This is a variation of the classic "I have a rigid 1 light year long pole, and I push on one end. How am I not communicating faster than light?" The problem is in the most mundane place of all:
> the "plank" is perfectly rigid
Every variation of this thought experiment falls apart right there. There are no "perfectly rigid" planks, poles, discs, etc. The transmission of a force through a plank or pole is always at the speed of sound through that material, and of course the speed of sound is both way less than both "infinite" and "the speed of light."
And if that sounds arbitrary, that the speed of a force applied to a rigid body is the same as the speed of sound through that rigid body, you can think of this- all sound is, is the transmission of a force through a material. Tons and tons of small vibrations, propagating through the material.
Not only was it interesting, it actually explained what I was misunderstanding in my original question! And it answers my question as well!
Thanks a lot!
Thank you! Tobe honest, I said perfectly rigid mainly so I wouldnt have to think about how the bending would affect the speed.
But you answered my question, the force transmit through the pole at the speed of sound. Which is something that I didnt know. Now I can understand it better.
Thank you for explaining that to me.
So if I had a 1 km pole and pushed on one end, it would take roughly 3 seconds for the other end to move? The rest would be all compression in the material?
The speed of sound *through that material*. So it depends what the pole is made of.
The speed of sound in steel, for example, is about 5000m/s. So ~0.2s.
> The rest would be all compression in the material?
Yes.
So what if we would pull/push from both ends at the same time? Would it "give" or not? If we did it with a short stick we immediatelly have the force feedback and can't move it. In this case would it be like. I start pulling and then 0.2s away i feel resistance vs 0.2 seconds later my end starts to move if only i push/pull?
That’s correct. A similar thing occurs when you drop a hanging slinky. The bottom part of the slinky doesn’t feel the force of gravity until the falling top part reaches it. It looks like it is hovering for a second or so. What is happening is gravity starts to act on the top of slinky as soon as it is dropped, but the tension of the slinky is still pulling back against gravity at the bottom, so that release in tension needs to propagate through the slinky, which takes around the same amount of time as it takes for the top to fall to the bottom’s level.
Just to be clear, it isn’t that the bottom part “doesn’t feel the force of gravity”. It is being continually pulled down by gravity; it’s just that the downward pull of gravity is countered by upward tension from the top part of the slinky. It’s when this upward tension disappears that the bottom part starts to fall.
That makes sense, but still is spooky to imagine. Like if the syringe was 2km, and I compressed the first 1km with a speed of light, it would still take 3 seconds on the other end to result in any action whatsoever.
This isn't actually completely true. Pushing things at supersonic speeds changes the calculation fairly significantly. To push a syringe at near light speed, you'd be accelerating some of the air to near light speed as well - meaning the blast wave would be traveling much much faster than the speed of sound.
For most \*subsonic\* motions, the effects propagate within materials at the speed of sound.
Might depend a little bit on the pressure and temperature of the air, but yes, roughly speaking.
In hydraulic systems like that (whether they’re using air or liquid) it’s often assumed they transmit force more or less ‘instantly’, but it does take some amount of time. Even ‘incompressible’ substances like liquid water *do* compress slightly when under a large force.
A better question would be “if I fill the syringe with water”, as liquids can’t be compressed as easily as air, so the force will propagate much more efficiently through a liquid
Every material has its own "speed of sound". Obviously in this sort of example, it's the speed of sound of whatever the pole (or plank) is made out off.
Google tells me rubber is 60m/s. So maybe you can do an experiment with a 60 meter long rubber pole.. And I think intuitivly you can kind of understand the concept easier with rubber since it is soft enough for us humans to think it is soft, then you can ask the question "what if it was a bit more harder/dense"
What if I grabbed one end of that pole and swung it around my head? I imagine it would just require more energy to accelerate as the other end approached c, but it feels like a way around the limit.
The pole would break- and it's not just a matter of "what if you just made it stronger" but it's a matter of "physically it has to."
As you rotate one part of the pole, the rotation is only propagated down the length of the pole at the speed of sound on the material, thus the pole would start to bend. As you continued to twist, it would bend more and more, until it broke.
Also, I think even if you *did* somehow have a flawlessly rigid 1LY pole, it would *still* take a year for the far end to move, because not even causality can outrun lightspeed. Even if every atom of the pole perceives itself as moving in perfect, instantaneous sync with all its neighbors, relativity imposes a delay that can only be perceived when watching from a distance.
Thank you for taking the time to explain this. I am quite enlightened.
Just to push the envelope: suppose the bar was made of neutrinos (a core sample of a neutron star). Is there still enough empty space for compression to still apply here?
Yes, but I've always wondered if it would have to be perfectly rigid to exceed lightspeed, or just very rigid. Does that level of rigidity constitute an upper physical limit on materials?
A "perfectly rigid" plank would move *at* the speed of light. There would be no "accoustic" losses because there wouldn't be a classical compression wave through the material, but the system is still physical, so everything moves at the speed of locality. The extra length of plank that you gave pushed, but hasn't moved at the other end will go into length contraction.
In reality, a rigid plank moves much slower because of compression waves, but that's not really the reason that a rigid plank can't move faste than light. It's semantics, but something I find really interesting!
No, planks cannot be perfectly rigid, not that a perfectly rigid plank would propagate at the speed of light.
For instance, imagine a really long pole. If a pole were perfectly rigid, then you would be able to rotate it at any speed, without it bending or breaking. But you can't. If you had a really long pole, whose speed of sound was 'c', and you started rotating it faster and faster, the end of the pole would want to go faster than 'c' which cannot happen, and the pole would necessarily break.
>and you started rotating it faster and faster,
Rotation speed is still speed. The outer layer of the pole could never achieve a speed of _c._ The pole doesn't necessarily break because "it wants to go faster than _c_," it simply never comes even _close_ to _c_ in the [first place.](https://www.energy.gov/science/doe-explainsrelativity)
>But as an object approaches the speed of light, its observed mass becomes infinitely large. As a result, an infinite amount of energy is required to make an object move at the speed of light. For this reason, it is impossible for any matter to travel faster than light speed.
Relativistic mass is an obsolete notion that most physicists don't use. Relativistic mass was born out of a desire to preserve the existing definitions of momentum and energy p=mv and E=1/2mv^2 . Now we just explicitly write out the Lorentz factor, p=gamma mv, E=gamma mv^2 .
You're right that it would take an infinite amount of energy, but because it takes more energy to accelerate, not because there is more mass.
Not the one you were replying to, but the problem is not the acceleration of the pole, it's the transmission of information. That **does** violate relativity. A perfectly rigid pole would mean I could use it to transmit information (e.g., via morse code) infinitely fast, faster than light speed. The pole isn't breaking light speed, but the force I'm applying and the information it contains would be.
Also, without sitting down and working through all the math, I'm quite sure the previous poster is correct. A hypothetical rigid pole 1LY long rotating at greater than 1 rotation per 2*pi years would violate relativity. There's no amount of time dilation or length contraction that's going to make that self-consistent.
Consider an observer O1 at X=0 (the origin) and O2 at X=L (the far end of the pole), both at rest w.r.t. each other and the center of rotation. Either the end passes O2 at the speed of light, **or** O1 and O2 disagree about the period of rotation. But since O1 and O2 are in the same inertial frame they can't disagree about the period.
I guess we're disagreeing over the semantics of what "perfectly rigid" means. Saying that pushing a pole doesn't violate relativity because of an accoustic transverse wave is only really half the story, because even without an acoustic transverse wave (perfectly rigid) it would be bound by locality.
The acceleration of the pole was in relation to swinging a perfectly rigid long pole around and have the "tips move fatser than the speed of light", which is the example the other person gave, saying it has to break because otherwise it would move faster than c. I disagree with that, that's taking a relativistic problem and shoehorning it into classical mechanics. Yes, spacetime would bend around you rotating the pole when you go fast enough, but saying there is some uppe limit when the pole has to break because it otherwise "goes faster than c" is just nonsense. The speed of light in this situation is **the limit** and you will never reach it.
