by Gary Zukav
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.
This is the basic Yukawa interaction. The strong force, as Yukawa theorized in 1935, is the multiple exchange of virtual pions between nucleons. The number of the exchanges (the strength of the force) increases at close range and decreases at a distance.
In a similar manner, neutrons never sit still and just be neutrons. Like protons and electrons they also constantly interact with themselves by emitting and re-absorbing virtual particles. Like protons, neutrons emit and re-absorb neutral pions. On the top of the next page is a Feynman diagram of a neutron emitting and re-absorbing a neutral pion.
In addition to emitting a neutral pion, a neutron also can emit a negative pion. However, when a neutron emits a negative pion, it momentarily transforms itself into a proton! First there is neutron, then there is a proton plus a negative pion, then there is a neutron again. Below is a Feynman diagram of this dance which continually changes a neutron into a proton and back into a neutron again.
If a neutron comes so close to a proton that their virtual pion clouds overlap, some of the pions that are emitted by the neutron are absorbed by the proton. Below is a Feynman diagram of a virtual-pion exchange between a neutron and a proton.
This is another strong-force interaction. In the left half of the diagram, a neutron emits a negative pion, temporarily transforming itself into a proton. However, before the negative pion can be re-absorbed, it is captured by a nearby proton which, in turn, becomes a neutron. The exchange of a negative pion causes a neutron to become a proton and a proton to become a neutron. As before, a pair of nucleons, bound together by a virtual-pion exchange, have changed roles.
There are many more strong-force interactions. Although pions are the particles most often exchanged in the creation of the strong force, the other mesons (such as kaons, eta particles, etc.) are exchanged as well. There is no “strong force”; there are only a varying number of virtual-particle exchanges between nucleons.
The universe, according to physicists, is held together by four fundamental types of glue. In addition to the strong force and the electromagnetic force, there is the “weak” force and the gravitational force.*
Gravity is the long-range force which holds together solar systems, galaxies, and universes. However, on the subatomic level its effect is so negligible that it is ignored altogether. Future theories, hopefully, will be able to take it into account.†
The weak force is the least known of the four forces. Its existence was inferred from the times required by certain subatomic interactions. The strong force is so short-range and powerful that strong-force interactions happen very, very fast, in about .00000000000000000000001 (10-23) seconds. However, physicists discovered that a certain other type of particle interaction which they knew involved neither the electromagnetic nor the gravitational forces, required a much longer time, about .0000000001 (10-10) seconds. They therefore deduced from this strange phenomenon that there must exist a fourth type of force. Since this new fourth force was known to be weaker than the electromagnetic force, it was called the weak force.
In the order of their strength, the four forces are:
Strong (nuclear) force
Electromagnetic force
Weak force
Gravity
Since the strong force and the electromagnetic force can be explained in terms of virtual particles, physicists assume that the same is true of the weak force and gravity. The particle associated with gravity is the graviton, whose properties have been theorized, but whose existence never has been confirmed. The particle associated with the weak force is the “W” particle, about which much has been theorized, but not much has been discovered.
The range of the strong force, relative to the electromagnetic force, is limited because mesons, relative to photons, have so much mass. Remember that the policeman who enforces the conservation law of mass-energy is willing to turn his back if the violation is quick enough, but the more flagrant the violation, the more quickly it must happen. The momentary creation of a meson out of nothing is a much more flagrant violation of the conservation law of mass-energy than the momentary creation of a photon out of nothing. Therefore, the creation and re-absorption of a meson must happen more quickly to stay within the protection, so to speak, of the uncertainty relation between time and energy. Because the life span of a virtual meson is limited, its range also is limited. The rule of thumb governing this phenomenon is this: The stronger the force, the more massive is the mediating particle, and the shorter is its range. The range of the strong force is only about one ten-trillionth (10-13) of a centimeter. Accordingly, the range of the electromagnetic force is much greater than the range of the strong force. In fact, the range of the electromagnetic force is infinite. This is because photons don’t have any rest mass!
“Wait a minute,” says Jim de Wit, agreeing with us for a change. “This doesn’t make sense. A virtual photon is a photon which is emitted and re-absorbed quickly enough to avoid violating the conservation law of mass-energy. Right?”
