2. Spinning arrows and squares
Photons
are the particles of electromagnetic radiation which often take the form
of visible light. "Classical," non-quantum-mechanical physics often teaches
that light travels as waves, and that as waves they experience superposition
effects such as those demonstrated by a double-slit experiment. However,
just shining a few photons at a time through a double-slit -- so that
it is impossible for "light-waves" to interfere with each other -- shows the
same effect of bright and dark spots.
This suggests a new particle-centric way of thinking
about light. QED [which from now on will signify only 
"quantum
electrodynamics"] imagines that there is a stopwatch tied to each photon
which turns extremely quickly. This is the analog of "frequency", so a
blue-photon stopwatch would spin a bit faster than a red-photon's and
a lot faster than a radio-photon's. As a photon moves from A to B, its
imaginary stopwatch would spin a certain number of times and stop in a
certain position.
The
direction the stopwatch is pointing corresponds
to a probability amplitude, a vector or "arrow" of length between 0 to
1. QED uses it to determine the probability that some action will occur;
the square of its length is the probability. (I won't explain how to determine
arrow length through theory, but it can be found experimentally. For instance,
arrows shrink .2 times when they are reflected off a glass surface.)
If
there is more than one possible path that a photon can take from A to
B (there almost always is), the arrows must be added vectorially. The
square of the resultant length then would be the probability. If the time
on one path from A to B results in an extra half-turn of the stopwatch
from another path, their arrows will point opposite directions and cancel
out. The square of the resultant would have no length, so there would
be no chance that a photon could travel those paths from A to B.
If photons were simply waves, this would be analogous to the "complete destructive interference" effect of superposition -- when a path takes half-a-wavelength longer than another, there won't be any disturbance in the medium. However, this QED effect will work even if there is only one photon.
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