Sunday, April 28, 2013

History of Science -- Part Seventeen: Bell’s Theorem

John Stewart Bell
By 1935, the basic form of quantum mechanics was clear. Schrödinger’s equation was the new universal law of motion. Although it was only required for objects on the atomic scale, quantum theory presumably governed the behavior of everything. The earlier physics, by then called “classical,” sort of like the ancient Greek theories, was the much easier to use approximation for macroscopic behavior. Nonetheless, quantum science has crept into modern technology in day-to-day objects such as transistors and microprocessors or lasers, items we take for granted today.

Although quantum theory works perfectly, it seems to imply something weird, almost absurd. That has been a problem for scientists and philosophers alike.

Yet quantum theory underlies all physics, which underlies all other sciences. So is all this theory built on sand? Copenhagen insists, and most scientists pragmatically accept the formulas for the practical reason that they work, what’s the problem?

(A minor note: mathematics is not based on physical science. Therefore, math does escape the paradox and does not require interpretation. It is still an unfettered and unrestricted tool, although a fellow by the name of Gödel proved his “Incompleteness Theorem” for mathematics in 1931, which is a sort of “Heisenberg Uncertainty” for math. But mathematical processes still are sharp tools for examining what we don’t know and proving what we can know. Not all is lost to crystal balls and stochastic processes.)

Schrödinger, himself, was bothered by the Copenhagen interpretation. He boiled his concerns down into a thought experiment, now quite famous, called “Schrödinger’s Cat.” It attempts to put the microscopic, quantum world into our macro-world and show the craziness and absurdity of what it implies.

I won’t describe the “cat in the box” story, but Google with quickly provide the details. This experiment has echoed down through the history of quantum theory and led to many an explanation, refutation, and even the title for a book. Stephen Hawkings once said, “When I hear about Schrödinger’s Cat, I reach for my gun.”

That quotation is taken out of context and doesn’t get into the subtleties of what Hawkings has said about it, so time for some more Google-ing. You can spend the better part of the day following the cat / rabbit trail.

As for another often-misquoted scientist, Albert Einstein, he said, “I think that a particle must have a separate reality independent of the measurements. That is, an electron has spin, location, and so forth even when it is not being measured. I like to think the moon is there even if I am not looking at it.”

Einstein rejected the Copenhagen interpretation and spent his lifetime in friendly jousting with Niels Bohr in an attempt to disprove Copenhagen.

Quantum theory has an atom being either a spread-out wave or a concentrated particle. If, on the one hand, you detect it in a single box (or through a single slit), you show it to be a compact particle. On the other hand, it can participate in an interference pattern that shows it to be an extended wave — an apparent contradiction. But the theory is protected from refutation by the Heisenberg uncertainty principle, which shows that checking to see through which slit an atom comes kicks it hard enough to blur any interference pattern. So you thus can’t demonstrate a contradiction.

To argue that quantum theory led to an inconsistency and was therefore wrong, Einstein attempted to show that even though an atom participated in an interference patter, it actually came through a single slit. To demonstrate this he had to evade the uncertainty principle. (Ironically, Heisenberg attributed his original idea for the uncertainty principle to a conversation with Einstein.)

Einstein presented his explanation at the 1927 Solvay conference. Niels Bohr then rose to point out a flaw in Einstein’s reasoning. With simple algebra, Bohr was able to show that the uncertainty principle would foil Einstein’s demonstration.

Three years later, at another conference, Einstein proposed an ingenious thought experiment claiming to violate a version of the uncertainty principle. This one stumped Bohr and he had a sleepless night. By morning, however, he was able to embarrass Einstein by showing that Einstein’s experiment actually violated Einstein’s own general theory of relativity. A humbled Einstein went home from the conference to concentrate on general relativity, his theory of gravity, or so Bohr assumed.

