06-01-2003, 03:33 PM
Hi,
you can't localize the energy in the gravitational field (you can always choose a reference frame in which the gravitational field vanishes locally).
IIRC, as measured from an accelerated frame that cancels the local field, the gravitational energy of the rest of the universe increases just enough that the total stays constant. Thus, it is meaningless to ask for the energy distribution but not for the total energy in the universe.
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.
If you are talking rest mass, I agree. However, just from the special theory that statement is not true for total energy. Consider two observers, each in an inertial frame moving relative to each other. Each will assign a different value to the total energy of that black hole. So either I'm missing something or I disagree with that statement.
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).
I'm a little bit confused here. The system (the universe) is not invariant under time translations. That has been pretty well established, the expansion of the universe not really being in doubt. But simply because the system is evolving does not mean that the laws governing the system are changing. From what I remember of Noether's theorem, the basic premise is that if the *origin* of the reference frame can be moved, then something (the conjugate variable in the Lagrangian sense, IIRC) related to that axis is conserved. Since the absolute time of an event doesn't matter, just the relative time between two events as measured in some frame, then unless the physical laws change between those two events, energy is conserved.
Yup, there's a beautiful quantum mechanical version of Noether's theorem (described, for example, in Vol III of Feynman's lectures on physics),
Thanks. I'll have to pull those red bastards out, blow the dust off, and give them another read :) Last time I went through them was Summer '76 for my prelims. I wish I knew as much physics as Feynman forgot during his life :)
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.
From the literature I've perused, I'd say that a lot of people think they know how to combine them. Of course, they all have different ideas, many contradictory, and none developed to the point that will meet the empirical test. But it gives a lot of smart folks a great game to play for now ;)
Well, my only real point is that there's no conclusive objection to time travel based on energetic considerations
In that we are in complete agreement.
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.
Right. However, sometimes, it is necessary to relate things which we can neither observe directly nor test conclusively to our everyday experience. It isn't so much a test of a theory as of its interpretation. Gedanken experiments are a useful way of exploring possibilities or clarifying concepts. Neither too much nor too little emphasis should be placed on them. After all, nature's logic may not be (probably isn't) ours.
--Pete
you can't localize the energy in the gravitational field (you can always choose a reference frame in which the gravitational field vanishes locally).
IIRC, as measured from an accelerated frame that cancels the local field, the gravitational energy of the rest of the universe increases just enough that the total stays constant. Thus, it is meaningless to ask for the energy distribution but not for the total energy in the universe.
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.
If you are talking rest mass, I agree. However, just from the special theory that statement is not true for total energy. Consider two observers, each in an inertial frame moving relative to each other. Each will assign a different value to the total energy of that black hole. So either I'm missing something or I disagree with that statement.
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).
I'm a little bit confused here. The system (the universe) is not invariant under time translations. That has been pretty well established, the expansion of the universe not really being in doubt. But simply because the system is evolving does not mean that the laws governing the system are changing. From what I remember of Noether's theorem, the basic premise is that if the *origin* of the reference frame can be moved, then something (the conjugate variable in the Lagrangian sense, IIRC) related to that axis is conserved. Since the absolute time of an event doesn't matter, just the relative time between two events as measured in some frame, then unless the physical laws change between those two events, energy is conserved.
Yup, there's a beautiful quantum mechanical version of Noether's theorem (described, for example, in Vol III of Feynman's lectures on physics),
Thanks. I'll have to pull those red bastards out, blow the dust off, and give them another read :) Last time I went through them was Summer '76 for my prelims. I wish I knew as much physics as Feynman forgot during his life :)
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.
From the literature I've perused, I'd say that a lot of people think they know how to combine them. Of course, they all have different ideas, many contradictory, and none developed to the point that will meet the empirical test. But it gives a lot of smart folks a great game to play for now ;)
Well, my only real point is that there's no conclusive objection to time travel based on energetic considerations
In that we are in complete agreement.
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.
Right. However, sometimes, it is necessary to relate things which we can neither observe directly nor test conclusively to our everyday experience. It isn't so much a test of a theory as of its interpretation. Gedanken experiments are a useful way of exploring possibilities or clarifying concepts. Neither too much nor too little emphasis should be placed on them. After all, nature's logic may not be (probably isn't) ours.
--Pete
How big was the aquarium in Noah's ark?