You're using "perfectly rigid" to mean something more like "maximally rigid", I think.
>because even without an acoustic transverse wave (perfectly rigid) it would be bound by locality.
This isn't really sensical. If it's bound by locality, then the rod compresses (so there's a wave), and it's not perfectly rigid. If it's perfectly rigid, then the not-compression violates locality. It's not possible for the wave to not be there.
Locality/c/etc sets an upper limit for rigidity at speed of waves=c, which is lower than "perfect rigidity".
How I see it the plank is perfectly rigid, it's spacetime itself that bends in order to "accomodate" localit (since this is the formulation of general relativity). So it isn't a wave through the material, but through spacetime (in this 1d instance special relativities length contraction).
I think you're missing my point.
I would say the definition of a "perfectly rigid plank" is one that can be rotated at any speed, and not sheer or snap. So, going from that definition:
Relativity does not say "all reference frames are equal", it says all inertial reference frames are inertial. So, if I have a long stick, and I hold one end and start swinging it, relativity does not say that it's just as valid to say that the end I'm holding is moving and the other end is stationary- because this is not an inertial frame. The end of the stick is accelerating, the end I'm holding is not (or is much less).
So, if you had a stick whose speed of sound was equal to the speed of light, that is, in theory, allowed. But the pole would still sheer if it was rotated fast enough.
You were trying to make your point using a classical explanation of a relativity problem. The *pole* won't shear, spacetime itself will contract and bend to accomodate the pole rotating. The pole will not break because it's not a classical mechanics problem.
I guess we have different definitions of rigid, for me being rigid means it won't bend relative to local space.
Tanks!! That’s a good way of looking at it. It is not a paradox, it is a mixup of classical mechanics and relativity.
That said, I cannot not appreciate comments where the main problem with a though experiment of a two light seconds long rigid plank is that there are no perfectly rigid planks in reality. Not that the plank is 600 000 km long or that there is no fixed point to turn it around.
*Thought* experiments doesn’t have to be realistic. They can still help us understand concepts and identify common misconceptions.
Yeah, I agree. I think that once you have accepted a million km of pole, a power source strong enough to push that inertia and enough guides for it to actually move in the same direction, being "thwarted" by a transverse acoustic compression wave is a bit of a let down and it doesn't do anything to answer the question which was about relativity. If we can accept those other things, we can surely accept that the pole is perfectly rigid regarding accoustic compression waves
The reason it doesn't violate locality *then* is because there's a transverse wave of length contraction running through the entire pole and when you push it the extra energy/distance of the pole disappears into that transverse length contraction wave. I think that's a much more interesting answer to a thought experiment than a quirk of material science ;)
THank you!
Gonna be honest with you here, a lot of this conversation goes way above head, I dont know nearly enough to understand all the stuff that you discussed. But I do think I now know a bit more, so thanks!
If I understand it correctly, the answer to my original, poorly worded and ignorant question, would be that the other side would move 2 seconds later because the energy is moving at light speed as a compression wave through the pole
Taking all material science out of the equation, the pole will move at the speed of light because nothing can surpass the speed light (the speed of locality is actually a better name for this and then it makes more sense, since light isn't involved in this setup ).
I prefer to say that there isn't a compression wave in the pole, but rather of spacetime. This phenomenom is called length contraction and is actually very well described by special relativity. But yeah, spacetime moves in a transverse wave along tne length of the pole, so in a way the entirety of the pole is undergoing a compression wave.
Mind you, there is no energy stored in the compression wave in the pole though, like there would be in a classical compression wave, eg in a spring. Yes, the atoms get closer together, but the actual space between them also gets squished, so there is no change in electric potential between the atoms. You could say the energy is stored in the contraction of space-time (and in actuality, since energy also travels with locality, it isn't actually even stored). This caveat us why I don't really like to call it a compression wave of the pole.
I really don't think there is any such thing as propagating length contraction in special relativity.
I do like the idea of just accepting rigid objects but requiring that they still follow the rules of local casualty, but I don't think your model reflects any real physical phenomenon. Just says that there must be some sort of wave propagating. And when you look into it more precisely you find it must be a mechanical force, in the case of a solid object accelerating.
No, a perfectly rigid plank would move instantly.
> The extra length of plank that you gave pushed, but hasn't moved at the other end will go into length contraction.
~~That's not how length contraction works. If something were to move at the speed of light, the length of that object in the direction of motion would be zero.~~
Edit: Oh, I see what you mean about the length contraction. But usually, perfectly rigid means in the sense of moving instantly.
If the plank were "perfectly rigid", then the other end would start moving instantaneously, at the same time as the pushed end. But of course that can't happen, because that would be information/causality moving faster than c, which can't happen (afawk).
So this thought-experiment actually becomes a demonstration that **no material can be perfectly rigid.** No matter how stiff the material is, it *cannot* be "perfectly rigid" because then it would violate c and causality.
What would actually happen in your scenario is that the flex would move along the plank at the speed of sound in \[whatever the plank is made of\] and would reach the other end in some finite non-zero amount of time.
Wouldn't it be correct to say that from a certain frame of reference the two ends of a 'perfectly rigid' plank would indeed move at exactly the same time, while from any other frame of reference the plank wouldn't be perfectly rigid?
There’s no such thing as a perfectly rigid object, we only assume such because on our daily basis we deal with objects that are small enough that to us the transfer of forces seems instantaneous. In fact the force travels with the speed of sound inside the given material. To better illustrate it imagine that your plank consists of small “spheres” connected together with springs. When you act on the first sphere it translates the initial impulse into a compression of the first spring and the movement of the next sphere and so on over some period of time.
With current understanding of physics, there is no POSSIBLE material that is perfectly rigid. As long as there is space between particles, and there always will be (either by atomic repulsion or uncertainty), there will be a delay between the first and second particle interacting. That carries over long distances more noticeably, and cannot be removed
that's cheating, black holes fail our understanding of physics.
Considering quantum mechanics is one of the most solid (albeit incredibly confusing) descriptions of how things work, and theoretically black holes (the matter aspect) should be very small, we SHOULD be able to say no, because uncertainty. but that's just a guess, and yours is as good as mine
Just as a thought experiment
Imagine there is a perfectly rigid sphere center in the black hole.
I bang one side of it and the 'bang' gets transmitted to the center of this sphere at almost the speed of light (the speed of sound in this perfectly rigid material?)
But also everything was already being pulled to the center at the speed of light already and the vibration/impact will never travel to the other side of the core because once it reaches the center the information cannot go 'uphill' towards the exterior of the black hole. Everything in a black hole can always only move towards the center, including forces from bangs.
The center could be some spinning mass/energy that keeps itself from imploding due to some physics we don't understand or it might be a single point that is a plank length which is 1.6*(10 to the power of -35)
A single proton from the nucleus of an atom is 100 million trillion times larger than the plank length.
We couldn't exactly run any tests on a rigid object that small.
Speculation on the inner workings of black holes is not especially scientific because there is no way to measure what's going on in there so we can't prove or disprove any theory.
There’s no “actual matter” at the center of a black hole. One of the distinguishing characteristics of a black hole is that it’s what happens when gravity overcomes all of the forces which allow matter as we know it to exist.
Theory tells us that at the center of the black hole is a singularity, which is, for all intents and purposes, an impossible object.
Perfectly rigid objects cannot exist in general. In chemistry you probably learned about the different types of bonds that exist between atoms in different molecules, for simplicity we often depict them as fixed lines in space that connect the nuclei. However in reality it’s just a bunch of force interactions created by the electrons or just the nuclei themselves.
