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Does gravity exist between quarks in a neutron?

I mean, I've learned that gravity exists between objects that have mass/energy. But does this apply between quarks in a neutron?

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  • $\begingroup$ Related: physics.stackexchange.com/q/130594/2451 , physics.stackexchange.com/q/215997/2451 and links therein. $\endgroup$ – Qmechanic May 5 '16 at 14:41
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    $\begingroup$ Since gravity obviously exists between quarks in seperated neutrons (otherwise no neutron stars), why would it not exist between quarks in the same neutron? $\endgroup$ – Lewis Miller May 5 '16 at 15:09
  • $\begingroup$ I don't see any reason that there wouldn't be any gravity between quarks in a neutron; they have mass and/or energy, but I could be corrected. $\endgroup$ – Anthony Holmes May 5 '16 at 15:29
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    $\begingroup$ I think you need a theory of quantum gravity in order to answer this question. If gravity is like the other forces in that it is mediated by virtual particles, then you have to deal with how frequently those gravitons can be exchanged since gravity is so weak. The answer would then be for a given pair of quarks in a neutron, there is a minuscule probability of virtual gravitons being exchanged while in a neutron star, there are so many quarks that are also densely-packed that many virtual gravitons are exchanged and we get the classical limit of gravity as a continuous field. $\endgroup$ – MSha May 5 '16 at 15:48
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    $\begingroup$ Define the phrases "gravity exists" and "quarks in a neutron". A neutron is a bound state of three quarks, there are no individual quarks "floating around". $\endgroup$ – ACuriousMind May 5 '16 at 17:07
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As far as we know the classical (i.e. non-quantum) laws of gravity apply at all length scales. There are theoretical reasons to suppose that the classical description fails at scales approaching a Planck length, but this is far, far smaller than the size of a neutron.

So inside a neutron we would expect the classical laws of gravity to apply, and in particular we would expect Newton's law to be good description - it doesn't seem likely we'd have to use general relativity. A simple calculation will show you that the gravitational energy is immeasurably small compared to the strong force binding energies, but in principle there will be some gravitational interactions.

But if you have an image of the neutron with the three quarks as little balls orbiting each other then you need to abandon that image. Firstly the quarks are delocalised so they exist as fuzzy objects distributed throughout the nucleus, and secondly 99% (ish) of the stuff inside a neutron is interaction energy not the three valence quarks. Exactly how you would calculate the gravitational interactions in such a system is unclear.

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  • $\begingroup$ The folks who are looking for post-Newtonian gravity are not expecting Newtonian gravity to hold down to the nuclear scale, neither are many quantum field theorists who would love to have macroscopic hidden dimensions. Down to 0.1mm, or so, no fun, though... $\endgroup$ – CuriousOne May 5 '16 at 20:07

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