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Expansion and conservation of energy 
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#1
Jun310, 08:21 AM

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According to quantum field theory there is an intrinsic energy of the vacuum or zero point energy (which is being related to cosmological constant by some cosmologists, i.e.:http://philsciarchive.pitt.edu/arch...osconstant.pdf ), so if space stretches with expansion, is the energy of this space vacuum being created all the time? if so, is this in conflict with the energy conservation law?



#2
Jun310, 01:44 PM

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In GR, energy is only (necessarily) conserved locally. This means that the stress tensor satisfies [tex]\nabla^{\mu}T_{\mu\nu} = 0[/tex]. The stress tensor that can be used to represent vacuum energy [tex]T_{\mu\nu} = Cg_{\mu\nu}[/tex] (for some constant C) certainly satisfies this.
Alternatively, if you want a Newtonian viewpoint, vacuum energy has a negative pressure, and the field does "negative work" to expand the universe. This "negative works" allows for extra energy in the field taking up more volume. It is the exact opposite situation as with photons, where photons have positive pressure and thus do work in expanding the universe, which exactly compensates for the energy loss (redshift) in the photons). 


#3
Jun310, 02:37 PM

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Still expansion is an observed fact not directly derived from GR which is a theory of gravitation. Maybe someone has a more direct answer to my question? 


#4
Jun310, 02:45 PM

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Expansion and conservation of energy



#5
Jun310, 03:38 PM

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Am I to conclude that the expansion of the universe is somewhat in conflict with global energy conservation ,but that it is a fact assumed by the scientific stablishment and either is not seen as a real problem or simply ignored, or seen as small problem and there is people already figuring it out? Or none of the above? 


#6
Jun310, 04:40 PM

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That said, the issue of energy is tricky in GR. There are physical descriptions that restore global energy conservation (google "pseudotensor"). If you have a problem with nonconservation, find comfort in these. 


#7
Jun310, 06:45 PM

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Ok, so there is no conflict because the first law of thermodynamics doesn't apply to timedependent situations such as expansion, is that it?
I guess what bugs me a little is that most of physics seems to be timeinvariant and yet expansion scapes this rule. 


#8
Jun410, 04:22 AM

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P: 4,782

One way of thinking of it is that energy is only one component of the stressenergy tensor, which is the object upon which gravity acts. Individual components of the stressenergy tensor are not conserved: the quantity as a whole is. And conservation of the totality of the stressenergy tensor (which includes things like momentum, pressure, and shear as well as energy) forces the nonconservation of individual components of the tensor, under the right conditions.
In general, you only get conservation of individual components like energy in a flat spacetime. Now, any small enough region of spacetime can be described as being flat (which is why it is possible to say that energy is conserved locally, but only if you use coordinates in which the spacetime is flat in that local region). But in general you can't describe spacetimes as being globally flat in this way, so energy conservation is forced to fail due to stressenergy conservation. 


#9
Jun410, 06:28 AM

P: 534

Sean Carroll has talked about energy conservation (or the lack thereof) in GR on his blog:
http://blogs.discovermagazine.com/co...notconserved/ 


#10
Jun410, 06:53 AM

P: 3,001

Thanks for the answers.
yenchin , the link is quite interesting, I found it yesterday. 


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