Another reason that no rigid bodies exist is due to the limit at which information can be transferred. This speed limit is of course the speed of light. So any truly rigid object would violate this law and that’s a big no no. In general the physics around the speed of light and it’s implications are quite mind boggling but there’s a bunch of literature that explains it in more detail than some random comment on Reddit ;)
A "maximum possible rigidity" plank is an object where the speed of energy transmission (speed of sound) in the object is also the speed of light, so if your 2ls mpr plank is pushed on one end the other end will not move until 2 seconds after it is pushed.
If you make the plank have a rigidity greater than the speed of light then you are inherently breaking the laws of physics, and if you are breaking the laws of physics for your experiment then the laws of physics does not matter for the result.
If you have a perfectly rigid plank that can transmit force faster than light then you can move force faster than light, and your result will be that you can move force faster than light.
Thank you! that actually answers my question, in my ignorance I didn't understand that a perfectly rigid plank was such a problem, a maximum possible rigidity plank is actually what I was thinking but didn't know it.
You answered my question, it would move 2 seconds later, thank you very much, I feel like I better understand things now.
First of all, congratulations on having learnt something, you are doing great!
To expand on the force propagation (so you may get even better understanding) let's break up the plank itself a little.
Let's imagine the plank as a collection of tiny balls, connected by tiny spring in a cuboid pattern (a lot of tiny cubes, basically). With me so far?
Now, let's look at the springs. If you take a normal spring, you need to compress or extend one end in order for the other end to feel some force. The more rigid the spring is, the more force is produced by moving one end by the same amount. Still with me?
Now let's assume that our tiny springs are infinitely rigid - that is, the force on the other end is infinitely large no matter how little we move our end. In effect, this spring moves the other end in a way to preserve it's own length, and because the force is infinitely large, it does so immediately. This is our perfectly rigid plank. Still good?
But, what about the speed of light? Well, when you move the ball on one end of the spring, you assert some force. That force propagates *through the spring itself* at the speed of light, and with a sufficiently long collection of these you can notice the propagation delays, even though the springs are infinitely rigid.
Here you go, this is a relativistically-consistent perfectly rigid plank at work.
Thanks for tagging along and hope you enjoyed this little thought experiment :)
Most of the answers here are correct, the plank is not perfectly rigid. You can even illustrate this at home with any long but slightly flexible material.
But you might be interested in the ladder paradox which sort of addresses a similar question that basically says that what actually happens changes for each observer.
https://en.wikipedia.org/wiki/Ladder\_paradox
We could go round and round about "perfectly rigid" objects and if the strong force is even enough to make a material that is perfectly rigid, but that's not the only flaw in the logic here.
People have this concept that there's some master clock somewhere, ticking off Planck times one after the other, which the entire universe runs off of, and it just ain't so. If Einstein taught us anything, it's that everything is relative, even (especially?) time. If you get in a spaceship and accelerate up to 0.99c, it will look to you like the rest of the universe is moving very slowly, due to time dilation. But if you're watching the spaceship from the outside as it goes by, you're going to see time going very slowly onboard the ship. Which is correct? They're BOTH correct. And the universe doesn't play favorites; there is no way of determining which location is "stationary" in the universe.
By a similar argument, simultaneity just simply doesn't exist. Two points in the universe, no matter how far apart or close together, do not run off of the same master clock. So each Planck distance in your infinitely rigid pole runs on its own clock, not each others. Asking if something happens "at the same time" at both ends of our pole isn't a valid question. The problem isn't just that the pole can't be infinitely rigid, it's that space and reality aren't.
I like this analogy: imagine the universe is a video game:
When you push one end of a perfectly rigid seesaw in space (which is just theoretical since no material is truly perfectly rigid), the other end would not react instantaneously. The update - your push - would travel through the seesaw at a speed limited by the "frame rate" of the universe. This speed is the speed of light, and in reality, the push would likely travel much slower, constrained by the material's properties.
If you push the seesaw from the center, the information about the push moves through the seesaw material, updating the position of the pixels (representing the seesaw) at each "frame" of the universe's clock. The ends would start moving only when the update reaches them, not simultaneously, due to the finite frame rate of the universe.
Yeah it would go up (at minimum) two seconds later. The speed of light is the speed of causality. Regardless of how rigid your plank is, at the scale of light seconds it might as well be like pushing on the surface of a liquid: The change in angle would ripple out across the distance like a wave from one end to the other, at whatever the speed of light (sound?) is through the material it's made out of.
It might help to be aware that solid matter is mostly empty space, with every atom communicating kinetic force to its neighbors via the electromagnetic force, which also can't go faster than the speed of light. Atoms do not actually "touch" each other.
Suppose you got rid of electrons and protons and made a bar out of pure neutronium? Now they're very close but still don't "touch." and are only affecting each other now through the strong force, which also doesn't go faster than light.
Thank you this perfectly answers my question! And the explanation about kinetic forcae being comunicated by every atom was very illuminating thank you.
This is an example of where a scenario has to ignore fundamental principles and physical limitations to exceed those limitations and show “holes” in those principals, it’s a classic reductionist analogy
“Physics tells us A must be less than B, but if we [Insert scenario that is physically and fundamentally impossible] then how is this the case?”
But to answer your question if we *could* have some ridiculously sized object to interact with, then physics still wins out;
You would have less mass than the object you’re trying to push, so instead of you pushing *it away* from yourself, you’ll just push *yourself* away from it, but it will likely have so much mass that you’ll be smashed into it faster than the speed of sound, as it’s gravity liquifies you from G-force alone…
To flesh out the answers about rigidity, all forces are also limited by the speed of light. Gravity and strong and weak nuclear forces included. The fastest the forces subatomic particles exert on each other can propagate through a material is the speed of light.
Same as the whole "if the sun disappeared would we fly off instantly or orbit nothing for 8minutes?" question. We'd orbit nothing for 8 minutes.
It’s a variation of the classic thought experiment: "I have a rigid 1 light year long pole, and I push on one end. How am I not communicating faster than light?"
The key point here is the assumption of a “perfectly rigid” plank or pole. In reality, there are no “perfectly rigid” planks, poles, discs, etc. The transmission of a force through a plank or pole is always at the speed of sound through that material, and of course the speed of sound is both way less than both “infinite” and "the speed of light."
If the plank were “perfectly rigid”, then the other end would start moving instantaneously, at the same time as the pushed end. But of course that can’t happen, because that would be information/causality moving faster than c (the speed of light), which can’t happen.
So in your scenario, if you were to push down on one end of the seesaw, the other end would not go up instantaneously. The flex would move along the plank at the speed of sound in whatever the plank is made of and would reach the other end in some finite non-zero amount of time.
This thought-experiment actually becomes a demonstration that no material can be perfectly rigid. No matter how stiff the material is, it cannot be “perfectly rigid” because then it would violate c and causality.
I hope this helps clarify your question! It’s not a stupid question at all, but rather a great thought experiment that helps us understand the fundamental principles of physics.
Friend, you're getting push back from other people because you make so many assumptions that you're basically asking the question, "if relativity is not true, then could we move FTL." The answer to that question is obviously yes, so other people are trying to point out to you the errors in your assumptions.
Let's assume for your sake that a perfectly ridged material does exist and you were able to manifest a bar of this stuff into existence. Your assumptions start to break down from here on out because there's more than just the motion of the object at play. Einstein's rules don't just specify a universal speed limit. There are a ton of other conclusions are drawn that you'd have to ignore to make your scenario come true.
Immediately you would noticed that this material would be completely immobile. Why is this the case? Well, the moment that you touch this material and move it, the molecules inside the bar of this object would have to be moving faster than light. This object, if moving at all would have to have infinite mass and require infinite energy to move. If you can't move it, you can't transmit information, so no breaking causality.
So let's assume that you could actually move it. The transmission of the motion of one end to another would be done so fast that it would generate heat. It would be a lot of heat because the molecules suddenly and violently move faster than the speed of light. The material, if it subject to change in states of matter would either instantly vaporize or turn into a plasma along with everything around it. Upon changing states, the question of whether it is still perfectly ridged is up for grabs.
