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Let There Be Light, Part I

I'd like to conclude by discussing the various interpretations of quantum mechanics around today. When I say interpretations, I mean descriptions of quantum theory that attempt to attach some real world model. While no serious scientists doubt that the theories are correct, there is considerable debate about what they mean. All viable interpretations make the same predictions about the experiments we can conduct in a lab with current technology. All the interpretations agree that, when unobserved, quantum events develop as wave functions. All the interpretations agree that whenever a particle is observed, it takes on a definite state.

Where the interpretations disagree is how these two facts are to be reconciled. Without going into great detail, I will outline the currently available options:

The Copenhagen Interpretation (CI)

The oldest interpretation, this is the one that is generally offered up in high school and college physics texts. The following represents a fairly succinct summary of the Copenhagen's salient points, from The Page of Uncertainty:

  1. The wave function is a complete description of a wave-particle. That is, any information that can't be derived from the wave function doesn't exist. For example, if the wave is spread out over a broad region, then we can't determine where the particle is located. And since the wave function doesn't tell us the location, the particle doesn't have a location. Similarly, if a wave is made up of many different momenta, then the wave-particle doesn't have a value for the momentum.
  2. When a measurement of a wave-particle is made, its wave function collapses. So for example, if we precisely measure the momentum of a particle, its wave function suddenly changes from a wave made up of many moment, to a wave with only one momentum. (This is termed a collapse, even though the wave doesn't actually get any smaller in this case. Remember, a wave with an exact momentum extends across the entire universe.)
  3. If two properties of a wave-particle are related by an uncertainty relation (such as the Heisenberg uncertainty principle), no measurement can simultaneously determine both properties to a precision greater than the uncertainty relation allows. In the case of the Heisenberg uncertainty principle, this means that if we measure the position of a particle, then there's a limit to the precision with which we can know the momentum. A consequence of this is that when we measure the position of a particle, we affect its momentum, and vice versa.

It should be noted that there is no one established Copenhagen Interpretation.

The biggest flaw with CI, one that was demonstrated almost immediately, is that measurement is ill-defined. No one has given a satisfactory description as to what kind of event is necessary to collapse a wave function. Nor, given the equations of QM, does it seem that it is possible to do so. This lead to the infamous Shrodinger's Cat thought experiment. If someone were to develop a refined CI that predicted that wave collapse were associated with a particular physical phenomenon, this could be measured, and CI could then be considered a viable model. However, this seems unlikely at present.

I will mention in passing that a minority of CI advocates claim that consciousness is the key event in the collapse. Not only does this seem like a suspiciously solipsistic theory, it doesn't solve the measurement problem. Instead of "what constitutes a measurement?" we are stuck with "what constitutes a consciousness?".

Hidden Variables (HV)

Einstein, who hated the uncertainties and fuzziness of QM, was a proponent of Hidden Variable interpretations. Basically HV asserts that particles carry unobservable information in them that corresponds to a description of the wave function they will follow.

A later experiment, would demonstrate that any Hidden Variable theory would require a superluminal (faster than light) communication system between particles.

Transactional Interpretations (TI)

The Transactional Interpretation asserts that every quantum event has two waves associated with it, an advanced wave that moves in normal time and a retarded wave that moves backwards in time. I would strongly encourage reading the Transactional Interpretation web reference, not just to understand the interpretation, but because the site covers many of the problems in QM.

Many Worlds Interpretation (MWI)

The most paradigm shattering interpretation of Quantum Mechanics is theMany Worlds Interpretation, aka the Everett Interpretation, or under a slightly different guise, Many Histories.

MWI claims that every quantum event is not an either-or proposition. Instead, all possible events occur. There exists a universe for every possible permutation of history that QM allows. This interpretation seems so far fetched at first blush, that it seems odd that it is taken seriously at all, particularly by such physicists as Stephen Weinberg, Murray Gell-Mann and Stephen Hawking.

Yet it has the distinct advantage of being free of all the paradoxes that plague traditional QM. It (almost) neatly resolves all the problems that have arisen as a result of QM: wave particle duality, the measurement problem, locality, etc.

Conclusion

I firmly believe that someday the mystery of Quantum Mechanics will be solved- we will know why light acts like a wave and looks like a particle.

Furthermore, I believe that understanding the implications of Quantum Mechanics will be necessary to develop new theories to explain the mysteries of both the quantum and macroscopic world.

I hope that this "puzzle" and its related links encourage you to learn more about the incredible almost magical physics that define our world.

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