Wikipedia:Reference desk/Archives/Science/2022 March 17

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March 17

Special relativity : 3.4 Relativity without the second postulate

There is a paradox in this chapter, Lorentz transformations should be excluded from it, because they only make sense if the speed of light is invariant in all frames of reference. This is in conflict with the wikipedia article "Lorentz transformation" and its sentence in the introduction: "For example, they reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events , but always such that the speed of light is the same in all inertial reference frames. The invariance of light speed is one of the postulates of special relativity." If the speed of light is not invariant in reference frames, then the Galilean transformations must apply. Malypaet (talk) 03:33, 17 March 2022 (UTC)

References

When you do not postulate P, it does not mean that you postulate its negation non-P.  --Lambiam 10:02, 17 March 2022 (UTC)

Sometimes an apparent Paradox is merely a statement that runs contrary to one's expectation. The Lorentz transformation explains both how the speed of light was observed to be independent of the reference frame, and the symmetries of Maxwell's equations of electromagnetism. The article Special relativity considers the Lorentz transformation and light speed invariance to be the fundamental postulates of special relativity. The background theory of general relativity has been so convincingly tested that it is widely regarded as mainstream science. Some of its predictions that are so-called paradox are indeed counter-intuitive but are not a paradox in the sense of a logical contradiction. Philvoids (talk) 13:24, 17 March 2022 (UTC)

I think the OP merely meant to point out a perceived inconsistency between statements in the article section Special relativity § Relativity without the second postulate and the article Lorentz transformation.  --Lambiam 09:52, 18 March 2022 (UTC)

Another possibility is that Lorentz transformations apply and there is an invariant speed, but that light does not travel at this speed. That’s the case, for example, in models with a small photon mass. By taking it as a postulate that the invariant speed is the speed of light in vacuum, we exclude this possibility by construction, although we cannot physically rule it out to unlimited precision. —Amble (talk) 19:23, 17 March 2022 (UTC)

In fact photon rest mass is ruled out experimentally to our highest achievable, though not unlimited, precision. Philvoids (talk) 20:57, 17 March 2022 (UTC)

I'm confused as to why OP is confounded. @Malypaet: Could you clarify a bit? IIRC, one can derive a transformation for different (velocity) inertial frames even without starting from a physical invariant speed of anything. You would then end up with a transformation relation that's a function of a parameter, say X. If X is infinite, we have Galilean. If X is finite, we have Lorentz. Usually that's where we associate it with c in vacuum. Of course, you can make your life easier by starting from invariant c; it might lead to a shorter derivation of Lorentz transformation. GeorgiaDC (talk) 19:35, 22 March 2022 (UTC)