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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?

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    $\begingroup$ Yes, they are the same. $\endgroup$ – jinawee Nov 30 '13 at 21:50
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    $\begingroup$ see also en.wikipedia.org/wiki/One-electron_universe $\endgroup$ – Christoph Nov 30 '13 at 22:17
  • $\begingroup$ @Christoph: So do you think there is no difference between electrons and positrons either? This is not an attempt at sarcasm: you made a good point, but I am not sure it does not prove more than it was intended to prove. $\endgroup$ – akhmeteli Nov 30 '13 at 22:46
  • $\begingroup$ @akhmeteli: well, we do describe both particles and anti-particles with a single Dirac field; the idea of a single worline for all electrons is not really workable (despite conjectured proton decay involving positrons), but I like it nevertheless ;) $\endgroup$ – Christoph Nov 30 '13 at 23:11
  • $\begingroup$ @Christoph: I agree, "we do describe both particles and anti-particles with a single Dirac field". However, the apparent conclusion seems to be: "electron is the same (or not the same) as positron to the same extent as two electrons with different spin projection on some axis." $\endgroup$ – akhmeteli Nov 30 '13 at 23:28
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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.

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  • $\begingroup$ Nice one, as soon as I tried answering I wondered whether I'd opened a can of worms! $\endgroup$ – innisfree Nov 30 '13 at 22:10
  • $\begingroup$ @innisfree Yea I feel like this is one of those questions that could easily get out-of-hand. For example, akhmeteli's answer about electrons having different spin projections upon measurement is, of course, not false provided you interpret the term "same" in a particular way, but it kind of flies in the face of the way the terms "same" or "identical" are conventionally used in physics when referring to elementary particles. $\endgroup$ – joshphysics Nov 30 '13 at 22:13
  • $\begingroup$ With the slight caveat that it may depend on it's surroundings or energy. A lone neutron doesn't behave like one in an atom - although it does behave like any other lone neutron $\endgroup$ – Martin Beckett Nov 30 '13 at 23:10
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    $\begingroup$ @Martin Beckett: I was under impression that neutron is not considered an elementary particle anymore. Am I wrong? $\endgroup$ – akhmeteli Nov 30 '13 at 23:30
  • $\begingroup$ @akhmeteli, correct, but it was the only common example I could think of. It doesn't change josh's answer $\endgroup$ – Martin Beckett Nov 30 '13 at 23:47
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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.

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

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