Monday, 6 October 2014

Quantum Mechanics: Part Two

Determinism or Not?

What we now see developing is a schism among the luminaries of early 20th century physicists. They were divided into two philosophical camps: those who supported the probabilistic Copenhagen Interpretation (Bohr, Heisenberg and others not yet mentioned) and those who supported a deterministic model of reality (Einstein, Schrödinger, Born and others). It might be surprising to note that Einstein Рthe man who turned classical Newtonian physics on its head Рshould be so vehemently opposed to this interpretation of Quantum Mechanics, especially since it appeared to be an inevitable conclusion arising out of his own theories. But, in my view, Einstein passionately believed that the universe is structured in a beautiful and logical manner, however strange that logic may appear to traditional science. As such, nothing (in the physical realm, at least) was ultimately beyond human comprehension. The Copenhagen Interpretation, on the other hand, introduced messy and irrational randomness. This was just intolerable for Einstein and, it seems, for a majority of scientists, engineers and technicians to this day. Nevertheless, the Copenhagen Interpretation remains, among quantum physicists, the current orthodoxy even though it has several challengers.

The crucial difference between the two standpoints was: determinism or not? Determinism states that every event has a cause, going back to the beginning of time, i.e. the Big Bang (or whatever the current theory of the beginning happens to be). Another way of stating it (theoretically) is to say that, if we could know all of the pre-existing conditions, we could accurately predict everything that will happen in the future. This, of course, has far reaching implications, not the least for the concept of human free will and accountability. For example, if someone goes out one morning and shoots his neighbour, can he be held ultimately responsible for his action if it was inevitable from the moment the universe came into being? On the other hand, quantum mechanics introduces probability at the most fundamental level. Another big philosophical question now begs: does quantum level probability allow for choice? If, by deciding to observe an electron, I collapse the probability wave and determine its position or momentum, does that signify that the universe does indeed allow for my free will?

Lest anyone be in any doubt about the quantum description of the electron vis-à-vis its position and/or momentum, we are not talking about a limitation of the measuring equipment to determine either or both, we are talking about the electron having no position nor momentum until we make the measurement of one or the other. This is crucial to the debate above.

Einstein was not about to lie down and quietly concede the point to Bohr and his Copenhagen confederates. In 1935 he, Boris Podolsky and Nathan Rosen invented a thought (gedanken) experiment designed to expose the incompleteness of QM. This became known as the EPR paradox. The measurement problem as described above is one of the bizarre outcomes of QM but it leads into another, even more bizarre, consequence and this is what Einstein, Podolsky and Rosen latched on to in describing the paradox.

The EPR Paradox

Two particles can exist in a state referred to as “entangled” – that is, they behave as one physical system. The EPR argument centred around entanglement together with a particular measurement. In addition to position and momentum, another property of a particle is that known as its “spin”. Using convenient terms, we could say that the spin is either “up” or “down”. So, with the entangled pair, if we measure the spin of one particle to be “up”, we can say with absolute certainty that the spin of the other will be “down”. The paradox is this: if we allow the pair to fly apart – even light years apart – the measurement of the spin of one particle should instantly yield certain knowledge of the spin of the other. As neither particle (according to QM) had a definite spin direction until the first measurement was taken, how would the remote particle receive the information determining which spin direction it should display. Einstein’s Special Relativity specifically rules out faster-than-light travel so how could information travel across light years in an instant? Einstein called this “spooky action at a distance” and thought it demonstrated that QM violated causality (a.k.a. determinism), thus rendering it inconsistent. In physics this spooky action at a distance is called “nonlocality”. Einstein maintained that something must be missing from QM – probably some form of hidden variable – that would account for the spookiness.

John Stewart Bell

For many years following the EPR paper, nobody tested the argument experimentally. In 1964, John Stewart Bell – a young physicist from Northern Ireland – produced a theorem that rejects all models of reality based on locality. The proof (Bell’s theorem) states that in order to assume locality, any model (including the hidden variable variety) must satisfy a mathematical inequality, known today as Bell’s Inequality. In 1982 actual experiments carried out by Alain Aspect and his team (and others since) appear to prove that Bell’s inequality is violated and left little doubt that nonlocality is a fact of nature – at least at the sub-microscopic level. Just so that we are sure about what nonlocality means, let’s use a big world analogy: two men are given flags and told that if one raises his flag, the other must drop his. They are sent a short distance apart and we ask first man to raise his flag; immediately the second man drops his. Ok, we say, the second man must have reacted when he saw the first flag go up. So we send the first man to New York and the other to Tokyo. We film and accurately time the proceedings and ask the first man to raise his flag. Immediately the second man drops his. How? Maybe the second man had a radio and received a signal? But no, we can even rule that out because his flag dropped before the time it would take for a radio signal – travelling at the speed of light, of course – could reach him. It is as if the space between the two men did not exist and the second man knows instantly what the first is doing. This is a very simplistic analogy, of course, and it must be pointed out that there is little present evidence of “big world” nonlocality although, recently, experiments by Anton Zeilinger and his group have confirmed that essential "spookiness" and confounded those hoping for a return to "rational" physics.

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