Alright /sci/, thought experiment time! Imagine you have two

If the lever is infinitely rigid, it would turn on the lightbulb faster than the speed of light. Which is why objects can't actually be infinitely rigid and unbreakable.

>>8276901
The atoms in the rod can only interact as fast as the speed of sound. So the force you applied pulling the lever has to travel across the entire rod at 340m/s (or whatever the speed of sound is) before the switch at the other end feels the force.

>>8276933
>The atoms in the rod can only interact as fast as the speed of sound

what

>>8276939
I mean in terms of using the rod as a lever, the force you apply is carried along by the atoms in the rod vibrating in sequence as a sound wave. Forgive my shitty wording.

>>8276912
Alright, so is there a physical limit on rigidity then? I can't guess to well at what that physical limit might be, but I'll give in and say that the vibration of whatever atoms composed the structure would have to be either constantly absorbed by some kind of padding or somehow directly converted into some other form of energy to prevent the rod's own vibration from destroying it.

>>8276950
I don't think that's how that works...

>>8276939
That's essentially what the speed of sound means.

>>8276963
I've always heard that "push" forces move like sound waves in solids.

Please correct me if I'm wrong though.

I think I read about this thought experiment in a Stephen Hawking book.

>>8276901
I remember asking my teach in high school something similar

Basically, if I had a stick that was as long as the distance between Earth, connecting me with some alien on Neptune, if I push the stick, would the alien instantly feel the stick being pushed? But if this is the case, then a force/information has traveled faster than light.

Or would the force of me pushing the stick have to travel at the speed of sound until it reaches Neptune? But if this is the case, then a part of the stick become existent, because if I pushed and the alien hasn't felt anything, then the stick just got shorter.

Does anybody know the answer? My teach refused to answer, saying "hurrr it's hypothetical no need to think about it", but what would happen?

>>8276981
Really?

If you could remember which book I'd really appreciate it.

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>>8276999
Part of the stick becomes in-existent*

And teacher instead of teach, I use teach as a slang a lot, pardons.

>>8277002
Either The Universe In A Nutshell or A Brief History of Time. I'm trying to find it right now.

>>8276976
That is true for energy moving through materials, but not necessarily for the movement of objects relatively. Objects can and do move faster than the speed of sound.

In this case, the amount of force that might need to be conjured up to "pull" the lever might be beyond my reasoning, but the point of the experiment is more to establish whether or not an action might (even if by some incredible and unlikely scenario) exceed the speed of light.

>>8276999
It's kind of a trick question, because saying the rod is "completely rigid" is the same thing as saying "it is made of a material in which the speed of sound* is indefinitely high." It's impossible to have a "completely" rigid rod for the same reason that it's impossible to have a sound wave travel faster than the speed of light.

So basically, if we take the impossible premise at face value, it makes sense that we get an impossible outcome (information traveling faster than light).

*Recall that the speed of sound is different in different materials.

>>8277012
>Objects can and do move faster than the speed of sound.
Without getting caught up in silly word interpretations (obviously we are not talking about why fighter jets and rockets can exceed the speed of sound in air, here), let's be clear that in this scenario the end of the rod could move before the "pulse" of the push reaches it, but only according to random vibrations. The observer on neptune would have no way to tell if he was seeing the very beginning of the push coming through, or just a few atoms randomly jostling around.

>>8277007
sorry can't find it

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>>8277015
I'm sorry for being retarded but what does rigidity change in all of this? Assuming the stick isn't hit by anything, why would we consider it breaking?

I understand that the speed of sound is different depending on the medium, but would me just pushing the stick be enough to destroy it? Plus assuming the force will just travel based on the speed of sound permitted by the stick, then won't the stick become shorter, because you pushed it on one end, while on the other end it hasn't moved?

I know this sounds stupid and I don't know much about physics but pls explain.

>>8277036
I also kinda realized something.

How about we assume the stick is made out of some extra-light material that isn't fragile. Because if the stick is big then I understand pushing it will require a ton of force, capable of destroying it.

