lightspeedrod

Can I Send a Signal Faster than Light by Pushing a Rigid Rod?

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One common proposal for achieving faster than light communication is to use a long perfectly rigid object and mechanically send signals to the other end by pushing, pulling, or tapping it. For instance; a hypothetical rigid rod linking two people several lightyears away. The fundamental idea is that when one end is moved the other end is disturbed instantaneously.

However, there is no such thing as a perfectly rigid rod: a mechanical disturbance at one end of any material can only move through the material at a finite speed. This speed is called the speed of sound in that material.

High stiffness materials like metal have a very high speed of sound and low stiffness materials like jello or air have a very low speed of sound. When you push on something made of jello, you can easily see that the disturbance propagates at a finite speed. When you push on something like metal, it is not so easy to see visually, but the disturbance still propagates at the finite speed of sound in the metal. (see e.g. https://www.physicsforums.com/showthread.php?p=4414855#post4414855)

The speed of sound in diamond is about 12000 m/s which is about 25 thousand times slower than the speed of light (299792458 m/s). But what about some hypothetical “unobtainium”? Why couldn’t unobtainium’s speed of sound be faster than the speed of light? The answer is that all materials, even unobtainium, are held together by electromagnetic forces at the molecular level. When one molecule moves then the change in its electromagnetic field propagates to its neighboring molecule at the speed of light. So even in principle it is not possible for any material to have a speed of sound faster than the speed of light.

The following forum members have contributed to this FAQ:
DaleSpam
Ryan_m_b
DrGreg
tiny-tim
with additional review and discussion by several others

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52 replies
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  1. russ_watters
    russ_watters says:

    [QUOTE="Chris Miller, post: 5633028, member: 608318"]Thanks. No need. The term "slinky drop" clears up my thinking.[/QUOTE]

    Since you asked earlier, I'm going to use you as an example of why I advocated for leaving this thread open.  It isn't always easy to tell from the first post whether someone legitimately doesn't understand the mechanics behind what happens – the fact that a long metal rod behaves very similarly to a slack spring.  But it is almost always clear from the second post, when either the person gets combative or in your case, the light bulb goes on.  On this particular topic it takes an awful lot of effort to keep the noise down so we can help people like you are are trying to learn.  So thanks for saying thanks.

  2. R
    RockyMarciano says:

    [QUOTE="Ibix, post: 5632825, member: 365269"]I think it's worth reading the context before taking any statement at face value. Especially from that thread. It's a very confusing thread.

    I think that Peter was pointing out that it is perfectly possible to have objects that behave rigidly by Born's definition under steady acceleration. That's enough for Einstein's purposes (building a grid of unaccelerated rods to use as a coordinate system), but isn't enough to transmit faster than light. That would require rigidity under varying acceleration as well.[/QUOTE]

    I think when you wrote steady acceleration you meant uniform straight motion, since Born rigidity is broken under constant proper acceleration and when you wrote varying acceleration you meant varying speed.

    I agree the thread was confusing or at least the statements of several posters made no sense to me. Since they are on topic in this thread I'll comment on them, IMHO getting the math right solves confusions most of the time. For instance it was stated in that thread that in situations that didn't involve rigid bodies subjected to a force in the manner the insigths article refers to (i.e. pushing the rod), Born rigidity allowed existence of rigid bodies in SR and their motion under certain restricted circumstances, like for instance pure lorentz boosts. It is true that Born rigidity motion that only involves three degrees of fredom  is compatible with pure lorentz boost with the same d.o.f.

    It is not correct that Lorentz transformations in the way they are understood in physics, i.e. the identity component of the group, that preserves both space and time orientation and that has six degrees of freedom is compatible with Born rigidity, there are just three d.o.f. missing. A pure boost(that is not connected continuously to the identity and therefore doesn't preserve causality unless the assumption is added independent of the mathematics like it is done in the standard undergraduate SR texts) is just not enough to convey the richness of physical (causal) Lorentzian transformations for extended rods to be valid objects in SR. You could maybe say a very limited motion (rotation-free boosts) is allowed in Minkowski spacetime, but the geometry of Minkowski spacetime is not exactly isomorphic to the physics of SR.

