversation discusses the concept of the relativity of simultaneity and how it relates to the theory of relativity. The scenario of a light wave being observed in two different inertial reference frames is used to illustrate the paradox of how two observers can have different sets of simultaneous events. The explanation given is that simultaneity is relative and different observers will have different notions of it. However, this explanation is considered incomplete as it does not fully explain why this paradox occurs. The conversation also touches on the importance of the speed of light in connecting events, rather than simultaneity.
peteb
I have recently been reading on the topic of the philosophy of relativity and the nature of spacetime. An interesting example of the difficulty of understanding the physical reality of the relativity of simultaneity has me very much at a loss to explain how the theory of relativity really physically manifests itself in the real world.

Consider the following scenario:

An inertial reference frame S' moves with respect to another inertial reference frame S in the positive x direction of S. The clocks in S and S' are synchronized at the instant t = t '= 0 when the coordinate origins O and O' of the two frames coincide. At this instant a light wave is emitted from the point O = O'. After time t it is observed in S that the light wave is spherical with a radius r = ct and is described by the equation r^2 = x^2 + y^2 + z^2 which means that the center of the light sphere as determined in S is at O. Consider now the shape of the light wavefront in S' at time t'. Is it also a sphere whose center is at O'? If so, does this lead to a paradox? If not, does this lead to a contradiction with the principle of relativity?

The relativity principle requires all physical phenomena to look the same in all inertial reference frames. Therefore an observer in S' should determine that the wavefront of the propagating light signal is also a sphere whose center is at O'. This conclusion is confirmed by the Lorentz transformations. But our everyday experience tells us that there must be something totally wrong here -- the center of the same light wave cannot be at two different places (at O and O' which may be thousands of kilometers apart). A standard explanation of this apparent paradox is the following: the wavefront of the propagating light sphere constitutes a set of simultaneous events and since according to relativity simultaneity is relative, the observers in S and S' have different sets of simultaneous events and consequently different light spheres. This is a correct explanation, but it certainly does not satisfy me.

The explanation is conceptually incomplete since it merely shifts the paradox from the specific case of light propagation to the relativity of simultaneity itself. What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events and therefore different light spheres (one centered at O and the other at O') given the fact that the two spheres originated from a single light signal. What physical meaning of relativity of simultaneity can be conceptually explained such that this paradox will be explained as well?

How can we really understand this world we live in?

Pete B

I'm not sure I understand your problem.
What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events
What is there to explain? Just like different observers have different notions of what "at the same place" means, they have different notions of what "at the same time" means. That's only fair.
I mean, how do you explain that there is a relativity of conlocality?
(I just made up this word. Is there an official word for "at the same place"?)

How do you 'synchronize' watches without instantaneous communication [which is forbidden]? There is no universal clock. Time is relative throughout this universe.

A thought experiment - moon receeding at superluminal velocity. If the moon suddenly decided to receed from Earth at superluminal velocity, what would we see? A moon that redshifts toward infinity, or abruptly winks out of existence?

It is perhaps worth pointing out that, in relativity, the concept of simultaneity is a convention rather than an experimentally meaningful idea. As nothing can be transmitted instantaneously from A to B, nature doesn't care about "simultaneity" at all. It's a man-made concept which eases our mathematical analysis within a frame of reference, but has no real "physical" significance.

In pre-relativistic physics, all observers agreed on what was simultaneous, which is why we intuitively feel simultaneity is important. In relativity, nobody agrees on simultaneity, but they all agree on the speed of light; it's the notion of being able to send light from event A to event B which is the important relation in connecting events (rather than simultaneity).

Chronos said:
A thought experiment - moon receeding at superluminal velocity. If the moon suddenly decided to receed from Earth at superluminal velocity, what would we see? A moon that redshifts toward infinity, or abruptly winks out of existence?
I'm not sure what this has to do with this thread but the first, obviously. Even if the moon were moving away faster than the speed of light, at any given instant, it would be a finite distance away from us and we would see the light from it after a finite time.

Hi.

peteb said:
The clocks in S and S' are synchronized at the instant t = t '= 0 when the coordinate origins O and O' of the two frames coincide.

Syncronized clocks still in S cannot be synchronized in S' and vice versa.

