So I am not sure if I can articulate this question but, so what is the whole point with the only moving as fast as the speed of sound? If the reactions of an item back towards an equilibrium are occuring at the speed of light (ie a stick I wave around doesn't seem to deform since it can equalize faster than I can wave it around) I am confused as to the transmittal of a signal though the medium at the speed of sound limitation.
I think you're confused because a few people are confusing their terminology in this thread. I'll try to clear it up a little.
First, "incompressibility" refers to a material's volume. A perfectly incompressible material's volume will not change due to the application of pressure or stresses, though its shape may change due to deformation.
Second, "rigid" refers to a material's stiffness (and, indirectly, its volume). If a material is perfectly rigid, it will not deform due to any applied pressures or stresses, no matter how large. This implies that the volume also does not change. Therefore, applied stresses or pressures can induce rotations or translations but never deformations.
Empirical evidence indicates that stresses in an incompressible medium propagate at a rate equal to the speed of sound as strain waves. However, a strictly "rigid" material does not transmit strain waves, as strain implies deformation. In other words, it would require infinite stress to induce strain (and, therefore, infinite energy) to induce infinitesimal strain in a rigid body. Therefore, the application of stress is relieved by translating the body. This translation would be governed by Newton's second law, F=ma.
Throckmorton
Lifer
- Aug 23, 2007
- 16,829
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If there was a 100% incompressible stick, the other end would move instantly right? That would mean that the information would travel instantly, which has nothing to do with the speed of light
Such a stick would by a physical impossibility. Don't let the material science definitions and equations distract you from the fundamental forces at play here. This really boils down to the electromagnetic force which has a maximum rate of propagation of the speed of light, and MUCH slower in any solid material the stick could be made out of.
No, incompressibility tells us nothing about how the material deforms except that its volume is independent of stress and pressure. For example, if I have an incompressible cylinder with a circular cross section with initial height H0 and initial radius R0, then the initial volume is pi*R0^2*H0. If I apply an axial deformation such that the new height is H, then I can immediately tell you the new radius, since the deformed volume pi*R^2*H is equal to the undeformed volume. However, the key thing to note here is that H can change and R can change, while the total volume must remain constant.
Now, if the cylinder were rigid, then H=H0 and R=R0, regardless of the applied loads. Thus, a rigid cylinder (rod) could transmit information faster than the speed of light. If it existed.
MrDudeMan
Lifer
- Jan 15, 2001
- 15,069
- 94
- 91
Originally posted by: CycloWizard
No, incompressibility tells us nothing about how the material deforms except that its volume is independent of stress and pressure. For example, if I have an incompressible cylinder with a circular cross section with initial height H0 and initial radius R0, then the initial volume is pi*R0^2*H0. If I apply an axial deformation such that the new height is H, then I can immediately tell you the new radius, since the deformed volume pi*R^2*H is equal to the undeformed volume. However, the key thing to note here is that H can change and R can change, while the total volume must remain constant.
Now, if the cylinder were rigid, then H=H0 and R=R0, regardless of the applied loads. Thus, a rigid cylinder (rod) could transmit information faster than the speed of light. If it existed.
If you made a completely rigid rod, what would be the physical limits compared to a normal rod in terms of shearing, bending, etc.?
You couldn't bend it or shear it without infinite force/energy. "Rigid," in terms of linear elasticity, implies an infinite elastic modulus (and, therefore, an infinite shear modulus). This means that infinite stress is required to achieve infinitesimal strain (i.e. no matter how hard you press on it, it's not bending, compressing, stretching, et cetera).
That is true. But any universe which actually contains a 100% incompressible/rigid stick probably doesn't share our speed-of-light limitations either.
It doesn't even matter how long the stick is, if the stick will not bend, compress, or deform in any way, then moving one end of the stick will move the other end up at the same time. I don't consider this cheating the speed of light as you're moving about an axis only and no portion of the stick has exceeded the speed of light. You've just moved a stick, no matter if the stick was only a few inches or a few lightyears long, the same thing happens.
Theoretically I guess this would be the fastest way to send a message over really long distances though. But anyway, the message is only being sent at the speed that the end is being moved at. Try it with a steel rod at home with a friend.
No, the "paradox" has nothing to do with the speed at which you move the stick. The "problem" is that you would be able to send information FTL (through "straight" spacetime) which is forbidden according to SR (and would give rist some to REAL paradoxes it it was possible).
But, again, the reason why it can't be done is that there is no such thing as a 100% incompressible stick.
If that's truly a paradox, I still insist that the same thing would happen with said stick of any length.
And still, no matter on the stick has moved faster than the speed of light. You have exerted a finite amount of force to move every particle in the stick. Besides, doesn't gravity transmit "information" in a similar way? As far as I know, gravity is an "instant" force acting over very long distances. Or is there some theory that shows gravity requires time to act?
For instance though, assume there's a single massive object that a planet is orbiting around. If this object moves away at the speed of light, will the change in the effect of gravity be felt instantly, or will it propagate <= to the speed of light?
Gravity propagates at the speed of light. Relativity disallows information from travelling at speeds faster than c, not just matter. Matter is only what we most commonly think of since it is the most obvious form for things that "travel."
NikolaeVarius
Lifer
- Oct 25, 2006
- 11,036
- 11
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Gravity that requires time to act.
There is something called relativity that answers your question.
Gravity is limited but the speed of light
And also the stick will move in a wave like motion. Its not a paradox.
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