Is Any Material Truly Incompressible Under Special Relativity?

[YoungPhysicist]

TL;DR Summary

Is everything compressible?

I thought that if something is incompressible, then when we push on this thing, the other end of it will move instantly, which is a kind of FTL information transport and is impossible. So does that mean literally everything, including atom nucleus or even some elementary particles(if they can be pushed), are compressible?

 

[jbriggs444]

Summary:: Is everything compressible?

I thought that if something is incompressible, then when we push on this thing, the other end of it will move instantly, which is a kind of FTL information transport and is impossible. So does that mean literally everything, including atom nucleus or even some elementary particles(if they can be pushed), are compressible?

Yes. Well observed.

Note that when you get down to the level of quantum mechanics, things get weird and the notion of something being incompressible does not really make sense. The two sides of an object have to actually have relative positions before you can talk about the object being compressed.

Edit: One might want to claim that truly elementary particles (e.g. the electron) are incompressible by virtue of having zero size. However, one could equally well point out that the notion of compressibility requires non-zero size to start with.

 

[sysprog]

As posited, to me your question seems somewhat contradictory. If something is really impossible, then it never happens. If there exists something that is incompressible, then it is not the case that everything is compressible. I venture to answer that even solids have more than zero compressibility. Gases are obviously very compressible. Liquids generally are not seen to be very compressible, but they are slightly so.

 

[YoungPhysicist]

As posited, to me your question seems somewhat contradictory. If something is really impossible, then it never happens. If there exists something that is incompressible, then it is not the case that everything is compressible.

What I am trying to do is show that there is no such thing as incompressible therefore proving everything is compressible.

 

[phinds]

What I am trying to do is show that there is no such thing as incompressible therefore proving everything is compressible.

Define "show"

 

[YoungPhysicist]

Define "show"

Like "prove"?

 

[phinds]

Like "prove"?

Prove HOW? We don't "prove" things in physics --- you're thinking of math. I think post #2 is as much as you're going to get.

 

[YoungPhysicist]

Prove HOW? We don't "prove" things in physics --- you're thinking of math. I think post #2 is as much as you're going to get.

So what should it be?

 

[phinds]

So what should it be?

What should WHAT be ? You have an explanation. I don't think you are going to get more.

 

[YoungPhysicist]

What should WHAT be ? You have an explanation. I don't think you are going to get more.

Ohh Ok. I was just not sure what you mean by post #7.

 

[jbriggs444]

A forum search here for terms such as "superluminal rigid rod" will turn up many threads. For instance: https://www.physicsforums.com/threads/can-information-travel-faster-than-light.238964/#post-1770404

 

[vanhees71]

Summary:: Is everything compressible?

I thought that if something is incompressible, then when we push on this thing, the other end of it will move instantly, which is a kind of FTL information transport and is impossible. So does that mean literally everything, including atom nucleus or even some elementary particles(if they can be pushed), are compressible?

It's also interesting to think about a ficititious strictly rigid body in the theory of relativity. This was first down around 1909 by Born and later worked out by Noether (Emmy Noether's brother Fritz) and Herglotz. It turns out that the most plausible definition of a rigid body, i.e., that proper distances of any two points of the body don't change, lead to very restrictive motions of such a continuum-mechanical system.

In contradistinction to the non-relativistic case (where the rigid body has 6 degrees of freedom, described by the translation of an arbitrary body-fixed point relative to the space-fixed reference frame and a rotation of an arbitrary body-fixed Cartesian basis system against the space-fixed Cartesian basis system) the rigid body has only three degrees of motion, and all the possible motions are either the translation of one of its fixed points without any intrinsic rotation of the body along a accelerated (but the acceleration is limited depending on the spatial extension of the body) or non-accelerated trajectory or a special class of rotational ("helical") motions characterized by subgroups of the Poinare group (like hyperbolic motion of one of its points plus a uniform rotation around the axis given by the direction of the hyperbolic motion, or uniform rotation, and some other quite restricted motions). For details, see

https://en.wikipedia.org/wiki/Born_rigidity

 

[Orodruin]

Like "prove"?

Based on what? Any proof requires a set of basic assumptions. Whether those assumptions are valid or not is a matter for experimental verification in any empirical science.

In the case of SR, a logical conclusion is that incompressible materials are incompatible with SR. Thus, if you find a truly incompressible material, that would violate SR. This in itself tells you nothing about the existence (or non-existence) of incompressible materials unless you assume relativity to be correct.

More to the point, compressibility is tightly linked to sound speed and in SR you cannot have a material with sound speed > c.

 

[YoungPhysicist]

Based on what? Any proof requires a set of basic assumptions. Whether those assumptions are valid or not is a matter for experimental verification in any empirical science.

In the case of SR, a logical conclusion is that incompressible materials are incompatible with SR. Thus, if you find a truly incompressible material, that would violate SR. This in itself tells you nothing about the existence (or non-existence) of incompressible materials unless you assume relativity to be correct.

Thanks for the term clarification! So the word "prove" cannot be used on logical problems but only like "based on this, I prove that". Am I right?

 

[jbriggs444]

Thanks for the term clarification! So the word "prove" cannot be used on logical problems but only like "based on this, I prove that". Am I right?

I think I get what you are saying, yes.

In mathematics, there are two basic possibilities. You either need to have some axioms to start with -- so the relevance of your proof is dependent on the correctness of those axioms. Or the thing you are proving needs to be a conditional -- so the correctness of the result is only as relevant as the truth of the associated condition.

Either way, all you get is a conditional result.

In physics and the sciences, all you get is "Every experiment we've run so far is consistent with this result. But we have not yet run tomorrow's experiment". You can disprove things to pretty high certainty. But you can never 100% prove them.

 

[Orodruin]

So the word "prove" cannot be used on logical problems but only like "based on this, I prove that". Am I right?

I would say that it can only be used on logical problem, but the question of whether incompressible materials exist or not is not a logical problem without further assumptions such as "assuming SR holds". Ultimately, whether relativity holds or not is an empirical and not a logical problem.

 

[snorkack]

Compressibility is through sound speed (maximum light speed) tightly tied to density. As pointed out, point particles are incompressible - by virtue of having infinite density.
Is there any rule of special relativity forbidding a material from having transverse wave speed exactly equal to light speed?