- #1
muonion
- 2
- 0
Let's consider Bohm's paradox (explaining as follows). A zero spin particle converts into two half-spin particles which move in the opposite directions. The parent particle had no angular momentum, so total spin of two particles is 0 implying they are in the singlet state.
Suppose we measured Sz of particle 1 which happened to be +1/2. Then automatically Sz of particle 2 would be -1/2.
From Weinberg's 'Lectures on Quantum Mechanics' Ch-12 (P. 394)
I don't get the bold lines above. Whenever we make a Sz measurement of 1 and then the same of 2 and then Sx measurement of 1- this x measurement destroys the previous info of particle 2. Hence particle 2 shouldn't have 2 definite components at a time, let alone 3 definite values.
What did Weinberg imply there?
Suppose we measured Sz of particle 1 which happened to be +1/2. Then automatically Sz of particle 2 would be -1/2.
From Weinberg's 'Lectures on Quantum Mechanics' Ch-12 (P. 394)
... the observer could have measured the x-component of the spin of particle 1 instead of its z-component, and by the same reasoning, if a value h/2 or −h/2 were found for the x-component of the spin of particle 1 then also the x-component of the spin of particle 2 must have been −h/2 or h/2 all along. Likewise for the y-components. So according to this reasoning, all three components of the spin of particle 2 have definite values, which is impossible since these spin components do not commute.
I don't get the bold lines above. Whenever we make a Sz measurement of 1 and then the same of 2 and then Sx measurement of 1- this x measurement destroys the previous info of particle 2. Hence particle 2 shouldn't have 2 definite components at a time, let alone 3 definite values.
What did Weinberg imply there?