Unintuitive physics - rigid objects and compression waves

[autodidude]

I was watching a video on YouTube called 'How Much Does A Shadow Weigh?' and towards the end, the following question was posed:

Suppose you had a button that was one light year away from you and you built a rigid stick one light year long. If you pushed that stick, would the other end of the stick push the button instantaneously?

The answer was no and the explanation was that when you push a rigid object, you're really putting a series of compression waves through it which travel at the speed of sound.

So if we had a 12km long steel rod and we pushed it at what end, then the person on the other end would see it move about 2 seconds later (speed of sound in steel: http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html). Would the steel rod then be momentarily contracted? Would the more we push, the more it becomes contracted?

 

[mfb]

Would the steel rod then be momentarily contracted? Would the more we push, the more it becomes contracted?

Right.
And those contracted regions travel as waves towards the other end.

 

[autodidude]

Whoa, that's pretty crazy. Is there a limit on how contracted you can make it? Hypothetically, if you could push it faster than the propagation of the compression wave, what would happen?

 

[mfb]

The required force would increase a lot, and you would get all sorts of nonlinear effects (including an increased speed of the propagation of the shockwave). You would probably evaporate the material in the process. A hypothetical upper limit on the density would be the formation of a black hole, but I don't think this is a realistic scenario.

 

[ZealScience]

Of course, there is not such thing as "rigid object" in real life. The sound speed is some function of the young's modulus. Apparently if it is infinitely stiff, it may violate causality which means that if such object exists and laws of physics still hold, you can never move that object.

 

[autodidude]

The required force would increase a lot, and you would get all sorts of nonlinear effects (including an increased speed of the propagation of the shockwave). You would probably evaporate the material in the process. A hypothetical upper limit on the density would be the formation of a black hole, but I don't think this is a realistic scenario.

What is a 'nonlinear effect'? Why would it evaporate? So basically what you are then diong is compressing so much that it's mass becomes concentrated in a super small space (hence the unrealistic black hole scenario?)

 

[russ_watters]

Think of a steel rod is a nearly perfect spring. But if you push on it faster than it can compress, you can permanently deform it.

 

[mfb]

What is a 'nonlinear effect'?

An amplitude-dependent or frequency-dependent propagation speed of compressions. Or even some conversion between different frequencies.

Why would it evaporate?

Heat from compression

So basically what you are then diong is compressing so much that it's mass becomes concentrated in a super small space (hence the unrealistic black hole scenario?)

Right

 

[autodidude]

Think of a steel rod is a nearly perfect spring. But if you push on it faster than it can compress, you can permanently deform it.

Thanks russ - what would the properties of a perfect spring be?

An amplitude-dependent or frequency-dependent propagation speed of compressions. Or even some conversion between different frequencies.
Heat from compression
Right

Got it...thanks

 

[Buckleymanor]

Suppose you had a button that was one light year away from you and you built a rigid stick one light year long. If you pushed that stick, would the other end of the stick push the button instantaneously?

The answer was no and the explanation was that when you push a rigid object, you're really putting a series of compression waves through it which travel at the speed of sound.

Maybe if you reversed the proposition. The rigid stick was put under tension (it is stretched) and lots of it.
Would the expansion waves still travel at the speed of sound to the button.

 

[autodidude]

Maybe if you reversed the proposition. The rigid stick was put under tension (it is stretched) and lots of it.
Would the expansion waves still travel at the speed of sound to the button.

Hmm...well, if it was under tension, wouldn't the waves propagate faster (based on what I think I remember)? Though if it's stretched, the molecules would be further apart...

 

[Darwin123]

Whoa, that's pretty crazy. Is there a limit on how contracted you can make it? Hypothetically, if you could push it faster than the propagation of the compression wave, what would happen?

You would probably cause a shock wave at some point. If you push something faster than the speed of the low amplitude limit of the compressional wave, eventually a discontinuity forms that moves faster than the low amplitude limit of the compressional

One type of “nonlinear effect” would be a shock wave. A shock wave could result in a near discontinuity in density that travels faster than the canonical speed of sound. A sonic boom starts out as a shock wave. When an airplane moves faster than the speed of sound, the air right on the airplane wing has to move faster than sound. The compression at contact has to keep up with with the airplane. This creates a build up of pressure, which results in a shock wave, which breaks down into normal sound waves.


