In addition to mass-energy, momentum is conserved in every particle interaction. The total momentum carried by particles going into an interaction must equal the total momentum of the particles leaving the interaction. This is why the spontaneous decay of a single particle always produces at least two new particles. A particle at rest has zero momentum. If it decays into a single new particle which then flies off, the momentum of the new particle will exceed the momentum of the original particle (zero). The momenta of at least two new particles flying off in opposite directions, however, cancel each other, producing a total momentum of zero.
Charge also is conserved in every particle interaction. If the total charge of the particles entering an interaction is plus two (for example, two protons), the total charge of the particles leaving the interaction must also equal plus two (after the positive and negative particles cancel each other). Spin, too, is conserved, although keeping the books balanced in regard to spin is more complicated than it is in regard to charge.
In addition to the conservation laws of mass-energy, momentum, charge, and spin, there are conservation laws of family numbers. For example, if two baryons, or heavy-weight particles (like two protons), go into an interaction, two baryons must be among the resulting new particles (like a neutron and a lambda particle).
This same baryon conservation law, along with the conservation law of mass-energy, “explains” why protons are stable particles (i.e., why they do not decay spontaneously). Spontaneous decays must be downhill to satisfy the conservation law of mass-energy. Protons cannot decay downhill without violating the conservation law of baryon family numbers because protons are the lightest baryons. If a proton were to decay spontaneously, it would have to decay into particles lighter than itself, but there are no baryons lighter than a proton. In other words, if a proton were to decay, there would be one less baryon in the world. In fact, this never happens. This scheme (the conservation law of baryon family numbers) is the only way that physicists so far have been able to account for the proton’s stability. A similar conservation law of lepton family numbers accounts for the stability of electrons. (There are no lighter leptons than an electron.)
Some of the twelve conservation laws are actually “invariance principles.” An invariance principle is a law that says, “under a change of circumstances (like changing the location of an experiment) all of the laws of physics remain valid.” “All of the laws of physics,” so to speak, is the “conserved quantity” of an invariance principle. For example, there is a time-reversal invariance principle. In order for a process to be possible, according to this principle, it must be reversible in time. If a positron-electron annihilation can create two photons (it can), then the annihilation of two photons can create a positron and an electron (it can).
Conservation laws and invariance principles are based on what physicists call symmetries. The fact that space is the same in all directions (isotropic) and in all places (homogeneous) is an example of symmetry. The fact that time is homogeneous is another example. These symmetries simply mean that a physics experiment performed in Boston this spring will give the same result as the same experiment performed in Moscow next fall.
In other words, physicists now believe that the most fundamental laws of physics, the conservation laws and invariance principles, are based upon those foundations of our reality that are so basic that they go unnoticed. This does not mean (probably) that it has taken physicists three hundred years to realize that moving an object, like a telephone, around the country does not distort its shape or size (space is homogeneous), nor does turning it upside down (space is isotropic), nor does letting it get two weeks older (time is homogeneous). Everyone knows that this is the way our physical world is constructed. Where and when a subatomic experiment is performed are not critical data. The laws of physics do not change with time and place.
It does mean, however, that it has taken physicists three hundred years to realize that the most simple and beautiful mathematical structures may be those that are based on these unobtrusively obvious conditions.
Theoretical physics, roughly speaking, has branched into two schools. One school follows the old way of thinking and the other school follows new ways of thinking. Physicists who follow the old way of thinking continue their search for the elementary building blocks of the universe in spite of the hall-of-mirrors predicament.
For these physicists, the most likely candidate at present for the title of “ultimate building block of the universe” is the quark. A quark is a type of hypothetical particle theorized by Murray Gell-Mann in 1964. It is named after a word in James Joyce’s book Finnegans Wake.
All known particles, the theory goes, are composed of various combinations of a few (twelve) different types of quarks. The great quark hunt could become very exciting, but no matter what is discovered, one thing about it already is certain: The discovery of quarks will open an entirely new area of research, namely, “What are quarks made of?”
The physicists who follow the new ways of thinking are pursuing so many different approaches to understanding subatomic phenomena that it is not possible to present them all. Some of these physicists feel that space and time are all that there is. According to this theory, actors, action, and stage are all manifestations of an underlying four-dimensional geometry. Others (like David Finkelstein) are exploring processes which lie “beneath time,” processes from which space and time, the very fabric of experiential reality, are derived. These theories, at the moment, are speculative. They cannot be “proven” (demonstrated mathematically).
The most successful departure from the unending search-for-the-ultimate-particle syndrome is the S-Matrix theory. In S-Matrix theory, the dance rather than the dancers is of primary importance. S-Matrix theory is different because it places the emphasis upon interactions rather than upon particles.
“S Matrix” is short for Scattering Matrix. Scattering is what happens to particles when they collide. A matrix is a type of mathematical table. An S Matrix is a table of probabilities.
