# Lorentz Contraction & Twin Paradox

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• Mickey1
If you refer to Lorentz and FitzGerald, you are referring to something that is not relativity. In summary, Lorentz had the maths to set up the twin paradox, but not the conceptual framework in which to think of it.

#### Mickey1

TL;DR Summary
Does Lorentz contraction point to the twin paradox
The twin paradox is connected to the special relativity but I wonder simply if one might construct the paradox (or something very similar) based on the Lorentz’ (and FitzGerald) work alone?

Several ingredients in the paradox, time dilation and Lorentz contraction, are often mentioned with reference only to Lorentz without any mention of relativity.

Mickey1 said:
The twin paradox is connected to the special relativity but I wonder simply if one might construct the paradox (or something very similar) based on the Lorentz’ (and FitzGerald) work alone?
I don't know.
Mickey1 said:
Several ingredients in the paradox, time dilation and Lorentz contraction, are often mentioned with reference only to Lorentz without any mention of relativity.

In its simplest form, the twin paradox is the analogy in Minkowski geometry of the triangle inequality in Euclidean geometry. More generally, the proper time that elapses along the worldline of an object is equivalent to the invariant spacetime distance along the worldline.

Dale, malawi_glenn, topsquark and 1 other person
Mickey1 said:
The twin paradox is connected to the special relativity but I wonder simply if one might construct the paradox (or something very similar) based on the Lorentz’ (and FitzGerald) work alone?
Well, length contraction alone won't get you there (and I don't think a theory with length contraction alone would really be self-consistent). Lorentz actually derived the Lorentz transforms, which are the mathematical core of relativity, before Einstein. As far as I know, though, he believed them to be just a mathematical fix for Maxwell's equations, so something that was only relevant to electromagnetic waves and fields and the like, until shown otherwise by Einstein.

So Lorentz had the maths to set up the twin paradox, but not the conceptual framework in which to think of it. So in answer to your question I'd say "maybe, it kinda depends what you think of as Lorentz's work".

Last edited:
topsquark and PeroK
Mickey1 said:
Several ingredients in the paradox, time dilation and Lorentz contraction, are often mentioned with reference only to Lorentz without any mention of relativity.

If you refer to Lorentz contraction, you are referring to something that's a part of relativity. Likewise for time dilation.

topsquark