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Very sorry if this is still considered a duplicate to this, but unfortunately the answer to this question cannot address this because mine is a nonrigid body and involve biological locomotion concepts

Basically, there is an annoyingly curious question asked by my friend (quoted here for reference), which I probably have knew that the answer is false but I lacked the key ideas to explain why

如果有一種生物的體積好像銀河系這麼大 連體積都超越很多很多光年 它爬一爬，就已經不知多少光速的千萬倍?

(English translation (brackets are his elaborations)): Say if there exists a lifeform the size of a galaxy, isn't it true that when it moves (e.g. crawl by its limbs), the speed of its movement will be many times of the speed of light c (lightyears of distance in a few seconds as measured in its rest frame)?

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Therefore, instead of asking the above question, I am more interested in the answer to the key element that form this question, which is as follows:

Q1. When we wave our arms in air from point A to point B like a fan, it does look like our entire arm is moving in unison from one point to another. Is the true picture that there is a negligible delay between the movement at the base of the arm and the palm from point A to B, thsat only become significant when the movement approaches the speed of light or the arm is lightyears in length?

Q2. Is the principle in Q1 applied to all non rigid bodies, thus whenever it was being moved from point A to point B, it looks like as if the whole thing moved in unison, but in reality e.g. the leftmost side reached point B faster than e.g. the rightmost side?

(PS I don't say "topmost" and "bottomost" side is to avoid the gravitational time dilation factor that might be at play, so that the key confusion and the fundamental mechanism at play can be put into focus)

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EDIT2: It was pointed that the answer to Q1 was the same as the answer to the rod However of all the answers in the rod link, only the following seemed to touched on the confusion of Q1

BebopButUnsteady

When you move one end of the steel rod, it makes part of it bend and stretch which exerts a force on the next section which makes that move and which makes a new part bend and stretch and so on and so on until you reach Alpha Centauri. This moves along at some speed which is characteristic for the metal which is fast enough that we don't really notice in day to day life. All relativity tells us is that that characteristic speed is less than the speed of light - it turns out for real metal its much less than the speed of light.

Elaboration on Q1: why does the hand looks like it is moving like an unbroken whole?

do the combined delay due to the nerve impulse and the sequence of muscle contraction is still not slow enough to caused our arm to look disjointed as each cell in the arm move from one place to another in the waving motion?

That is, is the principle mentioned by BebopButUnsteady in the link sufficient to address Q1, or is there other subtleties because of the nonrigid and biological nature of the arm?

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  • Why does the other question not apply? The answers on the other question do not really rely on the body being "rigid". – ACuriousMind Jul 02 '15 at 13:04
  • Perhaps my major confusion is whether the fact that we saw our hands (from elbow to palm) moving in unison is actually because the delay between the movement of the elbow and the palm is negligible. That is it looks instantenous to us but is is true that there's actualyl a delay between the ends? So that original question that qas quoted is actually inspired me to ask the confusion I actually had, since an arm is biological and even if there's a signal delay due to the nerve impulses, then why does the hand looks like it is moving like an unbroken whole? – Secret Jul 02 '15 at 13:16
  • In short my question is not related to the rigid rod question in the link, because it is this: why does the hand looks like it is moving like an unbroken whole (even with the nerve impulse delay in the muscle movement is taken into account)? (EDITED and placed on OP) – Secret Jul 02 '15 at 13:33
  • I don't follow. The hand looks "moving as a whole" for the same reason a "rigid rod" looks "moving as a whole". – ACuriousMind Jul 02 '15 at 13:33
  • The link addresses how a rigid body like a rod have info transmitted at max the speed of sound < c, and how relativity does not have rigid bodies, thus answering that question there. However I am not sure if the principle in BebopButUnsteady's answer that the density wave move at < c but fast enough to look instantenous applies also for the arm case, because the movement delay due to nerve impulse is already mentioned, but is this and the sequence of muscule contraction still fast enough to make the arm look like move as a whole, which is why it uses the same principle as the rod? – Secret Jul 02 '15 at 13:51
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    The length and range of speeds of a human arm is much too small a scale for relativity to make any noticeable difference. Remember the arm has bones. Those bones ensure everything remains in a more or less fixed position relative to the arm. So we can treat an arm exactly the same as a rigid rod for the purpose of this question – Jim Jul 02 '15 at 15:00

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