The Dancing Wu Li Masters Read online

  Photons do not exist by themselves. All that exists by itself is an unbroken wholeness that presents itself to us as webs (more patterns) of relations. Individual entities are idealizations which are correlations made by us.

  In short, the physical world, according to quantum mechanics, is:

  …not a structure built out of independently existing unanalyzable entities, but rather a web of relationships between elements whose meanings arise wholly from their relationships to the whole. (Stapp)4

  The new physics sounds very much like old eastern mysticism.

  What happens between the region of preparation and the region of measurement is a dynamic (changing with time) unfolding of possibilities that occurs according to the Schrödinger wave equation. We can determine, for any moment in the development of these possibilities, the probability of any one of them occurring.

  One possibility may be that the photon will land in region A. Another possibility may be that the photon will land in region B. However, it is not possible for the same photon to land in region A and in region B at the same time. When one of these possibilities is actualized, the probability that the other one will occur at the same time becomes zero.

  How do we cause a possibility to become an actuality? We “make a measurement.” Making a measurement interferes with the development of these possibilities. In other words, making a measurement interferes with the development in isolation of the observed system. When we interfere with the development in isolation of the observed system (which is what Schrödinger’s wave equation governs) we actualize one of the several potentialities that were a part of the observed system while it was in isolation. For example, as soon as we detect the photon in region A, the possibility that it is in region B, or anyplace else, becomes nihil.

  The development of possibilities that takes place between the region of preparation and the region of measurement is represented by a particular kind of mathematical entity. Physicists call this mathematical entity a “wave function” because it looks, mathematically, like a development of waves which constantly change and proliferate. In a nutshell, the Schrödinger wave equation governs the development in isolation (between the region of preparation and the region of measurement) of the observed system (a photon in this case) which is represented mathematically by a wave function.

  A wave function is a mathematical fiction that represents all the possibilities that can happen to an observed system when it interacts with an observing system (a measuring device). The form of the wave function of an observed system can be calculated via the Schrödinger wave equation for any moment between the time the observed system leaves the region of preparation and the time that it interacts with the observing system.

  Once the wave function is calculated, we can perform a simple mathematical operation on it (square its amplitude) to create a second mathematical entity called a probability function (or, technically, a “probability density function”). The probability function tells us the probabilities at a given time(s) of each of the possibilities represented by the wave function. The wave function is calculated with the Schrödinger wave equation. It deals with possibilities. The probability function is based upon the wave function. It deals with probabilities.

  There is a difference between possible and probable. Some things may be possible, but not very probable, like snow falling in the summer, except in Antarctica where it is both possible and probable.

  The wave function of an observed system is a mathematical catalogue which gives a physical description of those things which could happen to the observed system when we make a measurement on it. The probability function gives the probabilities of those events actually happening. It says, “These are the odds that this or that will happen.”

  Before we interfere with the development in isolation of an observed system, it merrily continues to generate possibilities in accordance with the Schrödinger wave equation. As soon as we make a measurement, however—look to see what is happening—the probability of all the possibilities, except one, becomes zero, and the probability of that possibility becomes one, which means that it happens.

  The development of the wave function (possibilities) follows an unvarying determinism. We calculate this development by using the Schrödinger wave equation. Since the probability function is based upon the wave function, the probabilities of possible happenings also develop deterministically via the Schrödinger wave equation.

  This is why we can predict accurately the probability of an event, but not the event itself. We can calculate the probability of a desired result, but when we make a measurement, that result may or may not be the one that we get. The photon may land in region B or it may land in region A. Which possibility becomes reality is, according to quantum theory, a matter of chance.

  Now back to the double-slit experiment. We cannot predict where a photon in a double-slit experiment will land. However, we can calculate where it is most likely to land, where it is next likely to land, and so on.* This is how it happens.

  Suppose that we place a photon detector at slit one and another photon detector at slit two. Now we emit photons from the light source. Sooner or later one of them will go through one slit or the other. There are two possibilities for that photon. It can go through slit one and detector one will fire, or it can go through slit two and detector two will fire. Each of these possibilities is included in the wave function of that photon.

  Let us say that when we examine the detectors we find that detector two has fired. As soon as we know this we also know that the photon did not go through slit one. That possibility no longer exists, and, therefore, the wave function of the photon has changed.

  The graphic representation (picture) of the wave function of the photon, before we made the measurement, had two humps in it. One of the humps represented the possibility of the photon passing through slit one and detector one firing. The other hump represented the possibility of the photon passing through slit two and detector two firing.

