Time Travel

[Thecla]

Unless I'm mistaken, it is an energy conservation in the sense that there can be no net flow of energy into or out of the universe. Making it more in the nature of a boundary condition. However, I believe that it really does not address the appearance or disappearance of energy within the universe.

Well, standard conservation of energy says that: rate of change of energy in an arbitrary region = flux of energy through the boundary of the region; but in general relativity it doesn't quite work that way because you can't localize the energy in the gravitational field (you can always choose a reference frame in which the gravitational field vanishes locally). But you can assign a definite mass/energy to an isolated object, like an isolated black hole, even though it's just one item in the universe.

Yes, if the laws of nature are invariant under time translations then a quantity is conserved that can be identified as energy. However, there is some question of the time invariance of physical laws. Hence the question of the constancy of G over the age of the universe.

Even if G is constant, then you don't have invariance under time translations if the universe is expanding, and this is closely related to the difficulties in defining energy conservation in general relativity (space-time is not invariant under time translations).

It's been almost 30 years since I've thought of Emmy and her theorem. Every invariance in four space corresponds to a conservation law -- a beautiful theoretical concept. So, displacement gives us momentum, rotation gives us angular momentum, and so on. In practice, it just gives us an additional way of finding or testing conservation laws. It's been too long. How does Noether's Theorem apply to the quantum conservations? It seems that I remember it as part of a classical mechanics course and the direct application to quantum, if any, eludes me. Of course, quantum has a very similar basis as reflected in the various commutative relations.

Yup, there's a beautiful quantum mechanical version of Noether's theorem (described, for example, in Vol III of Feynman's lectures on physics), which in many ways is simpler than the classical version: any operator that commutes with the Hamiltonian (which generates the time evolution of a quantum system) generates a conservation law. But no one really knows what's the physically correct combination
of quantum theory and general relativity (gravitation), though string -- or membrane -- theorists may disagree.

So, yeah, perhaps my statement was too general. However, neither special not general relativity really address the question of a sudden change in energy caused by an object being translated in time. Perhaps, we could extend the theory of an anti-particle being a particle going back in time (CPT conservation). The world line of the particle forms an "N" with extended start and finish. Before the "loop back" and after, there is only the one particle. During the "loop back", there are two particles and an antiparticle. When all the conserved quantities are summed, the two conditions are "identical".
Considerations of that type could, possibly, lead to some postulated limitations on time travel.

Well, my only real point is that there's no conclusive objection to time travel based on energetic considerations: the cosmologies that allow time travel allow it by global, topological means -- you travel around the universe, or some portion of it, and return earlier than when you started. There's no mention of ancestors, or descendents that kill them, in the theory of general relativity, any more than Schrodinger's cat is an integral part of the in the theory of quantum mechanics.