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The following paragraph is from Morin's Special Relativity: For the Enthusiastic Beginner (page 40, the 'rear clock ahead' section, remark number 6):

What if we have a train that doesn’t contain the above setup with a light source and two light beams? That is, what if the given events have nothing to do with light? The $\frac{Lv}{c^2}$ result still holds, because we could have built the light setup if we wanted to (arranging for the light-hitting-end events to coincide with the given events). It doesn’t matter if the light setup actually exists.

I don't see how we could have built the light setup proves that the rear clock ahead phenomenon happens without the light setup. There is no way we can know if this phenomenon we are witnessing is only due to our space changing its rules, i.e. conforming to the presence of light.

Is there a more formal and comprehensive explanation of why the relativistic phenomena still occur 'when there is no light in the train'?

Dale
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losmi247
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  • c is the speed of propagation of causality, and in relativity you can show that all massless particles must travel at this speed in vacuum, including photons (light). It is related to an invariant quantity called a "spacetime interval" between two events. – Marius Ladegård Meyer Sep 30 '21 at 18:21
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    The idea is that light is merely a tool (an ideal one at that) to probe this phenomenon which ultimately does not require the existence of that tool. If you try to come up with any other hypothetical way of simultaneously observing two clocks on a moving train, you will arrive at the same result, assuming you account for any non-ideal artifacts of your newly conceived way. An analogy would be, is an object round if we don't rub our hands around it and feel that it is so? Certainly if we feel a smooth sphere we'll know it's round, but what if we don't? Is the object still round? – Arturo don Juan Sep 30 '21 at 18:22
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    Light is special because it's comprised of photons, which are observable particles (in isolation, unlike gluons) which have exactly zero rest mass, and therefore are always observed to travel at the same speed by any massive observer. Any other zero-rest-mass particle would also travel at that speed. – Arturo don Juan Sep 30 '21 at 18:26

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Special relativity is essentially a theory about time and space. Perhaps the key relationship is that if two events are separated spatially by $\Delta x$, $\Delta y$ and $\Delta z$ and in time by $\Delta t$ in one inertial frame of reference and by $\Delta x'$, $\Delta y'$ and $\Delta z'$ and by $\Delta t'$ in another inertial frame then $$(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - k^2(\Delta t)^2 =(\Delta x')^2 + (\Delta y')^2 + (\Delta z')^2 - k^2(\Delta t')^2.$$ $k$ is a constant. Clearly it must have the dimensions of speed. It enables us to express the fourth dimension, that of time, in spatial units. Textbooks show that it is the fastest speed at which anything can travel without there being weird consequences.

Light travels at this speed. So we can put $c$ instead of $k$. I almost said "light happens to travel at this speed". This would be a controversial statement, but it would make the point that although we may use thought experiments involving light in order to derive the equations of Special Relativity from observed phenomena, Special Relativity is not best thought of as a theory about light, or even as one that is strongly bound up with light.

Philip Wood
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  • I still don't understand why the relativistic effects happen in absence of light. Are you saying it makes no sense to discuss the phenomena in the special relativity 'when there's no light'? – losmi247 Sep 30 '21 at 19:39
  • @losmi247 No, he's saying that $k$ is a conversion factor relating spatial distance to temporal duration. That is, 1 second of time has the same magnitude as 299792458 metres of distance. I discuss this further in https://physics.stackexchange.com/a/291346/123208 – PM 2Ring Sep 30 '21 at 20:06
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    "Are you saying it makes no sense to discuss the phenomena in the special relativity 'when there's no light'?" Quite the reverse! – Philip Wood Sep 30 '21 at 20:33
  • Your answer improved my understanding of this topic so I'll mark it as accepted. – losmi247 Oct 01 '21 at 08:03
  • Thank you. Many introductions to Special Relativity start with a bunch of thought experiments involving light, from which emerge the necessity for time dilation, length contraction and relativity of simultaneity. It's understandable (but not good!) that the student should think of light propagation as a key ingredient of Special Relativity. For a better perspective you might try Spacetime Physics by Taylor and Wheeler. It's a classic, written on an elementary level. – Philip Wood Oct 01 '21 at 08:49
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Is there a more formal and comprehensive explanation of why the relativistic phenomena still occur 'when there's no light in the train'?

Yes. The thing is that relativity is not about light, it is about the speed of light. The speed of light was so named historically, but what it should be called is the invariant speed. The invariant speed is a property of spacetime and not specifically tied to light.

It can be shown that there can only be one invariant speed and that speed is either finite or infinite. Experiments can then show that the invariant speed is finite and equal to the speed of light. Once that is established, then it is clear that relativistic phenomena exist wherever there is spacetime, regardless of whether or not there is light also.

Dale
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Yes. Everything that isn't mass travels at the speed of light. So any force between atoms (i.e. basically everything) i sunder the same limitation.

Señor O
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