Page 22 - GALIET PHYSICS BLOSSOMS IV+

2.1(b) Now suppose we do a measurement on the first Tokyo spin, and at a time t = 0 it is found that it has ↑ spin. What is the probability that the second Paris spin, measured a nanosecond after the first Tokyo measurement, will be ↑?
Quantum Mechanics’ entanglement principle would say that its probability is 100% given the correlations explained in the previous page. That is, if Tokyo finds that Spin A is up, then Paris will find that Spin B is necessarily up, too, with absolute certainty.
This we would know with certainty. And whatever is certain, says Einstein, expresses something real.10 This means that there is something real about Spin B’s state.
EPR THOUGHT EXPERIMENT
However, if we switched Spin A at the last minute, we would affect Spin B even though there is zero influence travelling between Spin A and B. The spin and apparatus are so far apart that no signals travel between them in the time after we change our minds. This is the EPR paradox!
• If we were to suddenly switch Spin A to measure left-right states instead of up-down states, then Spin A would be in any of those states, left or right with equal 50% probability.
o Consequently, Spin B ought also to be found in any of those states, left or right, with equal 50% probability. § Thatis,ifSpinAisleft,soisSpinB. IfSpinAisright,soisSpinB.
o However, Spin A still knows it is up or down!
o In this time, no possible influence could have travelled to Spin B that fast, or at the speed of light! So Spin B could not have changed! o To Einstein, this showed a flaw in Quantum Mechanics because the State of Spin B is uncertain; and hence, not real.
10 Dr. Stamp. From class lecture notes, and from Basic Ideas of Quantum Mechanics. II. Entangled States. 6. •22•