Thursday, June 19, 2014

Aaronson on quantum randomness

MIT computer science professor Scott Aaronson has posted the sequel to his earlier article on quantum randomness.

My earlier criticisms apply. He explains correctly how quantum mechanics is contrary to local hidden variable theories. This has been conventional wisdom since about 1930. He also explains that you can never truly prove randomness. His main purpose is to describe some recent results on how you can use some random numbers to generate other random numbers, under some quantum mechanical assumptions.

These results are of some interest in his field of abstract quantum computer complexity theory, but they are of no practical importance, and do not really shed any light on either quantum mechanics or randomness. He suggests utility, such as:
Pironio’s group has already done a small, proof-of-concept demonstration of their randomness expansion protocol, using it to generate about 40 “guaranteed random bits.” Making this technology useful will require, above all, improving the bit rate (that is, the number of random bits generated per second). But the difficulties seem surmountable, and researchers at the National Institute of Standards and Technology are currently working on them. So it’s likely that before too long, we will be able to have copious bits whose randomness is guaranteed by the causal structure of spacetime itself, should we want that. And as mentioned before, for cryptographic purposes it can matter a lot whether your randomness is really random.
No, those bits are no more random than coin tosses, and have no guarantees that are useful to cryptography.

He explains:
Before going further, it’s worth clarifying two crucial points. First, entanglement is often described in popular books as “spooky action at a distance”: If you measure an electron on Earth and find that it’s spinning left, then somehow, the counterpart electron in the Andromeda galaxy “knows” to be spinning left as well! However, a theorem in quantum mechanics—appropriately called the No-Communication Theorem—says that there’s no way for Alice to use this effect to send a message to Bob faster than light. Intuitively, this is because Alice doesn’t get to choose whether her electron will be spinning left or right when she measures it. As an analogy, by picking up a copy of American Scientist in New York, you can “instantaneously learn” the contents of a different copy of American Scientist in San Francisco, but it would be strange to call that faster-than-light communication! (Although this might come as a letdown to some science fiction fans, it’s really a relief: If you could use entanglement to communicate faster than light, then quantum mechanics would flat-out contradict Einstein’s special theory of relativity.)

However, the analogy with classical correlation raises an obvious question. If entangled particles are really no “spookier” than a pair of identical magazines, then what’s the big deal about entanglement anyway? Why can’t we suppose that, just before the two electrons separated, they said to each other “hey, if anyone asks, let’s both be spinning left”? This, indeed, is essentially the question Einstein posed—and the Bell inequality provides the answer. Namely, if the two electrons had simply “agreed in advance” on how to spin, then Alice and Bob could not have used them to boost their success in the CHSH game. That Alice and Bob could do this shows that entanglement must be more than just correlation between two random variables.

To summarize, the Bell inequality paints a picture of our universe as weirdly intermediate between local and nonlocal. Using entangled particles, Alice and Bob can do something that would have required faster-than-light communication, had you tried to simulate what was going on using classical physics. But once you accept quantum mechanics, you can describe what’s going on without any recourse to faster-than-light influences.
Those first 2 paragraphs are fine, but then the summary is nonsense. There is no "intermediate between local and nonlocal". It is true that you need quantum mechanics to explain electrons, and you cannot effectively simulate them with classical mechanics. Einstein, Bell, and their followers refuse to accept what the experts taught in 1930. That's all.

The electron does not really spin left in quantum mechanics. Measurements may find that, but the act of measuring forces that. It is possible that, just before the two electrons separated, they said to each other “hey, if anyone measures left spin, let’s both say yes.” Measuring spin in other directions gives other results. The Bell paradoxes only occur if the observer is allowed to choose the direction of the spin measurement, and you cling to some classical (non-quantum) model of spin.

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