I could never be a quantum mechanic. I have read and studied the subject on and off for more than forty years, and while I have become comfortable with many of the concepts, a number of things simply elude me. To approximate something Niels Bohr said, "If quantum theory doesn't seem crazy to you, you don't understand it."
The Age of Entanglement: When Quantum Physics Was Reborn, by Louisa Gilder, has clarified a point or two for me, but made the subject seem crazier than ever. I wonder how crazy it would seem if I did understand!
The focus of the book is, as the title states, the continuing struggle to understand entangled quanta, a fierce, emotional, eventually nearly no-holds-barred battle between those who, following Einstein (and the "EPR" paper by Einstein, Podolsky and Rosen) consider quanta to have real positions, velocities, and other "quantum states", which are partly hidden to our clumsy means of measuring them; and those who follow Bohr and consider that such quantities do not exist until they are measured. This latter is the Copenhagen Interpretation.
The question is not yet fully answered, decades after the deaths of the original knights in this battle. But as the book relates, physicists are closer to an answer since the work of John Stewart Bell and his "Bell's Inequality", the clearest statement of what must be true if "hidden variables" genuinely exist.
This is the machine that first peeled back the covers a bit to indicate that Bell's Inequality is violated. We'll see in just a minute how crazy that is. It is a pity that Bell did not live to see these results; he died at age 62.The small mechanism at the center produces a stream of very thin Calcium gas, which a lamp illuminates to send an electron in each of many of the atoms "up" two levels, which then drops back "down", one level after another, releasing two photons as a quick cascade. The illuminating light is ultraviolet (high energy), and the "cascade" photons are green and blue, with energies that add up to that of the original UV photon. The principle of conservation of angular momentum requires that the two photons be polarized at right angles to one another.
The big tapered sections contain glass plates that gradually polarize the light before each photon is counted by a large phototube at each end. In this case that means that certain photons get through, and others are blocked. The Heisenberg Uncertainty principle means you can't measure everything you'd like to with sufficient precision on a single pair of photons, so the experimenters (Clauser and Freedman), had to gather statistics from many pairs of photons. Depending which way the polarizers were set, Bell's Inequality predicted there should be certain ratios of photons of each color detected.
The rival theory, based on the Copenhagen (Bohr's) interpretation, predicted that the ratios ought to be larger at certain angles, compared to the Bell prediction. This is how the experiment turned out! Now let us see how crazy that is.
Suppose you have a room full of people, with plenty of diversity. Pick three "variables" that can be expressed in pairs: male/female, tall/short (cutoff at, say, 1.66m for both men and women), and right/left handed. This groups everyone in the room into one of eight groups: MTR, MTl, MsR, Msl, fTR, fTl, fsR, fsl. Bell's Inequality states that, for three quantum variables, A(not b) + B(not c) is greater than or equal to A(not c). Using "x" to refer to an unknown state, and >= to mean greater than or equal to, we can state the People Inequality thus:
Msx + xTl >= Mxl, or "Short men plus all tall, left-handed people will equal or outnumber the left-handed men." It sounds obvious, perhaps, and perhaps not. But it is proven thus:
Msx = MsR + Msl
xTl = MTl + FTl
Mxl = MTl + Msl
Look carefully: The left side includes both MTl and Msl, plus two other groups, while the right side includes just MTl and Msl. Only if MsR and FTl are zero will this be equal, otherwise the left side is certain to be greater. It cannot be less.
The violation of Bell's Inequality is like this: Suppose out of 30 people, those in Msx + xTl number 12. Then you ask just the Mxl people to gather, and you count 14! How did that happen? In the case of people, somebody lied (at least two people). But for photons, that is what the experimenters claim happened. I told you it is crazy!
This is supposed to prove entanglement, that measuring one of the photons forces the other one to have a particular state when it is measured, with greater probability than if "hidden variables" were determining the result. Quite a number of experiments, with better apparatus, and lasers and so forth, have been done since the contraption above was built in 1969. The result has been verified. Not only so, entangled photons are now routinely sent opposite ways through kilometer-long light fibers, and practical use will soon be made of them to encrypt messages in ways that cannot be broken. Entanglement is also behind the attempts to produce "quantum computers", which will be able to crack any encryption technique that doesn't depend on quantum entanglement. They will also be able, perhaps, to solve other "NP complete" problems that currently could not run on any conceivable "ordinary" computer in less than millions of years.
My mind boggles. Fortunately, being boggled was a pleasant experience in this case. I confess, when I started the book, I read the author's introduction, that she had written many conversations in a semi-fictionalized way, reconstructing them from letters between the persons, and I thought I would quickly get tired of that and give up after a while. However, the writing drew me in; the author doesn't overuse such conversations, and she really does give us a flavor of the way science is carried on among brilliant, passionate advocates for various points of view.
The book, centered on the breakthrough by Bell and his followers, and on the experiments that tested his work, helps me (a little bit) to understand the total weirdness of quantum theory. I can now better accept that certain difficult ideas are so, but I still cannot say why. Then again, neither can anyone else!
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