| Topic: |
Science > Physics |
| User: |
"DAH" |
| Date: |
20 Sep 2004 11:39:34 AM |
| Object: |
conservation of energy in GR? |
“But in Einstein’s general theory of relativity, which incorporated
gravity, the proof of local energy conservation no longer worked.
This deeply concerned Hilbert. Violating energy conservation was
considered a pretty serious crime. So he asked Noether to
investigate the mathematics of general relativity to try to figure
out what was going on.”
“Noether succeeded. She showed that while energy was not conserved
locally, it was conserved globally--in other words, if you considered
a big enough region of space, everything was fine. Energy
conservation held. It was just that in smaller regions, looked at
from different points of view, the measurement of energy content
could differ depending on that point of view. Actually, the issue of
conservation of energy in general relativity is more complicated than
this; in different situations the very notions of energy and
conservation are not easily defined.”
---Strange Matters, Tom Siegfried, page 66
Can someone offer enlightenment on this issue without getting hip deep
in the mathematical argument provided by Emmy Noether? Is this issue
a roadblock in formalizing a theory of quantum gravity?
thanks,
DAH 9/20/04
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| User: "Old Man" |
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| Title: Re: conservation of energy in GR? |
20 Sep 2004 08:19:10 PM |
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"DAH" <dharder@bnl-dot-gov.no-spam.invalid> wrote in message
news:414f07c6_1@127.0.0.1...
“But in Einstein’s general theory of relativity, which incorporated
gravity, the proof of local energy conservation no longer worked.
DAH is confused or deliberately attempting to confuse.
In GTR: locally, energy is conserved; globally, energy
conservation isn't guaranteed. Old Man recalls that, in
the external Schwarzschild metric, global energy can be
shown to be conserved.
[Old Man]
< ... snip .... >
thanks,
DAH 9/20/04
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| User: "Bjoern Feuerbacher" |
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| Title: Re: conservation of energy in GR? |
20 Sep 2004 12:05:33 PM |
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DAH wrote:
?But in Einstein?s general theory of relativity, which incorporated
gravity, the proof of local energy conservation no longer worked.
This deeply concerned Hilbert. Violating energy conservation was
considered a pretty serious crime. So he asked Noether to
investigate the mathematics of general relativity to try to figure
out what was going on.?
?Noether succeeded. She showed that while energy was not conserved
locally, it was conserved globally--in other words, if you considered
a big enough region of space, everything was fine. Energy
conservation held. It was just that in smaller regions, looked at
from different points of view, the measurement of energy content
could differ depending on that point of view. Actually, the issue of
conservation of energy in general relativity is more complicated than
this; in different situations the very notions of energy and
conservation are not easily defined.?
---Strange Matters, Tom Siegfried, page 66
Can someone offer enlightenment on this issue without getting hip deep
in the mathematical argument provided by Emmy Noether?
AFAIK, it's exactly the other way round: locally, energy is conserved,
globally it isn't!
This stems from the fact that in GR, only the covariant derivative
of the energy-momentum tensor is zero; but for a "real" conservation
law, one would need the *coordinate* derivative of that tensor to be
zero. See here for more details:
<http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html>
If you want to have a more down-to-earth explanation: classically,
gravitation conserves energy because one can define a gravitational
potential, based on the force of gravitation. But in GR, neither
gravitational forces nor a gravitational potential exists any longer -
gravity is a fictitious force, like inertia in non-inertial frames. See
the last section here:
<http://www.physics.adelaide.edu.au/~dkoks/Faq/General/Centrifugal/centri.html>
Is this issue
a roadblock in formalizing a theory of quantum gravity?
No, AFAIK.
[snip]
Bye,
Bjoern
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