The pseudo-explanation that the proton is stable because it has a lower mass than the rest is incomplete, because a particle formed by three u: uuu would have still a lower mass. I know that some answers will signal conservation of some physical quantities, but why must they be conserved or equivalently, why there exist the corresponding symmetries?

  • $\begingroup$ The charged current interaction in the SM Lagrangian for quarks. Look up Glashow Salam Weinberg model $\endgroup$ – InertialObserver Aug 2 at 17:39
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    $\begingroup$ The particle with three up quarks is the $\Delta^{++}$ and it has a mass of around 1232 MeV/$c^2$, so it is heavier than the proton not lighter. Presumably you are thinking that three up quarks would be lighter than a proton because the up quark has a lower rest mass than the down quark. However 99% of the mass of a proton is due to the quark interaction energy not the mass of the quarks, and the $\Delta^{++}$ has a higher interaction energy than the proton. The proton is stable because no other baryon has a lower total mass i.e. quarks plus interaction energy. $\endgroup$ – John Rennie Aug 2 at 17:44
  • $\begingroup$ Please be aware that titles are easily editable. (Click “edit” below the post.) Someone else may fix the typos, but there is no reason to expect others to clean them up. Thanks. $\endgroup$ – G. Smith Aug 2 at 17:52
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    $\begingroup$ Current physics cannot explain why there are certain symmetries and corresponding conservation laws. It is simply an observational fact on which the Standard Model is built. $\endgroup$ – G. Smith Aug 2 at 18:03
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    $\begingroup$ You have two quite different questions here. One is about the stability of the proton. The other is about the existence of symmetries and conservation laws. That makes the question too broad (IMO). However we have conservation laws because that's what we need for our (successful) mathematical models of physics to reproduce what we see. $\endgroup$ – StephenG Aug 2 at 23:57

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