Is Lorentz length contraction symmetrical in the direction of motion?

Question

Assuming a pole moving from left to right at a constant speed. According to Lorentz length contraction, will the leading end of the pole contract towards the trailing end of the pole, case (a) shown, or case (b) the trailing end towards the leading end or case (c) both ends of the pole will contract at equally amount towards the middle of the pole?

Is the contraction in the pole homogeneous or not? And if not what is the asymmetry?

@WillO But I thought Lorentz length contraction was a feature of special relativity depended only at speed and not in acceleration?! — Markoul11, Dec 13 '21 at 14:32
"Length contraction" has nothing to do with contraction in the sense of changing length. It is shorthand for the fact that the pole has different lengths in different frames, and yes, it depends only on speed. But you are talking about a pole actually changing length in some frame. To change length, it has to be either squashed or stretched. The exact nature of the squashing or stretching depends on exactly where, how and when you apply forces to it. Your question doesn't specify those forces and so has no well-defined answer. — WillO, Dec 13 '21 at 14:54

Marco Ocram · Answer 1 · 2021-12-13T14:03:12.303

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The pole appears to contract equally along its length, so your answer c) is the correct one. You should be able to guess that from your diagrams- if c) were not the answer then some sections of the pole would have contracted more than others.

Length contraction is an effect caused by the relativity of simultaneity. It is a property of spacetime, not of objects as such.

Suppose you have two points in space that are at rest relative to each other a distance d apart. If you measure the distance in any other frame in which the points are moving along the line that joins them you get a shorter value for d. The reason is that in the other frame simultaneous measurements of the positions of the two points are actually measurements at two separate moments in the rest frame. The position of the leading point is measured before the trailing point, which gives the trailing point a chance to move ahead before it is measured, so the recorded gap between the two points is shortened.

So you see that length contraction affects space itself, not just objects within it.

edited Dec 13 '21 at 14:03

answered Dec 13 '21 at 11:40

Marco Ocram

26,161

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And what makes you think that neither a) nor b) are correct? – Markoul11 Dec 13 '21 at 11:43
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I have said it in my answer- the Lorenz contraction applies to all elements of the line equally. Your diagrams for a) and b) show some elements of the line contracted and some not. – Marco Ocram Dec 13 '21 at 11:49
@Markoul11 why don't you tell us why you dispute his answer? – m4r35n357 Dec 13 '21 at 12:15
@m4r35n357 I don't know that is why I'm asking? Is the contraction in the pole homogeneous or not? And if not what is the asymmetry? – Markoul11 Dec 13 '21 at 12:25
Of course it is "symmetrical" (your words, not mine!). But if you take the time to do an SR course this is the sort of question that is answered in the introductory stages. You cannot learn this stuff by "intuition" or by asking specific targeted questions like this, you need to do it in a structured way. If you do not do this, you will not be in any position to understand the answers you get anyway! – m4r35n357 Dec 13 '21 at 12:42
IMO it is more like a Doppler shift effect since the coordinates of specific segments of the pole will continuously change according to the observer position. Thus, as the pole is approaching parallel to your position you will observe the leading end of the pole contracted towards its trailing end and when the pole passes you by and goes away you will see trailing end of the pole expanding. The geometrical center of the pole will contentiously shift position. When the center of the pole coincides parallel with your position you will see the inertial length of the pole. – Markoul11 Dec 13 '21 at 14:02
This is a terribly misleading answer.The correct answer to the question depends entirely on the details of how the pole accelerates. So an answer that ignores those details cannot be correct. – WillO Dec 13 '21 at 14:20
In general concerning 3D objects LLC IMO results in a deformation of the objects on the x-axis aligned with the direction of motion but for a 2D pole like in this question although you will observe contraction - expansion on the ends of the pole because these are symmetrical I don't believe you would experience any change in its total length. – Markoul11 Dec 13 '21 at 14:24
@WillO The question assumes a constant speed. – Markoul11 Dec 13 '21 at 14:26
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@Markoul11: If the speed is constant, nothing contracts. The pole has one length (always) in one frame and a different length (always) in the other. – WillO Dec 13 '21 at 14:52

Is Lorentz length contraction symmetrical in the direction of motion?

1 Answers1