I Lorentz Contraction & Twin Paradox

Mickey1
Messages
27
Reaction score
0
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.
 
Physics news on Phys.org
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.
 
  • Like
Likes 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:
  • Like
Likes 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.
 
In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
So, to calculate a proper time of a worldline in SR using an inertial frame is quite easy. But I struggled a bit using a "rotating frame metric" and now I'm not sure whether I'll do it right. Couls someone point me in the right direction? "What have you tried?" Well, trying to help truly absolute layppl with some variation of a "Circular Twin Paradox" not using an inertial frame of reference for whatevere reason. I thought it would be a bit of a challenge so I made a derivation or...
Back
Top