The Dancing Wu Li Masters

  Substituting “ø” for “H and D,” we are left with “ø, or H and V” on the right side of the statement. To solve for “H and V,” we follow the lines on the lattice downward from H and from V to their lowest common point. They also intersect at ø. Therefore, the lattice tells us that “H and V” equals “ø.” Substituting “ø” for “H and V” we now are left with “ø or ø” on the right side of the original statement. Both the lattice and common sense tell us that “ø or ø” equals “ø.”

  In short:

  “H” equals “H and D, or H and V”

  “H” equals “ø, or H and V”

  “H” equals “ø or ø”

  “H” equals “ø”

  But “H” does not equal “ø!” “H” is horizontally polarized light and “ø” is a non-experiment—a lack of any emission at all. The distributive law does not work!

  Here is Birkhoff and von Neumann’s proof again. It is important because, simple as it is, it could end an illusion millennia old: the illusion that symbols and experience follow the same set of rules. Except for the mathematical symbols that represent the connectives “and” and “or,” this is exactly the way that physicists read it:

  “H, and D or V” “H and D, or H and V”

  “H and I” “ø, or H and V”

  “H” “ø or ø”

  “H” ≠ “ø”

  Finkelstein’s theory is a theory of process. Quantum logic is only one part of it. According to this theory, the basic unit of the universe is an event, or a process. These events link in certain ways (allowed transitions) to form webs. The webs in turn join to form larger webs. Farther up the ladder of organization are coherent superpositions of different webs (things which are neither “this web” nor “that web” but distinct entities in themselves).

  The basic events of Finkelstein’s theory do not exist in space and time. They are prior to space and time. According to Finkelstein, space, time, mass, and energy are secondary qualities which are derived from the basic events of the universe. In fact, Finkelstein’s latest paper is called “Beneath Time.”

  This bold theory is a radical departure from conventional physics and from conventional thought. The mathematics of Finkelstein’s theory, which is called quantum topology, is remarkably simple compared to the complex mathematics of quantum theory and relativity. Quantum topology is as yet incomplete (lacking “proof”). Like many theories, it may never be complete. Unlike most other theories, however, it contains the potential to alter radically our conceptual framework.

  Von Neumann’s discovery that our thought processes (the realm of symbols) project illusory restrictions onto the real word is essentially the same discovery that led Einstein to the general theory of relativity. Einstein disproved the universality of Euclidean geometry. Until the general theory of relativity, Euclidean geometry had been accepted without question as the underlying structure of the universe. Birkhoff and von Neumann disproved the universality of classical logic. Until now, classical logic has been accepted without question as a natural reflection of the nature of reality.

  A powerful awareness lies dormant in these discoveries: an awareness of the hitherto-unsuspected powers of the mind to mold “reality,” rather than the other way round. In this sense, the philosophy of physics is becoming indistinguishable from the philosophy of Buddhism, which is the philosophy of enlightenment.

  1

  The End of Science

  A vital aspect of the enlightened state is the experience of an all-pervading unity. “This” and “that” no longer are separate entities. They are different forms of the same thing. Everything is a manifestation. It is not possible to answer the question, “Manifestation of what?” because the “what” is that which is beyond words, beyond concept, beyond form, beyond even space and time. Everything is a manifestation of that which is. That which is, is. Beyond these words lies the experience; the experience of that which is.

  The forms through which that which is manifests itself are each and every one of them perfect. We are manifestations of that which is. Everything is a manifestation of that which is. Everything and everybody is exactly and perfectly what it is.

  A fourteenth-century Tibetan Buddhist, Longchenpa, wrote:

  Since everything is but an apparition

  Perfect in being what it is,

  Having nothing to do with good or bad,

  Acceptance or rejection,

  One may well burst out in laughter.1

  We might say, “God’s in His heaven and all’s well with the world,” except that according to the enlightened view, the world couldn’t be any other way. It is neither well nor not well. It simply is what it is. What it is is perfectly what it is. It couldn’t be anything else. It is perfect. I am perfect. I am exactly and perfectly who I am. You are perfect. You are exactly and perfectly who you are.

  If you are a happy person, then that is what you perfectly are—a happy person. If you are an unhappy person, then that is what you perfect are—an unhappy person. If you are a person who is changing, then that is what you perfectly are—a person who is changing. That which is is that which is. That which is not is that which is. There is nothing which is not that which is. There is nothing other than that which is. Everything is that which is. We are a part of that which is. In fact, we are that which is.

  If we substitute “subatomic particles” for people in this scheme, we have a good approximation of the conceptual dynamics of particle physics. Yet, there is another sense in which this aspect of unity has entered physics. The pioneers of quantum physics noticed a strange “connectedness” among quantum phenomena. Until recently this oddity lacked any theoretical significance. It was regarded as an accidental feature which would be explained as the theory developed.

