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.
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.