Could the conservation laws be expanded so all times are included?
This is indeed the standard approach in modern physics, yes. But then it gets even weirder.
Suppose that the person activating the time turner is turned into a blob of neutrinos which radiate in all directions undetected. Or just stayed where the person used to be, somehow. But they still have to assemble into this person some time in the past, so they cannot be ordinary neutrinos, they have to be the special traveling-back-in-time ones. Now, in the usual particle physics a particle traveling back in time is equivalent to an antiparticle traveling forward in time. Same mass, but (nearly) every other numerical quantum property reversed. In this case even their mass has to be negative.
So, here is a workaround. When Hermione (or Harry in HPMoR) appears in the past, an undetectable ghost of equal and opposite mass separates from her, leaving the total mass unchanged (zero). While she goes about her business, this invisible negative mass ghost-Hermione gets to the final destination in the future when and where she activated her time turner in order to go back, then annihilates the poor girl. Well, the “real” Hermione is now the other one, so that’s OK. Voila, energy is conserved. If you don’t mind negative-mass ghosts walking around for a time.
From science fiction physics[1]: Could the conservation laws be expanded so all times are included?
[1] I don’t remember where I saw the notion, but possibly Heinlein or Poul Anderson.
This is indeed the standard approach in modern physics, yes. But then it gets even weirder.
Suppose that the person activating the time turner is turned into a blob of neutrinos which radiate in all directions undetected. Or just stayed where the person used to be, somehow. But they still have to assemble into this person some time in the past, so they cannot be ordinary neutrinos, they have to be the special traveling-back-in-time ones. Now, in the usual particle physics a particle traveling back in time is equivalent to an antiparticle traveling forward in time. Same mass, but (nearly) every other numerical quantum property reversed. In this case even their mass has to be negative.
So, here is a workaround. When Hermione (or Harry in HPMoR) appears in the past, an undetectable ghost of equal and opposite mass separates from her, leaving the total mass unchanged (zero). While she goes about her business, this invisible negative mass ghost-Hermione gets to the final destination in the future when and where she activated her time turner in order to go back, then annihilates the poor girl. Well, the “real” Hermione is now the other one, so that’s OK. Voila, energy is conserved. If you don’t mind negative-mass ghosts walking around for a time.