Why masses attract each other? According to the gravitational law, every mass attracts each other.
But why the masses attract each other? Why they don't repel each other?
 A: Mass is gravity's equivalent of electric charge, with two obvious differences:


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*Charges can be positive or negative, but masses are positive. We can discuss "what about the mass-energy stored in gravitational fields?" or any number of gotchas, but you and me and planets, as familiar examples, definitely have positive mass.

*If the dissimilarity ended there, you might expect masses to repel: after all, positive charges repel each other. Mathematically, we need to get a sign change from somewhere.


Where we get it from is a very complicated theoretical question. The first few chapters of Quantum Field Theory in a Nutshell derive the mathematics, but here's the short version:


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*Interactions are due to the exchange of particles of integer spin, coupling to a conserved tensor-valued current whose rank is that spin;

*Positive attracts positive if that spin is even, or repel if it's odd, because otherwise the action we minimise wouldn't have a kinetic cost, so would be unstable;

*The spin has to be $0$, $1$ or $2$;

*Electromagnetism is due to a spin-$1$ photon, coupling to a conserved vector current, so like charges repel;

*Gravity acts on all mass-energy contributions to the rank-$2$ stress-energy tensor, which requires a spin-$2$ graviton, which implies positive masses are attractive.