  In 1964, J. S. Bell, a physicist at the European Organization for Nuclear Research (CERN) in Switzerland, zeroed in on this strange connectedness in a manner that may make it the central focus of physics in the future. Dr. Bell published a mathematical proof which came to be known as Bell’s theorem. Bell’s theorem was reworked and refined over the following ten years until it emerged in its present form. Its present form is dramatic, to say the least.

  Bell’s theorem is a mathematical construct which, as such, is indecipherable to the nonmathematician. Its implications, however, could affect profoundly our basic world view. Some physicists are convinced that it is the most important single work, perhaps, in the history of physics. One of the implications of Bell’s theorem is that, at a deep and fundamental level, the “separate parts” of the universe are connected in an intimate and immediate way.

  In short, Bell’s theorem and the enlightened experience of unity are very compatible.

  The unexplained connectedness of quantum phenomena shows itself in several ways. The first way we already have discussed. It is the double-slit experiment. When both slits in a double-slit experiment are open, the light waves going through them interfere with each other to form a pattern of alternating light and dark bands on a screen. When only one slit in a double-slit experiment is open, the light waves going through it illuminate the screen in the ordinary way. How does a single photon in a double-slit experiment know whether or not it can go to an area on the screen that must be dark if both slits are open?

  The great multitude of photons of which a single photon eventually will be a part distributes itself in one way if one slit is open, and in an entirely different way if both slits are open. The question is, assuming that a single photon goes through one of the two slits, how does it know whether or not the other slit is open? Somehow it does. An interference pattern always forms when we open both slits, and it never forms when we close one of the slits.

  However, there is another experiment in which this apparent connectedness of quantum phenomena is even more perplexing. Suppose that we have what physicists call a two-particle system of zero spin. This means that the spin of each of the particles in the system cancels the other. If one of the parti
cles in such a system has a spin up, the other particle has a spin down. If the first particle has a spin right, the second particle has a spin left. No matter how the particles are oriented, their spins are always equal and opposite.

  Now suppose that we separate these two particles in some way that does not affect their spin (like electrically). One particle goes off in one direction and the other particle goes off in the opposite direction.

  The spin of a subatomic particle can be oriented by a magnetic field. For example, if a beam of electrons with randomly oriented spin is sent through a particular type of magnetic field (called a Stern-Gerlach device), the magnetic field splits the beam into two equal smaller beams. In one of them all of the electrons have a spin up and in the other all of the electrons have a spin down. If only one electron goes through this magnetic field, it will come out of it with either a spin up or a spin down. (We can design the experiment so that the odds are 50–50) (first drawing, previous page).

  If we reorientate the magnetic field (change its axis) we can give all of the electrons a spin right or a spin left instead of a spin up or a spin down. If only one electron goes through the magnetic field when it is oriented this way, it will come out of it with either a spin right or a spin left (equal chance either way) (second drawing, previous page).

  Now suppose that after we separate our original two-particle system we send one of the particles through a magnetic field that will give it either a spin up or a spin down. In this case, let us say that the particle comes out of the magnetic field with a spin up. This means that we automatically know that the other particle has a spin down. We do not have to make a measurement on the other particle because we know that its spin is equal to and opposite to that of its twin.

  The experiment looks like this:

  The original two-particle system with zero spin is at the center. One of the particles goes to area A. In area A it goes through a Stern-Gerlach device. In this case, the Stern-Gerlach device gives it a spin up. Therefore, we know without measuring that the other particle, which has gone to area B, has a spin down.

  Albert Einstein, Boris Podolsky, and Nathan Rosen thought up this experience over forty-five years ago. Actually, this version of the Einstein-Podolsky-Rosen experiment (using spin states) was thought up by David Bohm, a physicist at the University of London. This version usually is used to illustrate the Einstein-Podolsky-Rosen effect. (The original paper dealt with positions and momenta.)

  In 1935, Einstein, Podolsky, and Rosen published their thought experiment in a paper entitled, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”2 At that time, Bohr, Heisenberg, and the proponents of the Copenhagen Interpretation of Quantum Mechanics were saying that quantum theory is a complete theory even though it doesn’t provide any picture of the world separate from our observations of it. (They’re still saying it.) The message that Einstein, Podolsky, and Rosen wanted to convey to their colleagues was that the quantum theory is not a “complete” theory because it does not describe certain important aspects of reality which are physically real even if they are not observed. The message that their colleagues got, however, was quite different. The message that their colleagues got was that the particles in the Einstein-Podolsky-Rosen thought experiment somehow are connected in a way that transcends our usual ideas about causality.

  For example, if the axis of the Stern-Gerlach device in our hypothetical experiment were changed to make the particles spin right or left instead of up or down, the experiment would look like this:

  The particle in area A would have a spin right instead of a spin up. This means that the particle in area B would have a spin left instead of a spin down. Its spin is always equal and opposite that of its twin.