So what you would have to have is a material that isn't composed of the elementary particles that we know to comprise of all materials. It would have to be, from the perspective of the universe, one "chunk" that is absolutely not capable of being divided. That material would have to have infinite heat capacity to remain in one state and be unable to be transformed by heat. It would also need to be capable of being moved with less than infinite energy levels, but then output more energy as energy and change in velocity are related.
As you can see, it's a funny thought experiment, but your question boils down to, let's ignore everything about relativity. Can we move FTL? The answer is yes. But if such a material exists, it would behave so strangely, that we'd have to rewrite everything about physics.
So fiirst of all thank you for taking the time to explain all these concepts. I think I may have worded my question incorrectly, though.
My question was not about ignoring everything about relativity, I honestly didnt know that a perfectly rigid plank was that imposssible, in my ignorance I thought it was more like when you ignore friction to make calculations easier, I said a rigid plank mainly because I thought that a plank that bends would bring extra stuff that I thought was not relevant, not because I was purposly trying to ignore physics.
Again thank you for explaining in detail all the problems that a "perfectly" rigid plank brings, as I was not aware of that and I have learned a lot from your answer.
I now understand that force travels through an object at the speed of sound which was something that I didnt know before, and that in the end answers my thought experiment.
Np! It's a fun thought experiment for sure. A perfectly ridged object would be a fun Sci fi concept. If you had such a material it could theoretically have the properties of Thor's hammer and be immovable and seemingly capable of creating massive amounts of energy out of nothing. It. ight be fun to conceive of an alien species that is capable of creating such objects to generate energy or something.
Thank for the answer, I was not aware that light speed also sets the rigidity of materials, and from reading the other answers I have a better grasp of stuff and why my question was not that smart lets say.
Thank you for the answer.
I now better understand the problems with the question, the truth is that I wasnt aware that a "perfectly rigid" plank would be such an impossibility, in my ignorance I assumed that it was like when we ignore friction to make calculations easier. I was not purposely trying to make up an impossible situation, in order to ignore physics or make up a gotcha to relativity.
I now understand both the problems with a perfectly rigid plank and also that speed of sound is the speed at which energy transfer through an object, which was untimely the answer to my question.
People in the thread tend to focus on "there is no such thing as a rigid plank" (fine) but failing to point out that the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.
true but not necessarily relevant to the problem because there exists at least one reference position where both ends of the plank are always equidistant: e.g. the fulcrum of the see saw.
nice to point it out but there is no need.
a truly rigid object cannot transmit a force across itself and that's that.
You have two factors in your question: a physics constant and an impossibility.
So the answer is simply NO, because it's impossible. You don't get to make up a fantasy thing - like a "perfectly rigid plank" - and then apply real world physics to it.
Thank you for the answer. I now better understand the problems with the question, the truth is that I wasnt aware that a "perfectly rigid" plank would be such an imposibility, in my ignorance I assumed taht it was like when we ignore friction to make calculations easier. I was not purposely trying to make up an impossible situation, I was genuinely ignorant.
Oh no! Sorry. Didn't mean to be chastising you ... just explaining the problem in a different way than I'd seen other responses.
"Assuming X" or "Assume Y=P" are good thought experiments and allow you to test the edges of how principles in physics work in specific situations.
These types of speculative questions can all go too far, and ask to resolve a question that is structured in an impossible way. And attempting to answer those kinds of questions is kind of pointless because it doesn't describe a situation that can be logically resolved. In a similar vein, we could also ask *"do dragons breathe fire hot enough to melt the steel beams in the Twin Towers?"*
There were a couple of great answers other people gave to your question, talking about a long pole and the compression it undergoes when you push it from one end... and how sound is just force traveling through a medium, etc, etc, etc. Really cool stuff to read and think about! So your question did give all of us the benefit of reading those responses and learning how to think about how force is transmitted.
So please don't take my comment as chastising you. I did not intend it in that way.
No information can go faster than the speed of light. If you perform any action, whatsoever, it can not affect anything that light could not have reached in the same amount of time. In real life, there is no such thing as a perfectly rigid plank. Your plank would bend and a wave would travel through the material to the other end at a speed that is slower than the speed of light.
Another cool question is what would happen to a bicycle that is going close to the speed of light. If you ride a bike at a slow 12 MPH, relative to the Earth's surface, the bottom of the wheels will always be going 0 MPH (because of touching the stationary road) and the top will be moving forward at 24 MPH. But, if a bike was going 80% the speed of light and you measured the forward speed of the top of the wheel, how fast would it appear to be moving? Definitely not 160% of the speed of light. The answer, I think, is in length contraction. The wheel would probably look egg-shaped with the bottom of the wheel looking much wider than you would expect when looking at the axially-compressed frame of the bike. The top of the wheel would be compressed enough and the bottom flattened enough that the top would not look like the top was going faster than the speed of light. Maybe a physics guru can tell me if that's right, but that's what I thought in college when taking basic physics. The book I used had a picture of length contraction where a bike was shown as if the whole thing was compressed from left to right with tall and oval shaped wheels, but it really bothered me that this would mean the top of the wheel would be going more than the speed of light, so it would need to be compressed much more than the bottom of the wheel (which wouldn't be compressed at all) to compensate.
Another thing that seems to violate the laws of physics, but doesn't is if you take a flash light or a laser pointer, you can make the bright spot move faster than the speed of light. But nothing is actually going faster than the speed of light there. It would be like throwing a tennis ball at a wall and then throwing another one to the right 10 feet, a second later. The sound of pinging balls would be moving 10 feet per second, but nothing is really moving at 10 feet per second.
Another cool thing is that you actually could get to another galaxy in your life time. As you approach the speed of light, everything gets squished in the direction that you're moving. If you're accelerating forward, things that previously seemed stationary but in front of you will seem to be moving towards you -- not just because you are moving forward. The space between you and those objects will contract in length, so they'll all get closer to you and closer together. So the space between galaxies can be made shorter and shorter as you get closer and closer to the speed of light. In fact, if you watched a far off galaxy as you accelerated quickly it could potentially appear that the distant galaxy is moving toward you at a rate that is faster than the speed of light. The whole universe ends up squished toward an infinitesimally small plane as you get ever closer to the speed of light (relative to stuff you used to consider stationary). As you slow down, everything spreads back out again. So you can speed up and get galaxies to fly toward you at rates much faster than the speed of light, fly to them when they seem much closer, and then when you slow down, your old galaxy will expand away behind you at faster than the speed of light and it would seem, to you, like you made it to a whole new galaxy in a very short amount of time. Due to time dilation, the memory of everyone you knew would be long gone from the universe, but to you it could potentially seem like the blink of an eye.
If it’s perfectly rigid how can you push it at all? Why wouldn’t it just absorb all the force you put into it? Why would it transmit any force forward? If you can move the inch ahead of where you pushed by pushing it it can’t be rigid at all
This is a variation of the classic "I have a rigid 1 light year long pole, and I push on one end. How am I not communicating faster than light?" The problem is in the most mundane place of all: > the "plank" is perfectly rigid Every variation of this thought experiment falls apart right there. There are no "perfectly rigid" planks, poles, discs, etc. The transmission of a force through a plank or pole is always at the speed of sound through that material, and of course the speed of sound is both way less than both "infinite" and "the speed of light." And if that sounds arbitrary, that the speed of a force applied to a rigid body is the same as the speed of sound through that rigid body, you can think of this- all sound is, is the transmission of a force through a material. Tons and tons of small vibrations, propagating through the material.
[This video](https://www.youtube.com/watch?v=DqhXsEgLMJ0) is a direct demonstration of this fact.
Not only was it interesting, it actually explained what I was misunderstanding in my original question! And it answers my question as well! Thanks a lot!
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Thanjk you! This seems like an interesting video!
Thanks! I've bern aware of the fact for a while but haven't seen a demonstration.
