Friday, April 26, 2013

History of Science -- Part Fifteen: Interpreting Schrödinger

Schrödinger speculated that an object’s waviness was the smeared out object itself. Where, for example, the electron fog is densest, the material of the electron is most concentrated. The electron itself would thus be smeared over the extent of its waviness. The waviness of one of the states of the hydrogen electron might then morph smoothly into another state without the quantum jumping the Schrödinger detested.

This reasonable-seeming interpretation of waviness is wrong. This is the start of the real mystery. When one looks at a particular spot, one finds either a whole object or no object at that spot. For example, an alpha particle emitted from a nucleus might have a waviness extending over kilometers. But as soon as a Geiger counter detects an alpha, there is a whole alpha right there inside the counter and nowhere else. All the waviness is suddenly concentrated one spot where the particle is observed. If the particle was actually spread out throughout the wave, then it would have to collect at one point almost instantly, which would require traveling faster than the speed of light. That idea just doesn’t work.

Once the modern interpretation of his wavefunction was known, Schrödinger stated that he was sorry that he had anything to do with quantum theory. What his equation predicts is something a lot crazier than “those damn quantum jumps.”

The modern, accepted interpretation is that the waviness in a region is the probability of finding the object in that location. Be careful! It is not the probability of the object being there!

The object was not there before you found it there!!

Your happening to find it caused it to be there!!!

This is tricky and the essence of the weirdness of quantum mechanics — yet it works … every time!!!!

It is all about probability. It was, in fact, only a few months after Schrödinger announced his equation that Max Born realized that the waviness in a region is probability, the probability for the whole object being found in that region. Once the particle is detected, the probability becomes “1” at that point and “0” everywhere else. We say that the probability wavefunction “collapses” upon detection.

Max Born was born in 1882 in Breslau, Germany. He participated in all the great discoveries of both relativity and quantum mechanics in the first half of the twentieth century. He pioneered the use of matrices and other advanced mathematics in both relativity and quantum theory and was closely associated with many of the people I’ve mentioned in this history. He worked with J J Thomson in Cambridge on atomic particle scattering and he added to the fundamental principles first proposed by Einstein. He formulated the dynamics of a crystal lattices and he shared the Nobel Prize for Physics in 1954 with Walther Bothe for his probabilistic interpretation of quantum mechanics. Perhaps Born’s greatest contribution was his work introducing Matrices to physics and quantum calculations. (A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns, sort of like a crossword puzzle.)

Prior to his work, Matrices were rarely used by physicists, but he showed their powerful capabilities in exactly the type of problems being worked on in quantum mechanics. Today it seems odd to not use matrices in physics, but in the early years of last century they were much more the providence of mathematicians, rather than physicists.

So, if the wavefunction is about probability, you might say, “The waveform is a probabilistic prediction of where the particle is.” No, we actually interpret it that the particle is sort of physically spread out over the entire waveform … but not really … and the act of detecting the specific location causes the wavefunction to collapse.

Trust me, it is not easier to understand from the equations than from this explanation. It is mind-blowing no matter how you think about it. That’s the really weird part I spoke of earlier. Schrödinger’s equation will accurately predict the location and motion (and a lot in addition to that such as energy and spin), but it predicts it as a region with probabilities of detection. Upon actual detection, things seem to suddenly change. We say the wavefunction collapses.

Here is a little experiment that has actually been performed thousands of times. Any wave can be reflected. Semitransparent mirrors reflect part of a wave and allow the rest to go through just like a window pane that lets light in, but also reflects some too. A semitransparent mirror for light is also semitransparent for photons — the particle nature of light. We can also construct semitransparent mirrors for atoms. After all, matter also has the dual nature of wave - particle. Encountering such a mirror, an atom’s wavefunction splits into two wavepackets.

We can use such a construct to send half of the wavepacket into one box and half into another. Now the wavefunction is trapped in two boxes. Holding an atom in a box pair without disturbing its wave function would be tricky, but it can be done. So, which box is the atom actually in? You might say the probability is 50% for each box, and you would be right. If we put a detector into each box, sure enough, it will be in one or the other. Note that, after detection, the odds are now 100% it is in the box detected and 0% it is in the empty box.

