The Dancing Wu Li Masters

by Gary Zukav

  This is the static type of space-time picture described in Einstein’s theory of relativity. If we could survey an entire span of time as we can survey an entire region of space, we would see that events do not unfold with the flow of time but present themselves complete, like a finished painting on the fabric of space-time. In such a picture movements backward and forward in time are no more significant than movements backward and forward in space.

  The illusion of events “developing” in time is due to our particular type of awareness which allows us to see only narrow strips of the total space-time picture one at a time. For example, suppose that we place a piece of cardboard with a narrow strip cut out of it over the diagram so that all we can see of the interaction is what is visible through the cut-out. If we move the cardboard slowly upward, starting at the bottom, our restricted view discovers a series of events, each one happening after the other.

  First, we see three particles, two photons entering our view on the right and an electron entering from the left (1). Next, we see the photons collide to produce an electron-positron pair, the electron flying off to the right and the positron flying off to the left (2). Finally, we see the newly created positron meet the original electron to create two new photons (3). Only when we remove the entire cardboard (which was an artificial construction anyway) can we see the complete picture.

  “In space-time,” wrote de Broglie,

  everything which for each of us constitutes the past, the present, and the future is given in block…. Each observer, as his time passes, discovers, so to speak, new slices of space-time which appear to him as successive aspects of the material world, though in reality the ensemble of events constituting space-time exist prior to his knowledge of them.1

  “Wait a minute,” says Jim de Wit to a passing particle physicist. “It is easy to talk of movement backward and forward in time, but I never have experienced going backward in time. If particles can travel backward in time, why can’t I travel backward in time?”

  The answer which physicists gave to this question is actually quite simple: There is a growing tendency in any closed part of the universe, their explanation goes, for disorder (called “entropy”) to expand at the price of order (called “negentropy”). Suppose, for example, that we deposit a drop of black ink into a glass of clear water. Initially its presence is quite ordered. That is, all of the molecules of ink are located in one small area and are clearly segregated from the molecules of clear water.

  As time passes, however, natural molecular motion will cause the black ink molecules steadily to intersperse with the clear water molecules until they are distributed evenly throughout the glass, resulting in a murky homogeneous liquid with no structure or order whatever—only a bland uniformity (maximal entropy).

  Experience has taught us to associate increasing entropy with the forward movement of time. If we see a movie of a glass of murky water becoming clearer and clearer until all of the foreign substance in it collects into one small drop at the top, we know at once that the film is running backward. Of course, it is theoretically possible for this to happen, but it is so improbable that it simply never (probably) will happen. In short, time “flows” in the direction of high probability, which is the direction of increasing entropy.

  The theory of growing disorder, or “increasing entropy,” is called the second law of thermodynamics. The second law of thermodynamics is statistical. That means it won’t work unless there are many entities in a given situation to apply it to. Generally speaking, individual subatomic particles are conceived as such conceptually isolated, short-lived entities that the second law of thermodynamics does not apply to them.*, † It does apply, however, to molecules, which are quite complex compared to subatomic particles; to living cells, which are more complex than molecules; and to people, who are made of billions of cells. It is only at the subatomic, or quantum, level that the forward flow of time loses its significance.

  However, there is speculation, and some evidence, that consciousness, at the most fundamental levels, is a quantum process. The dark-adapted eye, for example, can detect a single photon. If this is so then it is conceivable that by expanding our awareness to include functions which normally lie beyond its parameters (the way yogis control their body temperature and pulse rate) we can become aware of (experience) these processes themselves. If, at the quantum level, the flow of time has no meaning, and if consciousness is fundamentally a similar process, and if we can become aware of these processes within ourselves, then it also is conceivable that we can experience timelessness.

  If we can experience the most fundamental functions of our psyche, and if they are quantum in nature, then it is possible that the ordinary conceptions of space and time might not apply to them at all (as they don’t seem to apply in dreams). Such an experience would be difficult to describe rationally (“Infinity in a grain of sand/And eternity in an hour”), but it would be very real, indeed. For this reason, reports of time distortion and timelessness from gurus in the East and psychotropic drug users in the West ought not, perhaps, to be discarded preemptorily.

  Subatomic particles do not just sit around being subatomic particles. They are beehives of activity. An electron, for example, constantly is emitting and absorbing photons. These photons are not full-fledged photons, however. They are a now-you-see-it-now-you-don’t variety. They are exactly like real photons except that they don’t fly off on their own. They are re-absorbed by the electron almost as soon as they are emitted. Therefore, they are called “virtual” photons. (“Virtual” means “being so in effect or essence, although not in actual fact.”) They are virtually photons. The only thing that keeps them from being full-fledged photons is their abrupt re-absorption by the electron that emits them.*

  In other words, first there is an electron, then there is an electron and a photon, and then there is an electron again. This situation is, of course, a violation of the conservation law of mass-energy. The conservation law of mass-energy says, in effect, that we cannot get something for nothing. According to quantum field theory, however, we do get something for nothing, but only for about one thousand trillionth (10-15) of a second. † The reason that this can happen, according to the theory, is the famous Heisenberg uncertainty principle.

  The Heisenberg uncertainty principle, as it originally was formulated, says that the more certain we are of the position of a particle, the less certain we can be about its momentum, and the other way round. We can determine its position precisely, but in that case we cannot determine its momentum at all. If we choose to measure its momentum precisely, then we will not be able to know where it is located.

  In addition to the reciprocal uncertainty of position and momentum, there also is a reciprocal uncertainty of time and energy. The less uncertainty there is about the time involved in a subatomic event, the more uncertainty there is about the energy involved in the event (and the other way round). A measurement as accurate as one thousand trillionth of a second leaves very little uncertainty about the time involved in the emission and absorption of a virtual photon. It does, however, cause a specific uncertainty about how much energy was involved. Because of this uncertainty, the balance books kept by the conservation law of mass-energy are not upset. Said another way, the event happens and is over with so quickly that the electron can get away with it.

  It is as if the policeman who enforces the conservation law of mass-energy turns his back on violations if they happen quickly enough. However, the more flagrant the violation, the more quickly it must happen.

  If we provide the necessary energy for a virtual photon to become a real photon without violating the conservation law of mass-energy, it does just that. That is why an excited electron emits a real photon. An excited electron is an electron that is in an energy level higher than its ground state. An electron’s ground state is its lowest energy level where it is as close to the nucleus of an atom as it can get. The only photons that electrons emit when they are in their ground state are vi
rtual photons which they immediately re-absorb so as not to violate the conservation law of mass-energy.

  An electron considers the ground state to be its home. It doesn’t like to leave home. In fact, the only time it leaves its ground state is when it literally is pushed out of it with extra energy. In that case, the electron’s first concern is to get back to its ground state (provided that it hasn’t been pushed so far from the nucleus that, in effect, it becomes a free electron). Since the ground state is a low-energy state, the electron must lose its excess energy before it can return to it. Therefore, when an electron is at an energy level higher than its ground state, it jettisons its excess energy in the form of a photon. The jettisoned photon is one of the electron’s virtual photons that suddenly finds itself with enough energy to keep going without violating the conservation law of mass-energy, and it does. In other words, one of the electron’s virtual photons suddenly is “promoted” to a real photon. The amount of energy (the frequency) of the promoted photon depends upon how much excess energy the electron had to jettison. (The discovery that electrons emit only photons of certain energies and no others is what made the quantum theory a quantum theory). Electrons are always surrounded by a swarm of virtual photons.*

  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 construction 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. Assum
ing 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. Selfinteraction makes the world of subatomic particles a kaleidoscopic reality whose very constituents are themselves unceasing processes of transformation.