Monday, January 19, 2009
The problem with interpretations
I’ve had another one of those enlightenment experiences today, when I bought and read a very comprehensible book about quantum mechanics. What the author did right, and what most other authors do wrong: It disregarded all the partly quite bizarre interpretations of the theory. If you forget about all the motivations and interpretations of a theory, what remains? Equations. That’s it.
For example, I’ve learned that a quantum state is simply a unit vector V. Things such as superpositions or in more colloquial terms being in multiple states simultaneously exist only in interpretations. The state vector is a fully determined value.
Then where do superpositions come from? It’s simple. They are no fundamental feature of a quantum state, but a feature of the measuring process. Measurement is always done in a certain base described by a number of base vectors. The outcome of the measurement of V depends on the description of V as a linear combination of these base vectors. The square of the absolute value of the coefficient of a particular base vector X is the probability of the outcome being X. That’s it. Quantum states are fully determined and not superposed. Superposition is a measurement effect, because the measurement destroys information.
Example: If you run a vertically polarized photon through a polarization filter, which lets through vertically and horizontally polarized photons, then the outcome is a vertically polarized photon. If you rotate your filter by 45°, the outcome is completely random. That’s not because the photon had a superposed polarization, but because the new base of the measurement has changed in a way, which makes the outcome “vertical” impossible. In other words, in the former experiment, there was no superposition, in the latter there was, even though the initial configuration is exactly the same with the only difference being the justification of the filter. So superposition doesn’t exist. It can be interpreted as a measurement effect.
I had that same experience with other things as well, for example group theory or monads. For some reason, people seem to prefer to depict abstract or unimaginable things and concepts as something complicated or mysterious. I think, this is related to our fascination for the incomprehensible and the satisfaction of amazing other people. Who isn’t amazed by the imagination that there may be more than the three (or four) dimensions you can see, or that a single thing can be at multiple locations at the same time, let alone relativistic effects? However, if you described these things as what they really are, you wouldn’t amaze anyone. Ask a physicist about quantum physics, you’ll get a straight, but disappointingly boring answer.
Monday, January 19, 2009