Light sphere is
S: x^2 + y^2 + z^2 = c^2 t^2
S':x'^2 + y'^2 + z'^2 = c^2 t'^2
where γ=1/√（1 - v^2/c^2),
x'=γ（x - v/c t),
ct'=γ（ct - v/c x),
y'=y,
z'=z.

Regards.

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peteb said:
What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events and therefore different light spheres (one centered at O and the other at O') given the fact that the two spheres originated from a single light signal.
The origin of the light sphere is the origin of O and O' at t=t'=0, which is a single location, not two locations. Where is the paradox?

peteb said:
What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events and therefore different light spheres (one centered at O and the other at O') given the fact that the two spheres originated from a single light signal. What physical meaning of relativity of simultaneity can be conceptually explained such that this paradox will be explained as well?

Pete B

This subject was addressed in the longest ever thread on this forum. It was called the light sphere question.

Matheinste.

Thanks for all the comments. Let me clarify something: this is not a thought experiment that I made up, this is taken verbatim freom a university textbook written by a Professor who studies and teaches the Philosophy of Physics. So the question does have meaning, it is not trivial or meaningless as someone implied. The comments and questions in my post were a blend of my own thoughts and (mostly) those of the author who provided it as an illustration of the difficulty of conceptualizing the physical reality of the principles of relativity.

I mention this because there appears to be some misunderstanding, for example one poster claims it is not possible to synchronize two clocks, one in each of two different frames of reference, to set each clock to zero at the same instant. This is indeed entirely possible and is furthermore mentioned in almost every book on the physics of relativity, usually in terms of two vehicles or trains passing each other or whatever, or as a spaceship that starts off from Earth with a clock synchronized with a clock on earth. In fact, if such were not possible, we could kiss GPS devices and satellite navigation systems goodbye.

To further clarify my discussion, as I see it, the heart of the problem is the issue presented by relativity dealing with the one flash of light generated and perceived as originating at the same physical point, physically coincident in the two frames at time t = t'= 0 at the **same** coincident physical location/origin in the two frames O = O'. When considered at a later time in the two different different inertial frames, the single, unique wavefront generated at the origin location must be treated as though each reference frame had originated its own individual unique spherical wavefront, specific only to that frame, that is identical to the spherical wavefront observed in the other frame of reference. The paradox occurs because the two different wavefronts **physically measured** in the two separated frames were generated by the same one flash of light and thus **in physical reality** shoild be ONE and the SAME wavefront. But that would cause a paradox because the physically same original wavefront should not physically appear identical in the two frames because the frames have moved thousands of kilometers apart since the wavefront was generated.

The observer in each inertial reference frame sees a perfect spherical wavefront in his reference frame, with dimensions as stated in my post, centered at the origin, O or O', of that observer's inertial frame. Yet the time lapsed since the generation of the wavefront means that the two origins, O and O', will be thousands or more kilometers apart from each other because the two frames of reference are in motion relative to each other. So relativity demands that each independent frame of reference will see that wavefront as a sphere generated at its own origin, which means the one unique flash of light is now somehow physically observed as two separate independent spherical wavefronts. one for the observer in each of the two independent inertial frames. How can one sphere morph into two separate spheres yet still physically be the one unique original sphere? We started with one sphere at the instant of generation, as the two frames moved relative to each other, the one sphere became two separate independent spheres as proven by the Lorentz transformations.

The question is, how is this **physically** possible? What does it mean in terms of what we perceive of our physical world? Two observers, moving independently relative to each other, see a spherical wavefront centered at one and the same unique physical location, but no matter how the two observers have moved apart, each observer sees identically the same spherical wavefront centered on that observer's own origin.

Logic would say that the observers will each see a different perspective of that wavefront if they have moved away from each other, and neither will see a sphere, rather they will see the sphere from two different locations and thus it will not appear the same to the two observers. Yet we know from relativity that such is noit the case.

So in my mind the question boils down to, is this a real physical phenomenon in the universe, or is it simply a mathematical calculation that has no real foundation in the physical world we perceive. IOW if it wre physically possible to actually conduct this exercise, would the results be as discussed her and specified by relativity, or would they physically be something else?

Somebody mentioned that this problem has been covered before in an earlier thread. If so, I do not want to rehash old material, can someone point me to that thread if it is still around? Or at least tell me what the final conclusion was in that discussion?

