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Tuesday, December 21, 2004

Confuse me with the facts


The most common way to be bozotic is not wanting to know something, which seems to afflict everybody in some form. You have some comforting belief, and you won't listen to anything that goes against it. We see this in politics, religion, and to some extent in science and even mathematics. In politics, it is those who cling to ideology of the right, the left, or wherever. In religion, the dogmatists. In science there are of course adherents of lunatic theories of all sorts, including inventors of perpetual motion machines. But even the top scientists get stuck sometimes. The difference there is that top scientists, however much they may dislike an idea, still pay attention to the experimental results that support it.

Einstein, for example, famously hated Quantum Mechanics, which he had a hand in creating. In 1905, his miracle year (annus mirabilis), in addition to his papers on Special Relativity and Brownian motion (conclusively establishing the atomic theory of matter), he wrote a paper on the photoelectric effect, conclusively establishing that light is absorbed in the discrete chunks that we have called quanta ever since. This rounded out Max Planck's 1899 theory that light was emitted in quanta, and set the stage for the development of quantum theory, one of the most successful physical theories ever, and by far the most troubling. Niels Bohr, the acknowledged leader of the process that led to Quantum Mechanics, frequently said things like, "If you are not troubled by Quantum Mechanics, you don't understand it." By that standard and several others, Einstein really understood what Quantum Mechanics was about.

The problem, from Einstein's point of view, was that Quantum Mechanics deals with probabilities, not inherent properties. The difficulty became clear in 1925 with Max Born's probabilistic interpretation of Schrödinger's application of the wave equation to quantum mechanics. It became intolerable to Einstein in 1927 with Heisenberg's Uncertainty Principle.

The wave equation applies to any kind of wave. For water waves, sound waves, the motion of a vibrating string, and many other phenomena, the wave is an observable physical state of matter in an obvious way, like the shape of a water wave, where the essential physical property is height. Sound moves in pressure waves, and there are temperature waves, bending and twisting waves, and other kinds.

But in quantum mechanics, the waves don't represent observable properties. The wave form determines the probability of observing any value of a property of the object such as position, energy, and so on. In general there is a high-probability value, with the probability dropping off very rapidly away from that value. These states do not present much of a problem, because the high-value states behave themselves pretty well. An atom observed in some location is likely to be found near there in the future. An object moving in some direction will be found continuing in that direction if it is not disturbed. In some cases there may be two or even more values of relatively high probability, meaning that there is no such thing as the actual value. In the extreme case, we get Schrödinger's cat, which is alive and dead at the same time, with a mixture of probabilities depending on the decay of one radioactive atom.

The Uncertainty Principle made things much worse. It is a principle of mathematics that a wave form does not have a definite frequency unless it is infinite in extent. More generally a finite wave form has a spread of possible frequencies that depends on its size in space, and the product of the spread in space and the spread in frequency must be greater than a certain constant amount. Since the size of the waveform determines the area in which the object can be found, and the frequency relates to the speed of the motion, determining the object's position means that we don't know its speed of motion, and determining how fast it is moving means that we don't know where it is.

The wave equation and the Uncertainty Principle make it clear that we cannot predict the future with complete precision, and in some cases we can't predict it at all. This is entirely different from Newtonian physics, which was entirely determinate. Of course, in certain areas, Newtonian physics doesn't work, so although we could make precise predictions with it, they would turn out to be completely wrong.

A further problem is that even God cannot predict the future if Quantum Mechanics is correct. This puts it in conflict with all religions that teach the omniscience of God not only concerning the present, but the eternal future. How can God give prophets a look at the future if there isn't only one? How can God have a plan for everything in the universe? This is a problem for many versions of Christianity, Judaism, and Islam, but not for other religions in general. Anyway, it was a problem for Einstein.

Einstein fought against probabilistic Quantum Mechanics with every resource he could muster. He analyzed the consequences of the theory in considerable detail, and whenever he found a seeming contradiction, he challenged physicists to resolve it. They always did, and they always resolved the seeming contraditions by experiment, that is by showing that the world actually does things that no reasonable person would expect, and that hardly anybody would believe without the evidence of the experiment.

Poor Einstein. It was hard on him, having his most cherished beliefs shattered. Still, he did pay attention to the experiments, and was therefore not a bozo on this point. In fact, he made major contributions to statistical Quantum Mechanics, in particular the Bose-Einstein statistics of indistinguishable particles that can be in the same quantum state, since amply verified.

Now, Quantum Mechanics is known to be wrong on some points, because it is inconsistent with Einstein's General Relativity, which has survived every experimental and observational test. There are some theories designed to replace Quantum Mechanics in a way compatible with General Relativity, although it is too soon to tell which of them may work out. So, in a way, Einstein will have a real victory over Quantum Mechanics. Still, the replacement theory is not going to reestablish determinacy and predictability, not even for God.

Unless, of course, God is just making it all up, and so doesn't need to predict anything. If you really don't want to listen to the facts, you can always find a way to claim that they don't matter.


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