...honestly, probably not well. It’s been too long. At a high level: Noether’s theorem implies that if you have a Lagrangian that’s invariant under a perturbation of coordinates, that corresponds to a conserved quantity of the system. In particular: invariance under time perturbations (a.k.a. continuous time-translation symmetry) corresponds to a conserved quantity that turns out to be conservation of energy.
Also, do you consider your loopholes like technicalities, or more serious problems?
For 1: it’s like someone showing how to break your 1024-bit hash in 2^500 operations. It isn’t a problem in and of itself, but it’s suggestive of deeper problems. (It requires both infinite precision and point particles to achieve, neither of which appear to be actually possible in our universe.)
For 2: I’d consider the issues with general relativity (and however quantum gravity shakes out) to be potentially an issue—though given that it’s not an issue for classical mechanics any loopholes would likely be in regimes where the Newtonian approximation breaks down.
That all being said, take this with a grain of salt. I’m not confident I remembered everything correctly.
Thanks for the comment!
Could you give more details on the path itself?
Also, do you consider your loopholes like technicalities, or more serious problems?
...honestly, probably not well. It’s been too long. At a high level: Noether’s theorem implies that if you have a Lagrangian that’s invariant under a perturbation of coordinates, that corresponds to a conserved quantity of the system. In particular: invariance under time perturbations (a.k.a. continuous time-translation symmetry) corresponds to a conserved quantity that turns out to be conservation of energy.
For 1: it’s like someone showing how to break your 1024-bit hash in 2^500 operations. It isn’t a problem in and of itself, but it’s suggestive of deeper problems. (It requires both infinite precision and point particles to achieve, neither of which appear to be actually possible in our universe.)
For 2: I’d consider the issues with general relativity (and however quantum gravity shakes out) to be potentially an issue—though given that it’s not an issue for classical mechanics any loopholes would likely be in regimes where the Newtonian approximation breaks down.
That all being said, take this with a grain of salt. I’m not confident I remembered everything correctly.