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Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) have this sort of dual relationship, I don
by mannerheim 5y ago
Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) have this sort of dual relationship, I don't think it makes sense to talk about entanglement with respect to them - they intrinsically have to be related to each other, and the position state (i.e., function) a particle is in fully determines its momentum state.
But it is possible to imagine usually unrelated properties of a particle being entangled, e.g. a two-peaked position function, spin up if it's over here and spin down if it's over there. So that's possible. Usually when discussing entanglement, though, we're talking about 'distinct'* particles. Electron A's spin entangled with electron B's spin. Not that it has to be spin, of course. But that's a common case because of how naturally this sort of entanglement occurs, for example, in atoms where electrons have to form spin pairs.
* This is complicated by QFT where particles are not exactly distinct, but exist as excitations in a particle field. E.g. there aren't two electrons but the electron field is excited by two quanta. At least, that's my understanding; I never went to grad school for physics, so I'm limited to undergraduate knowledge and some extracurricular reading.
- tines 5y ago> Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) Yep, sorry, artifact of the editing process. > they intrinsically have to be related to each other, and the position state (i.e., function) a particle is in fully determines its momentum state. Sure, but the momentum doesn't determine the position (due to the constant of integration) so you can have two particles with the same momentum functions and different locations, and that leads to my next question... > Usually when discussing entanglement, though, we're talking about 'distinct'* particles. That's what I actually meant to ask but didn't phrase clearly: since position and momentum are described by wave functions, can you entangle the positions of two particles? or entangle their momentum?
- mannerheim 5y ago> Sure, but the momentum doesn't determine the position (due to the constant of integration) so you can have two particles with the same momentum functions and different locations, and that leads to my next question... There's no constant of integration since the integral will be over all of space (or momentum space). > That's what I actually meant to ask but didn't phrase clearly: since position and momentum are described by wave functions, can you entangle the positions of two particles? or entangle their momentum? Certainly! I couldn't think of any examples of how it might occur, but I googled it and found an answer on Quora that seems to be correct: https://www.quora.com/In-quantum-mechanics-how-do-I-comprehend-the-claim-that-positions-of-entangled-particles-are-correlated/answer/Howard-Landman https://www.quora.com/In-quantum-mechanics-how-do-I-comprehe...