“Right,” says a particle physicist on his way to the cyclotron.
“Then how can a particle, or anything else, be emitted and re-absorbed within certain time limits, like the time limits imposed by the uncertainty principle, and still have an infinite range? It doesn’t make sense.”
De Wit has a point. At first glance it appears that he is correct. On closer examination, however, there is a subtle logic involved which does make sense. If the limitations of the conservation law of mass-energy are avoided by a balance of time and energy (mas
s) permitted by the uncertainty principle, and a virtual photon has no (rest) mass, then it has all the time in the world, literally, to go where it pleases. In other words, there is no practical difference between a “real” photon and a “virtual” photon. The only difference between them is that the creation of a “real” photon does not violate the conservation law of mass-energy and the creation of a “virtual” photon avoids the law momentarily via the Heisenberg uncertainty principle.
This is a good example of how “unreal” and “ivory-tower-like” the nonmathematical explanation of a successful physical theory can sound. The reason for this is that physical theories, in order to describe more accurately the phenomena under consideration, have become more and more divorced from everyday experience (i.e., more abstract). Although these highly abstract theories, such as quantum theory and relativity, are unaccountably accurate to an awesome degree, they truly are “free creations” of the human mind. Their primary link with ordinary experience is not the abstract content of their formalisms, but the fact that, somehow, they work.*
The distinction between a transient, virtual (nothing-something-nothing) state and a “real” one (something-something-something) is similar to the Buddhist distinction between reality as it actually is and the way that we usually see it. For example, Feynman himself described the difference between a virtual state and a real state (of a photon) as a matter of perspective.
…what looks like a real process from one point of view may appear as a virtual process occurring over a more extended time.
For example, if we wish to study a given real process, such as the scattering of light, we can, if we wish, include in principle the source, scatterer, and eventual absorber of the scattered light in our analysis. We may imagine that no photon is present initially, and that the source then emits light…. The light is then scattered and eventually absorbed…. From this point of view the process is virtual, that is, we start with no photons and end with none. Thus we can analyze the process by means of our formulas for real processes by attempting to break the analysis into parts corresponding to emission, scattering, and absorption.2
According to Buddhist theory, reality is “virtual” in nature. What appear to be “real” objects in it, like trees and people, actually are transient illusions which result from a limited mode of awareness. The illusion is that parts of an overall virtual process are “real” (permanent) “things.” “Enlightenment” is the experience that “things,” including “I,” are transient, virtual states devoid of separate existences, momentary links between illusions of the past and illusions of the future unfolding in the illusion of time.
Particle self-interactions become quite intricate when virtual particles emit virtual particles which emit virtual particles in a diminishing sequence. On the next page is a Feynman diagram of a virtual particle (a negative pion) transforming itself momentarily into two more virtual particles, a neutron and an anti-proton (Dirac’s 1928 theory also predicted anti-protons which were discovered at Berkeley in 1955).
This is the simplest example of self-interaction. On the exquisite dance of a single proton performed in the flicker of time permitted by the uncertainty principle. This diagram was constructed by Kenneth Ford in his book, The World of Elementary Particles.3 Eleven particles make their transient appearance between the time the original proton transforms itself into a neutron and a pion and the time it becomes a single proton again.
A proton never remains a simple proton. It alternates between being a proton and a neutral pion on the other hand, and being a neutron and a neutral pion on the other hand. A neutron never remains a simple neutron. It alternates between being a neutron and a neutral pion on the one hand, and being a proton and a negative pion on the other hand. A negative pion never remains a simple negative pion. It alternates between being a neutron and an anti-proton on the one hand, etc., etc. In other words, all particles exist potentially (with a certain probability) as different combinations of other particles. Each combination has a certain probability of happening.
Quantum theory deals with probability. The probability of each of these combinations can be calculated with accuracy. According to quantum theory, however, it is ultimately chance that determines which of these combinations actually occur.
The quantum view that all particles exist potentially as different combinations of other particles parallels a Buddhist view, again. According to The Flower Garland Sutra, each part of physical reality is constructed of all the other parts. (A sutra is a written account of the Buddha’s teachings.) This theme is illustrated in The Flower Garland Sutra by the metaphor of Indra’s net. Indra’s net is a vast network of gems which overhangs the palace of the god Indra.
