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Although they are very small, they are assumed to have gravity fields, because they have mass. But is this demonstrably true? I'd think that the field would be too small to measure with any existing technology.

If such fields cannot be measured, how can we be sure they even occur?

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    $\begingroup$ Possible duplicate of physics.stackexchange.com/questions/130594/… if we can't do it with atoms............. $\endgroup$
    – user108787
    Aug 17, 2016 at 16:13
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    $\begingroup$ Are you specifically thinking of free electrons? We know electrons in bound states, i.e. matter, gravitate because we can measure the gravitational field produced by a test mass and it isn't 1/2000 less than it should be. $\endgroup$ Aug 17, 2016 at 16:44
  • $\begingroup$ I guess I am thnking about free electrons. Interested in minimal fields. $\endgroup$
    – Jiminion
    Aug 17, 2016 at 17:28

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Before the existence of magnetometers, people were using compasses. We couldn't measure the magnetic field, but we knew it was there.

From another angle, how do you distinguish one type of mass-energy from another? Viewed purely from the perspective that particles carry a certain amount of mass-energy, without knowing what the mass-energies are, how do you distinguish between them? What determines whether or not the mass-energy is large enough to create a gravitational field?

There is no such defining line. All mass-energy contributes to the stress-energy tensor, which is used to find a set of solutions detailing possible metrics, i.e., the shape of the space in which these particles reside. Gravitational fields are simply manifestations of these shaped, or rather "curved", spaces

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