Q:

Wave behavior of particles

When people say that every moving particle has an associated wave, do they mean that the particles will move up and down physically, for example when we say that a moving electron has a wave associated with it, does the electron physically oscillate?  Or is it some other wave, like a probability wave? I really don't understand the latter.

A:

I agree with Pieter, especially when he refers to QED, writing

Feynman explains this (in his little book QED, I recommend to read
  that) with electrons having dials that turn around. Or one could
  represent phase as color.

It must be remarked however that Feynman was a strong opponent of the
so-called "wave particle duality. Let me quote from p. 15:

I want to emphasize that light comes in this form - particles. It is
  very important to know that light behaves as particles, especially for
  those of you wo have gone to school, where you were probably told
  something about light behaving as waves. I'm telling you the way it
  does behave - like particles.

And in note 3 at p. 23:

No reasonable model could explain this fact, so there was a period
  for a while in which you had to be clever: You had to know which
  experiment you were analyzing in order to tell it light was waves or
  particles. This state of confusion was called the "wave-particle
  duality" of light, and it was jokingly said that light was waves on
  Mondays, Wednesdays, ans Fridays, it was particles on Tuesdays,
  Thursday, and Saturdays, and on Sundays, we think about it! It is the
  purpose of these lectures to tell you how this puzzle was finally
  "resolved".

I entirely agree with Feynman. His purpose was to show how the
wave-like behaviour of particles could be modeled by assigning to each
particle an "amplitude" - a complex number, which Feynman depicts as
an arrow. 
In some notes of mine I further elaborated this point. Here is a
translation (original is in italian):

Conviction about wave character of light was based on a series of
  experimental facts [...] we only recall by their names:
  interference and diffraction. It was known, and it is easy still
  today to verify in the laboratory, that all known waves give rise to
  interference and diffraction: this holds true for surface waves on a
  liquid as well as for sound waves. From here it was concluded: since
  waves exhibit interference and diffraction and light too exhibits
  interference and diffraction, it follows that light is made of waves.
It is easy to see the on logical grounds such conclusion is
  unwarranted: all fishes live in water, dolphins live in water, then
  dolphins are fishes? We don't mean that for a century physicists had
  fallen into a so trivial logical error, but simply that it was an
  induction, not a deduction. It was very plausible, on the ground
  of the analogy with wavelike phenomena, to induce that light too were
  made of waves. Experimental sciences proceed this way very often, and
  are often successful. But it may also happen that ensuing research
  shows the induction was unjustified. This is what happened with light.
Our reasoning cannot stop at this point however, because if we
  assert light is made of particles (photons) we still have to explain
  how it can behave in ways we are used to attribute to waves. At least
  we must be prepared to accept that if we are dealing with particles,
  they are particles sui generis, very different from the idea of
  particle our everyday experience could suggest.

