I am teaching undergraduate quantum mechanics for the first time this semester. One thing I have discovered is that it is very easy to make mistakes when talking about quantum mechanics. Not mathematical mistakes (the math is fairly straightforward), but conceptual mistakes in the interpretation of the mathematics.
I was therefore pleased to read a recent paper by Blake Stacey entitled “Misreading EPR: Variations on an Incorrect Theme.” The “EPR” in the title stands for Einstein-Podolsky-Rosen (Einstein and his two postdocs at the time), and is used as shorthand for a famous thought-experiment these three published in 1935. The original paper is only 3 pages long and is very readable.
EPR starts with two particles prepared in a quantum-mechanical entangled state, and we consider the possibility of measuring one of a pair of incompatible (noncommuting) observables. The original EPR paper used position and momentum. Stacey boils down the subsequent thought-experiment to three key ideas:
The two particles cannot influence each other. This can be accomplished by sending the particles out in different directions, and waiting until they are far enough apart that information traveling between them at the speed of light would not arrive until after completion of the experiment. This assumes that superluminal or instantaneous signalling is not allowed. More generally, it is an assumption of locality.
We (the experimenters) make a choice about which of the two observables to measure. We then measure the chosen observable for one particle, and use the results of this measurement to argue about what would have happened if we had picked the other option. We do not measure both observables, and we do not measure the same observable twice.
Einstein, Podolsky, and Rosen make an assumption that they call a “criterion of reality” (this now gets called the Criterion of Reality). Quoting from their original paper:
“If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”
Stacey goes on to demonstrate how many popularizers of physics, and also some physicists, get these key ideas wrong when presenting the EPR thought-experiment.
EPR is often introduced as a lead-up to discussing Bell’s inequality. The standard interpretation of Bell’s inequality is that it shows that the locality assumption is suspect, though Stacey focuses on the meaning of probability. The last section in the paper (“EPR and Beyond the Intrinsic”) was new to me, and I would need to do more background reading to fully understand it. Stacey subscribes to the quantum Bayesianism, or QBism, interpretation of quantum mechanics, which I don’t understand. (Granted, I haven’t tried to understand it in detail, or any other interpretation of quantum mechanics besides out-of-the-box Copenhagen. Yes, I know this is not good.)
As Weinberg puts it, in the corrected 2nd edition of his quantum book which correctly presents EPR (Lectures on Quantum Mechanics, 2nd edition, page 394):
Bohm was led to suppose that either the content or the interpretation of quantum mechanics needs modification. Most physicists today would instead respond to both the Einstein–Podolsky–Rosen paradox and the Bohm paradox by accepting that no matter how far apart the two particles are, the measurement of the properties of one of them does affect the wave function of the other. Though the particles are far apart, their properties remain entangled.
I hope that I didn’t make any mistakes in how I stated things in this post, but I probably did. Please let me know!