When subatomic particles collide several things usually are possible. For example, the collision of two protons can create (1) a proton, a neutron, and a positive pion, (2) a proton, a lambda particle, and a positive kaon, (3) two protons and six assorted pions, (4) numerous other combinations of subatomic particles. Each of these possible combinations (which are the combinations that do not violate the conservation laws) occurs with a certain probability. In other words, some of them occur more often than others. The probabilities of various combinations in turn depend upon such things as how much momentum is carried into the collision area.
In an S Matrix all of these probabilities are tabulated in such a way that we can look up or calculate the possible results of any collision along with their probabilities if we know what particles initially collide and how much momentum they have. Of course, there are so many possible combinations of particles (each one of which can yield a variety of results) that a complete matrix (table) containing all the probabilities of all the possible combinations of particles would be enormous. In fact, such a complete table has not been compiled. This is no immediate problem, however, since physicists are concerned only with a small part of the S Matrix at any one time (for example, the part which deals with two-proton collisions). Such parts of the total S Matrix are called elements of the S Matrix. The major limitation of S-Matrix theory is that at present it applies only to the strongly interacting particles (mesons and baryons), which, as a group, are called hadrons (hay’drons).
On the next page is an S-Matrix diagram of a subatomic interaction. It is very simple. The collision area is the circle. Particles 1 and 2 go into the collision area and particles 3 and 4 come out of the collision area. The diagram tells nothing about what happened at the point of collision. It shows only what particles went into the interaction and what particles came out of the interaction.
An S-Matrix diagram is not a space-time diagram. It does not show the position of the particl
es in space or time. This is intentional because we do not know the exact positions of the interacting particles. We have chosen to measure their momenta and consequently their position is unknown (the Heisenberg uncertainty principle). For this reason, S-Matrix diagrams indicate only that an interaction took place in a certain area (inside the circle). They are purely symbolic representations of particle interactions.
Not all interactions involve only two initial particles and two final particles. Below are some other forms that an S-Matrix diagram can take.
Like Feynman diagrams, S-Matrix diagrams can be rotated. The direction of the arrowheads distinguishes the particles from the anti-particles. Here is an S-Matrix diagram of a proton colliding with a negative pion to produce a proton and a negative pion.
When this diagram is rotated it becomes a diagram of a proton/anti-proton annihilation producing a negative pion and a positive pion. (The positive pion is the anti-particle of the negative pion in the original reaction.)
Every time a diagram is rotated it depicts another possible interaction. This particular S-Matrix diagram can be rotated four times. All of the particles that can be depicted by rotating a single element of the S Matrix are intimately related to each other. In fact, all of the particles represented in an S-Matrix diagram (including those discovered by rotating the diagram) are defined in terms of each other. Which of them are “elementary” is a meaningless question.
Since the particles resulting from an interaction often become involved in other interactions, separate elements of the S Matrix can be assembled diagrammatically into a network of related interactions. Each network, as well as each interaction, is associated with a certain probability. These probabilities can be calculated.
According to S-Matrix theory, “particles” are intermediate states in a network of interactions. The lines in an S-Matrix diagram are not the world lines of different particles. Lines in an S-Matrix diagram of an interaction network are “reaction channels” through which energy flows. A “neutron,” for example, is a reaction channel. It can be formed by a proton and a negative pion.
If more energy is available, however, the same channel can be created by a lambda particle and a neutral kaon, and several other particle combinations as well.
In short, S-Matrix theory is based upon events, not upon things.*, † Dancers no longer stand apart as significant entities. In fact, the dancers are not even defined except in terms of each other. In S-Matrix theory there is only the dance.
We have come a long way from Newton and his proverbial apple. Nonetheless, apples are a real part of the apparent world. When we eat an apple we are aware of who is eating and what is being eaten as distinct from the action of eating.
The idea that objects exist apart from event is part of the epistemological net with which we snare our particular form of experience. This idea is dear to us because we have accepted it, without question, as the basis of our reality. It profoundly influences how we see ourselves. It is the root of our inescapable sense of separateness from others and environment.
The history of scientific thought, if it teaches us anything at all, teaches us the folly of clutching ideas too closely. To this extent it is an echo of eastern wisdom which teaches us the folly of clutching anything.
Part One
ENLIGHTENMENT
1
More Than Both
What does physics have in common with enlightenment? Physics and enlightenment apparently belong to two realms which are forever separate. One of them (physics) belongs to the external world of physical phenomena and the other of them (enlightenment) belongs to the internal world of perceptions. A closer examination, however, reveals that physics and enlightenment are not so incongruous as we might think. First, there is the fact that only through our perceptions can we observe physical phenomena. In addition to this obvious bridge, however, there are more intrinsic similarities.
