The Dancing Wu Li Masters (32 page)

If two electrons come close enough to each other, close enough so that their virtual-photon clouds overlap, it is possible that a virtual photon that is emitted from one electron will be absorbed by the other electron. Below is a Feynman diagram of a virtual photon being emitted by one electron and absorbed by another electron.

The closer the electrons come to each other, the more this phenomenon occurs. Of course, the process is two-way with both electrons absorbing virtual photons that were emitted by the other.

This is how electrons repel each other. The closer two electrons come, the more virtual photons they exchange. The more virtual photons they exchange, the more sharply their paths are deflected. The “repulsive force” between them is simply the cumulative effect of these exchanges of virtual photons, the number of which increases at close range and decreases at a distance. According to this theory, there is no such thing as action-at-a-distance—only more and fewer exchanges of virtual photons. These interactions (absorptions and
emissions) happen on location, so to speak, right there where the particles involved are located.
^*

The mutual repulsion of two particles of the same charge, like two electrons, is an example of an electromagnetic force. In fact, according to quantum field theory, an electromagnetic force
is
the mutual exchange of virtual photons. (Physicists like to say that the electromagnetic force is “mediated” by photons.) Every electrically charged particle continually emits and re-absorbs virtual photons and/or exchanges them with other charged particles. When two electrons (two negative charges) exchange virtual photons, they repulse each other. The same thing happens when two protons (two positive charges) exchange virtual photons. When a proton and an electron (a positive charge and a negative charge) exchange virtual photons they attract each other.

Therefore, since the development of quantum field theory, physicists generally have substituted the word “interaction” for the word “force.” (An interaction is when anything influences anything else). In this context—a mutual exchange of virtual photons—it is a more precise term than “force,” which labels that which happens between electrons but does not say anything about it. That part of quantum field theory (Dirac’s original part) which deals with electrons, photons, and positrons is called quantum electrodynamics.

Virtual photons, even if they were charged particles, would not be visible in a bubble chamber because of their extremely short lives. Their existence is inferred mathematically. Therefore, this extraordinary theory, that particles exert a force on each other by exchanging other particles, clearly is a “free creation” of the human mind. It is not necessarily how nature “really is,” it is only a mental construc
tion which correctly predicts what nature probably is going to do next. There might be, and probably are, other mental constructs that can do as good a job as this one, or better (although physicists have not been able to think of them). The most that we can say about this or any other theory is not whether it is “true” or not, but only whether it works or not; that is, whether it does what it is supposed to do.

Quantum theory is supposed to predict the probabilities of given subatomic phenomena to occur under certain circumstances. Even though quantum field theory as a whole is not totally consistent, the pragmatic reality is that it
works
. There is a Feynman diagram for every interaction, and every Feynman diagram corresponds to a mathematical formula which precisely predicts the probability of the diagrammed interaction to happen.
^*

In 1935, Hideki Yukawa, a graduate student in physics, decided to apply the new virtual particle theory to the strong force.

The strong force is the force that keeps atomic nuclei together. It has to be strong because the protons, which along with the neutrons make up the nucleus of an atom, naturally repel each other. Being particles of like sign (positive), protons want to be as far away from each other as they can get. This is because of the electromagnetic force between them. However, within the nucleus of an atom, these mutually repulsive protons not only are kept in close proximity, but they also are bound together very tightly. Whatever is binding these protons together into a nucleus, physicists reasoned, must be a very strong force compared to the electromagnetic force, which works against it. Therefore, they decided to call the strong force, naturally, the “strong force.”

The strong force is well named because it is one hundred times stronger than the electromagnetic force. It is the strongest force
known in nature. Like the electromagnetic force, it is a fundamental glue. The electromagnetic force holds atoms together externally (with each other to form molecules) and internally (it binds electrons to their orbits around atomic nuclei). The strong force holds the nucleus itself together.

The strong force is somewhat musclebound, so to speak. Although it is the strongest force known in nature, it also has the shortest range of all the forces known in nature. For example, as a proton approaches the nucleus of an atom it begins to experience the repulsive electromagnetic force between itself and the protons within the nucleus. The closer the free proton gets to the protons in the nucleus, the stronger the repulsive electromagnetic force between them becomes. (At one third the original distance, for example, the force is nine times as strong). This force causes a deflection in the path of the free proton. The deflection is a gentle one if the proton is distant from the nucleus and very pronounced if the proton should come close to the nucleus.