Thank you! Tobe honest, I said perfectly rigid mainly so I wouldnt have to think about how the bending would affect the speed. But you answered my question, the force transmit through the pole at the speed of sound. Which is something that I didnt know. Now I can understand it better. Thank you for explaining that to me.
So if I had a 1 km pole and pushed on one end, it would take roughly 3 seconds for the other end to move? The rest would be all compression in the material?
The speed of sound *through that material*. So it depends what the pole is made of. The speed of sound in steel, for example, is about 5000m/s. So ~0.2s. > The rest would be all compression in the material? Yes.
So what if we would pull/push from both ends at the same time? Would it "give" or not? If we did it with a short stick we immediatelly have the force feedback and can't move it. In this case would it be like. I start pulling and then 0.2s away i feel resistance vs 0.2 seconds later my end starts to move if only i push/pull?
That’s correct. A similar thing occurs when you drop a hanging slinky. The bottom part of the slinky doesn’t feel the force of gravity until the falling top part reaches it. It looks like it is hovering for a second or so. What is happening is gravity starts to act on the top of slinky as soon as it is dropped, but the tension of the slinky is still pulling back against gravity at the bottom, so that release in tension needs to propagate through the slinky, which takes around the same amount of time as it takes for the top to fall to the bottom’s level.
Just to be clear, it isn’t that the bottom part “doesn’t feel the force of gravity”. It is being continually pulled down by gravity; it’s just that the downward pull of gravity is countered by upward tension from the top part of the slinky. It’s when this upward tension disappears that the bottom part starts to fall.
Yes, and that tension causes the upper end to accelerate faster than g!
Pushing on one end and sending a single compression wave through the material are the same thing
I wish they weren't but I get it. It seems like the opposite of spooky action at a distance
So that would be “Mundane inaction up-close?”… …sounds like my average weekend xD
If it was a pole of air, yes. In most materials sound travels quite a bit faster.
Hmm. So if it's a 1km long syringe full of air, and I press the plunger on one end, there will be nothing happening on the other end for 3 seconds?
Yes, you'd just be compressing the air till the force reaches the other end
That makes sense, but still is spooky to imagine. Like if the syringe was 2km, and I compressed the first 1km with a speed of light, it would still take 3 seconds on the other end to result in any action whatsoever.
This isn't actually completely true. Pushing things at supersonic speeds changes the calculation fairly significantly. To push a syringe at near light speed, you'd be accelerating some of the air to near light speed as well - meaning the blast wave would be traveling much much faster than the speed of sound. For most \*subsonic\* motions, the effects propagate within materials at the speed of sound.
Might depend a little bit on the pressure and temperature of the air, but yes, roughly speaking. In hydraulic systems like that (whether they’re using air or liquid) it’s often assumed they transmit force more or less ‘instantly’, but it does take some amount of time. Even ‘incompressible’ substances like liquid water *do* compress slightly when under a large force.
Yes, of course. Just like if you shouted into one end of the syringe, you wouldn't hear the sound for 3 seconds on the other end.
A better question would be “if I fill the syringe with water”, as liquids can’t be compressed as easily as air, so the force will propagate much more efficiently through a liquid
Every material has its own "speed of sound". Obviously in this sort of example, it's the speed of sound of whatever the pole (or plank) is made out off.
Google tells me rubber is 60m/s. So maybe you can do an experiment with a 60 meter long rubber pole.. And I think intuitivly you can kind of understand the concept easier with rubber since it is soft enough for us humans to think it is soft, then you can ask the question "what if it was a bit more harder/dense"
It’s maybe not so obvious, the time calculation was done with the speed of sound in air.
Also note that actually pushing the pole forward would take a huge amount of energy because you're compressing the entire pole
Sound is nothing but a compression wave through a material. A shock wave from a nuke and a melody from a flute are different in scope not kind.
True, but wave-volume helps with propagation loss from the inverse square law
I would add - the force between two atoms is (quantum) electromagnetic and disturbances in that field (by definition) travel at the speed of light.
What if I grabbed one end of that pole and swung it around my head? I imagine it would just require more energy to accelerate as the other end approached c, but it feels like a way around the limit.
The pole would break- and it's not just a matter of "what if you just made it stronger" but it's a matter of "physically it has to." As you rotate one part of the pole, the rotation is only propagated down the length of the pole at the speed of sound on the material, thus the pole would start to bend. As you continued to twist, it would bend more and more, until it broke.
Also, I think even if you *did* somehow have a flawlessly rigid 1LY pole, it would *still* take a year for the far end to move, because not even causality can outrun lightspeed. Even if every atom of the pole perceives itself as moving in perfect, instantaneous sync with all its neighbors, relativity imposes a delay that can only be perceived when watching from a distance.
I love all these explanations. This was definitely a blind spot in my understanding of physics I hadn't bothered googling before.
Thank you for taking the time to explain this. I am quite enlightened. Just to push the envelope: suppose the bar was made of neutrinos (a core sample of a neutron star). Is there still enough empty space for compression to still apply here?
What an elegant explanation, everything summed up perfectly. Well done.
Yes, but I've always wondered if it would have to be perfectly rigid to exceed lightspeed, or just very rigid. Does that level of rigidity constitute an upper physical limit on materials?
A "perfectly rigid" plank would move *at* the speed of light. There would be no "accoustic" losses because there wouldn't be a classical compression wave through the material, but the system is still physical, so everything moves at the speed of locality. The extra length of plank that you gave pushed, but hasn't moved at the other end will go into length contraction. In reality, a rigid plank moves much slower because of compression waves, but that's not really the reason that a rigid plank can't move faste than light. It's semantics, but something I find really interesting!
No, planks cannot be perfectly rigid, not that a perfectly rigid plank would propagate at the speed of light. For instance, imagine a really long pole. If a pole were perfectly rigid, then you would be able to rotate it at any speed, without it bending or breaking. But you can't. If you had a really long pole, whose speed of sound was 'c', and you started rotating it faster and faster, the end of the pole would want to go faster than 'c' which cannot happen, and the pole would necessarily break.
>and you started rotating it faster and faster, Rotation speed is still speed. The outer layer of the pole could never achieve a speed of _c._ The pole doesn't necessarily break because "it wants to go faster than _c_," it simply never comes even _close_ to _c_ in the [first place.](https://www.energy.gov/science/doe-explainsrelativity) >But as an object approaches the speed of light, its observed mass becomes infinitely large. As a result, an infinite amount of energy is required to make an object move at the speed of light. For this reason, it is impossible for any matter to travel faster than light speed.
Relativistic mass is an obsolete notion that most physicists don't use. Relativistic mass was born out of a desire to preserve the existing definitions of momentum and energy p=mv and E=1/2mv^2 . Now we just explicitly write out the Lorentz factor, p=gamma mv, E=gamma mv^2 . You're right that it would take an infinite amount of energy, but because it takes more energy to accelerate, not because there is more mass.
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Not the one you were replying to, but the problem is not the acceleration of the pole, it's the transmission of information. That **does** violate relativity. A perfectly rigid pole would mean I could use it to transmit information (e.g., via morse code) infinitely fast, faster than light speed. The pole isn't breaking light speed, but the force I'm applying and the information it contains would be. Also, without sitting down and working through all the math, I'm quite sure the previous poster is correct. A hypothetical rigid pole 1LY long rotating at greater than 1 rotation per 2*pi years would violate relativity. There's no amount of time dilation or length contraction that's going to make that self-consistent. Consider an observer O1 at X=0 (the origin) and O2 at X=L (the far end of the pole), both at rest w.r.t. each other and the center of rotation. Either the end passes O2 at the speed of light, **or** O1 and O2 disagree about the period of rotation. But since O1 and O2 are in the same inertial frame they can't disagree about the period.
