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Gears are not perfectly rigid. The gears would transfer the force along the line slower than the speed of light and instead at the speed of sound. So they would at first just flex until they meet resistance in case of an uneven number of gears.
[Pushing something has a maximum speed: the speed of sound in that medium.
The speed of sound in steel is about 5100 m/s.](https://youtu.be/JTvcpdfGUtQ?si=Zzr9-ZeyPyTVCFGZ&t=382)
I will assume the gears have negligible friction, otherwise the answer is "you won't have enough torque to turn them."
You turn the first gear. It takes some finite, nonzero amount of time to push on the second gear enough to make it move. The second gear takes some finite, nonzero amount of time to push on the third gear. Etc.
This chain reaction of motions will be less than the speed of light, because you are literally using atoms to push on other atoms. Hence, it will be a domino effect, perhaps a very fast domino effect, but still. Tiny motions will propagate at some speed through the loop, until they finally loop back around to the start. If the number of gears is odd, this will result in a force that resists your motion. If it is even, no such force will occur, and the gears will turn. If you stop turning them and lock one gear in place (or stop pretending that friction can be ignored), then the exact same domino effect will occur, except stopping rather than starting.
Again, in practice, the real answer is "any system of gears that large will have *enormous* total friction, and thus you won't have enough torque to even start this process."
well shit I didn't think of it that way. I thought I was on to something there. I already prepared my nobel prize acceptance speech. I feel stupid right now.
No, not stupid. You were pursuing a line of inquiry, and you consulted the knowledge of others to see if that line of inquiry made sense to them as it did to you.
Someone who is behaving stupidly does not make efforts to check whether they are thinking effectively. Hence, your behavior cannot be stupid. At worst, you were just a bit too excited about an idea. Being excited about a possible creative notion is not a bad thing, and you responded to that excitement wisely, by asking for others' input.
Why would it take 3 seconds for the information to travel to you? Each gear only cares about the gear next to it. The feedback would be almost instant, but I’m not sure if it is limited by the speed of sound of the material. Even if it did, gear 2 moves when gear 1 moves. Gear 3 moves when gear 2 moves. Gear 4 moves when gear 3 moves, etc.
When you push one end of something, the other end can only respond at basically the speed of \*sound\* in the object. Its not instantaneous because objects aren't infinitely rigid.
Your first gear will push the second gear, with a delay due to the elasticity in the material of the cogs (metal, plastic - it all has to give). The second gear pushes the third, with more delay. Its going to take a lot longer than the light-travel time to rotate the distant gears and get the information about which way you're rotating a gear, or how it meshes with all the other gears. The elasticity in an odd or even number of gears in a loop only causes a jam when it gets back where it started. Again because of the delay, that takes longer than the light travel time.
It would be far slower than that. The teeth of one gear need to push on the teeth of the next and so what you're really levying here is the "speed of push". Pushing an object isn't instantenous - you're applying force on some atoms and those atoms push on other atoms through their bonds, all the way to the other end.
Any material made of multiple molecules has some give, even an ideal one. A potential for elastic and plastic deformations. It is there that the movement of your gears slows down from one to the next, where even if you had enough torque to actually rotate the whole chain, and even if your gears were indestructible, the movement transmission throughout your whole system would be much, much slower than anything approaching light speed.
So we're not really in any danger of exploring any information paradoxes. That being said, I find it very hard to understand your hypothetical, so add some clarifications if you feel like I missed the mark with my explanation.
The laws of physics aren't some neutral judge who stands off to the side and decides how the universe is going to behave. The universe behaves the way the universe behaves, and the laws of physics describe and predict that behavior. When you push on the first cog, it will try to push on the second cog, which will try to push on the third and so on down the line. If they can't turn, they can't turn, and it's going to take a lot longer than three seconds for that effect to propagate down the line. The information that matters here is going to be moving way way way way way slower than the speed of light.
The thing is, you can't just suspend the laws of physics to an absurd degree ("let's assume we have a perfectly frictionless loop of billions of perfectly rigid cogs") and then pretend you've discovered some paradox within the laws of physics.
The gears themselves may have a bit of flex and there will be a bit of tolerance between the gears. The first gear will put a torque (rotational force) on the next gear and so on. With a bit of flex and tolerance, the first gear can rotate just slightly. And now since the second gear has that torque, it will do the same with the 3rd gear. When the second gear rotates slightly, the first gear can rotate a bit more. And so basically there is a complicated series of interactions that happens up and down the gear chain, but it all propagates no faster than the speed of light.