In the words of an English interpreter:
In the heaven of Indra, there is said to be a network of pearls, so arranged that if you look at one you see all the others reflected in it. In the same way each object in the world is not merely itself but involves every other object and in fact is everything else.4
The appearance of physical reality, according to Mahayana Buddhism, is based upon the interdependence of all things.*, †
Although this book is not about physics and Buddhism specifically, the similarities between the two, especially in the field of particle physics, are so striking and plentiful that a student of one necessarily must find value in the other.
Now we come to the most psychedelic aspect of particle physics. Below is a Feynman diagram of a three-particle interaction.
In this diagram no world line leads up to the interaction and no world line leads away from it. It just happens. It happens literally out of nowhere, for no apparent reason, and without any apparent cause. Where there was no-thing, suddenly, in a flash of spontaneous existence, there are three particles which vanish without a trace.
This type of Feynman diagram is called a “vacuum diagram.* That is because the interactions happen in a vacuum. A “vacuum,” as we normally construe it, is a space that is entirely empty. Vacuum diagrams, however, graphically demonstrate that there is no such thing. From “empty space” comes something, and then that something disappears again into “empty space.”
In the subatomic realm, a vacuum obviously is not empty. So where did the notion of a completely empty, barren, and sterile “space” come from? We made it up! There is no such thing in the real world as “empty space.” It is a mental construction, an idealization, which we have taken to be true.
“Empty” and “full” are “false distinctions” that we have created, like the distinction between “something” and “nothing.” They are abstractions from experience which we have mistaken for experience. Perhaps we have lived so long in our abstractions that instead of realizing that they are drawn from the real world we believe that they are the real world.
Vacuum diagrams are the serious product of a well-intentioned physical science. However, they also are wonderful reminders that we can intellectually create our “reality.” It is not possible, according to our usual conceptions, for “something” to come out of “empty space”; but, at the subatomic level, it does, which is what vacuum diagrams illustrate. In other words, there is no such thing as “empty space” (or “nothing”) except as a concept in our categorizing minds.
The core sutras of Mahayana Buddhism (the type of Buddhism practiced in Tibet, China, and Japan) are called the Prajnaparamita Sutras.† Among the most central of the Prajnaparamita Sutras (there are twelve volumes of them) is a sutra which is called simply, The Heart Sutra. The Heart Sutra contains one of the most important ideas of Mahayana Buddhism:
…form is emptiness, emptiness is form.
Below is a vacuum diagram of six different mutually interacting particles.
It depicts an exquisite dance of emptiness becoming form and form becoming emptiness. Perhaps, as the wise people of the East have written, form is emptiness and emptiness is form.
In any case, vacuum diagrams are representations of remarkable transformations of “s
omething” into “nothing” and “nothing” into “something.” These transformations occur continuously in the subatomic realm and are limited only by the uncertainty principle, the conservation laws, and probability.*
There are roughly twelve conservation laws. Some of them affect every type of subatomic interaction. Some of them affect only some types of subatomic interaction. There is a simple rule of thumb to remember: The stronger the force, the more its interactions are restrained by conservation laws. For example, strong interactions are restrained by all twelve conservation laws; electromagnetic interactions are restrained by eleven of the conservation laws; and weak interactions are restrained by only eight of the conservation laws.† Gravitational interactions, those involving the most feeble force in the subatomic world, have not been studied yet (no one has found a graviton), but they may violate even more conservation laws.
Nonetheless, where the conservation laws have jurisdiction, they are inviolable rules which shape the form of all particle interactions. For example, the conservation law of mass-energy dictates that all spontaneous particle decays be “downhill.” When a single particle spontaneously decays, it always decays into lighter particles. The total mass of the new particles is always less than the mass of the original particle. The difference between the mass of the original particle and the total mass of the new particles is converted into the kinetic energy of the new particles (which fly away).
“Uphill” interactions are only possible when kinetic energy, in addition to the energy of being (mass) of the original particles, is available for the creation of new particles. Two colliding protons, for example, can create a proton, a neutron, and a positive pion. The total mass of these new particles is greater than the mass of the two original protons. This is possible because some of the kinetic energy of the projectile proton went into the creation of the new particles.