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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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3 Answers3

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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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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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