Are we doing troll science memes again?

Anyway, this has already been answered. The force cannot be transmitted through the rod faster than light, and realistically only moves as fast as the atoms interact.

>>8277036
"Rigid" doesn't mean unbreakable. It means the rod isn't at all "springy." Real objects that actually exist are all a little bit springy, at least on a microscopic scale.
Thus, this is exactly what happens:
>then won't the stick become shorter, because you pushed it on one end, while on the other end it hasn't moved?
Matter is just compressible. Some matter can be compressed quite a lot (like air and other gasses), and some (like say, a hard stone or metal) can barely be compressed at all. We say these less-compressible objects are more rigid.

If, for the purposes of a thought experiment, we imagine a rod that is completely rigid, then of course this slight compression is not permitted, and so the end of the rod would have to (impossibly) move sooner than the laws of physics would normally permit.

>>8277020
Not really what I was getting at, but it brings up an interesting idea.

I was more focused on the fact that the speed of any vibration through an object is dictated by the energy exposed to it by the force in question. It happens whenever you "push" a thing that if you've exceeded the energy level an object can reasonably experience it's molecular bonds break. You put dynamite in a rock and the rock explodes. The "vibration" the parts of the rock might experience if the force were not converted into kinetic energy would be like your sound waves.

All that really says is that the object has to break because we can't actually use an indefinitely rigid material like the previous poster brought up.

>>8277048
Alright that sounds reasonable, thanks man. Sorry for my mistake there, mixed rigidity with hardness there.

>>8277040
What material then, carbon? That stuff'll break after bending all over the place

>>8277040
>capable of destroying it
To be clear, it has absolutely nothing to do with destroying the rod or not. Imagine pushing on a piece of rubber. You can squish (compress) it without destroying it or causing it to become "non-existent." You are just temporarily pushing some atoms closer to each other than they normally would like to be.

In the case of the rod, other atoms will move out of the way behind them to make room, all the way through the material, until the other end eventually gets pushed back too. The time it takes for all this to happen depends on how hard the atoms are pushing each other out of the way.

Now, some smartass will probably ask something like
>What if the rod were made not of atoms, but of nucleons without electrons spacing them out, like a neutron star or a giant atomic nucleus?
In that case, instead of "atoms" in the above paragraphs, we would be dealing with individual nucleons, but I believe astronomers can confirm they would still behave broadly in the way I described by observing seismology (that is, the effects of pressure waves traveling through) of neutron stars.

>>8277051
>All that really says is that the object has to break because we can't actually use an indefinitely rigid material
Yes, I suppose any "perfectly rigid" object would also be "utterly fragile," unable to transmit any forces without breaking. Or to put it more simply, an atomic bond that can only exist at a single radius instantly breaks under any force that moves one of the bonded particles. (Which makes sense because they are no longer at the specified radius.)

I'm not actually convinced, even in the case of infinite rigidity, that the action is instantaneous. To me, the information (moving the lever) still must be communicated via particle interactions (i.e. at the speed of light). This is distinct from any notion of compression or rigidity, because atoms halfway along need to know to move. Information about the force must reach them, but the particle interaction can only travel at the speed of light.

It's not actually logically inconsistent, in relativistic theories, to have the lever pushed for one observer and static for the other, because they are in different (presumably inertial) frames. And I'm not talking about length contraction; I am talking about different observers not agreeing on events.

>>8277100
>Information about the force must reach them, but the particle interaction can only travel at the speed of light.
Certainly. But this is not at all distinct from the concept of rigidity: if it is true that the interactions take some time to propagate down the rod (which they certainly do, in the real universe), then the rod must become somewhat compressed, and is therefore not rigid.

>because they are in different (presumably inertial) frames
Why should the two observers be in different inertial frames? If one observer were accelerating relative to the other, it would be very difficult to perform this experiment! It makes much more sense for both observers to have no relative velocity throughout the duration of the experiment.