Enlightenment entails casting off the bonds of concept (“veils of ignorance”) in order to perceive directly the inexpressible nature of undifferentiated reality. “Undifferentiated reality” is the same reality that we are a part of now, and always have been a part of, and always will be a part of. The difference is that we do not look at it in the same way as an enlightened being. As everyone knows(?), words only represent (re-present) something else. They are not real things. They are only symbols. According to the philosophy of enlightenment, everything (everything) is a symbol. The reality of symbols is an illusory reality. Nonetheless, it is the one in which we live.
Although undifferentiated reality is inexpressible, we can talk around it (using more symbols). The physical world, as it appears to the unenlightened, consists of many separate parts. These separate parts, however, are not really separate. According to mystics from around the world, each moment of enlightenment (grace/insight/samadhi/satori) reveals that everything—all the separate parts of the universe—are manifestations of the same whole. There is only one reality, and it is whole and unified. It is one.
We already have learned that understanding quantum physics requires a modification of ordinary conceptions (like the idea that something cannot be a wave and a particle). Now we shall see that physics may require a more complete alteration of our thought processes than we ever conceived or, in fact, than we ever could conceive. Likewise we previously have seen that quantum phenomena seem to make decisions, to “know” what is happening elsewhere. Now we shall see how quantum phenomena may be connected so intimately that things once dismissed as “occult” could become topics of serious consideration among physicists.
In short, both in the need to cast off ordinary thought processes (and ultimately to go “beyond thought” altogether), and in the perception of reality as one unity, the phenomenon of enlightenment and the science of physics have much in common.
Enlightenment is a state of being. Like all states of being it is indescribable. It is a common misconception (literally) to mistake the description of a state of being for the state itself. For example, try to describe happiness. It is impossible. We can talk around it, we can describe the perspectives and actions that usually accompany a state of happiness, but we cannot describe happiness itself. Happiness and the description of happiness are two different things.
Happiness is a state of being. That means that it exists in the realm of direct experience. It is the intimate perception of emotions and sensations which, indescribable in themselves, constitute the state of happiness. The word “happiness” is the label, or symbol, which we pin on this indescribable state. “Happiness” belongs to the realm of abstractions, or concepts. A state of being is an experience. A description of a state of being is a symbol. Symbols and experience do not follow the same rules.
This discovery, that symbols and experience do not follow the same rules, has come to the science of physics under the formidable title of quantum logic. The possibility that separate parts of reality (like you and I and tugboats) may be connected in ways which both our common experience and the laws of physics belie, has found its way into physics under the name of Bell’s theorem. Bell’s theorem and quantum logic take us to the farthest edges of theoretical physics. Many physicists have not even heard of them.
Bell’s theorem and quantum logic (currently) are unrelated. Proponents of one seldom are interested in the other. Nonetheless, they have much in common. They are what is really new in physics. Of course, laser fusion (fusing atoms with high-energy light beams) and the search for quarks generally are considered to be the frontiers of theoretical physics.* In a certain sense, they are. However, there is a big difference between these projects and Bell’s theorem and quantum logic.
Laser fusion research and the great quark hunt are endeavors within the existing paradigms of physics. A paradigm is an established thought process, a framework. Both quantum logic and Bell’s theorem are potentially explosive in terms of existing frameworks. The first (quantum logic) calls us back from the realm of symbols to the realm of experience. The s
econd (Bell’s theorem) tells us that there is no such thing as “separate parts.” All of the “parts” of the universe are connected in an intimate and immediate way previously claimed only by mystics and other scientifically objectionable people.
The central mathematical element in quantum theory, the hero of the story, is the wave function. The wave function is that mathematical entity which allows us to determine the possible results of an interaction between an observed system and an observing system. The celebrated position held by the wave function is due not only to Erwin Schrödinger, who discovered it, but also to the Hungarian mathematician John von Neumann.
In 1932, von Neumann published a famous mathematical analysis of quantum theory called The Mathematical Foundations of Quantum Mechanics.1 In this book von Neumann, in effect, asked the question, “If a ‘wave function,’ this purely abstract mathematical creation, actually should describe something in the real world, what would that something be like?” The answer that he deduced is exactly the description of a wave function that we already have discussed.
This strange animal constantly would change with the passage of time. Each moment it would be different than the moment before. It would be a composite of all the possibilities of the observed system which it describes. It would not be a simple mixture of possibilities, it would be a sort of organic whole whose parts are changing constantly but which, nonetheless, is somehow a thing-in-itself.
This thing-in-itself would continue to develop indefinitely until an observation (measurement) is made on the observed system which it represents. If the “observed system” is a photon “propagating in isolation,” the wave function representing this photon would contain all of the possible results of the photon’s interaction with a measuring device, like a photographic plate.* (For example, the possibilities contained in the wave function might be that the photon will be detected in area A of the photographic plate, that the photon will be detected in area B of the photographic plate, and that the photon will be detected in area C of the photographic plate.)