# I Prediction of GR for the gravitational pull

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1. Apr 21, 2017

### ftr

It is said that GR in the weak field limit it produces Newtons familiar law, so why can't GR produce other formulas for "strong field" which I guess it means at short distances.

2. Apr 21, 2017

### Drakkith

Staff Emeritus
What do you mean? Are you asking why you can't reduce the equations for very strong field strengths, such as near neutron stars and black holes, to simple formulas like Newton's Law of Universal Gravitation?

3. Apr 21, 2017

### ftr

no I mean like why can't GR predict this
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.021101

4. Apr 21, 2017

### Staff: Mentor

What makes you think it can't?

5. Apr 21, 2017

### Staff: Mentor

6. Apr 22, 2017

### ftr

Because it seems EQ 1 in the paper assumes the potential form, is it derivable from GR?

7. Apr 22, 2017

### pervect

Staff Emeritus
If you could scale up the experiment to large enough plates (how large is something I haven't attempted to calculate), eventually you could get into a region where strong fields were important. Of course, it'd be useless for testing gravity at small distances, which is what the author is interested in. Another realm where strong fields could be important would be to increase the density of the materials used, keeping the experimental setup the same size.

In either case, it's unlikely that you could actually build such an experiment - no known form of matter wouldn't be strong enough to hold the required shape (a plate with holes in it). Even for something as small as a planet, the strength of the matter making up the planet is mostly ignorable - to a good approximation they can be treated as perfect fluids, not rigid bodies. And planets aren't big enough to generate "strong gravity" in the sense that the nonlinearities in Einstein's field equations become important - they're too small. Or not dense enough, take your pick.

8. Apr 22, 2017

### Staff: Mentor

The paper does not derive it from GR, it just assumes it. But it assumes it as an alternative hypothesis to the standard $1 / r$ potential that is derived from GR. Then it proceeds to show experimental data that confirms the GR potential and rules out the alternative potential described in equation 1. So the upshot of the paper is that GR does predict what we actually observe.

9. Apr 22, 2017

### Staff: Mentor

Another thing about equation 1 in the paper, the potential described there is in fact the standard form of the interaction potential you get in the classical limit if you assume a massive gauge boson instead of a massless one in quantum field theory. The constant $\lambda$ in the potential is related to the mass of the gauge boson.

Standard GR is the classical limit of the field theory of a massless spin-2 gauge boson; so the potential in equation 1 in the paper would not be derivable from standard GR, but only from a variant of it that was the classical limit of the field theory of a massive spin-2 gauge boson. One way of interpreting the results given in the paper is therefore as setting limits on the possible mass of the spin-2 gauge boson, i.e., the graviton. This would be similar to experimental results that set limits on the mass of the photon in electromagnetism.

10. Apr 22, 2017

### ftr

They motivate in the first paragraph with details in this paper, which has over 200 citations ! My interpretation is that they are trying to look for things like extra dimensions and other quantum correction to classical results. However, I don't know of any calculations for GR at those scales, I assume it is the inverse square law.

11. Apr 22, 2017

### Staff: Mentor

Yes, and so far none have been found.

GR's predictions are not scale-dependent; for the special case under consideration (see below), GR predicts the inverse square law independently of the distance scale being probed.

However, it's important to understand exactly what the "special case under consideration" is that GR predicts the inverse square law for. That special case is the case of an object which is dropped from rest, in a purely radial direction (or held at rest by a purely radial force), in the vacuum region surrounding a spherically symmetric (i.e., non-rotating) isolated massive object, whose surface radius is sufficiently large compared to its mass. As soon as you violate any one of these conditions, GR's prediction becomes more complicated, and in general can't be interpreted as a central Newtonian "force" at all. So if your question is whether GR can "produce other formulas" for other cases, certainly it can. You just have to be clear about what case a given formula applies to.

12. Apr 25, 2017

### dextercioby

Related to the arxiv preprint mentioned above with alleged 200 citations. Were I to write an article, I wouldn't call a chapter "Theoretical Speculations". A no-no word in physics...