Experimental tests of zero divergence for stress-energy?

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bcrowell

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We expect the stress-energy tensor to have zero divergence, because this is required for local conservation of energy-momentum, which has been verified to high precision in laboratory and solar system experiments. The standard review article is Will, "The Confrontation between General Relativity and Experiment." Will does explicitly discuss PPN parameters that would violate conservation of momentum: http://relativity.livingreviews.org/Articles/lrr-2006-3/articlesu5.html#x11-190003.2 [Broken]

What remains unclear to me is:

(1) Why does PPN appear to treat energy and momentum differently, when they're actually part of the same four-vector? Or is this difference just in Will's presentation? If we assume (a) no preferred frame and (b) conservation of energy in some frame, then it follows that we must have conservation of momentum. But since PPN explicitly allows preferred frames, the situation seems hazy to me.

(2) How would one test whether dark energy gives a stress-energy tensor with zero divergence? We can't do it in the lab, because we have no access in the lab to any empirical tests of the properties of dark energy (e.g., its equation of state). So do cosmological observations tell us anything about this, or are we assuming that dark energy has zero divergence purely because the rest of physics works that way?

(3) At scales where dark energy has a negligible effect, which is the better test of conservation of energy-momentum: laboratory experiments, or solar-system/space probe data?
 
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Why does PPN appear to treat energy and momentum differently, when they're actually part of the same four-vector?
What different treatment are you referring to? The fact that there are different PPN parameters for the violation of energy and momentum (and angular momentum) conservation, instead of just one?

How would one test whether dark energy gives a stress-energy tensor with zero divergence?
The simplest test would be to test whether dark energy density is constant everywhere and at all times (in practice, we can't avoid assessing both since we are looking along our past light cone); if it is, then its stress-energy tensor is just that constant times the metric, which obviously has zero divergence. As far as I know, all of our observations to date are consistent with this, although I don't know how tightly it is pinned down.

If the density is not constant everywhere, then I think one would have to be able to somehow measure the different components (density and pressure, at a minimum) in order to be able to explicitly measure the stress-energy tensor and take its divergence. I'm not sure what cosmological observations would help with that.

At scales where dark energy has a negligible effect, which is the better test of conservation of energy-momentum: laboratory experiments, or solar-system/space probe data?
My intuitive guess would be laboratory experiments, simply because it's possible to control things so much more precisely.
 

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