Re: Wave / Particle contradiction

On Apr 17, 8:48 pm, part...@xxxxxxxxx wrote:
"Everyone knows" there's a contradiction between the wave and particle
concepts - a wave can't be a particle and vice versa. I never
understood it. Can someone please explain?

I understand wave to be any physical phenomena that satisfies the wave
equation. For a particle I didn't find any definition, but intuitively
it means something with energy, momentum and maybe velocity, defined
in some region of space/time. Why can't such a thing also satisfy the
wave equation? The only problem is that it may be somewhat hard to
imagine.

In classical mechanics a point particle might be defined as an object
that occupies only a single point in space at a given time. A
solution to the wave equation assigns some value to every point in
space at once. A single classical mechanical particle would have to
be at many different places at once in order for some property of the
particle to satisfy the wave equation. A classical probability
distribution would be better, but then you run into the problem that
probability is always positive. You could do it with multiple
classical particles -- think sound waves -- but experiments have
demonstrated the interference is still there when only one particle is
in the apparatus at a time.

Ultimately, the problem is resolved by quantum mechanics. For a
single particle, the laws of quantum mechanics are essentially that
the particle obey a certain wave equation. And further down the road,
a bunch of particles obeying quantum mechanical laws is equivalent to
a solution of the wave equation obeying what you might call a quantum
mechanical version of the appropriate wave equation. And yes, you
could say quantum mechanics is hard to imagine; I'd say it's hard to
understand what's going on in between observations of a system.

--
Jim E. Black

.

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