One last thing: I am not a physicist. I am a retired EE who has had a lifelong interest in physics, but I am not an expert. If I made mistakes here, please be gentle with me in correcting my errors. I am just insatiably curious about these things.

Pete B

peteb said:
can someone point me to that thread if it is still around?

Several of the regular posters here posted various examples showing how relativity of simultaneity works in the "light sphere" situation, in a futile attempt to convince one person who kept insisting that we had to be wrong.

peteb said:
**in physical reality** shoild be ONE and the SAME wavefront.
That's how it is.
peteb said:
But that would cause a paradox because the physically same original wavefront should not physically appear identical in the two frames because the frames have moved thousands of kilometers apart since the wavefront was generated.
What do you exactly mean by "should not physically appear identical"? That the center of the light sphere coincides with different physical locations, in different frames?

That is not paradoxical, because unlike the wavefront itself, the light sphere center is not a physical object. It is just an abstract coordinate, calculated from those coordinates which are hit by the wavefront simultaneously, according to some arbitrary simultaneity convention.

If you are interested in physical reality, then you have to realize that the light sphere center has no physical relevance at all.

peteb said:
The observer in each inertial reference frame sees a perfect spherical wavefront in his reference frame, with dimensions as stated in my post, centered at the origin, O or O', of that observer's inertial frame. Yet the time lapsed since the generation of the wavefront means that the two origins, O and O', will be thousands or more kilometers apart from each other because the two frames of reference are in motion relative to each other. So relativity demands that each independent frame of reference will see that wavefront as a sphere generated at its own origin, which means the one unique flash of light is now somehow physically observed as two separate independent spherical wavefronts. one for the observer in each of the two independent inertial frames.
In relativity, there is only one spherical wavefront, not two. In O, the center of the wavefront remains at the origin of O, while the origin of O' is in motion relative to the light sphere's center. At any given time t > 0, in O, the origin of O' is no longer at the center of the light sphere because the origin of O' moved.

The reason that in O', the origin of O' remains at the center of the light sphere is because the sphere itself is defined by clocks, and two clocks in O' on either side (equal distance) of its origin will have the same reading when the light reaches them. In O, the light reaches those clocks at two different times, because in O, the origin and clocks of O' are in motion relative to the center of the sphere.

OK I admit I just quickly browsed the beginning of that other thread, whch did indeed discuss the same problem, but it seemed concerned with the mathematical proof or demonstration of the scenario. My concern is with the implications in physical reality of the scenario. What are the physical phenomena that occur in the real physical world as a result of this phenomenon? The math is rather simple and IMO is indisputable, I am concerned with how this outcome is physically perceived in our real universe.

The most recent reply about the paradox seems to indicate it is not a paradox because the whole thing is just an arbitrary mathematical abstraction rather than a physically real phenomenon. That is what I am seeking to find out, whether this is just an abstract mathematical concept, or is it an actual physically perceivable, theoretically observable phenomenon we can observe and measure in our universe.

Pete B

peteb said:
The most recent reply about the paradox seems to indicate it is not a paradox because the whole thing is just an arbitrary mathematical abstraction rather than a physically real phenomenon.
It's physically real, and not a paradox. The wavefront of a single light sphere must be spherical in every inertial frame as a consequence of the constant speed of light postulate.

The fact that this presented a paradox in Newtonian physics is what motivated SR, since SR was created specifically to resolve this apparent paradox, and successfully does so.

In SR, the single wavefront is spherical in each frame, since synchronized clocks in each frame show the light to travel at c isotropically in each respective frame. Those same clocks are out of synch in other frames, since in other frames the clocks are in motion relative to the origin of the light.

Hi.
peteb said:
I mention this because there appears to be some misunderstanding, for example one poster claims it is not possible to synchronize two clocks, one in each of two different frames of reference, to set each clock to zero at the same instant. This is indeed entirely possible and is furthermore mentioned in almost every book on the physics of relativity, usually in terms of two vehicles or trains passing each other or whatever, or as a spaceship that starts off from Earth with a clock synchronized with a clock on earth. In fact, if such were not possible, we could kiss GPS devices and satellite navigation systems goodbye.

Please pay a little bit attention on the difference of adjustment and synchronization.

