My thoughts on this are not going to be fully coherent, because I am in the process of possibly changing my mind.
I agree that if we take the uniform motion of centre of mass as an absolute principle then the weird light-in-circles machine does not work. However, I had never before encountered this principle, and (to me) it still carries the “I learned about this last week, how much do I trust it?” penalty. But, even accepting it, that doesn’t explain why the machine fails. Does it remain the case that the actual mechanical momentum and energy transport directions are opposite in the right metamaterial (as claimed in, for example: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.75.053810 ), but the machine fails for some other reason (eg. recoils on the interfaces)? Showing the machine to be impossible while leaving this unanswered doesn’t get to the roots of my various related confusions, I still don’t know whether energy flow and momentum can ‘really’ point opposite directions, or whether it’s all just an accounting trick.
The uniform motion of centre of mass implies other things. For example, it means anything like a portal from the game “portal” is impossible as the centre of mass would change discontinuously as something went through the portal. [We can even “re-skin” of the photon loop by instead having a train with portals, so it can keep reusing the same track on our space ship repeatedly].
I agree that you can confidently believe that something won’t work because of some high-level principle, but still be curious for a nuts-and-bolts lower-level explanation of why it doesn’t work. That’s a perfectly healthy and fun and pedagogical activity. A classic example is questions in the genre “Why does this particular proposal for a perpetual machine not actually work?” Another is “What’s the flaw in this apparent proof that 0=1?”
I was just saying that we should be confident about the high-level principle here, not that there’s anything wrong with being curious about the thing that you’re curious about. :)
I agree that if we take the uniform motion of centre of mass as an absolute principle then the weird light-in-circles machine does not work. However, I had never before encountered this principle, and (to me) it still carries the “I learned about this last week, how much do I trust it?” penalty.
Start from the fact that the fundamental laws of physics are the same regardless of where you are. Then Noether’s theorem gets us from there to conservation of momentum. And then conservation of momentum implies uniform motion of the center of mass, right? (I think that second step involves spatial integration to get from a local continuity equation to a global conservation law, and so general relativity might or might not mess up that part, not sure. But anyway, we’re assuming flat space here.)
“And then conservation of momentum implies uniform motion of the center of mass, right?”—This is the step I am less than 100% on. Certainly it does for a collection of billiard balls. But, as soon as light is included things get less clear to me. It has momentum, but no inertial mass. Plus, as an admittedly weird example, the computer game “portal” has conservation or momentum, but not uniform motion of the centre of mass. Which means at the very least the two can logically decouple.
Plus, as an admittedly weird example, the computer game “portal” has conservation or momentum, but not uniform motion of the centre of mass. Which means at the very least the two can logically decouple.
That’s related to what I wrote here:
I think that second step involves spatial integration to get from a local continuity equation to a global conservation law, and so general relativity might or might not mess up that part, not sure. But anyway, we’re assuming flat space here.
The spatial integration step, to get from local properties (continuity equation for momentum density) to global properties (center of mass motion), can get screwed up by weird topology (e.g. teleportation portals), just like it can get screwed up by curved spacetime. You do have to assume that spacetime is normal flat Minkowski space.
Certainly it does for a collection of billiard balls. But, as soon as light is included things get less clear to me. It has momentum, but no inertial mass.
Maybe this link is a proof? It kinda looks right but I didn’t check it super-carefully. It uses the stress-energy tensor which applies to both matter and electromagnetic waves. Note the part where they integrate over space and set the boundary term at infinity to zero—that part doesn’t work with curved space or wormholes.
It’s also trivial to make a perpetual motion machine with Portal portals. Just have a portal in the floor that teleports you to the ceiling directly above it, then drop a ball into it. It’ll fall forever, accelerating until it hits terminal velocity (at which point all the gravitational potential energy goes to heating the air it falls through).
If you don’t want to just throw out conservation of energy, using a portal to “lift” things would have to take the same amount of energy as lifting it through normal space does.
