# Relativity, ultimate rigidity and the speed of light.

Hello,

Surfing the web I came across a question posted by someone. Basically the question asked if I were to have a very, very long rod, say 1000 ly long, and at each end I place an observer. If observer A pushes the rod, would observer B instantly detect the nudge?

I do understand that this is pretty much impossible because the nudge would travel at the limited speed of sound in the regular rod, but it got me wondering. Say I have a perfectly rigid rod, with no vacuum whatsoever between the atoms composing the rod. A super compressed rod—a black hole of a rod, so to speak—if I were to use that instead, would observer B instantly detect the nudge?

Or, let me put it this way. Say that a (hypothetical) detector is placed at the far eastern end of a 1000 ly wide black hole. It so happens that a meteor strikes the western end of said black hole and thereby gets sucked by it. Would the detector instantly know of this disturbance, given that both objects are within the event horizon of the black hole?

I hope this makes sense. :P

Related Special and General Relativity News on Phys.org
D H
Staff Emeritus
There is no such thing as a perfectly rigid rod. When observer A pushes on the rod, the compression wave will travel down the rod at the speed of sound in the rod. This will be orders of magnitude slower than speed of light.

Yes, that's exactly what I said.

I'm asking if it WERE a perfectly rigid one. My question is purely hypothetical.

D H
Staff Emeritus
There's no such thing as a perfectly rigid rod. Not in condensed matter physics, not in relativity. Your question is along the lines of "what do the known laws of physics say would happen in this hypothetical situation where the known laws of physics are violated?"

Hello,

Surfing the web I came across a question posted by someone. Basically the question asked if I were to have a very, very long rod, say 1000 ly long, and at each end I place an observer. If observer A pushes the rod, would observer B instantly detect the nudge?

I do understand that this is pretty much impossible because the nudge would travel at the limited speed of sound in the regular rod
That's right.
, but it got me wondering. Say I have a perfectly rigid rod, with no vacuum whatsoever between the atoms composing the rod. A super compressed rod—a black hole of a rod, so to speak—if I were to use that instead, would observer B instantly detect the nudge? [..]
Atoms consist mostly of vacuum, and the speed of sound will always be less than the speed of light. You can also look at this in another way: infinitely fast signalling is incompatible with relativity, as the Lorentz transformations only can be maintained with a limit speed c (the speed of light) that is less than infinite.

Yes. Exactly. I want an opinion. There's nothing wrong with a hypothetical question. :P

Okay, but say if it happened in a black hole. As I understand, a black hole has no 'vacuum' in it, so what would happen in that case?

You said infinitely fast signalling is impossible, I'm not disagreeing with that. I'm just wondering if the signal in the black hole would travel at the speed of light (delayed detection) or infinitely faster (instantaneous detection). That is all.

PAllen
2019 Award
Okay, but say if it happened in a black hole. As I understand, a black hole has no 'vacuum' in it, so what would happen in that case?

You said infinitely fast signalling is impossible, I'm not disagreeing with that. I'm just wondering if the signal in the black hole would travel at the speed of light (delayed detection) or infinitely faster (instantaneous detection). That is all.
Actually, the classic eternal black hole solutions in GR are all vaccuum - they have no matter at all. You could try to say all the matter is in the singularity inside the event horizon, but the singularity is not not part of the universe within the math used for GR (it is not part of the manifold representing the black hole solution).

As a result, your question cannot be posed within relativity. Just like your other version it amounts to: suppose physics were completely different - what would happen?

(Note, if you go outside relativity, there are hypothetical quantum models of maximally compact objects. I don't know it this question could be meaningfully posed in that context, but no such theory is complete or generally accepted yet).

When you push something, the atoms get closer to the other atoms, the electromagnetic force makes them repel etc and the movement or pressure wave gets carried on. Light is an electromagnetic wave and electromagnetic forces or waves cannot travel faster than the speed of light. Also, the atoms that move to create the pressure wave have mass, meaning that they cannot reach the speed of light. So there really is no mechanism for a pressure wave to travel faster than the speed of light. The atoms themselves cannot travel at the speed of light and the force created by the proximity of the atoms cannot travel faster than the speed of light. Also, gravity nor any other force can travel faster than the speed of light. How would you imagine a faster than light nudge propulsion?

Meir Achuz
Homework Helper
Gold Member
You may want to look at <http://arxiv.org/PS_cache/arxiv/pdf/1105/1105.3899v2.pdf>. [Broken]

Last edited by a moderator:
phinds
Gold Member
2019 Award
... There's nothing wrong with a hypothetical question. :P
No there's nothing wrong with a hypothetical question, BUT there is nothing useful about a hypothetical question that requests an answer that would be inherently self-contradictory.

Yes. Exactly. I want an opinion. There's nothing wrong with a hypothetical question. :P
Any answer other than "this situation is impossible" is false. You can't use the laws of physics to explain something that violates those same laws.

PAllen
2019 Award
You may want to look at <http://arxiv.org/PS_cache/arxiv/pdf/1105/1105.3899v2.pdf>.[/QUOTE] [Broken]

That might actually confuse the OP, as it doesn't stress the Born rigid objects cannot actually exist; and that the trick for rigidity is that the all parts of such an object know how to move to meet the definitional constraints without any signaling.

Last edited by a moderator:
Dale
Mentor
Hi najd, you may feel that we are being a little dismissive, but this is a very frequently asked question. Here is a link to our FAQ

Regarding hypothetical questions, this forum is for discussing mainstream physics, as you agreed to when you signed up for your account. So hypothetical questions about the laws of physics are perfectly ok, but hypothetical questions which contradict the known laws of physics are not.

Last edited by a moderator:
pervect
Staff Emeritus
There is a problem when hypothetical questions contain impossible assumptions. It's a well-known problem.