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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.

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