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In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?

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From the perspective of classical general relativity at least, spacetime is really more like a container for objects that can possess energy or momentum. Einstein's equations $$ G_{\mu\nu} + g_{\mu\nu}\Lambda = 8\pi T_{\mu\nu} $$ then basically tell you how such objects curve spacetime. The left hand side of this equation contains quantities that determine what spacetime looks like, and the right hand side represents the energy and momentum of all the stuff you put in it. So the answer from the perspective of classical general relativity is no, spacetime does not possess momentum, but it is affected by things that do.


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The answer isn't quite that simple. For example, the Schwarzschild metric is everywhere flat, but if a particle falls into the black hole singularity, a net momentum will be tranferred to it as the black hole grows. There is certainly a sense in which this momentum could be said to "belong to the spacetime" at late times. –  Jerry Schirmer Jan 29 '13 at 23:08
And, to add another example to @JerrySchirmer 's point, a gravitational wave should certainly be regarded as possessing energy and momentum. –  sjasonw Jan 29 '13 at 23:28
@JerrySchirmer Yeah that's a good point, thanks for the comment! –  joshphysics Jan 29 '13 at 23:32
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In the case of an asymptotically flat spacetime (basically, one in which all of the matter is confined to a finite area of the spacetime), there is a quantity called the ADM Momentum that will tell you the total momentum contained in the spacetime, factoring both the matter and a contribution "from the geometry". There are other schemes that let you do stuff like this if you have a timelike or null killing vector defined on a timelike or null 3-d surface. Then, you can talk about the momentum (and energy) contained "within" this surface. There is a review article on the topic here

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