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1. Quantum mechanics

Paul Budnik paul@mtnmath.com

Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to build nuclear weapons. It is strange because, unlike all previous fundamental physical theories, it does not model what happens physically. It only models how probabilities change over time. Yet no previous theory has come remotely close to the accuracy that quantum mechanics is at times capable of.

Waves and particles

Quantum mechanics uses partial differential equations to model how probability densities evolve over time. This produces `waves' of probability densities not unlike the waves on the surface of the ocean. The higher the wave at a given point the more likely the particle is to be located at that point. Everything that exists has a wave aspect. One cannot model what the particle does between observations of the particle. One can only model how the probability of observing it changes over time. These probabilities have a wave like character. Everything also has a particle aspect. Every particle interacts with other particles as if it were located at a single point in space.

It is these two aspects of a particle that causes physicists to speak of the ``collapse'' of the wave function. Prior to observing a particle it could be located at anywhere the wave function is not zero. After observing it the particle is known to be within a much smaller region of space. The wave function has collapsed. Of course there cannot be a physical wave function that collapses because this would violate special relativity. However the wave function does at times seem to be a physical entity because wave functions from two particles can interfere with each other just as physical waves do.

More information is available in sections of my online book.

Quantum mechanics

The uncertainty principle

Quantum entanglement

Combining quantum mechanics and relativity


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