The mass of a proton is $1.673 \times 10^{-27}$ kg and the mass of a neutron is $1.675\times10^{-27}$ kg. (Approximate.) Would anything be different if they had different masses? Is there a "reason" that they are so close in terms of mass? What is being the same mass doing for them?

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    $\begingroup$ Besides the fact that a neutron decays in to a proton and two very light particles? $\endgroup$ – Jon Custer Aug 24 '16 at 20:01
  • $\begingroup$ A photon can decay into an electron and positron, it doesn't mean anything about its mass $\endgroup$ – Martin Beckett Aug 27 '16 at 4:31
  • $\begingroup$ @MartinBeckett the photon does not decay. you are describing an interaction of the photon with a field . hyperphysics.phy-astr.gsu.edu/hbase/particles/lepton.html#c6 . Think, in the center of mass of the electron and positron the momentum is zero, but a photon , which also should exist for this center of mass, can never have zero momentum. Thus it is a two particle interaction, photon+ field $\endgroup$ – anna v Aug 27 '16 at 5:23

Most of the mass of proton and neutron arises due to the invariant mass of the system of moving virtual quarks and gluons that make up the protons and neutrons. Although gluons are massless, yet their energy makes up the mass of protons and neutrons, by the virtue of mass-energy equivalence. The mass of protons and neutrons are roughly of the order of $10^2$ more than of the 3 valence quarks (uud for proton and udd for neutron) that "supposedly" make them up and most of it comes from these virtual gluons and quarks. In addition some of these quarks form additional bound structures like mesons, which mediate strong force between nucleons.

The significance of protons and neutrons having the roughly same mass is that the strong interaction has a much larger contribution to the Hamiltonian than the electromagnetic interaction or weak interaction at the given distance (or energy) scales. Indeed this was the exact reason why Heisenberg introduced the isospin model. Simply put,

$$ H = H_{strong} + H_{weak} + H_{electromagnetism}$$

Since the strong interaction dominates over weak and the electromagnetic ones at this scale,

$$ H \approx H_{strong} $$ and since the strong interaction doesn't depend on the nature of the nucleons in question, the masses of proton and neutrons are equal.

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  • $\begingroup$ "are equal " within the width introduced by the existence of electromagnetic and weak contributions in higher orders $\endgroup$ – anna v Aug 27 '16 at 5:25

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