Labyrinth said:
How does the exchange of photons/virtual photons give rise to the electrostatic or electromagnetic force?
Why do like charges repel and opposite charges attract?
You see this question often here... Key is to understand the role
of the wave behavior of the electron.According to the Pauli-Weisskopf interpretation, the wavefunction
should be regarded as a distributed charge/spin density. Now imagine
an electron wave-packet moving in an initial direction, with an initial
momentum and energy. At the end of an interaction it will move in
a final direction with a final momentum/energy.
Between the two states it can be viewed as being in a superposition
of these two states. The two states will interfere with each other
giving rise to an interference component (technically: \bar{\psi}_f \gamma_\mu \psi_i )
The interference component is a sinusoidal charge/spin distribution.
Such a distribution will radiate electromagnetically, basically just
like it would do classically. This radiation can be associated with
the (virtual) photon.
A photon can be emitted or absorbed. In the latter case external
radiation comes in and the reaction of the charge/spin density to
the external excitation causes opposite radiation which cancels the
incoming electromagnetic fields: The photon is absorbed.
The magnetic spin/distribution of the wave function plays an very
important role since it determines the polarization of the photon.
Feynman diagrams typically describe a scattering zone. They use,
for simplicity, a plane wave representation. The Fourier domain of
plane waves with, in principle, infinite size and duration. Nevertheless,
this can be an extremely good representation, giving results which
are accurate in 12 or more digits compared with experiments.
When is this representation accurate and when not? Let's look at
some cases.
1) A free electron's wave function may easily expand to a size of
1 micrometer. It collides with an X-ray photon with a one nano
meter wavelength. The ratio scattering zone versus wavelength
is ~1000:1. The plane wave representation is a good representation.
2) A bound electron has a much smaller size, less than one nanometer.
It interacts with an incoming photon with a wavelength of one micro-
meter. This situation is typically not described by Feynman diagrams
since the bound electron isn't a plane wave.
Now, even though there is a 1:1000 ratio now spatially,
temporally, there
is a long overlapping time since the wave function of the electron is
"infinite" in time and the photon oscillates many times. The ratio interaction
time versus oscillation time is >> 1 so the picture of photon absorption
and emission, caused by the interference between the initial and final
state of the electron's wave function is very accurate.
3) The bound electron now interacts with a strong single cycle laser
pulse. The interaction thus has a very short duration. The electric field of
the single pulse is transversal to the direction motion and can be controlled
to be either to the left or to the right. What happens in the experiment?
Well. the atom becomes ionized and the electron flies off either to the
left or the right depending on the direction of the electric field.
So, the geometry plays a very important role, nevertheless, all inter-
actions are the result of the
same physics, and the various pictures
may be used universally.
Now, take the picture of a "classical" electron in an electron field.
We can use here the picture of the electron's wave function in
a initial state interfering with the final state of the wave function.
The interference pattern can be seen as a very small fraction of
a sinusoidal period. The gradient of the resulting radiation is just
the gradient of the potential field.
Very important however is the concept of quantization, photons
come in single units and have unitary propagation. There are various
formal methods to incorporate this behavior in our mathematical
description of quantum physics: canonical quantization, path
integral quantization.
Even so, the unitary behavior of photons, proved in many experiments
remains quite a mystery. Its total range of validity, especially at the
very low frequencies, is still a research topic.
Regards, Hans.