“But bringing up the quantum Hamiltonian? FTL signalling? Su3su2u1′s analysis is correct.”
Is it? Noether’s theorem implies the Hamiltonian is conserved. The Hamiltonian is the quantum operator that give you the energy of a system. If energy conservation is violated, either the basic equations of quantum mechanics don’t hold, or (magical) physics is not time invariant. I’m not saying Harry is being technically precise but he’s not completely wrong, either.
No, he’s certainly not completely wrong, but he’s bringing up irrelevant complications and missing the main point. Quantum vs classical has nothing to do with it, for example.
The fact that quantum mechanics conserves energy is stronger evidence for the hypothesis that reality conserves energy than the fact that classical mechanics conserves energy. He is saying “our best model of reality conserves energy” which is very relevant.
If quantum mechanics allowed for small violations of energy conservation (which sometimes people even say that it does, on short time periods, although this is not really correct), then McGonagall’s tranformation would still violate physical law as we know it. In physics, you don’t always push everything down to the most fundamental theory, which is a good thing, since we don’t actually have a most fundamental theory of physics. There is no such thing as ‘our best [single] model of reality’; there are some ways in which our quantum models are (so far) worse than our classical ones.
“But bringing up the quantum Hamiltonian? FTL signalling? Su3su2u1′s analysis is correct.”
Is it? Noether’s theorem implies the Hamiltonian is conserved. The Hamiltonian is the quantum operator that give you the energy of a system. If energy conservation is violated, either the basic equations of quantum mechanics don’t hold, or (magical) physics is not time invariant. I’m not saying Harry is being technically precise but he’s not completely wrong, either.
No, he’s certainly not completely wrong, but he’s bringing up irrelevant complications and missing the main point. Quantum vs classical has nothing to do with it, for example.
The fact that quantum mechanics conserves energy is stronger evidence for the hypothesis that reality conserves energy than the fact that classical mechanics conserves energy. He is saying “our best model of reality conserves energy” which is very relevant.
If quantum mechanics allowed for small violations of energy conservation (which sometimes people even say that it does, on short time periods, although this is not really correct), then McGonagall’s tranformation would still violate physical law as we know it. In physics, you don’t always push everything down to the most fundamental theory, which is a good thing, since we don’t actually have a most fundamental theory of physics. There is no such thing as ‘our best [single] model of reality’; there are some ways in which our quantum models are (so far) worse than our classical ones.