FUNDAMENTAL BUILDING BLOCKS 273
Summing probabilities
In 1947, German physicist Hans
Bethe suggested a way of fixing
the equations so that they mirrored
real laboratory results. In the late
1940s, Japanese physicist Sin-Itiro
Tomonaga, Americans Julian
Schwinger and Richard Feynman,
and others took Bethe’s ideas and
developed them to produce a
mathematically sound version
of QED. It produced meaningful
results by considering all the
possible ways that interactions
could take place according to
quantum mechanics.
Feynman made this complex
subject approachable through his
invention of “Feynman diagrams”—
simple pictorial representations
of possible electromagnetic
interactions between particles,
which provide an intuitive
description of the processes at
work. The key breakthrough was
to find a mathematical way of
modeling an interaction as a
sum of the probabilities of each
individual pathway, which include
pathways in which particles move
backward in time. When summed,
many of the probabilities cancel
each other out: for example, the
probability of a particle traveling
in a particular direction may be
the same as the probability of it
traveling in the opposite direction,
so adding these probabilities gives
a sum of zero. Summing every
possibility, including the “strange”
ones involving backward time
travel, produces familiar results
such as light appearing to travel
in straight lines. However, under
certain conditions, the summed
probabilities do produce strange
results, and experiments have
shown that light does not always
necessarily travel in straight lines.
As such, QED provides an accurate
description of reality even if it feels
alien to the world we perceive.
QED proved so successful that
it has become a model for similar
theories of other fundamental
forces—the strong nuclear force
has been successfully described
by quantum chromodynamics
(QCD), while the electromagnetic
and weak nuclear forces have
been unified in a combined
electroweak gauge theory. Only
gravitation so far refuses to
conform to this kind of model. ■The “strange theory
of light and matter”
produces correct
results.Particles interact by
exchanging photons.This exchange can
happen in many different
ways, each with its
own probability.Summing the
probabilities of all
possible events gives
an accurate description
of experimental results.See also: Erwin Schrödinger 226–33 ■ Werner Heisenberg 234–35 ■
Paul Dirac 246–47 ■ Sheldon Glashow 292–93
Richard Feynman
Born in New York in 1918,
Richard Feynman showed a
talent for mathematics at an
early age, and earned a
degree at Massachusetts
Institute of Technology (MIT)
before attaining a perfect
score in mathematics and
physics for his graduate
entrance exam to Princeton.
After receiving his PhD in
1942, Feynman worked under
Hans Bethe in the Manhattan
Project to develop the atomic
bomb. Following the end of
World War II, he continued
his work with Bethe at
Cornell University, where
he did his most important
work on QED.
Feynman showed a flair for
communicating his ideas. He
promoted the potential of
nanotechnology, and late in
his life wrote bestselling
accounts of QED and other
aspects of modern physics.Key works1950 Mathematical
Formulation of the Quantum
Theory of Electromagnetic
Interaction
1985 QED: The Strange
Theory of Light and Matter
1985 Surely You’re Joking,
Mr. Feynman?