I Movement of a guitar string at relativistic speeds

[Frabjous]

I think there is some confusion about sound speed. A rigid body has infinite sound speed because information about what happens at a single point is known instananeously by the entire body. For bodies that can deform, this information is transferred via material deformation with a sound speed of (relevant modulus/density)^0.5

 

[PeterDonis]

I'm a bit puzzled.

See post #48.

 

[PeterDonis]

A rigid body

There is no such thing as a perfectly rigid body in relativity.

 

[Frabjous]

There is no such thing as a perfectly rigid body in relativity.

I do not know what you mean by breaking strength. I hear it and think of an elastic-failure or like @vanhees71 an elastic-plastic-failure criterion.

I do not understand how a non-rigid body can have an infinite wave speed. I’ll grant that my knowledge of high speed flows is incomplete, but I am not aware of a non-relativisitic supersonic flow problem that has an infinite sound speed solution, although if there is one I would be really interested in it. Is it coming from theoretical strength calculations? I would also be interested in the details of that calculation. If you are driving E/10 to infinity, why isn’t that a “rigid body”?

 

[PeterDonis]

I do not know what you mean by breaking strength.

It's also called "ultimate strength"--the maximum stress the material can sustain without breaking apart. This is different from (and greater than) the elastic limit, which is the maximum stress the material can sustain and still remain in the elastic regime (i.e., if a force causing stress is removed the material will return to its original shape).

I do not understand how a non-rigid body can have an infinite wave speed.

It can't. Who said it could?

a non-relativisitic supersonic flow problem

Has nothing to do with the topic of this thread.

 

[Frabjous]

I see. I call theoretical strength (commonly approximated as E/10) what you call breaking/ultimate strength. I read your post #48 too quickly.

 

[pervect]

I have only skimmed it, but https://arxiv.org/abs/gr-qc/0605025 is a PHD thesis recommended by Greg Egan on the topic of relativistic elasticity and dynamics. There's quite a lot of material there.

 

[Sagittarius A-Star]

Greg Egan's page on Relativistic Elasticity, in which the above mentioned PHD thesis is recommended for further reading:
http://www.gregegan.net/SCIENCE/Rindler/SimpleElasticity.html

Gron: Covariant formulation of Hooke's law:
https://www.researchgate.net/profile/Oyvind_Gron2/publication/252618282_Covariant_formulation_of_Hooke%27s_law/links/58a34b75458515d15fd98f25/Covariant-formulation-of-Hookes-law.pdf

 

[vanhees71]

I do not understand how a non-rigid body can have an infinite wave speed.

No body can have an infinite speed of sound, because that would mean you could use a sound wave to propagate information instantaneously and that violates relativistic causality. The conclusion is the opposite: There cannot be a rigid body in relativity and there cannot be an elastic body with a speed of sound larger than $c$. The material closest to a rigid body would be a hypothetical material where the speed of sound is $c$.

 

[Frabjous]

T

No body can have an infinite speed of sound, because that would mean you could use a sound wave to propagate information instantaneously and that violates relativistic causality. The conclusion is the opposite: There cannot be a rigid body in relativity and there cannot be an elastic body with a speed of sound larger than $c$. The material closest to a rigid body would be a hypothetical material where the speed of sound is $c$.

I understand that. I was tring to come to terms with the infinite breaking strength/sound speed idea. Out of curiosity, what is the sound speed of a string in string theory? Is it c or something else?

 

[Joda]

If anyone sees this, I'd like to ask another question:

How do we know that the Nambu-Goto action is the one we want to minimize to get the correct equation of motion for the string?

 

[Sagittarius A-Star]

If anyone sees this, I'd like to ask another question

Maybe it can be seen better, if you start for the new question also a new thread with a headline, which asks specifically for the Nambu-Goto action.

Eventually you could ask a moderator, if the new thread should be issued here in the relativity forum or better in the quantum theory forum. I think, formally it belongs to the relativity form, because it is in literature discussed regarding classical (non-quantized) relativistic strings. But eventually, you find in the quantum theory forum more users, who have better knowledge about it, because of the D-dimensional Minkowski space and also the additional dimension of the particle.

How do we know that the Nambu-Goto action is the one we want to minimize to get the correct equation of motion for the string?

I don't know. I can only provide additional links:
https://www.damtp.cam.ac.uk/user/tong/string/string.pdf
https://en.wikipedia.org/wiki/Nambu–Goto_action