The Inequality of Dr Bell

May 12, 2013

History, Science

Maybe they're just dizzy.A Particle Man’s Life
is Always Intense

How can a pair of tiny particles remain connected, remain related, and perfectly responsive to each other, in spite of being separated beyond their ability to communicate at subluminal speeds? It’s as if a pair of twins are born but are never truly separate beings. They remain in some sense a single being, even if one of them travels in a spaceship to a distant planet. That’s absurd on a human scale. Real twin humans are not like that. When one changes into a black shirt the other doesn’t automatically change to a white shirt without receiving proper notification to do so, a message that absolutely arrives no faster than light, by all that is holy. But superposition and entanglement of quantum particles appears to be rather spooky in this sense. The orthodox interpretation that arises from quantum theory implies that the Universe on the tiniest levels is deeply interconnected. It’s as if the two particles are twins and yet are never entirely separate things at all.

Scott Kelly (L) and Mark Kelly (R) (I think I got that right).
The EPR paradox was something proposed by three men whose names happen to start with those letters (what are the odds of that?). Einstein, Podolsky and Rosen presented the problem in an effort to clarify their position which ran counter to the spooky interpretation of quantum mechanics. For these men, as with other so-called “realists,” the disturbing implications of the superposition of quantum states represented a shortcoming of the theory. They did not mean to suggest that quantum theory was wrong, not at all. They simply felt it was probably incomplete. Though the realists were very much a small minority, the proposed paradox presented a substantial enigma for the mainstream, or “orthodox” interpretation. Mainstream physics had no ready resolution to the paradox. For a while it seemed the stand-off might be eternal.
Still pretty complicated.
The standard interpretation by mainstream physics is that certain properties, or “states” of a particle remain as vague undeclared values until they have been observed. And observation doesn’t mean some guy in a lab coat took a peek. It means the particle interacted with the macroscopic universe in a way that makes that state value meaningful and relevant. If “up” has no context, then the particle is truly neither up nor down. But as soon as up has meaning in a larger sense than just the particle alone, it adopts a defined value. It chooses to be up or down at that point and sticks with it. But here’s the weirdest part. Here’s the bizarro world of quantum part. At the instant it declares to be up or down, its twin automatically declares the opposite value, without being told to or even which value his brother chose. No communication is required for the original declaration to effect a declaration from the other particle. And it doesn’t matter how far apart they are. According to Einstein and his cadre of doubters, that’s fucked up.

If you don't hear from me meet me back here.The essence of the challenge to the orthodox interpretation by the EPR paradox is that two spatially separated particles, with correlated quantum states (e.g. up and down), can’t be correlated temporally at superluminal speeds, without violating special relativity. This assumes that some sort of communication has to travel between the particles, that they are completely separate entities in space and time. The EPR solution to the paradox was to assume there is some subluminal (local) variable missing from the equation – somehow hiding from us. Once found, the missing variable should allow us to interpret the situation without any spookiness. We’re ignorant, you see. Maybe by being clever we will discover the variable’s hiding place. Maybe not. Maybe we’re inherently too stupid to find it. Maybe it hides that good.
But worth it.
In 1964 John Bell amazed the physics world by showing mathematically that not only was quantum mechanics incompatible with local hidden variable theories, but that the issue was most certainly resolvable by actual physical experimentation in a laboratory. Bell proposed that two arbitrarily rotated detectors measure two correlated quantum vectors (e.g. plus or minus one), and the product of the values recorded. Then the average of an ensemble of such events calculated. Orthodox quantum theory predicts that the probable result of such an experiment for two vectors a and b, is;

Use of calculator is ok.
On the other hand, any local hidden variable introduces another vector c. Without assuming the number or distribution of hidden variables, a simple normalization of the probability shows that;

Requires one of those special calculators.
Which is known as Bell’s inequality. Simply stated, if there are hidden local variables, then results of such experiments will always produce values less than or equal to “1” and if so then EPR got it right. But if the results are occasionally greater than “1” then quantum is complete, sans local hidden variables, and EPR got it wrong.
Bring me that grumpy meme cat!
Experiments designed to explore Bell’s inequality were rather popular in the 1970’s and 1980’s, but the most notable and famous was one by Aspect, Grangier, and Roger (AGR), in 1982. For their “pair of twins” the AGR experiment used the quantum correlation of photon atomic transitions. The resulting conclusion from this and all the other experiments is unambiguous;

Orthodox Quantum 1, EPR 0.

EPR got it wrong. Any remaining unorthodox theorists out there must therefore rely on some “non-local” means of hiding their mysterious variables. Twin particles are apparently not entirely separate, or at least not in quite the same way as two twin human conglomerate of particles seem to be. If that sounds confusing, then you’ve been paying attention. It’s a weird damn deal. As Einstein himself once articulated, the Universe is not only stranger than we imagine, it’s stranger than we can imagine.
And half the people say half of the stuff I said half as well as I said it
In 1990 John Bell was nominated for a Nobel Prize but before he could be notified he died suddenly of a brain hemorrhage. Nobel Prizes are never awarded posthumously.

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