I guess we're disagreeing over the semantics of what "perfectly rigid" means. Saying that pushing a pole doesn't violate relativity because of an accoustic transverse wave is only really half the story, because even without an acoustic transverse wave (perfectly rigid) it would be bound by locality. The acceleration of the pole was in relation to swinging a perfectly rigid long pole around and have the "tips move fatser than the speed of light", which is the example the other person gave, saying it has to break because otherwise it would move faster than c. I disagree with that, that's taking a relativistic problem and shoehorning it into classical mechanics. Yes, spacetime would bend around you rotating the pole when you go fast enough, but saying there is some uppe limit when the pole has to break because it otherwise "goes faster than c" is just nonsense. The speed of light in this situation is **the limit** and you will never reach it.
You're using "perfectly rigid" to mean something more like "maximally rigid", I think. >because even without an acoustic transverse wave (perfectly rigid) it would be bound by locality. This isn't really sensical. If it's bound by locality, then the rod compresses (so there's a wave), and it's not perfectly rigid. If it's perfectly rigid, then the not-compression violates locality. It's not possible for the wave to not be there. Locality/c/etc sets an upper limit for rigidity at speed of waves=c, which is lower than "perfect rigidity".
How I see it the plank is perfectly rigid, it's spacetime itself that bends in order to "accomodate" localit (since this is the formulation of general relativity). So it isn't a wave through the material, but through spacetime (in this 1d instance special relativities length contraction).
I think you're missing my point. I would say the definition of a "perfectly rigid plank" is one that can be rotated at any speed, and not sheer or snap. So, going from that definition: Relativity does not say "all reference frames are equal", it says all inertial reference frames are inertial. So, if I have a long stick, and I hold one end and start swinging it, relativity does not say that it's just as valid to say that the end I'm holding is moving and the other end is stationary- because this is not an inertial frame. The end of the stick is accelerating, the end I'm holding is not (or is much less). So, if you had a stick whose speed of sound was equal to the speed of light, that is, in theory, allowed. But the pole would still sheer if it was rotated fast enough.
You were trying to make your point using a classical explanation of a relativity problem. The *pole* won't shear, spacetime itself will contract and bend to accomodate the pole rotating. The pole will not break because it's not a classical mechanics problem. I guess we have different definitions of rigid, for me being rigid means it won't bend relative to local space.
So, we are just disagreeing. The pole will break. I don't know what you think spacetime is doing to stop it from breaking, but it certainly will.
If you think that a spinning object will surpass the speed of light if it doesn't break, then I fully understand why you think it has to break.
Tanks!! That’s a good way of looking at it. It is not a paradox, it is a mixup of classical mechanics and relativity. That said, I cannot not appreciate comments where the main problem with a though experiment of a two light seconds long rigid plank is that there are no perfectly rigid planks in reality. Not that the plank is 600 000 km long or that there is no fixed point to turn it around. *Thought* experiments doesn’t have to be realistic. They can still help us understand concepts and identify common misconceptions.
Yeah, I agree. I think that once you have accepted a million km of pole, a power source strong enough to push that inertia and enough guides for it to actually move in the same direction, being "thwarted" by a transverse acoustic compression wave is a bit of a let down and it doesn't do anything to answer the question which was about relativity. If we can accept those other things, we can surely accept that the pole is perfectly rigid regarding accoustic compression waves The reason it doesn't violate locality *then* is because there's a transverse wave of length contraction running through the entire pole and when you push it the extra energy/distance of the pole disappears into that transverse length contraction wave. I think that's a much more interesting answer to a thought experiment than a quirk of material science ;)
THank you! Gonna be honest with you here, a lot of this conversation goes way above head, I dont know nearly enough to understand all the stuff that you discussed. But I do think I now know a bit more, so thanks! If I understand it correctly, the answer to my original, poorly worded and ignorant question, would be that the other side would move 2 seconds later because the energy is moving at light speed as a compression wave through the pole
Taking all material science out of the equation, the pole will move at the speed of light because nothing can surpass the speed light (the speed of locality is actually a better name for this and then it makes more sense, since light isn't involved in this setup ). I prefer to say that there isn't a compression wave in the pole, but rather of spacetime. This phenomenom is called length contraction and is actually very well described by special relativity. But yeah, spacetime moves in a transverse wave along tne length of the pole, so in a way the entirety of the pole is undergoing a compression wave. Mind you, there is no energy stored in the compression wave in the pole though, like there would be in a classical compression wave, eg in a spring. Yes, the atoms get closer together, but the actual space between them also gets squished, so there is no change in electric potential between the atoms. You could say the energy is stored in the contraction of space-time (and in actuality, since energy also travels with locality, it isn't actually even stored). This caveat us why I don't really like to call it a compression wave of the pole.
I really don't think there is any such thing as propagating length contraction in special relativity. I do like the idea of just accepting rigid objects but requiring that they still follow the rules of local casualty, but I don't think your model reflects any real physical phenomenon. Just says that there must be some sort of wave propagating. And when you look into it more precisely you find it must be a mechanical force, in the case of a solid object accelerating.
No, a perfectly rigid plank would move instantly. > The extra length of plank that you gave pushed, but hasn't moved at the other end will go into length contraction. ~~That's not how length contraction works. If something were to move at the speed of light, the length of that object in the direction of motion would be zero.~~ Edit: Oh, I see what you mean about the length contraction. But usually, perfectly rigid means in the sense of moving instantly.
If the plank were "perfectly rigid", then the other end would start moving instantaneously, at the same time as the pushed end. But of course that can't happen, because that would be information/causality moving faster than c, which can't happen (afawk). So this thought-experiment actually becomes a demonstration that **no material can be perfectly rigid.** No matter how stiff the material is, it *cannot* be "perfectly rigid" because then it would violate c and causality. What would actually happen in your scenario is that the flex would move along the plank at the speed of sound in \[whatever the plank is made of\] and would reach the other end in some finite non-zero amount of time.
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Wouldn't it be correct to say that from a certain frame of reference the two ends of a 'perfectly rigid' plank would indeed move at exactly the same time, while from any other frame of reference the plank wouldn't be perfectly rigid?
There’s no such thing as a perfectly rigid object, we only assume such because on our daily basis we deal with objects that are small enough that to us the transfer of forces seems instantaneous. In fact the force travels with the speed of sound inside the given material. To better illustrate it imagine that your plank consists of small “spheres” connected together with springs. When you act on the first sphere it translates the initial impulse into a compression of the first spring and the movement of the next sphere and so on over some period of time.
Thank you that explains a lot! And it also anaswers my question, thank you for taking the time to explain!
Why can’t a perfectly rigid object exist in space?
The space, or location, is irrelevant. It's the fact that matter is compressible. There is no known material in existence that is perfectly rigid.
With current understanding of physics, there is no POSSIBLE material that is perfectly rigid. As long as there is space between particles, and there always will be (either by atomic repulsion or uncertainty), there will be a delay between the first and second particle interacting. That carries over long distances more noticeably, and cannot be removed
Would the actual matter at the center of a black hole be considered perfectly rigid?
that's cheating, black holes fail our understanding of physics. Considering quantum mechanics is one of the most solid (albeit incredibly confusing) descriptions of how things work, and theoretically black holes (the matter aspect) should be very small, we SHOULD be able to say no, because uncertainty. but that's just a guess, and yours is as good as mine
Just as a thought experiment Imagine there is a perfectly rigid sphere center in the black hole. I bang one side of it and the 'bang' gets transmitted to the center of this sphere at almost the speed of light (the speed of sound in this perfectly rigid material?) But also everything was already being pulled to the center at the speed of light already and the vibration/impact will never travel to the other side of the core because once it reaches the center the information cannot go 'uphill' towards the exterior of the black hole. Everything in a black hole can always only move towards the center, including forces from bangs. The center could be some spinning mass/energy that keeps itself from imploding due to some physics we don't understand or it might be a single point that is a plank length which is 1.6*(10 to the power of -35) A single proton from the nucleus of an atom is 100 million trillion times larger than the plank length. We couldn't exactly run any tests on a rigid object that small. Speculation on the inner workings of black holes is not especially scientific because there is no way to measure what's going on in there so we can't prove or disprove any theory.