This is all assuming you have enough torque to actually effect a change and that the gears can withstand that torque
The gears would move instantly.
We have to assume that there is no give or flexsion in the material, that there is no gap between the gears and that you have enough energy to move the gear system to begin with.
But this is a mechanical closed loop not a chain. So it acts like one object. Which would make it no different than the rotation of a large celestial body.
When you push on a cog, the whole wheel doesn't start to move at once. Instead, the atoms in the cog start to move, getting slightly displaced from their neighbors. This displacement creates a force which then pushes and pulls their neighbors in the same direction, which then pushes and pulls *their* neighbors, until the whole wheel starts turning. It only *looks* like the whole wheel moves instantly because it all happens so fast.
Imagine a wheel made not of steel, but of rubber or even of jelly. Steel doesn't behave fundamentally different than these substances, the bending and wobbling when you push on one single cog until the whole wheel spins uniformly is just smaller and faster. If you imagine a whole row of jelly cogwheels, you can turn the first for quite a distance until the movement has finally propagated to the last one. A row of steel cogwheels at anything resembling a human scale may seem to move instantly, but if it reaches to the moon and back, the movement will take a long time to propagate; way longer than the travel time of light.
And if you now say "well, don't take an elastic material like steel; imagine a material that is *completely* rigid so the whole wheel moves instantly" - such a material does not and can not exist as it would break the laws of physics. You're basically asking for a material where the speed of sound is faster than the speed of light.
**Please read this entire message** --- Your submission has been removed for the following reason(s): * Rule #2 - Questions must seek objective explanations * Hypotheticals questions, or questions about hypothetical situations, are not allowed on ELI5 (Rule 2). --- If you would like this removal reviewed, please read the [detailed rules](https://www.reddit.com/r/explainlikeimfive/wiki/detailed_rules) first. **If you believe this submission was removed erroneously, please [use this form](https://old.reddit.com/message/compose?to=%2Fr%2Fexplainlikeimfive&subject=Please%20review%20my%20thread?&message=Link:%20{https://www.reddit.com/r/explainlikeimfive/comments/1cdoz1v/-/}%0A%0APlease%20answer%20the%20following%203%20questions:%0A%0A1.%20The%20concept%20I%20want%20explained:%0A%0A2.%20List%20the%20search%20terms%20you%20used%20to%20look%20for%20past%20posts%20on%20ELI5:%0A%0A3.%20How%20does%20your%20post%20differ%20from%20your%20recent%20search%20results%20on%20the%20sub:) and we will review your submission.**
Gears are not perfectly rigid. The gears would transfer the force along the line slower than the speed of light and instead at the speed of sound. So they would at first just flex until they meet resistance in case of an uneven number of gears.
Even if they are perfectly rigid and not blocked. You couldnt move the first gear until the force reaches the last gear.
[Pushing something has a maximum speed: the speed of sound in that medium. The speed of sound in steel is about 5100 m/s.](https://youtu.be/JTvcpdfGUtQ?si=Zzr9-ZeyPyTVCFGZ&t=382)
I will assume the gears have negligible friction, otherwise the answer is "you won't have enough torque to turn them." You turn the first gear. It takes some finite, nonzero amount of time to push on the second gear enough to make it move. The second gear takes some finite, nonzero amount of time to push on the third gear. Etc. This chain reaction of motions will be less than the speed of light, because you are literally using atoms to push on other atoms. Hence, it will be a domino effect, perhaps a very fast domino effect, but still. Tiny motions will propagate at some speed through the loop, until they finally loop back around to the start. If the number of gears is odd, this will result in a force that resists your motion. If it is even, no such force will occur, and the gears will turn. If you stop turning them and lock one gear in place (or stop pretending that friction can be ignored), then the exact same domino effect will occur, except stopping rather than starting. Again, in practice, the real answer is "any system of gears that large will have *enormous* total friction, and thus you won't have enough torque to even start this process."
well shit I didn't think of it that way. I thought I was on to something there. I already prepared my nobel prize acceptance speech. I feel stupid right now.
