According to the gravitational law, every mass attracts each other. But why the masses attract each other? Why they don't repel each other?
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1$\begingroup$ I think anything which contains WHY is a matter of philosophy. $\endgroup$– user240696Jan 5, 2020 at 16:43
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2$\begingroup$ Does this answer your question? physics.stackexchange.com/q/11542 $\endgroup$– SamJan 5, 2020 at 16:46
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1 Answer
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Mass is gravity's equivalent of electric charge, with two obvious differences:
- 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:
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.
