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What is the difference between indistinguishable particles and identical particles?

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As far as I know, these are just two different names with the same meaning. –  C.R. Jan 24 '13 at 16:33
I've been doing physics for a while now, and I've never heard these terms used for different things; I agree with @C.R. –  joshphysics Jan 24 '13 at 16:40
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up vote 7 down vote accepted

If I create an electron on earth and someone else creates an electron on Andromeda, they're identical particles. They have the same quantum numbers, they're both excitations of the electron field. However they're distinguishable by means of their spatial separation. Their wavefunctions don't overlap.

Edit: perhaps I should add that not everyone uses the two words in this strict sense. Sometimes they're used interchangeably, but blurring them carries with it the danger of taking seriously the entanglement implied by antisymmetrizing across all existing electrons.

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I'm skeptical that this is standard, but I like it! –  joshphysics Jan 24 '13 at 16:44
@joshphysics for more information to allay your skepticism, see here –  twistor59 Jan 24 '13 at 16:51
To put it another way, if they weren't distinguishable, then whenever I solve the Schrodinger equation for an electron, I'd have to solve it for all the electrons in the universe, using an antisymmetrized wavefunction. –  twistor59 Jan 24 '13 at 16:55
Thanks! I think the distinction you draw is very useful, and I'll certainly propagate this terminology to my students in the future. –  joshphysics Jan 24 '13 at 17:49
@josh and twistor: Probably a less ambiguous word for this than 'distinguishable' would be 'distinct'. –  BlueRaja - Danny Pflughoeft Jan 24 '13 at 19:18
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Two particles are the same if you can't tell the difference, that is if the exchanging operator commutes with all observables. In this QM context thus indistinguishable and identical particles mean the same thing.

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