  3. C
    Chris Miller says:

    [QUOTE="PeterDonis, post: 5633515, member: 197831"]Where?[/QUOTE]

    Don't remember, it was long ago, and the slinky example has cleared up my thinking. And even if the two ends did respond to letting go and gravity "simultaneously" I still don't think it would qualify as FTL.

  4. PeterDonis
    PeterDonis says:

    [QUOTE="RockyMarciano, post: 5634056, member: 585697"]Born rigidity is broken under constant proper acceleration[/QUOTE]

    It depends on how you interpret "constant proper acceleration". It is perfectly possible to have an object undergoing constant proper acceleration that is Born rigid, as long as we are clear that "constant proper acceleration" means "the proper acceleration of any given point inside the object is constant, but different points can have different constant proper acceleration". In other words, the object's worldlines describe a Rindler congruence. This is the kind of motion Ibix was describing.

    If "constant proper acceleration" means "the proper acceleration of every point inside the object is constant and exactly the same", then you are correct that such a motion is not Born rigid. This set of worldlines describes a Bell congruence, which has a positive expansion (and this fact is why the string stretches and finally breaks in the Bell spaceship paradox).

    The most general theorem on the requirements for Born rigid motion is the Herglotz-Noether theorem. A reasonable summary of what the theorem says is in the posts by myself and PAllen in this thread:

    https://www.physicsforums.com/threads/herglotz-noether-theorem-understanding.711793/

  5. R
    RockyMarciano says:

    [QUOTE="PeterDonis, post: 5634068, member: 197831"]It depends on how you interpret "constant proper acceleration". It is perfectly possible to have an object undergoing constant proper acceleration that is Born rigid, as long as we are clear that "constant proper acceleration" means "the proper acceleration of any given point inside the object is constant, but different points can have different constant proper acceleration".

    [/QUOTE]

    This is fine, but if the acceleration of the "body" is completely determined by one of its points' three degrees of freedom, what is the point in calling it a "rigid body" or "rigid rod" or implying we are referring to an extended body in general. The math is actually describing the acceleration of a material point, why pretend it is about rigid bodies we are talking about in this accelerated case?

  6. PeterDonis
    PeterDonis says:

    [QUOTE="RockyMarciano, post: 5634089, member: 585697"]The math is actually describing the acceleration of a material point[/QUOTE]

    No, it isn't, it's describing a congruence of worldlines that has zero expansion and shear. The fact that the entire congruence of worldlines is determined once we specify one of them does not mean it's just one worldline.

  7. R
    RockyMarciano says:

    [QUOTE="PeterDonis, post: 5634097, member: 197831"]No, it isn't, it's describing a congruence of worldlines that has zero expansion and shear. The fact that the entire congruence of worldlines is determined once we specify one of them does not mean it's just one worldline.[/QUOTE]

    You can consider the entire congruence but what is the point is my question if it also describes a material point worldline wich is a simpler object and has direct linking to point particles of QFT. Let's use some physical Ockham razor here.

  8. D
    Dale says:

    [QUOTE="Dale, post: 5629728, member: 43978"]There have been 23 posts deleted, one full ban, and one thread ban. The forum rules apply here and they apply to you![/QUOTE]Now 29 posts, one full ban, and 2 thread bans. All of the forum rules apply!

  9. Chronos
    Chronos says:

    Consider how would you test the propagation velocity in a 'perfectly rigid' material? You would need a signal device to tell you when the distant end of your hypothetical rod moved, was pushed, etc. The receiving end of your detector would need to acknowledge the signal before the near end of the rod moved. The only possible non null result would be If the near end of the rod moved before the signal registered, which would only prove the reaction time [hysteresis] of your signaling system was slower than the propagation speed of your 'perfectly rigid' material. This is reminiscent of Galileo's attempt to measure the speed of light using lanterns on distant hills. He concluded he was only measuring the reaction times of his students and the speed of light was very much faster [possibly infinite], which was entirely logical given the measurement precision possible in his test setup.

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