5 ms·
Reminds me of a thought experiment that's always bugged me: if you had an incredibly long see-saw or lever, like the length of the galaxy, would movement at one
by Tycho 16y ago
Reminds me of a thought experiment that's always bugged me: if you had an incredibly long see-saw or lever, like the length of the galaxy, would movement at one end instantaneously be matched by movement at the other end? (I think the reason it bugs me is because the object itself is preposterous, but I still want to know)
- Herring 16y agoWell you already know it won't be instantaneous, & there's only a few ways it can fail. What do you think will happen?
- JanezStupar 16y agoOh - yes, the unobtainium rod thought experiment :) Well - I guess that when you move an object - you firstly move (push away) - due to electromagnetic force the closest atoms first - which in turn push away the next... etc. until the whole object moves. I guess that what happens is actually an oscillation between atoms. So you would notice the far end moving in the time a photon would take from one end to other - in best case scenario. You know that information cannot travel faster than light? Even if you try to send it via wiggling of unobtainium rod :)
- Luc 16y agoIf it were a physical object (say, a long steel bar), the atoms would communicate at the speed of light, so your object would bend or squish, with a wave travelling along it. Now, let's say you move an ideal laser across an ideal screen some distance away. The further the screen is, the faster the laser dot will move. At some point the dot will move faster than c... But the dot is not an object. If you think in terms of individual photons, no speed limit is being broken. IANAPhysicist...
- philh 16y ago>Now, let's say you move an ideal laser across an ideal screen some distance away. The further the screen is, the faster the laser dot will move. At some point the dot will move faster than c... I'm pretty confident that you're wrong about this, but I don't really understand the scenario you're describing. Could you clarify? edit: I eat my words and stand corrected.
- doki_pen 16y agoIt seems he is correct. If you imagine a laser pen light being swung on an angle, the further away the screen is, the faster the dot will "move". If the screen is sufficiently far away, the dot will appear to move faster then the speed of light.
- kscaldef 16y agoHe's right. Say you have a laser pointer and point it at a screen some distance away. Now, you rotate the pointer such that the tip is moving at, say 1/10th the speed of light. Simple geometry tells you that the spot on the screen will move much faster than the speed of light. The important point, though, is that no physical object and no informaaation is actually moving faster than light. Each photon moves at exactly c in a straight line from the pointer to the screen.
- Luc 16y agoFor fun: the moon has a radius of about 1730 km. At full moon we can see about half of the moon, so the distance from one side to the other is about pi * 1730 km. So how fast do you need to move a laser pointer across the moon surface to make the dot attain the speed of light? http://www.google.com/search?q=%28%281730000+*+pi%29+m%29+%2F+c+in+s http://www.google.com/search?q=%28%281730000+*+pi%29+m%29+%2... A bit less than 2/100 of a second. That seems quite feasible really! (of course the moon is not a flat screen, but hey, back of the envelope and all that).
- Tycho 16y agoSo say the dot was fairly large and you had a vantage point on the moon near where the dot sweeps by... What would you actually see??
- philh 16y agoSuppose you're on the midpoint of a straight line 6e8 m long, which the dot traverses at uniform velocity. If the dot moves at c, you would see nothing for 1s. Then there would be an instant where the first half of the line is entirely illuminated, as light from the dot at each point reaches you simultaneously. After that, it would look like an ordinary dot moving away from you at c/2: if the dot moves for x seconds, it takes 2x seconds for the light from the dot at that point to reach you. (Note that a dot moving at c/2 would appear to be moving at c/3.) If it's moving faster than light (say, kc, k>1), then when the dot arrives at you, you'd see a dot appear at your position, then move back to the original position at (k c / (k-1)), and vanish. (k/(k-1) is because you see it reach the start point 1s after it starts moving, and you first see it 1/k s after it starts moving.) If the dot had been stationary at that point before it began moving, you'd still see the dot there until the new one reached it, at which point they would both vanish. Simultaneously, you'd see a dot move from your position to the end position at (k * c / (k+1)). I'm not going to try to work out what happens if you're just standing near the path of the dot. (I'm not sure about this, but it's what I get when I try to work it out. I'm especially not sure that I'm allowed to discount relativistic effects. I think I am because there are no massive bodies undergoing acceleration, but I don't pretend to fully understand relativity.)
- sp332 16y agoActually, the atoms would move much more slowly, something like the speed of sound through the material.
- deleted 16y ago[deleted]
- InclinedPlane 16y agoAlmost. The speed of light is the upper limit on how fast any forces could propagate along the object, in practice they would travel at the speed of sound in the material.
- philh 16y agoIf you move it, you're really moving some of the atoms at one end. They 'bump' into nearby atoms, which 'bump' into more atoms, and so on, and eventually the atoms at the far end get 'bumped', and the far end moves. Sound waves travel in the same way. So if you move one end, that movement propagates at the speed of sound (in whatever material the lever is made of).
- Tycho 16y agoHmm, I'd take your word over mine but this doesn't fee quite right to me. What I'm thinking is, say you reverse the action so that instead of bumping one end of the see-saw, you release your grip on it having been holding it down. So in normal circumstances the other end would fall while the near end rises (of course now an external gravitational field has entered the thought experiment). But if movement is still due to the bumping of atoms , how does it work, where does it start? and if it's something else, then what, and is it still not instantaneous?
- pavel_lishin 16y agoIt's the same scenario, except in this case the force isn't you pushing down on your end, but gravity pushing down on the other.
- doki_pen 16y agoI think it would snap. It would take a tremendous amount of force to move it and no material could withstand that force.
- adamtj 16y agoIt would bend or stretch before it snapped. Nearly all, if not absolutely all, materials that you might want to build a see-saw from will deform before they snap. Maybe it won't deform much, but that ok, and is enough to transmit a push from one end of the lever to the other. Remember, a lever is just a collection of individual atoms linked together by elecromagnetic forces. You push of the atoms on one end, and they are going electromagnetically push on nearby atoms, and that push is going to propagate as a wave at around the speed of light.
- lutorm 16y agoLike others have said, any movement will propagate at the speed of sound through the rod. But moreover, as the end of the rod speeds up, it will experience relativistic mass increase from your point of view, so it would still take an infinite amount of energy to accelerate it to c, regardless of how long your lever was. (Though special relativity, dealing with inertial frames, is strictly not applicable to a rotating rod, but you can probably make use of a succession of infinitesimal inertial frames to figure that out.)
- guelo 16y agoGood point. An unobtainium rod as JanezStupar calls it, would be the immovable object, stuck in the universe's gullet gumming up the works. I wonder if God would be able to move it after he created it.