# Why masses attract each other? [duplicate]

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

• I think anything which contains WHY is a matter of philosophy.
– user240696
Jan 5, 2020 at 16:43
– Sam
Jan 5, 2020 at 16:46

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.