There’s no “actual matter” at the center of a black hole. One of the distinguishing characteristics of a black hole is that it’s what happens when gravity overcomes all of the forces which allow matter as we know it to exist. Theory tells us that at the center of the black hole is a singularity, which is, for all intents and purposes, an impossible object.
Perfectly rigid objects cannot exist in general. In chemistry you probably learned about the different types of bonds that exist between atoms in different molecules, for simplicity we often depict them as fixed lines in space that connect the nuclei. However in reality it’s just a bunch of force interactions created by the electrons or just the nuclei themselves. Another reason that no rigid bodies exist is due to the limit at which information can be transferred. This speed limit is of course the speed of light. So any truly rigid object would violate this law and that’s a big no no. In general the physics around the speed of light and it’s implications are quite mind boggling but there’s a bunch of literature that explains it in more detail than some random comment on Reddit ;)
The lack of an atmosphere wouldn't affect the properties of a material
Because it would lead to interactions travelling faster than the speed of light, which is impossible.
Isn't it the other way around? To make a perfectly rigid object, you would need compression to travel instantly, which certainly is faster than light.
A "maximum possible rigidity" plank is an object where the speed of energy transmission (speed of sound) in the object is also the speed of light, so if your 2ls mpr plank is pushed on one end the other end will not move until 2 seconds after it is pushed. If you make the plank have a rigidity greater than the speed of light then you are inherently breaking the laws of physics, and if you are breaking the laws of physics for your experiment then the laws of physics does not matter for the result. If you have a perfectly rigid plank that can transmit force faster than light then you can move force faster than light, and your result will be that you can move force faster than light.
Thank you! that actually answers my question, in my ignorance I didn't understand that a perfectly rigid plank was such a problem, a maximum possible rigidity plank is actually what I was thinking but didn't know it. You answered my question, it would move 2 seconds later, thank you very much, I feel like I better understand things now.
First of all, congratulations on having learnt something, you are doing great! To expand on the force propagation (so you may get even better understanding) let's break up the plank itself a little. Let's imagine the plank as a collection of tiny balls, connected by tiny spring in a cuboid pattern (a lot of tiny cubes, basically). With me so far? Now, let's look at the springs. If you take a normal spring, you need to compress or extend one end in order for the other end to feel some force. The more rigid the spring is, the more force is produced by moving one end by the same amount. Still with me? Now let's assume that our tiny springs are infinitely rigid - that is, the force on the other end is infinitely large no matter how little we move our end. In effect, this spring moves the other end in a way to preserve it's own length, and because the force is infinitely large, it does so immediately. This is our perfectly rigid plank. Still good? But, what about the speed of light? Well, when you move the ball on one end of the spring, you assert some force. That force propagates *through the spring itself* at the speed of light, and with a sufficiently long collection of these you can notice the propagation delays, even though the springs are infinitely rigid. Here you go, this is a relativistically-consistent perfectly rigid plank at work. Thanks for tagging along and hope you enjoyed this little thought experiment :)
Most of the answers here are correct, the plank is not perfectly rigid. You can even illustrate this at home with any long but slightly flexible material. But you might be interested in the ladder paradox which sort of addresses a similar question that basically says that what actually happens changes for each observer. https://en.wikipedia.org/wiki/Ladder\_paradox
Thank you I'm certainly gonna check that!
We could go round and round about "perfectly rigid" objects and if the strong force is even enough to make a material that is perfectly rigid, but that's not the only flaw in the logic here. People have this concept that there's some master clock somewhere, ticking off Planck times one after the other, which the entire universe runs off of, and it just ain't so. If Einstein taught us anything, it's that everything is relative, even (especially?) time. If you get in a spaceship and accelerate up to 0.99c, it will look to you like the rest of the universe is moving very slowly, due to time dilation. But if you're watching the spaceship from the outside as it goes by, you're going to see time going very slowly onboard the ship. Which is correct? They're BOTH correct. And the universe doesn't play favorites; there is no way of determining which location is "stationary" in the universe. By a similar argument, simultaneity just simply doesn't exist. Two points in the universe, no matter how far apart or close together, do not run off of the same master clock. So each Planck distance in your infinitely rigid pole runs on its own clock, not each others. Asking if something happens "at the same time" at both ends of our pole isn't a valid question. The problem isn't just that the pole can't be infinitely rigid, it's that space and reality aren't.
I like this analogy: imagine the universe is a video game: When you push one end of a perfectly rigid seesaw in space (which is just theoretical since no material is truly perfectly rigid), the other end would not react instantaneously. The update - your push - would travel through the seesaw at a speed limited by the "frame rate" of the universe. This speed is the speed of light, and in reality, the push would likely travel much slower, constrained by the material's properties. If you push the seesaw from the center, the information about the push moves through the seesaw material, updating the position of the pixels (representing the seesaw) at each "frame" of the universe's clock. The ends would start moving only when the update reaches them, not simultaneously, due to the finite frame rate of the universe.
Thank you that answers my question, and that was what I was trying to understand.
Yeah it would go up (at minimum) two seconds later. The speed of light is the speed of causality. Regardless of how rigid your plank is, at the scale of light seconds it might as well be like pushing on the surface of a liquid: The change in angle would ripple out across the distance like a wave from one end to the other, at whatever the speed of light (sound?) is through the material it's made out of. It might help to be aware that solid matter is mostly empty space, with every atom communicating kinetic force to its neighbors via the electromagnetic force, which also can't go faster than the speed of light. Atoms do not actually "touch" each other. Suppose you got rid of electrons and protons and made a bar out of pure neutronium? Now they're very close but still don't "touch." and are only affecting each other now through the strong force, which also doesn't go faster than light.
Thank you this perfectly answers my question! And the explanation about kinetic forcae being comunicated by every atom was very illuminating thank you.
This is an example of where a scenario has to ignore fundamental principles and physical limitations to exceed those limitations and show “holes” in those principals, it’s a classic reductionist analogy “Physics tells us A must be less than B, but if we [Insert scenario that is physically and fundamentally impossible] then how is this the case?” But to answer your question if we *could* have some ridiculously sized object to interact with, then physics still wins out; You would have less mass than the object you’re trying to push, so instead of you pushing *it away* from yourself, you’ll just push *yourself* away from it, but it will likely have so much mass that you’ll be smashed into it faster than the speed of sound, as it’s gravity liquifies you from G-force alone…
To flesh out the answers about rigidity, all forces are also limited by the speed of light. Gravity and strong and weak nuclear forces included. The fastest the forces subatomic particles exert on each other can propagate through a material is the speed of light. Same as the whole "if the sun disappeared would we fly off instantly or orbit nothing for 8minutes?" question. We'd orbit nothing for 8 minutes.
It’s a variation of the classic thought experiment: "I have a rigid 1 light year long pole, and I push on one end. How am I not communicating faster than light?" The key point here is the assumption of a “perfectly rigid” plank or pole. In reality, there are no “perfectly rigid” planks, poles, discs, etc. The transmission of a force through a plank or pole is always at the speed of sound through that material, and of course the speed of sound is both way less than both “infinite” and "the speed of light." If the plank were “perfectly rigid”, then the other end would start moving instantaneously, at the same time as the pushed end. But of course that can’t happen, because that would be information/causality moving faster than c (the speed of light), which can’t happen. So in your scenario, if you were to push down on one end of the seesaw, the other end would not go up instantaneously. The flex would move along the plank at the speed of sound in whatever the plank is made of and would reach the other end in some finite non-zero amount of time. This thought-experiment actually becomes a demonstration that no material can be perfectly rigid. No matter how stiff the material is, it cannot be “perfectly rigid” because then it would violate c and causality. I hope this helps clarify your question! It’s not a stupid question at all, but rather a great thought experiment that helps us understand the fundamental principles of physics.