There are many clocks everywhere and stay still in S.
here ______________________ somewhere

S clock0：00 →synchronized1← clock0：00

S' clock0：00

There are many clocks everywhere and stay still in S'.
here ______________________ somewhere

S clock0：00

S' clock0：00 →synchronized2← clock0：00However,in integration,

here ______________________ somewheres

S clock0：00 →synchronized1← clock0：00 "We are synchronized. Their way of synchronization2 is wrong."

S' clock0：00 →synchronized2← clock0：00 "We are synchronized. Their way of synchronization1 is wrong."

As an example, In another passing-by at not "here",

S clock0:00 "We are now in adjustment by passing at "here". Your clock is ten minutes forward in synchronization"
↑
discrepancy
↓
S' clock0:10 "We have finished adjustment by passing by at "here" ten minutes ago. Your clock is ten minutes behind in synchronization"

Regards.

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peteb said:
I mention this because there appears to be some misunderstanding, for example one poster claims it is not possible to synchronize two clocks, one in each of two different frames of reference, to set each clock to zero at the same instant. This is indeed entirely possible and is furthermore mentioned in almost every book on the physics of relativity, usually in terms of two vehicles or trains passing each other or whatever, or as a spaceship that starts off from Earth with a clock synchronized with a clock on earth. In fact, if such were not possible, we could kiss GPS devices and satellite navigation systems goodbye.

Pete B

Yes, it is of course possible to synchronize two passing clocks, moving with respect to each other at the event of their meeting, in the sense that they can be set to show the same time.

Clocks at rest with respect to one another in an inertial frame are usually synchronized using the Einstein synchronization procedure and will remain in synchronization with each other to an observer in that frame. If this is done seperately in the two reference frames concerned, two clocks meeting at the same point, which we can designate as the origin, can be set to the same time (synchronized) for all observers for that moment. However, thereafter, clocks in one reference frame, although synchronous with other clocks in the same frame when observed by an observer in that frame, will not show the same time as passing clocks in the other frame. That is, clocks in one frame will not remain synchronized to an observer in the other frame.

Matheinste.

take a photo at the nigth sky and date it.
we have captured light from events that we call simultaneous, even if they happened/originated at diferent moments by some hypotetical 'master' clock. it is the observer that determines what is simultaneous, by convention. this way, observer rules,causality is preserved.

'Reality itself' is not observer dependent because one 'object' ,say, has to have multiple objective realities, one for each observer candidate.
then the 'reality we see' is dependent on 'reality itself' and also observer dependent (motion, field, mass distribution, and more, yet to be told ).
this calls for a 'modification' on the observer. But this is hard to directly measure because as we change, as observer, also our rulers change, and we get a null result on such a direct test.

heldervelez said:
take a photo at the nigth sky and date it.
we have captured light from events that we call simultaneous, even if they happened/originated at diferent moments by some hypotetical 'master' clock.

A photograph does not capture light from events that occurred simultaneously using the normal convention of simultaneity.

Matheinste.

Evey musician who plays in ensembles knows that simultaneity (two musicians playing so that each of their notes sound "at the same time") is only absolute for musicians in exactly the same location. So you cannot have ensemble playing for musicians separated by large distances. Maybe this would be possible if the speed of light were infinite, since you could convert sound into light and have that travel infinitely fast, then convert it back into sound, but that turns out not to be the case.

Mathinste you say well.
I've used that 'image' to make clear the observer dependence of 'simultaneous'.
Einstein method imply the possibility of measure 'time interval'.
The way I've used is limited.
mr atyy also used a nice 'and sound' example. In the concert hall the 'earing' is also diferent at distinct positions.
The orchestra 'master conductor' try to obtain some sort of syncronization at his privilege position and we hope that the acoustic engs had done a good design.

but when refering

>Please pay a little bit attention on the difference of adjustment and synchronization.

I have about fifty different physics books in my library that have no problem with what I said about clocks in two different inertial frames being synchronized to t = t' =0. So I am not going to discuss this particular issue any further.

Pete B

peteb said:
>Please pay a little bit attention on the difference of adjustment and synchronization.

I have about fifty different physics books in my library that have no problem with what I said about clocks in two different inertial frames being synchronized to t = t' =0. So I am not going to discuss this particular issue any further.

Pete B

Perhaps a closer study of what those books actually say may pay dividends. All of my realtivity books stress that clocks in relatively moving frames do not remain in synchronization.

