Does spacetime have a "mass" value? or What is "Spacetime" made out of?

Question

When measuring the MASS within the Universe, does "space" or "spacetime" have a value?

I only ask, because when speaking of expansion, space is expanding. Could it be possible, to reverse the process, by "uncreating" space?

For if it can be created, surely it can be destroyed. And if it is "created", it must be created out of something. What is this "something", and is it only gravity that can manipulate it.

Answer 1

The questions you ask are really difficult to answer. Mass is not a property of space (or space-time itself), but of physical objects in classical physics. In General relativity, it is difficult to speak about mass clearly, there is no good general definitions.

Now, there are two naive metaphysics about space-time. The substantivalists think that space-time exists by itself, even if its not "made" out of something, and that if you remove all matter from it it is still here (but empty). The relationalists on the other hands, think that space-time is emerging from the relations between matter and that it does not make sense to speak of space-time itself without matter. For substantivalists, space-time has points that "really" do exists, while for relationalists it does not.

I said that these two approach where naive. Why ? If you're a substantivalist, you would have to explain why space-time has points and why, if you do a Leibniz shift of all the matter inside it (that is, you shift all matter by a constant and add some constant velocity with respect to some inertial frame), then the resulting universe we measure is actually the same while its a different configuration. Is there really a need to believe in points if two different configurations are indiscernible ? There is also the hole argument from Einstein in general relativity, but its much subtler (see http://en.wikipedia.org/wiki/Hole_argument).

Now, if you're a relationalist, you would have to explain why is acceleration absolute ? How comes that even if I'm alone in space-time, without referring to anything near or far away from me, I can know for sure if I'm accelerating (say, rotating) or not ? This shows that space-time is not entirely relational, you can look at Newton's bucket for this deep argument.

What we can say, is that space-time is a weird thing we don't really understand. Yet, it is certain that it has an "inertial structure" that allows you to discriminate what it means to accelerate or to be "not moving" (that is, being inertial or following a geodesics in GR). How is that possible to reconcile the presence of an inertial structure without having points ? Nobody knows right now.

Answer 2

No one really knows the answers to you questions. Spacetime is most assuredly made of something as it is not a void and, by General Relativity, shown to be inhomogeneous: curvature over here in this piece of spacetime can be different from the curvature in that piece over there, so it has position-dependent properties.

You could construe the cosmological constant term $\Lambda\,g$, where $g$ is the metric tensor and $\Lambda$ the cosmological constant, as a kind of mass or gravitational source property of "empty" spacetime, but you need to take heed that this term behaves quite differently from the other source terms in Einstein's equations. $\Lambda\,g$ is wiped out outright by the covariant derivative ($\nabla_X (\Lambda\,g)=0$), for example, whereas general energy distributions represented by the stress energy tensor are not (although the SE tensor's divergence is nought, expressing local conservation of energy/momentum). Indeed, some people call the $\Lambda\,g$ term Dark Energy.

You could say that the whole field of quantum gravity is directed at learning exactly what spacetime is made of, and how it gives rise to things such as the Einstein equations and this of course is very much an ongoing endeavour.

Answer 3

Given that all existing matter and space had a common origin, it seems reasonable to assume that there is a possibility that if you could calculate the net mass of all the matter in the universe this value might be matched by a negative mass of what remains (i.e. space). If this was true then space itself would have a negative mass, and given this mass would be spread out amongst all existing space the negative mass would be very small when compared to a matching volume of matter. Whilst this might sound like strange thinking you have to factor in that if this was true then large amounts of space (e.g. the space between galaxies) might go some way to explaining the cause of why the expansion of our universe is actually accelerating rather slowing down.