Proving Lorentz Transform Without Light Signal

[Shrish]

The thought experiment used to prove Lorentz transform uses a light signal as an assumption. What if there was something other than the light signal then Lorentz transformation would have totally different term in place of 'c'(speed of light).

 

[mfb]

There are no proofs in physics.
Special relativity is based on the assumption that light in vacuum has the same speed for all observers. Experimental tests verified that assumption to a really good precision. There is nothing special about light, however. Everything else with the property "has the same speed for all observers" (e. g. "the upper speed limit for matter") leads to the same Lorentz transformations.

 

[BvU]

The assumption (postulate) is that the light signal travels with a speed that is the same for both frames of reference.
"something other" wouldn't help much in deriving the Lorentz transformation.

 

[Dale]

There can only be one invariant speed, not two.

 

[Ibix]

The reason you use the light signal is that it travels at the postulated invariant speed, so its transformation between frames is trivial. To use something else in the thought experiment you would first have to establish (presumably by actual experiment) what is the transformation law for velocities. You could then recover that the transformation law was consistent with the invariance of the speed of light.

If we lived our lives on energy scales where relativistic effects were obvious, that's probably how we'd have done it.

 

[mfb]

If we lived our lives on energy scales where relativistic effects were obvious

We are going... no, running, in that direction ;).

 

[Shrish]

There can only be one invariant speed, not two.

Why?

 

[PWiz]

This might probably help: http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf
(Fellow PF member bhobba had posted this link here sometime ago)

 

[mfb]

Why?

There is no consistent framework that would have two of those speeds which are the same for all observers. It's a mathematical impossibility in the same way 1 cannot be 0 (using "1" and "0" as integers or real numbers). One universal speed already fixes the structure of spacetime, and you can derive that all other speeds are observer-dependent.

 

[Mister T]

The thought experiment used to prove Lorentz transform uses a light signal as an assumption. What if there was something other than the light signal then Lorentz transformation would have totally different term in place of 'c'(speed of light).

No, it would have the same form. The point is that there's a speed that's the same to all observers, regardless of their speed relative to each other. So, for example, if you are an observer on a moving train and I'm an observer stationary on the train platform, and we both measured this speed relative us, we get the same result. If you study the topic in any depth you understand that if such a speed exists, it must be the maximum possible speed.

Light itself seems to be the only thing we know of that travels at this special speed. But suppose it didn't. Suppose that it's discovered that light travels at a speed just under this special speed. It would change nothing. There would still be this special speed that's the same to all observers, and the maximum possible speed.