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According to length contraction, for an inertial observer, an object's length contracts in the direction of its motion as it moves faster.

However, as an object's length contract, it would contract about a specific point such that this point remains in the same location before and after the contraction, much like the eigenvector during a matrix transformation.

The question is, does this point exist? If so, how is it determined?

joshua mason
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  • To clarify, are you describing accelerated motion here, or motion with constant velocity? – Marius Ladegård Meyer May 10 '22 at 07:27
  • Have you heard of Lorentz Transformations? – BioPhysicist May 10 '22 at 07:34
  • @MariusLadegårdMeyer motion with constant velocity compared to object at rest – joshua mason May 10 '22 at 08:31
  • @BioPhysicist yes. but i'm unsure how to apply that here – joshua mason May 10 '22 at 08:31
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    @joshuamason : The point where observer is located That point will definitely be observed 'correctly' in both frames. – Sabat Anwar May 10 '22 at 10:25
  • "motion with constant velocity compared to object at rest" Ok, that is what I thought. In this case, the length of the object never changes, from either observers perspective. The length is always $\ell_0$ in the frame where the rod is at rest, and the length is always $\ell$ in the frame where the rod is moving. Neither observer will see the rod "contract"; but they will disagree on how long the rod is, when they compare their measurements. And if neither observers see the length change, there is no special point like your question asks for. – Marius Ladegård Meyer May 10 '22 at 11:20
  • @MariusLadegårdMeyer Not gonna lie, that is a very mystical way of approaching it haha. What about the case where it is accelerating? Such that the observer sees its length contraction unfolding. – joshua mason May 10 '22 at 12:35
  • I get that ;) the reason I am making a big deal out of this is that when my students hear "length contraction", many of them imagine that they are looking at a rod and can "see" the rod contracting as time progresses. But for a rod moving at constant speed relative to you, you will see it fly by with a completely fixed length. It's just that this length will be shorter than if you were to measure the length of the same rod while it was stationary next to you. Hence, "contracted". – Marius Ladegård Meyer May 10 '22 at 16:17

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