According to the gravitational law, every mass attracts each other. But why the masses attract each other? Why they don't repel each other?

  • 1
    $\begingroup$ I think anything which contains WHY is a matter of philosophy. $\endgroup$
    – user240696
    Jan 5, 2020 at 16:43
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    $\begingroup$ Does this answer your question? physics.stackexchange.com/q/11542 $\endgroup$
    – Sam
    Jan 5, 2020 at 16:46

1 Answer 1


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.


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