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Two different protons could be in a different state because of its parts "moving" in some sense?

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Protons can be distinguished from each other in particular interactions using conservation rules for energy momentum and angular momentum, otherwise they are exchangeable.

Protons are complicated bound states of their constituents. As in all quantum mechanical formulations there are excited states as the answer in the link provided says, and the links therein .

The theory for calculations is lattice QCD and is not simple. One must have a course in quantum field theory before tackling lattice QCD

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