# Is it contradictory with any theory or experimental result to have a negative gravitational force mass?

I am aware that there are many similar questions here about this in this site, but most answers concentrate on negative inertial and gravitational energy. My question is more specific.

QM together with special relativity tells us that we can generate interactions in which same charges repel if using spin one force carriers (photons). And same charges attract if using spin 2 carriers (gravitons?). I do not see anything wrong if, by symmetry you could have two mass charges, negative and positive. Of course, I am assume they work only as charges, so the inertial mass will still be positive, same too with the active mass of general relativity responsible for curvature. Here the principle of equivalence would work only for positive masses, or best, for the absolute values of the masses regardless of sign.

So is there any reason in which general relativity forbids a gravitational force of opposite sign? (do not call it gravity is that helps). In such a scenario I suspect that same charges will clump separately from positive charges and repel each other. So perhaps we have in nature galaxies made of negative matter whose dynamics would be otherwise indistinguishable from galaxies with positive matter.

Is this scenario plausible or does GR forbids it?

• Dumb question by somebody not familiar with renormalization: would the existence of such hypothesized particles help in reducing the difficulties of renormalizing quantum gravity ? – user83548 May 18 '16 at 18:07
• More on negative mass and gravity. – Qmechanic May 18 '16 at 18:58
• that answer deals with negative inertial, as opposed to gravitational, mass – user83548 May 18 '16 at 19:04

## 1 Answer

Negative energy or mass is not forbidden in Relativity, but gravity is not a force but geometry, so if you have a negative mass it would repell positive mass as well as negative mass, just like positive mass would attract negative and positive mass all together.

If you place a positive and a negative mass near each other the positive mass would attract the negative one while the negative mass repells the positive one, and they would both accelerate in direction of the positive mass until they get close to the speed of light.

The technical term for this is runaway pair, see video, presentation and plot.

• This do not provide a answer, the OP explicitly says that inertial mass is positive, something violated in the video presentation – user83548 May 18 '16 at 18:26
• If inertial and gravitational mass were not equal it would be forbidden by Relativity. – Gendergaga May 18 '16 at 18:30
• I know it would be no longer standard GR, but would modifying the principle of equivalence just slightly, "would work for the absolute values of the masses regardless of sign", have any major consequences? – user83548 May 18 '16 at 18:36
• @brucesmitherson: You can't modify anything in science except for the purpose of hypothesis building, but then you have to immediately progress to destroying the hypothesis by testing it against all known data. If you modify the equivalence principle even "slightly", then you either run into problems with the data or you have created the case of a currently indistinguishable theory. – CuriousOne May 18 '16 at 21:19
• In Newtonian mechanics both are numerically the same, but one could in principle distinguish between the gravitational and the inertial mass when hypothesizing about exotic matter. In general relativity this is as far as I know not possible any more, they both have to have the same sign no matter what, may it be positive or negative. – Gendergaga May 18 '16 at 22:21