  Now suppose that the axis of the Stern-Gerlach device is changed while the particles are in flight. Somehow the particle traveling in area B “knows” that its twin in area A is spinning right instead of up and so it spins left instead of down. In other words, what we did in area A (changed the axis of the magnetic field) affected what happened in area B. This strange phenomenon is known as the Einstein-Podolsky-Rosen (EPR) effect.

  Einstein, Podolsky, and Rosen’s thought experiment is the Pandora’s Box of modern physics. It inadvertently illustrated an unexplainable connectedness between particles in two different places. The particle in area B seems to know instantaneously the spin status of the particle in area A.* This connectedness allows an experimenter in one place (area A) to affect the state of a system in another place (area B).

  “It is rather discomforting,” remarked Erwin Schrödinger, in reference to this phenomenon,

  that the [quantum] theory should allow a system to be steered or piloted into one or the other type of state at the experimenter’s mercy in spite of his having no access to it.3

  At once physicists realized that this peculiar situation raises a critical question: “How can two of anything communicate so quickly?”

  According to the usual ideas in physics, information is carried from one place to another by a signal. Without a carrier there is no communication. For example, the most common form of communication is talking. The information that we convey by talking is carried (in a face-to-face conversation) by sound waves. Sound waves only travel so fast (about 700 miles per hour). Therefore, how long it takes my information to get from me to you depends upon how far away from me you are. The fastest communication signal is an electromagnetic wave, like a light wave or a radio wave. These travel at approximately 186,000 miles per second. Almost all of physics rests upon the assumption that nothing in the universe can travel faster than the speed of light.* The extraordinarily high velocity of light makes communication by light signal seem instantaneous. I seem to see you nod your head at the moment that you actually do it. Nonetheless, communication by light signal is not instantaneous. How long it takes my information to travel via light signal from me to you depends upon how far away from me you are. In most instances, the travel time required is so brief that it scarcely can be measured. It takes several seconds, however, for a radio signal to travel from the earth to the moon and back.

  Now suppose that area A and area B are very far apart. It will take a certain amount of time for a light signal to travel from area A to area B. If area A and area B are so far apart that there is insufficient time for a light signal to connect an event that happens in area A with an event that happens in area B, there is no way, according to the usual ideas in physics, that the event in area B can know about the event in area A. Physicists call this a “space-like” separation. (One event is space-like separated from another event if there is insufficient time for a light signal to connect them.) Communication between space-like separated events defies one of the most basic assumptions of physics. Yet this is exactly what the Einstein-Podolsky-Rosen thought experiment seems to illustrate. Even though they are space-like separated, the state of the particle in area B depends upon what the observer in area A decides to observe (which way he orients his magnetic field).

  In other words, the Einstein-Podolsky-Rosen effect indicates that information can be communicated at superluminal (faster than light) speeds contrary to the accepted ideas of physicists. If the two particles in the Einstein-Podolsky-Rosen thought experiment somehow are connected by a signal, that signal is traveling faster than the speed of light. Einstein, Podolsky, and Rosen may have created the first scientific example of a superluminal connection.

  Einstein himself denied this conclusion. It is not possible, he argued, that the setting we choose for a measuring device here can affect what happens somewhere else. In his autobiography, written eleven years after the Einstein-Podolsky-Rosen paper, he wrote:

  …on one supposition we should, in my opinion, absolutely hold fast; the real factual situation of the system S2 [the particle in area B] is independent of what is done with the system S1 [the particle in area A], which is spatially separated from the former.4

  This opinion is, in effect, the principle o
f local causes. The principle of local causes says that what happens in one area does not depend upon variables subject to the control of an experimenter in a distant space-like separated area. The principle of local causes is common sense. The results of an experiment in a place distant and space-like separated from us should not depend on what we decide to do or not to do right here. (Except for the mother who rose in alarm at the same instant that her daughter’s distant automobile crashed into a tree—and similar cases—the macroscopic world appears to be made of local phenomena.)

  Since phenomena are local in nature, argued Einstein, quantum theory has a serious flaw. According to quantum theory, changing the measuring device in area A changes the wave function which describes the particle in area B, but (according to Einstein) it cannot change “the real factual situation of the system S2 [which] is independent of what is done with the system S1…”

  Therefore, one and the same “factual situation” in area B has two wave functions, one for each position of the measuring device in area A. This is a flaw since it is “impossible that two different types of wave functions could be coordinated with the identical factual situation of S2.”5

  Here is another way of looking at the same situation: Since the real factual situation in area B is independent of what is done in area A, there must exist simultaneously in area B a definite spin up or down and a definite spin right or left to account for all the results that we can get by orienting the Stern-Gerlach device in area A either vertically or horizontally. Quantum theory is not able to describe such a state in area B and, therefore, it is an incomplete theory.*

  However, Einstein closed his argument with an incredible aside:

  One can escape from this conclusion [that quantum theory is incomplete] only by either assuming that the measurement of S1 ((telepathically)) changes the real situation of S2 or by denying independent real situations as such to things which are spatially separated from each other. Both alternatives appear to me entirely unacceptable.6