4 ms·
The necessity of time symmetry for energy conservation can be a little overstated. As long as the laws are holonomic, there will be a conserved quantity corresp
by whatshisface 2y ago
The necessity of time symmetry for energy conservation can be a little overstated. As long as the laws are holonomic, there will be a conserved quantity corresponding to the motion. You can call that quantity the energy. It won't be conserved if you jump forwards in time without allowing the state to change, but that can't ever happen, so is it really an issue?
- mjburgess 2y agoThe problem with 'motion' as the load-bearing property here is that there's an infinite number of derivatives at stake: x', x'', x''', etc. -- what is "the motion" ? What is supposed to be conserved about that motion? The intuition here seems to be that there's a continuity of some property involved in the "transmission of matter over time" which is unbroken, but its not clear what this is supposed to imply. It doesnt seem to imply, for example, that the universe operates like a closed system of motion simply because this property (whatever it is) is unbroken. There can be "global motion" without the need for discontinutiy/randomization/discretizatino/etc. in the trajectories of matter.