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(Disclaimer: the following might fit better on Worldbuilding - on the one hand, I'm not looking to write a story, but on the other, I don't know enough physics to know whether this is a trivial "no, save it for science fiction". Also could be considered a follow-up to this question).

Suppose for a moment that gravity is symmetric with electromagnetism, only with like "charges" attracting rather than repelling, and opposite charges repelling rather than attracting.

At the macro scale, billions of years of opposite gravitational polarities mean a sort of segregation of positively and negatively "charged" particles, which seems a plausible surface explanation for the lack of antigravity in day-to-day life - but, as I said, I don't know the physics well enough (read: at all) to say how well that explanation holds up under closer scrutiny.

At the micro scale, I don't know that we've had the capacity to observe the effects of gravity one way or the other on individual particles (to the extent that "individual particles" makes sense in modern physics), but while I'm on this hypothetical/crackpot bent I'd note that as long as the repulsive force from antigravity is exceeded by an attractive force from one of the other fundamental forces you could have, say, (obviously less stable) "hybrid" atoms, with a corresponding reduction in the observed gravitational force due to that atom.

Averaged over lots* of atoms, and you'd have what appears to be gravity that's significantly weaker than other forces, due to some of it being cancelled out by the mixed-in antigravity particles (presumably both fall off at $1/r^2$, and I'm also assuming there's no catastrophic mutual annihilation as with antimatter).

So. "totally uncharged" is obviously a consistent option. Are there any nonzero magnitudes for charged gravity that would be consistent with observations?

Probably more importantly for physics, but less important from a personal-interest perspective, how would we test this? Or, if this has already been disproved elsewhere, what experiments have we performed to rule this out?

*For experimentally confirmed values of "lots", ideally

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    Apart from deeper theoretical reasons why repelling gravity shouldn't exist, there is a rather trivial one: if there are both, repelling and attractive forces, the result is not that they "get sorted out", but the result is screening with an effective potential that has an exponential character. This is well observed in e.g. plasma physics: https://en.wikipedia.org/wiki/Debye_length. As you can see, the screening effect gives rise to a new scale, the Debye length and the observation of such a scale would be one tell-tale sign for repulsive gravity. – CuriousOne Mar 18 '16 at 06:10
  • I've chosen what seems an obvious duplicate, but there are lots of questions related to negative mass. – John Rennie Mar 18 '16 at 08:51
  • @JohnRennie Thanks, that's helpful; the behavior I'm describing looks like it matches dark energy more than negative mass, but it's interesting to learn about the counterintuitive behavior of "negative-mass particles would chase positive-mass particles". – Stephen Voris Mar 18 '16 at 11:50
  • @CuriousOne That sounds like an answer to me; I'm not entirely sure what you mean by "screening", though. Could you expand that term? – Stephen Voris Mar 18 '16 at 11:57
  • @JohnRennie Okay, after looking through those other questions - and other answers - and giving it a bit of time to simmer, I think this question is salvageable from the duplicates-bin if I focus it more on the experimental bounds than the theoretical ones. But also got a bit confused by the accepted answer here -http://physics.stackexchange.com/questions/44934/does-matter-with-negative-mass-exist - which really doesn't match the behavior I'm describing, and makes me think that what I'm describing isn't actually negative mass. – Stephen Voris Mar 18 '16 at 16:02
  • @StephenVoris: if you feel I've closed your question fairly post a comment here and I'll retract my close vote. However I think you should read up a bit on exotic matter first before doing so. While I've used negative mass as an example it is just one example of a range of types of matter/energy that break the energy conditions. See for example Significances of energy conditions or the Wikipedia article. – John Rennie Mar 18 '16 at 16:31

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