Relation between mass and spacetime

Question

I am trying to understand whether spacetime possesses an intrinsic "elasticity" that is acting as a sort of counter-force to mass trying to bend it.

Note that gravitational waves can propagate through spacetime. To me, that makes spacetime “elastic” in some sense, but I think it’s fairly rare for relativists to actually use this term. People don’t usually call the electromagnetic field elastic just because EM waves propagate through it. But with metric perturbations changing distances between events, the term seems somewhat more appropriate. — Ghoster, Dec 09 '22 at 19:22
there is also a back-reaction effect that happens when gravitational waves are generated, which shows that you can "push off of spacetime" — Zo the Relativist, Dec 09 '22 at 19:22

score 2 · Answer 1 · answered Dec 09 '22 at 20:15

In 1967, Andrei Sakharov proposed, in a very brief one-page paper, that vacuum fluctuations in quantum field theory resulted in empty space having an associated energy, that implied curvature of spacetime was resisted by a sort of generalised 'elastic' force.

The presence of the action (1) leads to a "metrical elasticity" of space, i.e., to generalized forces which oppose the curving of space.
Here we consider the hypothesis which identifies the action (1) with the change in the action of quantum fluctuations of the vacuum if space is curved. Thus, we consider the metrical elasticity of space as a sort of level displacement effect (cf. alsoRef. I).

A.D. Sakharov. Vacuum quantum fluctuations in curved space and the theory of gravitation. Doklady Akad. Nauk S.S.S.R., 177:70–71, 1967. [Sov. Physics Doklady, 12:1040–1041, 1968].

Sakharov's paper didn't give a lot of detail, but a very quick search suggests there is subsequent work based on the same idea. For example:

Millette, Pierre. (2013). Elastodynamics of the Spacetime Continuum. The Abraham Zelmanov Journal, ISSN 1654-9163. 5. 221-277.

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score 1 · Answer 2 · answered Dec 09 '22 at 20:16

There is a note by Kirk T. McDonald, Princeton university, discussing the Young modulus of elasticity of spacetime. The title of the note is: What is the stiffness of spacetime?

McDonald arrives at a number for Young's modulus of elasticity, of spacetime, that is in the order of $10^{20}$ times larger than that of steel.

McDonald mentions that his note was triggered by the response by Kip Thorne (during the question time after a lecture) to an audience question about the modulus of elasticity of spacetime. This response is at 1:21:20 of the Kip Thorne Lecture

Upon being asked about the modulus of elasticity of spacetime Kip Thorne looks up to the audience and says: "Ray, help me.". Rainer Weiss then proceeds to give the order of magnitude indication of $10^{20}$ higher than steel modulus of elasticity.

score 1 · Answer 3 · answered Dec 10 '22 at 01:12

See the 2018 paper by Melissinos, which is a rejoinder to McDonalds 'classical' result in the reproduced answer by Cleonis.

Melissinos points out that in our quantum Universe, the Youngs Modulus of space-time is frequency independent, limited only by the energy density of the medium through which the gravity wave propagates.

From the recently observed propagation of gravitational waves through space-time an upper limit can be deduced for the stiffness of space-time through which the gravitational wave propagates. The upper limit is extremely weak, implying that the stiffness of space-time is at least 14 orders of magnitude weaker than that of jello.

The radical difference between the classical and quantum results is another way to express the so-called cosmological constant problem.

Relation between mass and spacetime

3 Answers3