Einstein’s Boxes. In an interesting precursor to the EPR paradox, Einstein proposed the following gedanken experiment: Imagine a particle confined to a box (make it a one-dimensional infinite square well, if you like). It’s in the ground state, when an impenetrable partition is introduced, dividing

Question

Einstein’s Boxes. In an interesting precursor to the EPR paradox, Einstein proposed the following gedanken experiment: Imagine a particle confined to a box (make it a one-dimensional infinite square well, if you like). It’s in the ground state, when an impenetrable partition is introduced, dividing the box into separate halves, $B_{1} \text { and } B_{2}$ , in such a way that the particle is equally likely to be found in either one. Now the two boxes are moved very far apart, and a measurement is made on $B_{1}$ to see if the particle is in that box. Suppose the answer is yes. Immediately we know that the particle will not be found in the (distant) box $B_{2}$ .

(a) What would Einstein say about this?
(b) How does the Copenhagen interpretation account for it? What is the wave function in $B_{2}$ , right after the measurement on $B_{1}$ ?

(a) What would Einstein say about this?
(b) How does the Copenhagen interpretation account for it? What is the wave function in [latex] B_{2} [/latex] , right after the measurement on [latex] B_{1} [/latex] ?

Accepted Answer

(a) The particle must have been in box [latex] B_1 [/latex] all along, since there is no way that opening [latex] B_1 [/latex] could have instantaneously affected the outcome of opening faraway box [latex] B_2 [/latex].

(b) The measurement at [latex] B_1 [/latex] collapses the wave function to a narrow spike at the particle's measured position; the wave function is now zero everywhere in box [latex] B_2 [/latex], and the box will be empty when it is opened.

Question 12.2: Einstein’s Boxes. In an interesting precursor to the EPR par...

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