Yes, you could fix it by making the portal pay for lifting. An alternative fix would be to let gravity go through portals, so the ball feels the Earth’s gravity by the direct route and also through the portal. Which I think makes the column between the two portals zero G, with gravity returning towards normal as you move radially. This solution only deals with the steady-state though, at the moment portals appear or disappear the gravitational potential energy of objects (especially those near the portal) would step abruptly.
My thoughts on this are not going to be fully coherent, because I am in the process of possibly changing my mind.
I agree that if we take the uniform motion of centre of mass as an absolute principle then the weird light-in-circles machine does not work. However, I had never before encountered this principle, and (to me) it still carries the “I learned about this last week, how much do I trust it?” penalty. But, even accepting it, that doesn’t explain why the machine fails. Does it remain the case that the actual mechanical momentum and energy transport directions are opposite in the right metamaterial (as claimed in, for example: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.75.053810 ), but the machine fails for some other reason (eg. recoils on the interfaces)? Showing the machine to be impossible while leaving this unanswered doesn’t get to the roots of my various related confusions, I still don’t know whether energy flow and momentum can ‘really’ point opposite directions, or whether it’s all just an accounting trick.
The uniform motion of centre of mass implies other things. For example, it means anything like a portal from the game “portal” is impossible as the centre of mass would change discontinuously as something went through the portal. [We can even “re-skin” of the photon loop by instead having a train with portals, so it can keep reusing the same track on our space ship repeatedly].
I agree that you can confidently believe that something won’t work because of some high-level principle, but still be curious for a nuts-and-bolts lower-level explanation of why it doesn’t work. That’s a perfectly healthy and fun and pedagogical activity. A classic example is questions in the genre “Why does this particular proposal for a perpetual machine not actually work?” Another is “What’s the flaw in this apparent proof that 0=1?”
I was just saying that we should be confident about the high-level principle here, not that there’s anything wrong with being curious about the thing that you’re curious about. :)
Start from the fact that the fundamental laws of physics are the same regardless of where you are. Then Noether’s theorem gets us from there to conservation of momentum. And then conservation of momentum implies uniform motion of the center of mass, right? (I think that second step involves spatial integration to get from a local continuity equation to a global conservation law, and so general relativity might or might not mess up that part, not sure. But anyway, we’re assuming flat space here.)
“And then conservation of momentum implies uniform motion of the center of mass, right?”—This is the step I am less than 100% on. Certainly it does for a collection of billiard balls. But, as soon as light is included things get less clear to me. It has momentum, but no inertial mass. Plus, as an admittedly weird example, the computer game “portal” has conservation or momentum, but not uniform motion of the centre of mass. Which means at the very least the two can logically decouple.
That’s related to what I wrote here:
The spatial integration step, to get from local properties (continuity equation for momentum density) to global properties (center of mass motion), can get screwed up by weird topology (e.g. teleportation portals), just like it can get screwed up by curved spacetime. You do have to assume that spacetime is normal flat Minkowski space.
Maybe this link is a proof? It kinda looks right but I didn’t check it super-carefully. It uses the stress-energy tensor which applies to both matter and electromagnetic waves. Note the part where they integrate over space and set the boundary term at infinity to zero—that part doesn’t work with curved space or wormholes.
It’s also trivial to make a perpetual motion machine with Portal portals. Just have a portal in the floor that teleports you to the ceiling directly above it, then drop a ball into it. It’ll fall forever, accelerating until it hits terminal velocity (at which point all the gravitational potential energy goes to heating the air it falls through).
If you don’t want to just throw out conservation of energy, using a portal to “lift” things would have to take the same amount of energy as lifting it through normal space does.
Yes, you could fix it by making the portal pay for lifting. An alternative fix would be to let gravity go through portals, so the ball feels the Earth’s gravity by the direct route and also through the portal. Which I think makes the column between the two portals zero G, with gravity returning towards normal as you move radially. This solution only deals with the steady-state though, at the moment portals appear or disappear the gravitational potential energy of objects (especially those near the portal) would step abruptly.
Its quite a fun situation to think about.