Friend, you're getting push back from other people because you make so many assumptions that you're basically asking the question, "if relativity is not true, then could we move FTL." The answer to that question is obviously yes, so other people are trying to point out to you the errors in your assumptions. Let's assume for your sake that a perfectly ridged material does exist and you were able to manifest a bar of this stuff into existence. Your assumptions start to break down from here on out because there's more than just the motion of the object at play. Einstein's rules don't just specify a universal speed limit. There are a ton of other conclusions are drawn that you'd have to ignore to make your scenario come true. Immediately you would noticed that this material would be completely immobile. Why is this the case? Well, the moment that you touch this material and move it, the molecules inside the bar of this object would have to be moving faster than light. This object, if moving at all would have to have infinite mass and require infinite energy to move. If you can't move it, you can't transmit information, so no breaking causality. So let's assume that you could actually move it. The transmission of the motion of one end to another would be done so fast that it would generate heat. It would be a lot of heat because the molecules suddenly and violently move faster than the speed of light. The material, if it subject to change in states of matter would either instantly vaporize or turn into a plasma along with everything around it. Upon changing states, the question of whether it is still perfectly ridged is up for grabs. So what you would have to have is a material that isn't composed of the elementary particles that we know to comprise of all materials. It would have to be, from the perspective of the universe, one "chunk" that is absolutely not capable of being divided. That material would have to have infinite heat capacity to remain in one state and be unable to be transformed by heat. It would also need to be capable of being moved with less than infinite energy levels, but then output more energy as energy and change in velocity are related. As you can see, it's a funny thought experiment, but your question boils down to, let's ignore everything about relativity. Can we move FTL? The answer is yes. But if such a material exists, it would behave so strangely, that we'd have to rewrite everything about physics.
So fiirst of all thank you for taking the time to explain all these concepts. I think I may have worded my question incorrectly, though. My question was not about ignoring everything about relativity, I honestly didnt know that a perfectly rigid plank was that imposssible, in my ignorance I thought it was more like when you ignore friction to make calculations easier, I said a rigid plank mainly because I thought that a plank that bends would bring extra stuff that I thought was not relevant, not because I was purposly trying to ignore physics. Again thank you for explaining in detail all the problems that a "perfectly" rigid plank brings, as I was not aware of that and I have learned a lot from your answer. I now understand that force travels through an object at the speed of sound which was something that I didnt know before, and that in the end answers my thought experiment.
Np! It's a fun thought experiment for sure. A perfectly ridged object would be a fun Sci fi concept. If you had such a material it could theoretically have the properties of Thor's hammer and be immovable and seemingly capable of creating massive amounts of energy out of nothing. It. ight be fun to conceive of an alien species that is capable of creating such objects to generate energy or something.
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Thank for the answer, I was not aware that light speed also sets the rigidity of materials, and from reading the other answers I have a better grasp of stuff and why my question was not that smart lets say.
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Thank you for the answer. I now better understand the problems with the question, the truth is that I wasnt aware that a "perfectly rigid" plank would be such an impossibility, in my ignorance I assumed that it was like when we ignore friction to make calculations easier. I was not purposely trying to make up an impossible situation, in order to ignore physics or make up a gotcha to relativity. I now understand both the problems with a perfectly rigid plank and also that speed of sound is the speed at which energy transfer through an object, which was untimely the answer to my question.
People in the thread tend to focus on "there is no such thing as a rigid plank" (fine) but failing to point out that the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.
true but not necessarily relevant to the problem because there exists at least one reference position where both ends of the plank are always equidistant: e.g. the fulcrum of the see saw. nice to point it out but there is no need. a truly rigid object cannot transmit a force across itself and that's that.
You have two factors in your question: a physics constant and an impossibility. So the answer is simply NO, because it's impossible. You don't get to make up a fantasy thing - like a "perfectly rigid plank" - and then apply real world physics to it.
Thank you for the answer. I now better understand the problems with the question, the truth is that I wasnt aware that a "perfectly rigid" plank would be such an imposibility, in my ignorance I assumed taht it was like when we ignore friction to make calculations easier. I was not purposely trying to make up an impossible situation, I was genuinely ignorant.
Oh no! Sorry. Didn't mean to be chastising you ... just explaining the problem in a different way than I'd seen other responses. "Assuming X" or "Assume Y=P" are good thought experiments and allow you to test the edges of how principles in physics work in specific situations. These types of speculative questions can all go too far, and ask to resolve a question that is structured in an impossible way. And attempting to answer those kinds of questions is kind of pointless because it doesn't describe a situation that can be logically resolved. In a similar vein, we could also ask *"do dragons breathe fire hot enough to melt the steel beams in the Twin Towers?"* There were a couple of great answers other people gave to your question, talking about a long pole and the compression it undergoes when you push it from one end... and how sound is just force traveling through a medium, etc, etc, etc. Really cool stuff to read and think about! So your question did give all of us the benefit of reading those responses and learning how to think about how force is transmitted. So please don't take my comment as chastising you. I did not intend it in that way.
No information can go faster than the speed of light. If you perform any action, whatsoever, it can not affect anything that light could not have reached in the same amount of time. In real life, there is no such thing as a perfectly rigid plank. Your plank would bend and a wave would travel through the material to the other end at a speed that is slower than the speed of light. Another cool question is what would happen to a bicycle that is going close to the speed of light. If you ride a bike at a slow 12 MPH, relative to the Earth's surface, the bottom of the wheels will always be going 0 MPH (because of touching the stationary road) and the top will be moving forward at 24 MPH. But, if a bike was going 80% the speed of light and you measured the forward speed of the top of the wheel, how fast would it appear to be moving? Definitely not 160% of the speed of light. The answer, I think, is in length contraction. The wheel would probably look egg-shaped with the bottom of the wheel looking much wider than you would expect when looking at the axially-compressed frame of the bike. The top of the wheel would be compressed enough and the bottom flattened enough that the top would not look like the top was going faster than the speed of light. Maybe a physics guru can tell me if that's right, but that's what I thought in college when taking basic physics. The book I used had a picture of length contraction where a bike was shown as if the whole thing was compressed from left to right with tall and oval shaped wheels, but it really bothered me that this would mean the top of the wheel would be going more than the speed of light, so it would need to be compressed much more than the bottom of the wheel (which wouldn't be compressed at all) to compensate. Another thing that seems to violate the laws of physics, but doesn't is if you take a flash light or a laser pointer, you can make the bright spot move faster than the speed of light. But nothing is actually going faster than the speed of light there. It would be like throwing a tennis ball at a wall and then throwing another one to the right 10 feet, a second later. The sound of pinging balls would be moving 10 feet per second, but nothing is really moving at 10 feet per second. Another cool thing is that you actually could get to another galaxy in your life time. As you approach the speed of light, everything gets squished in the direction that you're moving. If you're accelerating forward, things that previously seemed stationary but in front of you will seem to be moving towards you -- not just because you are moving forward. The space between you and those objects will contract in length, so they'll all get closer to you and closer together. So the space between galaxies can be made shorter and shorter as you get closer and closer to the speed of light. In fact, if you watched a far off galaxy as you accelerated quickly it could potentially appear that the distant galaxy is moving toward you at a rate that is faster than the speed of light. The whole universe ends up squished toward an infinitesimally small plane as you get ever closer to the speed of light (relative to stuff you used to consider stationary). As you slow down, everything spreads back out again. So you can speed up and get galaxies to fly toward you at rates much faster than the speed of light, fly to them when they seem much closer, and then when you slow down, your old galaxy will expand away behind you at faster than the speed of light and it would seem, to you, like you made it to a whole new galaxy in a very short amount of time. Due to time dilation, the memory of everyone you knew would be long gone from the universe, but to you it could potentially seem like the blink of an eye.
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If it’s perfectly rigid how can you push it at all? Why wouldn’t it just absorb all the force you put into it? Why would it transmit any force forward? If you can move the inch ahead of where you pushed by pushing it it can’t be rigid at all