Re: Wave / Particle contradiction

In article <1176879447.290313.265880@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, Jim Black <tramspap@xxxxxxxxx> writes:
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.

There is a bit more than this to it. The key property of a particle
(be it classical or quantum mechanical, doesn't matter) is that it
interacts as a single entity. A partiucle may interact or fail to
interact but you cannot have "a part of a particle interacting". A
wave (classical wave, to be exact) can "partially interact". A
classical wave propagates from source to whatever destination point we
ma be interested in along all possible trajectories at the same time
and there is nothing especially puzzling about it, for us, since it is
a diffuse entty present in many locations simultaneously.

So here is the baffling thing about QM. The dynamics of a particle is
described by a wave equation. But, when it comes to interactions. it
ineracts particle like, as a single indivisible entity. The wave
doesn't determine how much of the particle arrives at a given spot,
just with what probability it arrives there. In the old parlance this
was referred to as "collapse", nowadays this term appears to go out of
fashion but I wouldn't say that better replacements exist.

Mati Meron | "When you argue with a fool,
meron@xxxxxxxxxxxxxxxxx | chances are he is doing just the same"
.

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