But, without putting a detector in each box, if you open a little hole in both box and shine the wavefunction onto a detection screen, you’ll get the familiar interference pattern. That implies that “something” is in each box. Is it the atom? No, when we measure (or detect) in each box, we find the atom in only one box … so what causes the interference? Something must be in both boxes if we perform the second experiment with the little holes. (Note carefully that you must perform one or the other experiment. You can’t do both. If you put a detector in the box, the wavefunction collapses, and now the atom will only be in one box … no interference pattern!)

So, the second experiment seems to makes more sense to say that part of the atom is in each box. That would explain the interference pattern when that experiment is performed. But what about the first experiment where you actually detect the atom? That shows it is all in one box.

The most accurate way to describe this in non-mathematical English is to say that a physical thing was in two places at the same time. The quantum mechanical term for such a situation is “superposition state.” And that is the state that “collapses” (we now say “decoherence”) when the particle is detected. An object in two places at once is counter-intuitive and inevitably confusing.

"Superposition" seems even stranger than the dual nature of waves and particles. How can something be in two (or a lot more) places at once. Yet that is the interpretation of many of the experiments. A wave is spread-out. Now we've reached the most fundamental strange and weird property of Quantum Theory. Yet it has been proven true tens of thousands of times and is the basis for about one-third of our current economy. It works! Strange or not.

To quote Paul Dirac, who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics, and first predicted the existence of antimatter (without which the Star Ship Enterprise would be dead in the water):

The general principle of superposition of quantum mechanics applies to the states [that are theoretically possible without mutual interference or contradiction] … of any one dynamical system. It requires us to assume that between these states there exist peculiar relationships such that whenever the system is definitely in one state we can consider it as being partly in each of two or more other states. The original state must be regarded as the result of a kind of superposition of the two or more new states, in a way that cannot be conceived on classical ideas. Any state may be considered as the result of a superposition of two or more other states, and indeed in an infinite number of ways. Conversely any two or more states may be superposed to give a new state …

This is the modern explanation of the double-slit experiment and the two boxes experiment I just described.

Anton Zeilinger, an Austrian quantum physicist and professor of physics at the University of Vienna, famous for his work in “quantum information” and particle “entanglement” referring to the prototypical example of the double-slit experiment, has elaborated regarding the creation and destruction of quantum superposition:

"[T]he superposition of amplitudes … is only valid if there is no way to know, even in principle, which path the particle took. It is important to realize that this does not imply that an observer actually takes note of what happens. It is sufficient to destroy the interference pattern, if the path information is accessible in principle from the experiment or even if it is dispersed in the environment and beyond any technical possibility to be recovered, but in principle still "out there." The absence of any such information is the essential criterion for quantum interference to appear.

Does this make sense? Of course not. Does Nature’s fundamental law, the Schrödinger equation, give only a probability? Einstein felt that there must be an underlying deterministic explanation. “God does not play dice with the Universe,” is his often-quoted remark. (Bohr told him not to tell God how to run the Universe.)

But randomness was not Einstein’s most serious problem with quantum mechanics. What disturbed Einstein and Schrödinger, and more people today, is the quantum mechanics’ apparent denial of ordinary physical reality — or, maybe the same thing, the need to include the observer in the physical description — that just doesn’t seem to make sense.

Newton’s laws didn’t need an observer. The famous philosophical question, “If no one hears a tree falling in the forest, does it make a sound?” is typically answered, “Yes!” Why would you need an observer to hear the sound to make the sound occur. That seems like crazy talk and bad science. Yet it is the observer that seems to cause the waveiness to collapse into a single location. WHAT ?!!?

If you’re not a bit baffled at this point, then you missed the point. According to Richard Feynman, who understood quantum mechanics as well as anyone ever did said, “Nobody understand quantum mechanics.”

Yet this is the most tested and most successful theory in the history of theories and one estimate put one-third of our economy based on quantum mechanics from lasers to transistors to MRI machines to a future of quantum computers. (The latter does not exist yet.)

Quantum mechanics isn’t just hard to understand because the math is hard … although the math is plenty hard … it is hard to understand because it seems to not fit our reality at all. I can conceive of quantum steps in electron energy, that isn’t too hard to understand. The dual wave-particle nature … well maybe I can fit my little brain around that concept. But this is the final straw.

This is so weird that Schrödinger actually resorted to a good old thought experiment to either explain it or to prove it wrong. It is called "Schrödinger’s Cat." You should Google it sometime. But don’t blame me if it keeps you up at night or gives you nightmares when you do sleep. Welcome to my world!

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