Are all elementary particles of the same type exactly the same?

Question

Are all elementary particles of the same type EXACTLY the same? Is there some variation in what an electron is, for example, or are they all the same?

Answer 1

This thread will inevitably descend into a semantic and/or philosophical discussion unless we have some at least somewhat precise notion of what it means for particles to be the "same".

In modern physics, elementary particles are fundamentally treated quantum-mechanically, and in quantum mechanics, they are modeled as being exactly the same in the following precise sense:

If a system consists of two or more elementary particles, then the state of the system only changes by a multiplicative constant (which happens to be $+1$ for bosons an $-1$ for fermions) when one permutes the labels of all of the particles. Now, it is also the case that in quantum mechanics, two states that differ by such a multiplicative constant are physically equivalent, so permuting the labels of all of the particles leads to a physically equivalent state of the system.

Answer 2

All elementary particles of a particular type, e.g. all electrons, are excitations of the same quantum field, and are all identical and indistinguishable.

Because of the uncertainty principle, one cannot distinguish such particles by even their trajectories.

Answer 3

I'd say two electrons can differ, e.g., by their spin projection on some axis.