06-01-2003, 06:46 AM
Hi,
Well, some form of conservation of energy is a consequence of Einstein' general theory of relativity: the Einstein field equations (G = Einstein curvature tensor, T = energy-momentum tensor):
G = 8 pi T
impy that Div T = 0 (via the Bianchi identities), which is a form of energy-momentum conservation;
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. Which, of course, can happen for short times according to the time-energy commutation relationship. If one loophole, why not more?
In special relativity (flat space-times), or classical mechanics, conservation of energy is much more straightforward, and in all cases it's connected with the fundamental concept (via Noether's theorem) of the invariance of the laws of nature under time translations.
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.
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.
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.
--Pete
Well, some form of conservation of energy is a consequence of Einstein' general theory of relativity: the Einstein field equations (G = Einstein curvature tensor, T = energy-momentum tensor):
G = 8 pi T
impy that Div T = 0 (via the Bianchi identities), which is a form of energy-momentum conservation;
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. Which, of course, can happen for short times according to the time-energy commutation relationship. If one loophole, why not more?
In special relativity (flat space-times), or classical mechanics, conservation of energy is much more straightforward, and in all cases it's connected with the fundamental concept (via Noether's theorem) of the invariance of the laws of nature under time translations.
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.
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.
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.
--Pete
How big was the aquarium in Noah's ark?