Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very slight degree? Is there a theory which proves that?
Imagine an alien of size of order of Milky-way galaxy examining our solar system with a probe of size of 10's of solar system dimension and concludes that all planets are identical.
Answer
One good piece of evidence that all particles of a given type are identical is the exchange interaction. The exchange symmetry (that one can exchange any two electrons and leave the Hamiltonian unchanged) results in the Pauli exclusion principle for fermions. It also is responsible for all sorts of particle statistics effects (particles following the Fermi-Dirac or Bose-Einstein distributions) depending on whether the particles are fermions or bosons.
If the particles were even slightly non-identical, it would have large, observable effects on things like the allowed energies of the Helium atom.
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