When you refer to the propagation of "the compressional wave", you are probably talking about the low amplitude limit of compressional waves. The speed of compressional wave increases with amplitude, but slowly. The speed of sound is actually the low amplitude limit.



The shock wave still wouldn’t travel faster than the speed of light in a vacuum. Thus, you couldn’t beat relativity using shock waves. However, you could send signals faster than the true speed of sound using a shock wave. Hence this is not really a topic in relativity.


If you push that “rigid” rod hard enough, you could get a shock wave. A large amplitude compressional wave could become a shock wave. The shock wave would travel faster than the low amplitude limit. Thus, you may be able to send a signal faster than the speed of sound. Light waves in the vacuum would race ahead of it.

Furthermore, the shock wave would probably cause damage in the rod. There could be some “breakage” that follows the discontinuity. Part of the rod may vaporize. However, that would be an entirely different subject. The signals in a shock wave would not be faster than c.

See this link on shock waves.

http://en.wikipedia.org/wiki/Shock_wave
“A shock wave (also called shock front or simply "shock") is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium (solid, liquid, gas or plasma) or in some cases in the absence of a material medium, through a field such as the electromagnetic field. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium.[1] Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow. In supersonic flows, expansion is achieved through an expansion fan. A shock wave travels through most media at a higher speed than an ordinary wave.”

There is no strict limit to how much a material can be compressed. However, the material will undergo phase changes as the pressure and temperature of the material increase. In practice, your rigid rod is going to break in a way consistent with "classical physics" way before you have to worry about relativity. The material could break, vaporize, ionize, and collapse into any number of degenerate fluids. The nucleii of the material could fission, fuse, emit radiation, or any number of strange effects. However, most of these effects would occur long before SR became an issue.

The only strict SR rule is that no signal can go faster than light. Therefore, there have to be hypothetical limits to materials that keep the signals from going faster than c. Hence, there may be a relativistic limit to the compressibility of the material at some point. For instance, one couldn't achieve a density greater than that of a black hole without the material collapsing into a black hole or singularity state. However, the rod would have been rendered unrecognizable way before this point.

 

[Menaus]

So what if you created a shock wave of light? Should it then create a FTL wave of light itself? Maybe there's a way to make a shock wave of light using, say, a capacitor and spark gap?

Furthermore, say we have an object which has a very high density / low elasticity ratio so that waves which travel through this object at a speed faster than light?

 

[mfb]

That is possible in a medium, where you can go faster than the (local) speed of light. There is an equivalent to the shock wave, and the result is Cherenkov radiation.

 

[Darwin123]

So what if you created a shock wave of light? Should it then create a FTL wave of light itself? Maybe there's a way to make a shock wave of light using, say, a capacitor and spark gap?

Furthermore, say we have an object which has a very high density / low elasticity ratio so that waves which travel through this object at a speed faster than light?

One can't create a shock wave with light in a vacuum.

In air, the shock wave is caused by the fact that the compressional wave can't keep up with the air molecules. Therefore, there is the density of the air "builds up" into a discontinuity. In vacuum, there is no analogue to the air molecules.

Or to put it another way, the speed of the compressional wave slowly increases with amplitude because the interaction potential between air molecules has a rather nonlinear (i.e., funky) form. No molecules, no nonlinearity.

Or to put it in a more succinct form:

Special relativity says that that nothing can go faster than the speed of light in a vacuum. Therefore, there can't be such a thing as a shock wave for light in a vacuum.

There are some caveats to the speed limit of c in SR. I briefly worked with one. Not the tachyons, something else. No one outside of SF has been able to get past the cosmic speed limit.

These caveats don't come about because of any extrapolation from Newtonian to relativistic physics. I am not saying that it is completely impossible to send a signal faster than the speed of light in a vacuum. I am saying that if anyone finds it, it won't be something "obvious".

 

[russ_watters]

Thanks russ - what would the properties of a perfect spring be?

Elastic (instead of plastic) deformation, conservation of energy (reversible).

 

[russ_watters]

Maybe if you reversed the proposition. The rigid stick was put under tension (it is stretched) and lots of it.
Would the expansion waves still travel at the speed of sound to the button.

A spring works pretty much the same under tension and compression.