However, if we push the free proton to within about one ten-trillionth (10
^-13
) of a centimeter of the nucleus, it suddenly is sucked
into
the nucleus with a force one hundred times more powerful than the repulsive electromagnetic force. One ten-trillionth of a centimeter is about the size of the proton itself. In other words, the proton is relatively unaffected by the strong force, even at a distance only slightly greater than its own magnitude. Closer than that, however, and it is completely overpowered by the strong force.

Yukawa decided to explain this powerful but very short-range “strong” force in terms of virtual particles.

The strong force, theorized Yukawa, is “mediated” by virtual particles like the electromagnetic force is “mediated” by virtual photons. According to Yukawa’s theory, just as the electromagnetic force
is
the exchange of virtual photons, the strong force
is
the exchange of another type of virtual particle. Just as electrons never sit idle, but constantly emit and re-absorb virtual photons, so nucleons are not inert, but constantly emit and re-absorb their own type of virtual particles.

A “nucleon” is a proton or a neutron. Both of these particles are called nucleons, since both of them are found in the nuclei of atoms. They are so similar to each other that a proton, roughly speaking, can be considered as a neutron with a positive charge.

Yukawa knew the range of the strong force from the results of published experiments. Assuming that the limited range of the strong force was identical to the limited range of a virtual particle emitted from a nucleon in the nucleus, he calculated how much time such a virtual particle would require, at close to the speed of light, to go that distance and return to the nucleon. This time calculation allowed him to use the uncertainty relation between time and energy to calculate the energy (mass) of his hypothetical particle.

Twelve years and one case of mistaken identity later, physicists discovered Yukawa’s hypothetical particle.
^*
They called it a meson.
An entire family of mesons
, it later was discovered, are the particles which nucleons exchange to constitute the strong force. The particular meson which physicists discovered first, they called a pion. “Pion” is short for pi (pronounced “pie”) meson. Pions come in three varieties: positive, negative, and neutral.

In other words, a proton, like an electron, is a beehive of activity. Not only does it continually emit and re-absorb virtual photons, which makes it susceptible to the electromagnetic force, it also emits and re-absorbs virtual pions, which makes it susceptible to the strong force as well. (Particles which do not emit virtual mesons, like electrons, for example, are not affected at all by the strong force).

When an electron emits a virtual photon which is absorbed by another particle, the electron is said to be “interacting” with the other particle. However, when an electron emits a virtual photon and then re-absorbs it, the electron is said to be interacting with itself. Self
interaction makes the world of subatomic particles a kaleidoscopic reality whose very constituents are themselves unceasing processes of transformation.

Protons, like electrons, can interact with themselves in more ways than one. The simplest proton self-interaction is the emission and re-absorption, within the time permitted by the uncertainty principle, of a virtual pion. This interaction is analogous to an electron emitting and re-absorbing a virtual photon. First there is a proton, then there is a proton and a neutral pion, then there is a proton again. Below is a Feynman diagram of a proton emitting and re-absorbing a virtual neutral pion.

Because all protons are identical, we can assume that the original proton suddenly ceases to exist and that, at the same point in space and time, another proton and a neutral pion just as abruptly come into existence. The new proton and the neutral pion constitute a violation of the conservation law of mass-energy since their mass together is greater than the mass of the original proton. Something (the neutral pion) literally has been created out of nothing and quickly disappears again (making this a virtual process). The life span of the new particles
is limited to the time calculated via the Heisenberg uncertainty principle. They quickly merge, annihilating each other, and create another proton. One blink of an eye, figuratively speaking, and the whole thing is over.

There is another way in which a proton can interact with itself. In addition to emitting and re-absorbing a neutral pion, a proton can emit a positive pion. However, by emitting a positive pion, the proton momentarily transforms itself into a neutron! First there is a proton, then there is a
neutron
(which by itself has more mass than the original proton) plus a positive pion, then there is a proton again. In other words, one of the dances that a proton does continually changes it into a neutron and back into a proton again. Below is a Feynman diagram of this dance.

Every nucleon is surrounded by a cloud of virtual pions, which it constantly emits and re-absorbs. If a proton comes close enough to a neutron so that their virtual-pion clouds overlap, some of the virtual pions emitted by the proton are absorbed by the neutron. On the next page is a Feynman diagram of a virtual-pion exchange between a proton and a neutron.

In the left half of the diagram, a proton emits a positively charged pion, momentarily transforming itself into a neutron. Before the pion can be re-absorbed, however, it is captured by a nearby neutron. This pion capture causes the neutron to transform itself into a proton. The exchange of the positive pion causes the proton to become a neutron and the neutron to become a proton. The two original nucleons, now bound together by this exchange, have changed roles.