- #1
Ken Ucarp
BELOW IS SOMETHING I COPIED FROM AN OLD THREAD (2004). Would anyone be willing to spend a little time explaining in laymen's terms a few things. In particular, when I as a complete ignoramus read this it sounds like utter mathematical abstraction being used in a manner that seems to posit truth about an actual physical system. Is this pure abstraction or do these things correspond to reality in some way.
START
Suppose that we have two particles, 1 and 2, with corresponding Hilbert spaces H1 and H2. Suppose that particle 1 is in the state |ψ> Є H1, and that particle 2 is in the state |φ> Є H2, and all of this is before the two particles interact. Then, prior to the interaction, the state of the joint system is simply
|ψ>|φ>.
Now, suppose that the interaction between these two particles is such that
|ψ>|φ> → Σk ak|ψk>|φk> ,
where each ak ≠ 0, and there are at least two distinct values for k (and, of course, the |ψk> (|φk>) are linearly independent).
Then, the state of the joint system after the interaction can no longer be written as a simple (tensor) product of one element from H1 with one element from H2 – it must be written as a linear combination of such products. The two particles are now said to be in an "entangled" state.
END
START
Suppose that we have two particles, 1 and 2, with corresponding Hilbert spaces H1 and H2. Suppose that particle 1 is in the state |ψ> Є H1, and that particle 2 is in the state |φ> Є H2, and all of this is before the two particles interact. Then, prior to the interaction, the state of the joint system is simply
|ψ>|φ>.
Now, suppose that the interaction between these two particles is such that
|ψ>|φ> → Σk ak|ψk>|φk> ,
where each ak ≠ 0, and there are at least two distinct values for k (and, of course, the |ψk> (|φk>) are linearly independent).
Then, the state of the joint system after the interaction can no longer be written as a simple (tensor) product of one element from H1 with one element from H2 – it must be written as a linear combination of such products. The two particles are now said to be in an "entangled" state.
END