-------------------
Waves or particles?
-------------------

Since Newton's time, there have been two competing pictures for the 
behavior of light and matter - particles and waves (or rather fields). 
Some phenomena can be reasonably interpreted in both pictures. But on 
the submicroscopic level, where experience can only be indirect, both 
pictures are somewhat limited because a quantum field - the reality 
underlying it all - is too abstract to be easily visualized.

If one chooses the particle picture, one earns paradoxes about being 
nowhere unless measured, passing to through both slits or only one, 
explaining why an interference pattern exists at all, etc.. There is 
no way to get a particle picture show wave effects - all that becomes 
very counterintuitive. (But the Copenhagen brain washing still shows 
its power - people became used to the fact that these alleged 
''particles'' are very strange objects.) On the other hand, waves can 
simulate particle properties by regarding the latter as wave packets 
- localized excitations of waves. 

Now light showed obvious interference effects, difficult to interpret 
with particles, and (polarization effects,  impossible to explain by 
even the most contrived particle picture. As a result, since around 
1850 if not earlier (the double slit experiment dates from 1801), 
physicists universally adopted the wave view of light. 


For matter, the development was much slower since matter is much 
heavier. This makes interference more difficult, since it is far more 
difficult to keep matter waves coherent. And they follow a Klein-Gordon 
or Dirac equation rather than a Maxwell equation. But these are stiil 
wave equations, so the qualitiative behavior - a superposition of two 
spherical waves after passing the slits, and the resulting form of the 
interference pattern - is the same.

The wave properties of matter such as electron diffraction 
    http://en.wikipedia.org/wiki/Electron_diffraction 
were only discovered after the advent of quantum mechanics. But here 
also the field view proved to be more versatile and won the competition.
Modern QED (the most accurate of all physical theories) and all high 
energy physics (based on the standard model and derived field theories) 
are framed in the language of quantum field theory, where quantum 
fields are the primary objects and particles are regarded as localized 
excitations of these fields.


So. if one knows that one produced single photons or atoms at a time, 
as localized wave packets, it is appropriate to talk about particles. 
In that case, the wave arriving and the particle arriving are 
synonymous. 

But their fate as particles after passing a slit more narrow than 
their wavelength (or a beam splitter and similar devices) becomes 
dubious since the slit delocalizes the field to an expanding spherical 
wave. Now this wave arrives at a far away detector at all places 
simultaneously, while the detector responds randomly at one place. 
Thus the particle view and the wave view diverge, and only the latter 
is a reasonable (i.e., semiclassical) explanation of what happens.

... except if one adheres to a strict Copenhagen view, according to 
which one cannot assert anything about a quantum system when it is not 
observed. This view has severe difficulties, though, once the quantum 
system becomes big enough to behave classically.