I think if you use the word "set" instead of synchronize it would be more accurate usage.

But if you choose to stay with your interpretation so be it.

Matheinste.

Thanks again for the helpful replies. Note that I am not disputing nor refuting the accuracy or truth of the actual relativistic physics and mathematics involved in analyzing and answering my thought problem. As I said, the reults for this established by relativity are indeed correct and have been verified. What puzzles me is how this phenomenon manifests itself as a physical phenomenon in the real physical world: does it represent what really, physically happens, or does it represent simply an abstract mathematically-based description of the correspondence of physical outcomes with the mathematically calculated results?

It is the correspondence of our physical perceptions of relativistic phenomena with what the theory of relativity proves is the correct description of phenomena that concerns me.

Pete B

Hi peteb,

First, regarding your specific question of the light spheres I direct you (as others have done) to https://www.physicsforums.com/showthread.php?t=358404. I and others who participated in that thread are exhausted of the question.
peteb said:
physical reality ... really physically ... real world
peteb said:
physical reality ... **physically measured** ... **in physical reality** ... **physically** possible ... physical world ... a real physical phenomenon ... real foundation in the physical world
Yes, all of this has been experimentally validated and therefore reflects physical reality. See the FAQ:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html
peteb said:
This is a correct explanation, but it certainly does not satisfy me.
How can you be unsatisfied by a correct explanation? More to the point, what do you expect from us if you can be given an explanation which you acknowledge to be correct but still don't accept? It seems to me that the problem here is not science, but attitude. Experimental results always trump preconceived expectations.
peteb said:
What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events
As DrGreg said, one of the key results of relativity is understanding that simultaneity itself is just a convention and has no physical significance. The universe cares about causality, not simultaneity. If event A causes event B then all reference frames will agree that A preceded B. But if event A is simultaneous with event C in some reference frame then A cannot possibly be the cause of C and therefore their order doesn't matter in any experimental sense.

I have read all the posted answers here. Since my questions and lack of understanding of the physical conceptualization of this thought problem are being taken as hostility be me to accepting the explanations offered here by Dale and others, I will just bow out of this discussion. I received argument even about things quoted directly from a textbook written by a college professor and physics instructor with a PhD in Philosophy of Physics.

It disappoints me that because I simply do not understand something, some of you here find fault with me for asking further questions about the matter and/or the explanations offered. I thought this forum would be an ideal place to get my questions answered without being treated like I am somehow at fault for not understanding what you all apparently do, but I guess I was wrong in that, too. Tolerance of and patience with those not as intellectually gifted as all of you here is apparently not of much importance to some here.

Pete B

peteb said:
I have about fifty different physics books in my library that have no problem with what I said about clocks in two different inertial frames being synchronized to t = t' =0. So I am not going to discuss this particular issue any further.

Pete B
I'll bet that all fifty of those books also say that those clocks match at t = t' = 0 and only at t = t' = 0. At any other time in either frame the clocks don't match.

t = t' = 0 represents only the origin of the light, not the wavefront of the light sphere. The wavefront of the light sphere at any later time is represented by t not equal to t'. There is no other point on the (single) wavefront where t = t'

peteb said:
It disappoints me that because I simply do not understand something, some of you here find fault with me for asking further questions about the matter and/or the explanations offered. I thought this forum would be an ideal place to get my questions answered without being treated like I am somehow at fault for not understanding what you all apparently do, but I guess I was wrong in that, too. Tolerance of and patience with those not as intellectually gifted as all of you here is apparently not of much importance to some here.

Pete B
I'd say tolerance and patience describe this thread (and others similar) to a T. Who was hostile? Who found fault with asking questions?

Unless you're referring to the correction of misconceptions as hostile?

Does special relativity explain anything?

Special relativity is an assertion that there are "inertial frames" or preferred frames of reference in which the laws of physics take their "standard form". Here we have needed to define "inertial frame" and "standard form". These definitions involve the "light sphere". There is no explanation for why such things exist, it is simply asserted that they do. The assertion is consistent with many known experiments.

SR further asserts that the Lorentz transformations are the correct coordinate transformations between any pair of inertial frames. Again, this is not an explanation, but an assertion that is consistent with experiment.

No explanation so far. Predictions only. However, special relativity does explain, I think, how we got along with Galilean relativity for so long, even though it's inconsistent with the totality of observations!

