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Quantization



 

This was very strange. In classical physics radiation is the oscillation of a medium of propagation. Sound is the oscillation of air. There is no problem in creating a wave of arbitrary amplitude at any frequency. This is not true of electromagnetic radiation. It comes in minimum size chunks as if it were a particle. Increasingly it became clear that whatever exists at the quantum level it is unlike any existing physical objects or mathematical models. The fundamental building blocks of nature all have a frequency like classical waves and all come in discrete energy packets like particles.

Things got much worse. A classical wave  cannot have both a definite position and a definite frequency. Only an impulse has an exact position and an impulse  is the integral over all frequencies. But classical waves are not quantized. The wave nature of the fundamental particles prevents us from simultaneously determining the position and momentum of a particle. If we prepare the wave so it has an accurate position we will spread out the momentum and vice versa. How is one to predict what happens with these particles that have a frequency? There seems to be no way to predict exactly what will happen. There is an equation the describes the exact evolution of the quantum mechanical wave function. However we cannot use the wave function to predict what is observed. All we can get from it is the probability that we will get a particular observation. Worse once an observation is made we must use that observation to constrain the future evolution of the wave function. Worse we can only model the single particle wave function in physical space. If we have an N particle system than we must model the evolution of the wave function in a space in which there are a separate set of spatial dimensions for every particle. For N particles there are 3N+1 dimensions. This is called configuration space  . Worse once two particles interact they become entangled. An observation of one particle can constrain observations of another in a way that can only be modeled if information about that observation propagates nonlocally so it can influence the second observation.

In other words the theory is an absolute mess. Einstein felt the more successful the theory became the sillier it became. He felt that we would need to start over with something completely different.

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