Four years later, in 1935, Einstein wrote a paper with two young colleagues, Boris Podolsky and Nathan Rosen. This paper hit Bohr like a “bolt out of the blue.” The paper, now famous as “EPR” for the three authors, did not claim that quantum theory was wrong, just that it was incomplete. They designed a thought experiment intended to reveal what they believed to be inadequacies of quantum mechanics. To that end they pointed to a consequence of quantum mechanics that its supporters had not noticed.

According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function, which encodes the probabilities of the outcomes of experiments that may be performed on the two systems, whether jointly or individually.

For example, there is something called “twin-state” particles, such as two photons created together and moving in opposite directions. Quantum theory predicted a particular state for each photon depending on the state of the other. Basically, they are described by a single wavefunction, just like the split electron in two boxes I described in a previous chapter.

So what if the two photons traveled some great distance before one is observed. Then, once observed the wavefunction would collapse to a particular state. But that implied the other photon, now some great distance away, would also have to "decohere" to the opposite state. How would the photon so far away, under the limitations of instant communications denied by relativity, obtain the opposite polarization? How would it “know” that its twin had been “observed”?

In modern terminology we say that the two particles are “entangled”; and it is called “quantum entanglement.” Einstein called it “spooky actions at a distance” and proposed a much simpler explanation that defied quantum theory, namely that the states of the two particles were established when they were emitted and didn’t require an observer or any long distance communications. Recall, he didn’t believe “God plays dice.”

These ideas are often explored in a set of experiments with polarized light. The original paper talked of a complex combination of position and momentum of particles instead of photons of light, but the polarization explanation is considered equivalent and much easier to understand, even to a layperson.

Bohr refuted EPR in a paper, but, like the Copenhagen interpretation, it did leave one with a feeling that something was missing; the explanation seemed more philosophical than scientific, and the argument went on.

Einstein seems in later years to have given up a bit on his view. Although he continued to search for the secrets of the universe, he did write to a friend later, “I have second thoughts. Maybe God is malicious.”

I suspect the continual agreement of all experiments with the descriptions and equations of quantum theory eventually wore Einstein down. (Not that some theories proposed in the intervening years didn’t turn out to be incorrect or incomplete, but the core of Schrödinger’s equations never was found in error … ever.)

The argument was laid to rest in 1970 when John Stewart Bell published his theorem. Bell’s theorem has been called “the most profound discovery in science in the last half of the twentieth century.” It rubbed physics’ nose in the weirdness of quantum mechanics. As a result of Bell’s theorem and the experiments it stimulated, a once “philosophical” question has now been answered in the laboratory.

There is universal connectedness. Einstein’s “spooky interactions” in fact do exist. There is some sort of connection between two particles in certain situations that can exist over great distances and seemingly defy relativistic speed constraints.

These “entanglements,” as modern science calls them, are part of the new frontier of physics. Bell’s theorem lays to rest, once and for all, Einstein’s argument about hidden variables. No, matter and behavior at atomic levels actually is probabilistic and cause-effect has a new interpretation.

Both Einstein and Bohr died before Bell’s explanation. We are sure Bohr would have predicted the experimental result confirming quantum theory. It is not clear what Einstein would have predicted had he seen Bell’s proof. He said he believed that quantum theory’s predictions would always be correct. How would he feel if the predicted result was an actual demonstration of what he denied as “spooky actions”?

The universal connectedness predicted by quantum theory (“Thou canst not stir a flower / Without troubling a star”) is now demonstrated routinely in the laboratory. So, is "non-locality" incompatible with fundamental relativity? Or is space-time folded — just one speculated result of Bell's theorem.

It supports wild speculations. It also, like the rest of quantum mechanics, just works. Now let’s use it to dig deeper into the nucleus.



1 comment:

  1. I enjoyed your point of view but think you are a bit hard on Einstein.

    Bell's theorem, as stated by Bell, concerns the breakdown of local causality, not that sub-quantum variables must be non-local.

    "..almost absurd"

    Well non-locality (instant-action-at-a-distance)is absurd and has no place in a complete physical theory. Issac Newton recognized his own theory of gravity was incomplete because this is what he thought of non-locality,

    “That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.” Isaac Newton 1693.

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