8 The Most Accurate Theory in Physics
157
Is there any way we can allow rays far away from the primary ray to make
their presence felt? Yes, there is. We can scratch lines across the mirror with a
spacing such that only those rays with a path length equal to a multiple of the
wavelength of the incident light are reflected. (We are assuming here that the
incident light is monochromatic.) In this case, the probabilities from these
rays will add up, and all rays will make a contribution to the reflected light
arriving at point B. Such a scratched mirror is called a diffraction grating.
We have discussed this example in some detail to make a point that is
necessary in what follows: all possible paths contribute to the probability of
finding a photon arriving at point B. However, contributions from particular
paths often cancel each other, leaving the majority of the contribution to
relatively few of the possible paths.
We now return to what is the core of QED, the interaction of electrons with each other, and with photons. In so doing we will encounter
some strange effects that will stretch our credulity. Some readers may be
unwilling to accept these effects because they are too “crazy”. However,
Richard Feynman summed up his reaction to this objection: “It’s the way
nature works. If you don’t like it, go somewhere else. Go to another universe where
the rules are simpler, and philosophically more pleasing” [3]. The fact is that the
accuracy of QED in describing natural phenomena, with the exceptions of
gravity and nuclear phenomena, is mind-boggling, and we cannot just discard
it because we find its principles contrary to our preconceptions.
In the classical model, a stationary electron is pictured as an electric charge
sitting in space, surrounded by an electric field. In QED the energy in the
electric field results in the spontaneous creation of photons and/or electron–
positron pairs. This situation is represented in Fig. 8.8.
Figure 8.8a displays the classical situation, with the electron remaining at
the same position in space as time progresses. (In these diagrams, time is
plotted vertically, and spatial distance horizontally, even if the axes are not
specifically plotted). In Fig. 8.8b, a photon has been spontaneously produced
by the electron and has been reabsorbed a short time later. (The photon’s
path is represented by the wiggly line). Figure 8.8c shows a more complex case
where two photons have been produced, and reabsorbed. There are an infinite
number of such possibilities. These diagrams are called Feynman diagrams,
after their inventor.
As we saw earlier, if its energy is sufficiently high, a photon can knock an
electron out of the Dirac Sea, and leave behind a hole, which is interpreted
as a positron. The corresponding Feynman diagram is shown in Fig. 8.8d.
The electron and positron may recombine (or annihilate) a short time later
to produce another photon, as shown in Fig. 8.8e.
157
Is there any way we can allow rays far away from the primary ray to make
their presence felt? Yes, there is. We can scratch lines across the mirror with a
spacing such that only those rays with a path length equal to a multiple of the
wavelength of the incident light are reflected. (We are assuming here that the
incident light is monochromatic.) In this case, the probabilities from these
rays will add up, and all rays will make a contribution to the reflected light
arriving at point B. Such a scratched mirror is called a diffraction grating.
We have discussed this example in some detail to make a point that is
necessary in what follows: all possible paths contribute to the probability of
finding a photon arriving at point B. However, contributions from particular
paths often cancel each other, leaving the majority of the contribution to
relatively few of the possible paths.
We now return to what is the core of QED, the interaction of electrons with each other, and with photons. In so doing we will encounter
some strange effects that will stretch our credulity. Some readers may be
unwilling to accept these effects because they are too “crazy”. However,
Richard Feynman summed up his reaction to this objection: “It’s the way
nature works. If you don’t like it, go somewhere else. Go to another universe where
the rules are simpler, and philosophically more pleasing” [3]. The fact is that the
accuracy of QED in describing natural phenomena, with the exceptions of
gravity and nuclear phenomena, is mind-boggling, and we cannot just discard
it because we find its principles contrary to our preconceptions.
In the classical model, a stationary electron is pictured as an electric charge
sitting in space, surrounded by an electric field. In QED the energy in the
electric field results in the spontaneous creation of photons and/or electron–
positron pairs. This situation is represented in Fig. 8.8.
Figure 8.8a displays the classical situation, with the electron remaining at
the same position in space as time progresses. (In these diagrams, time is
plotted vertically, and spatial distance horizontally, even if the axes are not
specifically plotted). In Fig. 8.8b, a photon has been spontaneously produced
by the electron and has been reabsorbed a short time later. (The photon’s
path is represented by the wiggly line). Figure 8.8c shows a more complex case
where two photons have been produced, and reabsorbed. There are an infinite
number of such possibilities. These diagrams are called Feynman diagrams,
after their inventor.
As we saw earlier, if its energy is sufficiently high, a photon can knock an
electron out of the Dirac Sea, and leave behind a hole, which is interpreted
as a positron. The corresponding Feynman diagram is shown in Fig. 8.8d.
The electron and positron may recombine (or annihilate) a short time later
to produce another photon, as shown in Fig. 8.8e.