A an example of Feynman Diagrams, by Len
Bugel.
A modern Physics View of Force
The Standard Model of Elementary Particles and Forces
(Standard Model for short), which describes the building blocks of
the universe and the interactions among these building blocks, recognizes
just two fundamental types of particles and four forces. The particles
of matter can be divided into quarks and leptons, and the forces are
the strong force. The weak force, the electromagnetic force, and gravity.
The theories that describe the first three of these interactions are
Quantum Field Theories (gravity, for the time being, is the odd man
out), and all quantum field theories treat forces in the same interesting
way: forces between particles result from the exchanging of Gauge
Bosons, particles which are said to mediate the forces. It is this
interesting feature of modern physics I would like to discuss, in
terms understandable to high school physics students, after they have
learned about conservation of momentum. The space shuttle presents
an ideal stage on which to illustrate the main idea here, and hopefully
all students have seen some video images of astronauts at work in
the shuttle's cargo bay. Specifically, the space shuttle, being in
free fall through space, is the ideal place to see Newton's first
law at work. Objects in motion really do tend to remain in motion
at constant velocity when we remove the annoying interference of gravity
and air resistance! Here then is the opportunity to demonstrate a
force as the exchange of a particle. Two astronauts, Amy and Bart,
working in the cargo bay, have pushed off from one wall, and are drifting
at constant velocity down the bay. (See Figure 1) Bart notices that
Amy has a nice big wrench, and asks to borrow it. At point 1 in the
diagram, A gives the wrench a toss. Since the wrench now has some
transverse momentum, and the momentum of the system A + W must be
conserved, A's velocity vector must change -- she must acquire some
transverse motion in the direction opposite the wrench. At some later
time, point 2 in the diagram, B catches the wrench, and now the conservation
of momentum for B + W requires B's velocity vector to change. (I've
drawn the path of the wrench with a wiggly line because Amy gave it
a bit of spin as she tossed it.) Now if you imagine all this taking
place in the dark, with A and B each wearing a light, an observer
would not see the wrench at all, but instead would see two particles
repel each other! The little diagram inside the cargo bay tells us
exactly what went on here, and since it does such a fine job of explaining
the interaction between two humans, I am going to refer to it as the
fine man diagram (pun definitely intended).
From this point, it is easy to replace A and B in
the fine man diagram with two particles of like charge, say two electrons,
replace the wrench with a photon, and we have the Feynman diagram
for a typical electromagnetic interaction (Figure 2). As before, the
exchanged particle is shown as a wiggly line. (Richard Feynman, inventor
of this handy little diagramming technique, received the Nobel Prize
in physics for his work on quantum electrodynamics, the currently
accepted theory of electromagnetism.)
Of course the repulsion of two like-charged particles
is not the only sort of force in nature - a good thing for us! - but
in fact all forces can be thought of in this same way. An immediate
question, and one your students will bring up, is how do you explain
an attraction, such as that between an electron and a proton. In our
analogy we can replace the tossed wrench with an extended pole of
some sort, so each astronaut can tug on it. (Not only will the pole
be under tension, but the analogy is being stretched pretty taut as
well!) The best description of what happens in quantum field theory
is that the exchanged particle carries negative momentum - not an
easy thing to visualize. The exchanged gauge bosons are in fact all
virtual particles, can never be directly observed, and "borrow" momentum
from the quantum field, subject only to the limitations of the Heisenberg
Uncertainty relation. (Real, observable versions of these bosons can
also exist, but they no longer mediate forces. The real photon becomes
the quantum of light, for instance.)
Mr. Bugel goes on in further detail, but I have chosen not to include
the rest of the essay as the above accomplishes a fair understanding
of how the Feynman diagrams work in a very clear manner. So I guess
it wasn't quite so technical after all. If you would like to read
the full essay I have included a link at the top of the page.