  When the photon was detected passing through slit two, the possibility that it would go through slit one ceased to exist. When that happened, the hump in the graphic representation of the wave function representing that possibility changed to a straight line. This phenomenon is called the “collapse of the wave function.”

  Physicists speak as if the wave function exhibits two very different modes of development. The first is a smooth and dynamic development, which we can predict because it follows the Schrödinger wave equation. The second is abrupt and discontinuous (that word, again). This mode of development is the collapse of the wave function. Which part of the wave function collapses is a matter of chance. The transition from the first mode to the second mode is called a quantum jump.

  The Quantum Jump is not a dance. It is the abrupt collapse of all the developing aspects of the wave function except the one that actualizes. The mathematical representation of the observed system literally leaps from one situation to another, with no apparent development between the two.

  In a quantum mechanical experiment, the observed system, traveling undisturbed between the region of preparation and the region of measurement, develops according to the Schrödinger wave equation. During this time, all of the allowed things that could happen to it unfold as a developing wave function. However, as soon as it interacts with a measuring device (the observing system), one of those possibilities actualizes and the rest cease to exist. The quantum leap is from a multifaceted potentiality to a single actuality.

  The quantum leap is also a leap from a reality with a theoretically infinite number of dimensions into a reality which has only three. This is because the wave function of the observed system, before it is observed, proliferates in many mathematical dimensions.

  Take the wave function of our photon in the double-slit experiment for example. It contains two possibilities. The first possibility is that the photon will go through slit one and detector one will fire, and the second possibility is that the photon will
go through slit two and detector two will fire. Each of these possibilities, alone, would be represented by a wave function that exists in three dimensions and a time. This is because our reality has three dimensions, length, width, and depth, along with time.

  If we want to describe a physical event accurately, we must say where it happened and when.

  To describe where something happens requires three “coordinates.” Suppose that I want to give directions to an invisible balloon floating in an empty room. I could say, for example, “Starting in a certain corner, go five feet along a certain wall (one dimension), four feet directly out from the wall (second dimension), and three feet up from the floor (third dimension).” Every possibility exists in three dimensions and has a time.

  If the wave function represents possibilities associated with two different particles, then that wave function exists in six dimensions, three for each particle. If the wave function represents the possibilities associated with twelve particles, then that wave function exists in thirty-six dimensions!*

  This is impossible to visualize since our experience is limited to three dimensions. Nontheless, this is the mathematics of the situation.

  The point to think about is that when we make a measurement in a quantum mechanical experiment—when the observed system interacts with the observing system—we reduce a multidimensional reality to a three-dimensional reality compatible with our experience.

  If we calculate a wave function for possible photon detection at four different points, that wave function is a mathematical reality in which four different happenings exist simultaneously in twelve dimensions. In principle, we can calculate a wave function representing an infinite number of events happening at the same time in an infinite number of dimensions. No matter how complex the wave function, however, as soon as we make a measurement, we reduce it to a form compatible with three-dimensional reality, which is the only form of experiential reality, instant by instant, normally available to us.

  Now we come to the question, “When, exactly, does the wave function collapse?” When do all of the possibilities that are developing for the observed system, except one, vanish?

  Up to now, we have said that the collapse occurs when somebody looks at the observed system. This is only one point of view. Another opinion (any discussion about this question is opinion) is that the wave function collapses when I look at the observed system. Still another opinion is that the wave function collapses when any measurement is made, even by an instrument. According to this view, it is not important whether we are there to see it or not.

  Suppose for the moment that there are no human experimenters involved in our experiment. It is entirely automatic. A light source emits a photon. The wave function of the photon contains the possibility that the photon will pass through slit one and detector one will fire, and also the possibility that the photon will pass through slit two and detector two will fire.

  Now suppose that detector two registers a photon.

  According to classical physics, the light source emitted a real particle, a photon, and it traveled from the light source to the slit where detector two recorded it. Although we did not know its location while it was in transit, we could have determined it, if we had known how.

  According to quantum mechanics, this is not so. No real particle called a photon traveled between the light source and the screen. There was no photon until one actualized at slit two. Until then, there was only a wave function. In other words, until then, all that existed were tendencies for a photon to actualize either at slit one or at slit two.