>>8277117

They're at difference spacetime points, so I consider them different observers inasmuch as I'm happy for them to disagree on the length of the rod. Maybe I didn't mean different frames.

>the rod must become somewhat compressed, and is therefore not rigid.

Let's look at it in terms of two electrons repelling each other. One moves slightly closer. Photons are exchanged. This is happening at c, so there is a finite time in which the first electron is closer to the second than is suitable for equilibrium. After this, there is a force generated, the second electron gets displaced and the whole thing continues.

If we argue that the point where the electron is slightly closer than it should be is compression (i.e. particles are displaced), then you're right. But then how can any particle interaction happen if perfect rigidity is enforced? How can the rod actually know to move?

>>8277143
>But then how can any particle interaction happen if perfect rigidity is enforced?
This is exactly my point about "perfect rigidity" being a nonsense proposition. I think the discussion did reach a rather interesting point leading up to this post >>8277065 though:
>an atomic bond that can only exist at a single radius instantly breaks under any force that moves one of the bonded particles.

If the object is to be completely rigid, while having particles that still react individually to forces in the usual way, then its particles can't move with respect to each other without becoming detached.

Thus, to be "perfectly rigid" either means to have a (physically impossible) means of transmitting forces instantaneously (an infinite sound speed), or to be so fragile as to break at the slightest disturbance.

Interestingly, this is intuitive when you consider the everyday notion of brittleness. Very firm objects tend to chip and fracture, while soft objects deform without breaking.

>>8277143
That's where the brunt of the argument fell. It was argued more that no perfectly rigid object could exist, so the experiment was flawed.

We could make things a bit more difficult and say that the material has 99.9% efficiency of changing to kinetic energy, increase the distance maybe.

>>8277150
>We could make things a bit more difficult and say that the material has 99.9% efficiency of changing to kinetic energy
Then it's still just a race between the sound speed in the rod and the speed of light in a vacuum. If you define the sound speed in the rod as being faster than c, you have specified an impossible object. If not, it is less than or equal to c, and the force either loses to or ties with the beam of light.

I guess that begs the question, "what makes it physically impossible for an object to be rigid enough to have an impossible sound speed?" To answer that, I think you would need to investigate the microphysics of the atomic bonds.

Surprised no one has come up with a version of this using the trolley problem. If yoiu had a perfectly rigid lever to change the tracks ...

>>8276901
>unfathomable material that is unbreakable and completely rigid

no

>>8276901
Why would you post a picture of candlejack? are you new or som-

I'm confused, isn't it obvious that the laser would arrive first due to the speed of electrons moving through a wire not being able to match that of light in a vacuum?

>>8276958
>Alright, so is there a physical limit on rigidity then?

The fundamental force that carries the impulse for the molecules in the rod to start moving can't move faster than the speed of light, so I would say that's the upper limit. I don't think vibration or mechanical strength really has anything to do with it, it's more to do with the "range" of the force.

If you pull the rod, then a change in the electrostatic field propogates down the rod at the speed of light, and eventually reaches the other end of the rod. This generates a miniscule impulse for the end of the rod to move, which arrived at the speed of light. However due to the drop-off in force (likely on an inverse-square basis) the effect would not be noticed by the person on the other end of the rod. It would be dominated by random fluctuations from the environment.

>>8276901
To summarize:

I remember seeing this exact question asked on /b/ a veeeeery long time ago. And the short answer is, that a perfectly rigid ("Born rigidity") object cannot exist under special relativity. See https://en.wikipedia.org/wiki/Ehrenfest_paradox

The movement of a solid object is a process of sending along information among its constituent particles via the action of a force. This can be seen as analogous to the wave-like pattern of traffic on a congested roadway.

The speed at which this wave of force propagates is also known as the speed of sound. It is mediated by a mixture of classical electrostatic repulsion between electrons, and quantum mechanical processes like Pauli exclusion.

Also note that, unless the rod is kept fairly cold, or the force is applied very quickly and strongly, thermal fluctuations would likely drown out the "signal" sent by the pulse of material strain by the time it finally arrives at the destination.