Similarly, special relativity can only be explained when it is found inconsistent with new data, and a more far-reaching theory takes its place. General relativity does a bit of this.

peteb said:
It disappoints me that because I simply do not understand something, some of you here find fault with me for asking further questions about the matter and/or the explanations offered. I thought this forum would be an ideal place to get my questions answered without being treated like I am somehow at fault for not understanding what you all apparently do, but I guess I was wrong in that, too. Tolerance of and patience with those not as intellectually gifted as all of you here is apparently not of much importance to some here.

For heaven's sake, you are asking about Philosophy here, not physics. Philosophers always deserve to be attacked

peteb said:
Tolerance of and patience with those not as intellectually gifted as all of you here is apparently not of much importance to some here.

Actually it is the other way around: You are much to intellectual and philosophical. If you stick to measurable physical quantities SR is much simpler to grasp.

peteb said:
my questions and lack of understanding of the physical conceptualization of this thought problem are being taken as hostility be me to accepting the explanations offered here by Dale and others
Since I was singled out by name here I would very much like to know what I said that you found so objectionable and why it offended you. I certainly meant to provoke thought rather than just provoke you.

peteb said:
What puzzles me is how this phenomenon manifests itself as a physical phenomenon in the real physical world: does it represent what really, physically happens, or does it represent simply an abstract mathematically-based description of the correspondence of physical outcomes with the mathematically calculated results?

Peteb, I think that science is the art of inventing concepts for solving practical problems. Well, that’s true for any intellectual discipline… Hmm, maybe some would say that the legal field, which is mine, is an exception, because, even when we know we are not right, our job is creating confusion in the judge’s mind through crafty use of concepts… But forget that. I didn’t say it. We are here to solve problems, let us assume that.

So you have two observers with different states of motion and a light sphere is created at that very instant. After some time, when the observers are thousands of miles away from each other, both of them continuously hold that they are right in the centre of the sphere. In other words, S holds that the two wavefronts are always simultaneously touching some space points that are equidistant from him; instead S’ maintains that the wavefronts simultaneously touch points equidistant from her…

So what? What is the problem with this discrepancy? I still do not see any. To stop here and start asking “who is really in the centre of the sphere, S or S’?” would be a mistake. That would be philosophy in the sense that atty feels authorised to attack, because it would be a useless exercise. Regardless the answer, the universe is the same. That’s what I think people in the thread mean when they told you that the concept “being at the centre of the sphere” or “two events being simultaneous” has no physical meaning. Look at the verb you used:

peteb said:
does it represent what really, physically happens…?

The question itself is premature. Nothing “happens” just because you attribute the centre of the sphere to S or S’, no events change just because we prefer the judgment of simultaneity of S or S’. Otherwise, SR would be admitting two realities, two universes, and that alone would disavow the theory. (Well, some authors end up admitting many universes through a complicated route involving GR, but that’s another story…)

A different thing is if you bring in a practical concern. For example: two men in S frame (Back and Front) shoot at each other when they are simultaneously, as judged in S frame, touched by the two wavefronts. However, a guy in S’ frame, who is standing by Back, points out that for him Front has not yet received its own wavefront, so in theory he could kill Front before he even shot. What will “happen”, one thing or the other? Will the guy who is by Back be able to prevent Front from shooting or not? Ah, that is, as Dale noted, “causality”, that’s a physically meaningful question.

So it can only have one answer. You can get it on the basis of the measurements of both frames. In S the answer is direct: the two events are simultaneous, so it’s too late for any action to prevent Front from shooting. In S’ the reasoning needs to take into account another factor: even if the two events happen at different moments (one wavefront reaches Back before the other reaches Front), the separation between the two of them is spacelike, which means that not even the fastest known signal, a light signal, could travel from one place to the other and arrive in time to kill Front before he shoots. Actually, both frames use different concepts to describe the same reality.

Conclusion: I would agree with you that the “phenomenon” is, as you seem to suggest, an intellectual trick, as long as you agree that it cannot be otherwise, that it *cannot* reflect what “really happens” because it is just, as DrGreg said, a “man-made concept”. Please note: it’d be so even if the two frames agreed on who is at the centre and on what is simultaneous and what is not. What is *real* is only what the assistants can do or cannot when touched by the light and in that there’s no disagreement.

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