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What am I missing? (quantum physics)

by kithpendragon1 min read21st Aug 202011 comments

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Quantum MechanicsEpistemologyWorld Modeling
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I've read many times about an experiment: take a 2-particle system and measure that it has a spin of 0. This tells us that the particles have opposite spin. Now, take the particles far away from each other and measure one. If you measure spin up, for example, you now know the other particle has spin down.

Why would anybody be surprised by this?

Let's imagine a similar classical experiment that uses literal spin. Take a system of two gyroscopes, each spinning at the same fixed speed, each in it's own sealed box. They can be powered or whatever so they stay spinning for the duration. Stack the two boxes ("entangling" their spin), and measure 0 spin to confirm that the gyroscopes are in fact spinning in opposite directions (some helicopters use this principle for stabilization on the y-axis instead of a tail propeller). Now, send the boxes far apart and measure one of them using the right hand rule. If it turns out to have spin up, the other will intuitively turn out to have spin down. But nobody will be surprised by this because we knew from the beginning that the pair was spinning in opposite directions; we just didn't know which was which before measuring one of them.

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Update: 2020Apr24
Thanks for all the comments, explanations, and links! I'm not ignoring them, just trying to find time between work and family responsibilities to digest and understand them before I ask my follow-up questions. I appreciate your patience!

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Because it's possible to do things that would be impossible with a hidden local variable theory such as you're describing. See Bell's theorem or https://en.wikipedia.org/wiki/CHSH_inequality, a game at which a quantum strategy can beat any classical strategy.

Like yourself, people aren't surprised by the outcome of your experiment. The surprising thing happens only if you consider more complicated situations. The easiest situations where surprising things happen are these two:

1) Measure the spins of the two entangled particles in three suitably different directions. From the correlations of the observed outcomes you can calculate a number known as the CHSH-correlator S. This number is larger than any model where the individual outcomes were locally predetermined permits. An accessible discussion of this is given in David Mermin's Quantum Mysteries for Anyone. The best discussion of the actual physics I know of is by Travis Norsen in his book Foundations of Quantum Mechanics.

2) Measure the spins of three entangled particles in two suitably different directions. There, you get a certain combination of outcomes which is impossible in any classical model. So you don't need statistics but just a single observation of the classically impossible event. This is discussed in David Mermin's Quantum Mysteries Revistited.

The fact is surprising when coupled with the fact that particles do not have a definite spin direction before you measure it. The anti-correlation is maintained non-locally, but the directions are decided by the experiment.

A better example is: take two spheres, send them far away, then make one sphere spin in any orientation that you want. How much would you be surprised to learn that the other sphere spins with the same axis in the opposite directions?