Reading David Mermin's Moon paper for the fifth or fourth time, I hope that I'm starting to grasp the entirety of it.
That the classical setup described cannot produce the needed outcomes is reasonably obvious. What has been getting me are the descriptions of the quantum measurement experiments. However, I think I am starting to understand how they work. Take Mermin's hypothetical Stern-Gerlach apparatus duo, measuring spin along any of 3 angles, separated by 120 degrees:
1. Assume the measured angles are the same. Because the two particles have opposite spin due to their common origin, although the value of each particle is random, the outcome will always be +- or -+. This is fairly clear.
2. Assume the measured angles are at 120 degrees. The outcome is random, but the equation governing the outcome has the property that the spin of the two particles is different only 25% of the time.
The second one has been annoying me a bit, but thinking about it, it is no stranger than the first. Picturing a godly die that has the outcomes "+-" or "-+" is really no less strange than one with the outcomes "++", "++", "++", "--, "--", "--", "+-" and "-+" etched into it - the weird thing is rather that the die is cast at the time of measurement, rather than at the time of emission; and not only that, the die of choice seems to depend on the relative angle of the measuring apparati! Or, in other words, measuring one particle at a given angle tells us that the other particle will always have an opposite value at the same angle, and an opposite value 25% of the time at the other two. And the reason this cannot be setup classically is that if this relation holds between angle 1 and 2/3, it cannot at the same time hold between angle 2 and 3, since they would then be opposite ~44% of the time - the correlation would be wrong.
Ignoring the disturbing quantum metaphysical questions, are there any vital subtleties or nuances to this that I have missed? Thanks.
That the classical setup described cannot produce the needed outcomes is reasonably obvious. What has been getting me are the descriptions of the quantum measurement experiments. However, I think I am starting to understand how they work. Take Mermin's hypothetical Stern-Gerlach apparatus duo, measuring spin along any of 3 angles, separated by 120 degrees:
1. Assume the measured angles are the same. Because the two particles have opposite spin due to their common origin, although the value of each particle is random, the outcome will always be +- or -+. This is fairly clear.
2. Assume the measured angles are at 120 degrees. The outcome is random, but the equation governing the outcome has the property that the spin of the two particles is different only 25% of the time.
The second one has been annoying me a bit, but thinking about it, it is no stranger than the first. Picturing a godly die that has the outcomes "+-" or "-+" is really no less strange than one with the outcomes "++", "++", "++", "--, "--", "--", "+-" and "-+" etched into it - the weird thing is rather that the die is cast at the time of measurement, rather than at the time of emission; and not only that, the die of choice seems to depend on the relative angle of the measuring apparati! Or, in other words, measuring one particle at a given angle tells us that the other particle will always have an opposite value at the same angle, and an opposite value 25% of the time at the other two. And the reason this cannot be setup classically is that if this relation holds between angle 1 and 2/3, it cannot at the same time hold between angle 2 and 3, since they would then be opposite ~44% of the time - the correlation would be wrong.
Ignoring the disturbing quantum metaphysical questions, are there any vital subtleties or nuances to this that I have missed? Thanks.
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