If in the Lorentz transformation the invariance of the speed of light is not presumed (as it was assumed later with special relativity), then what was the usage and meaning of the Lorentz transformations? Where did this t-prime formula come from?
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$\begingroup$ This is an excellent question, but it might be a better question for hsm.stackexchange.com $\endgroup$– user4552Commented Nov 26, 2019 at 14:59
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$\begingroup$ There is a pretty complete answer to this question here: hsm.stackexchange.com/questions/4941/… The history isn't simple. People were conceptually muddled and were not interpreting things correctly. Re time specifically, there was some concept of "local time," which is apparently not the same thing as what we mean by proper time or a time coordinate. See en.wikipedia.org/wiki/History_of_Lorentz_transformations $\endgroup$– user4552Commented Nov 26, 2019 at 20:51
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Prior to Einstein’s derivation of the Lorentz transforms from his two postulates the transforms were already known. To my knowledge they arose in two contexts:
1) they were a symmetry of Maxwell’s equations. This was before symmetries became so central to theoretical physics.
2) the were an ad-hoc explanation for the Michelson-Morley null results. The Michelson-Morley null result required length contraction in the amount of the Lorentz transform.
There may be other contexts in which they were known, but those are the two that I am aware of
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$\begingroup$ Thank you for the answer. Did this transform have c (speed of light) in it or is it more general (i.e. c can be something else than speed of light)? If it was exactly the speed of light, then what Einstein did more than just paraphrasing this? i do not imply anything, just want to get info. $\endgroup$– PashaCommented Nov 26, 2019 at 14:40
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$\begingroup$ Yes, c was the speed of light. Einstein realized that it applies to mechanics also. $\endgroup$– DaleCommented Nov 26, 2019 at 16:29
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1$\begingroup$ This doesn't seem to address the core of the question, which is how the equation for time would have been interpreted before Einstein. $\endgroup$– user4552Commented Nov 26, 2019 at 18:23