There are several ways to interpret the mathematical formalism of Quantum Mechanics. The two that we care about here are the realist and orthodox (AKA Copenhagen) interpretations. To introduce the two, we'll reconsider the experiment we thought up in the last post.
What Quantum Mechanics Tells Us
Quantum mechanics is all about probabilities. It can always answer questions like "What is the probability that the measurement of this electron's spin will yield result x?" but cannot always answer questions like "What is the spin of this electron?" In other words, instead of concrete, black and white predictions, QM often can only provide us with probabilistic answers.
So, for example, in the EPR-Bohm experiment we talked about earlier (the one with the decaying pion) Quantum Mechanics cannot tell us what the spin of the electron or the positron is until one of them is measured by the detector. We only know that the total spin must be zero. The two obvious possibilities are that either the positron is spin up and the electron is spin down or the other way around, with the electron being spin up and the positron spin down. QM tells us that the system is actually in some combination (i.e. superposition) of those two states. What that means physically, don't ask me. See "Schrodinger's Cat" for more superposition fun.
Realists have issues with this probabilistic gobbledygook (Einstein's "God does not play dice" characterizes their position pretty well) while followers of the Orthodox interpretation take Quantum mechanics at face value. Now, indulge me as I have an argument with myself about the merits of each interpretations:
The Realist Position:
What the hell kind of nonsense is this? If a physicist can't make 100% accurate, completely dependable predictions of the results of measurements, then his physics isn't right! If Quantum Mechanics can't give us concrete answers instead of some kind of probabilistic garbage, then it must be missing something! There must be some kind of hidden variables that haven't been taken into account.
Here's what happens in the EPR-Bohm experiment: After the pion decays the electron and the positron both get a spin in some well defined direction. If we knew all the hidden variables then we would know, without any measurement, exactly which of the two particles has spin up and which has spin down. The fact that QM can't tell us that kind of thing just proves that it is an incomplete theory.
Therefore, with the knowledge of all the hidden variables in the problem, we could predict the results of the two measurements with total certainty. That's physics!
The Orthodox Position:
Quantum Mechanics has never made any wrong predictions before and has proven useful in tons of different arenas. Let's just trust it at face value, bizarre as it might seem.
When the pion decays the electron and the positron go into a kind of state of indecision. This state is the result of adding (actually subtracting, but it's not relevant) the two obvious states we mentioned earlier:
(Superposed State) = (Electron Up, Positron Down State) + (Electron Down, Positron Up State)
When the measurement is carried out on the system, it has to choose between one of the two obvious states. In this case, either has a 50-50 chance of being chosen. Once the measurement has been made we know the state the system is in and the realists among us can rest easy. So, for example, if we measure it to be in the (Electron Up, Positron Down State) we can then safely say that the electron has a spin pointing up and the positron has one pointing down. We could not say this before the measurement, though. In other words, we have to accept the proposition that the measurement itself affects the system in a dramatic way.
The Realist's Response: The EPR Paradox
Suppose the detectors are one light year away from one another. Also, let's say that the electron detector is significantly closer to the decaying pion's initial location than the positron detector. Then it's safe to assume that the electron will reach its detector in less time than the positron. Now imagine the electron's detector returns the result that the electron was spin up. If we know the electron is spin up then the positron must, at that very same instant, be spin down in order to conserve angular momentum.
So, according to an orthodox interpretation the fact that the electron was measured as spin up somehow travels across one light year of space instantaneously and causes the positron to become spin down. This violates locality and requires faster than light transfer of information!
Summary
That's the EPR paradox: If we believe the orthodox interpretation of QM then locality is violated, as demonstrated in our simple thought experiment. This implies that, in order to preserve locality we need to put our stock in the realist interpretation, which claims that Quantum Mechanics is an incomplete theory and there are are some kind of hidden variables lying around somewhere that no one knows about.
In other words, because of the EPR paradox either locality or QM is wrong. Both can't be right.
Experiments like the one we discussed above have convincingly shown (see Bell's Theorem) that QM is a correct theory and that locality is, in fact, violated. The concepts we discussed in the previous three posts lie at the heart of ridiculously exciting recent experiments in quantum teleportation and computation.
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