# Is it possible to directly test whether of not the vacuum gravitates?

According to GR, all sources of stress-energy (e.g. everything on the $T_{\mu\nu}$ side of the EFE) should gravitate (e.g. affect the curvature/$G_{\mu\nu}$ side of the EFE). We observe the expansion of the universe, which (for now) fits the expected expansion of a small cosmological constant. However, that does not mean that the expansion is due to a cosmological constant (the expansion may be a slowly moving scalar field, for ex., or something else). Also GR (while well tested) may be a limit of a more fundamental theory. Particle physics expects the cosmological constant to be much greater than what is observed in cosmology.

How would we go about testing whether or not the vacuum itself gravitates? The only way I can think of is something involving combining an Eot-Wash experiment with a casimir force measurement.

p.s. The casimir force itself (as I understand) might not even be probing the vacuum.....there was a paper i saw a year ago explaining the casimir effect as the result of a van der waals force between the plates or something like that (i'd have to dig to find it if anyone is curious).

• There is a basic misunderstanding here, which is the common misconception that dark energy/$\Lambda$ is needed in order to explain cosmological expansion. Actually dark energy is only needed in order to explain the anomalous part of the acceleration of cosmological expansion. – Ben Crowell Jul 25 at 21:26

How would we go about testing whether or not the vacuum itself gravitates?

Do we need to? General relativity is one of the best-tested theories we've got, see Clifford M Will's paper at http://arxiv.org/abs/1403.7377. And in the Foundation of The General Theory of Relativity Einstein did say this: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". The space around a star is vacuum, and it itself gravitates.

One could argue that flat galactic rotation curves and gravitational lensing in the bullet cluster are direct tests of this. It's not as if anybody has actually detected any WIMPs. Let's not forget that we don't know of any breaches of conservation of energy, and that the raisin-cake analogy tells us that space expands between the galaxies but not within. That ought to suggest that vacuum energy density is now greater where the galaxies are. And we ought to expect it to act gravitatively in the same way as any other kind of energy. Space is dark, it has its vacuum energy, and this has a mass-equivalence.

As for the cosmological constant, there's plenty of references where it's described as a negative pressure. A negative pressure is a tension. And where have we seen that before? In the balloon analogy:

Image courtesy of the one-minute astronomer.

If you have a balloon in a vacuum, the pressure of the air inside is balanced by the tension in the skin, and there's two ways to make it expand. One way is to blow more air into the balloon. However energy = pressure x volume so this in breach of conservation of energy. But there is another way that isn't: make the skin weaker.

• Yes we do need to. For example, unimodular (also called trace-free) gravity can be shown to be exactly equivalent to GR except: 1. the vacuum does not gravitate (e.g. the oft-stated 120 orders of magnitude problem goes away...actually it's less than this) and 2. you lose $\nabla^\mu T_{\mu\nu}=0$. This is a big trade-off, but it is interesting. – Bob Aug 3 '15 at 18:50
• I'm not arguing that GR has holes in it....just that this would be a (another) strong test that GR is the correct theory of gravity. Also, I don't see how your balloon analogy applies here. The vacuum I refer to is the cosmological constant. Not an absence of air. – Bob Aug 3 '15 at 18:52
• AFAIK any concentration of energy gravitates, Bob. The balloon analogy is an example of how a reducing negative pressure aka tension can cause expansion. Step up a dimension, and see arxiv.org/abs/0912.2678 where Milgrom says this on page 5: "We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime (except perhaps its strength), as is done in f(R) theories and the like". I'm not a MOND fan by the way. – John Duffield Aug 3 '15 at 19:03
• The space around a star is vacuum Depending on your definition of "vacuum" this may be true, but really isn't for most useful definitions of vacuum. If it were matter-based, then there's roughly 1 atom/cc in the ISM & more if there's a stellar wind, so not true there. If it were energy-based, then you've got $\sim10^{45}$ photons coming out from the sun each second, so not true there either. – Kyle Kanos Aug 3 '15 at 19:15
• Any concentration of energy gravitates in GR. In Trace free gravity, all forms of energy gravitate except the vacuum. Otherwise, the two theories are equivalent as far as what does or does not gravitate, and by how much. In a sense, this is asking for a test that can discriminate between GR and another theory of gravity. From the point of view of the cosmological constant problem $\Lambda\sim (10^{-3} eV)^4$, Trace free gravity matches the data much better than GR. I mainly want to argue that a test of whether or not the vacuum gravitates is well motivated. – Bob Aug 3 '15 at 19:15