Theories of the Universe: Born of Probability
Born of Probability
Schrdingers's picture of the atom relied on a complicated and hard to imagine wave function. Nevertheless, it worked, and the atom's electron was indeed a wave. The atom radiated not because its electrons leaped from orbit to orbit, but because of a continuous process of harmonic beats. Light was emitted when the atom “played” both the upper and lower energy frequencies at the same time. The difference between the two electron matter/wave frequencies, which also corresponded to Bohr's conception of the atom as the difference in the electron's orbital energies, was exactly the frequency of the light observed.
In the last section and to this point, we've covered the quantum ideas and theories of some of the key scientists. They've been presented in a way so that you could see how each one, more or less, unfolded into or gave birth to the next. Before going further, it's a good idea that you to have a clear idea of how this stream of development occurred. Because from here on in the rest of the theories will get a little more unusual. So it's a good idea to have a clear picture of the state of quantum mechanics right now.
Eventually, Schrdinger's musical picture of the musical atom was replaced by a new one, but his mathematical equations remained intact. The problem with a pure wave model was that it didn't account for the electron's other feature, that of a particle. No matter how the wave shook and danced, there had to be a particle somewhere. Max Born (1882-1970), another German physicist, was the first to provide an interpretation of this particle discontinuity. He realized that the wave was not the electron. It was a wave of probability.
We can now add the notion of probability as another chief feature of quantum mechanics to de Broglie's contribution that all matter exhibits wave/particle duality. Probability is a strange characteristic to have as a fundamental building block of the universe. It somehow seems to reflect an incomplete picture of our understanding of how the quantum world operates. This is exactly how Einstein felt and was reflected in his famous statement, “God does not play dice with the universe.” He never fully accepted this flaw of quantum mechanics and always felt a more complete picture would be developed down the road. However, after more than fifty years of experiments, it seems that matter must be described in an essentially probabilistic manner, at least at this point in time.
The difficulty with an electromagnetic wave of any kind is that it's impossible to locate the position of any one particle, like an electron, within it. Born realized this and developed a way to determine its probable location. By calculating the magnitude or intensity of a wave, he found that in places where the wave was large there was a greater probability for the electron to be found. And where the intensity was small, the probability was less.
Probability is something we're all familiar with from tossing coins at sports events to bet-ting in casinos. It is also the basis for statistical analysis and when used in that framework has a very precise mathematical system. It can be usefully applied to predict certain out-comes, but also has the ability to be manipulated to reflect whatever outcome someone wants. It all depends on what you want to use it for. As a tool in quantum mechanics, it is the only method that can show us enough about the microcosmic universe to understand it at this point.
Probability Leads to Uncertainty
The role of probability became a crucial part of quantum mechanics. And because it did, it became the fount from which sprang other core theories and concepts that defined the quantum world in strange and exotic ways. The deeper physicists probed into the quantum world, the more the explanations veered from normal everyday experience. It seemed as though the fundamental structure of the universe operated in ways that were mysterious and profound at the same time. In the upcoming pages remaining in this section, we'll look at some of these ideas so you can see for yourself just how weird it can all get.
Richard Feynman believed that the double slit experiment encapsulated the “central mystery” of quantum mechanics. He said it is “a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery … the basic peculiarities of all quantum behavior.”
The only way a scientist can start to understand something is to describe it, measure it, and name it. You can't begin to measure something until you make some assumptions about what that something is. You can't measure the amount of beauty in a contestant without defining in some sense what beauty is any more than you can measure success, distance, motion, time, or intelligence without defining what it is. And measurement itself is as much a mode of perception as seeing and hearing. Reality and the way we measure it begins and ends with ourselves. And as Werner Heisenberg said, “We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.”
This may seem an unusual idea, because after all what is more scientific than measurement? Yet as we'll soon see, our ability to measure what goes on in the quantum world is what causes all of these theories to be developed in the first place. Let's begin with a return to the double slit experiment.
Back in “The Dual Nature of Light,” we saw how the act of measuring a beam of light defined it either as a wave or particle. We could not measure it as both a wave and a particle at the same time. If we extend that idea to include two other measurements—position and momentum—we'll have discovered Heisenberg's uncertainty principle, another cornerstone of quantum mechanics. Let me explain. Position is a property of a particle while momentum is a property of a wave. Since we can only know if a beam of light or any form of matter is either a particle or a wave, we can therefore only measure its position or its momentum, but not both.
To sum it up, the Heisenberg uncertainty principle can be expressed as follows:
- You can't accurately measure the position of a subatomic particle unless you're willing to be uncertain about its momentum.
- You can't accurately measure the momentum of a subatomic particle unless you're willing to be uncertain about its position.
This summary also shows that it all comes back to the person doing the observing. Not only does this principle reflect the uncertainty of what you can measure, but also that the very act of measuring affects the outcome of the experiment. It is not possible to separate the experiment from the experimenter. To put it succinctly, “To observe is to disturb.”
Excerpted from The Complete Idiot's Guide to Theories of the Universe © 2001 by Gary F. Moring. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.
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