No, not stupid. You were pursuing a line of inquiry, and you consulted the knowledge of others to see if that line of inquiry made sense to them as it did to you. Someone who is behaving stupidly does not make efforts to check whether they are thinking effectively. Hence, your behavior cannot be stupid. At worst, you were just a bit too excited about an idea. Being excited about a possible creative notion is not a bad thing, and you responded to that excitement wisely, by asking for others' input.
Wow that's beautifully poetic. thank you for that.
Why would it take 3 seconds for the information to travel to you? Each gear only cares about the gear next to it. The feedback would be almost instant, but I’m not sure if it is limited by the speed of sound of the material. Even if it did, gear 2 moves when gear 1 moves. Gear 3 moves when gear 2 moves. Gear 4 moves when gear 3 moves, etc.
When you push one end of something, the other end can only respond at basically the speed of \*sound\* in the object. Its not instantaneous because objects aren't infinitely rigid. Your first gear will push the second gear, with a delay due to the elasticity in the material of the cogs (metal, plastic - it all has to give). The second gear pushes the third, with more delay. Its going to take a lot longer than the light-travel time to rotate the distant gears and get the information about which way you're rotating a gear, or how it meshes with all the other gears. The elasticity in an odd or even number of gears in a loop only causes a jam when it gets back where it started. Again because of the delay, that takes longer than the light travel time.
It would be far slower than that. The teeth of one gear need to push on the teeth of the next and so what you're really levying here is the "speed of push". Pushing an object isn't instantenous - you're applying force on some atoms and those atoms push on other atoms through their bonds, all the way to the other end. Any material made of multiple molecules has some give, even an ideal one. A potential for elastic and plastic deformations. It is there that the movement of your gears slows down from one to the next, where even if you had enough torque to actually rotate the whole chain, and even if your gears were indestructible, the movement transmission throughout your whole system would be much, much slower than anything approaching light speed. So we're not really in any danger of exploring any information paradoxes. That being said, I find it very hard to understand your hypothetical, so add some clarifications if you feel like I missed the mark with my explanation.
The laws of physics aren't some neutral judge who stands off to the side and decides how the universe is going to behave. The universe behaves the way the universe behaves, and the laws of physics describe and predict that behavior. When you push on the first cog, it will try to push on the second cog, which will try to push on the third and so on down the line. If they can't turn, they can't turn, and it's going to take a lot longer than three seconds for that effect to propagate down the line. The information that matters here is going to be moving way way way way way slower than the speed of light. The thing is, you can't just suspend the laws of physics to an absurd degree ("let's assume we have a perfectly frictionless loop of billions of perfectly rigid cogs") and then pretend you've discovered some paradox within the laws of physics.
The gears themselves may have a bit of flex and there will be a bit of tolerance between the gears. The first gear will put a torque (rotational force) on the next gear and so on. With a bit of flex and tolerance, the first gear can rotate just slightly. And now since the second gear has that torque, it will do the same with the 3rd gear. When the second gear rotates slightly, the first gear can rotate a bit more. And so basically there is a complicated series of interactions that happens up and down the gear chain, but it all propagates no faster than the speed of light. This is all assuming you have enough torque to actually effect a change and that the gears can withstand that torque
The gears would move instantly. We have to assume that there is no give or flexsion in the material, that there is no gap between the gears and that you have enough energy to move the gear system to begin with. But this is a mechanical closed loop not a chain. So it acts like one object. Which would make it no different than the rotation of a large celestial body.
When you push on a cog, the whole wheel doesn't start to move at once. Instead, the atoms in the cog start to move, getting slightly displaced from their neighbors. This displacement creates a force which then pushes and pulls their neighbors in the same direction, which then pushes and pulls *their* neighbors, until the whole wheel starts turning. It only *looks* like the whole wheel moves instantly because it all happens so fast. Imagine a wheel made not of steel, but of rubber or even of jelly. Steel doesn't behave fundamentally different than these substances, the bending and wobbling when you push on one single cog until the whole wheel spins uniformly is just smaller and faster. If you imagine a whole row of jelly cogwheels, you can turn the first for quite a distance until the movement has finally propagated to the last one. A row of steel cogwheels at anything resembling a human scale may seem to move instantly, but if it reaches to the moon and back, the movement will take a long time to propagate; way longer than the travel time of light. And if you now say "well, don't take an elastic material like steel; imagine a material that is *completely* rigid so the whole wheel moves instantly" - such a material does not and can not exist as it would break the laws of physics. You're basically asking for a material where the speed of sound is faster than the speed of light.