  From the classical point of view, a real photon travels between the light source and the screen. The odds are 50–50 that it will go to slit one and 50–50 that it will go to slit two. From the point of view of quantum mechanics, there is no photon until a detector fires. There is only a developing potentiality in which a photon goes to slit one and to slit two. This is Heisenberg’s “strange kind of physical reality just in the middle between possibility and reality.”5

  It is difficult to make this sound less vague. The translation from mathematics to English entails a loss of precision but that is not the problem. We can experience a more clearly defined picture of this phenomenon by learning enough mathematics to follow the development of the Schrödinger wave equation. Unfortunately, clarifying the picture only helps to boggle the mind.

  The real problem is that we are used to looking at the world simply. We are accustomed to believing that something is there or it is not there. Whether we look at it or not, it is either there or it is not there. Our experience tells us that the physical world is solid, real, and independent of us. Quantum mechanics says, simply, that this is not so.

  Suppose that a technician, not knowing that our experiment is automatic, enters the room to see which detector has recorded a photon. When he looks at the observing system (the detectors), there are two things that he can see. The first possibility is that detector one has recorded the photon, and the second possibility is that detector two has recorded the photon. The wave function of the observing system (which now is the technician), therefore, has two humps in it, one for each possibility.

  Until the technician looks at the detectors, quantum mechanically speaking, both situations in some way exist. As soon as he sees that detector two has fired, however, the possibility that detector one has fired vanishes. That part of the wave function of the measuring system collapses, and the reality of the technician is that detector two has recorded a photon. In other words, the observing system of the experiment, the detectors, has become the observed system in relation to the technician.

  Now suppose that the supervising physicist enters the room to check on the technician. He wants to see what the technician has learned about the detectors. In this regard, there are two possibilities. One is that the technician has seen that detector one has recorded a photon, and the other is that the technician has seen that detector two has recorded a photon, and so on.*

  The division of the wave function into two humps, each one representing a possibility, has progressed from photon to detectors to technician to supervisor. This proliferation of possibilities is the type of development governed by the Schrödinger wave equation.

  Without perception, the universe continues, via the Schrödinger equation, to generate an endless profusion of possibilities. The effect of perception, however, is immediate and dramatic. All of the wave function representing the observed system collapses, except one part, which actualizes into reality. No one knows what causes a particular possibility to actualize and the rest to vanish. The only law governing this phenomenon is statistical. In other words, it is up to chance.

  The division into two parts of the wave function of the photon, detectors, technician, supervisor, etc., is known as the “Problem of Measurement” (or, sometimes, “The Theory of Measurement”). † If there were twenty-five possibilities in the wave function of the photon, the wave function of the measuring system, technician, and supervisor similarly would have twenty-five separate humps, until a perception is made and the wave function collapses. From photon to detectors to technician to supervisor we could continue until we include the entire universe. Who is looking at the universe? Put another way, How is the universe being actualized?

  The answer comes full circle. We are actualizing the universe. Since we are part of the universe, that makes the universe (and us) self-actualizing.

  This line of thought is similar to some aspects of Buddhist psychology. In addition, it could become one of many important contributions of physics to future models of consciousness.

  The Copenhagen Interpretation of Quantum Mechanics says that it is unnecessary to “peer behind the scenes to see what is really happening as long as quantum mechanics works (correlates experience correctly) in all possible experimental situations. It is not necessary to know how light can manifest itself both as particles and waves. It is enough to know that it does and to be able to use this phenomenon to predict probabiliti
es. In other words, the wave and particle characteristics of light are unified by quantum mechanics, but at a price. There is no description of reality.

  All attempts to describe “reality” are relegated to the realm of metaphysical speculation.* However, this does not mean that physicists do not speculate. Many do, in particular Henry Stapp, and their reasoning goes like this.

  The fundamental theoretical quantity in quantum mechanics is the wave function. The wave function is a dynamic (it changes as time progresses) description of possible occurrences. But what does the wave function describe, really? According to western thought, the world has only two essential aspects, one of which is matter-like and the other of which is idea-like.

  The matter-like aspect is associated with the external world, most of which is conceived to be made of inanimate stuff that is hard and unresponsive, like rocks, pavement, metal, etc. The idea-like aspect is cur subjective experience. Reconciling these two has been a central theme of religion through history. The philosophies which champion these aspects are Materialism (the world is matter-like, regardless of our impressions) and Idealism (reality is idea-like, regardless of appearances). The question is, which one of these aspects does the wave function represent?

  The answer, according to the orthodox view of quantum mechanics elucidated by Stapp, is that the wave function represents something that partakes of both idea-like and matter-like characteristics.*

  For example, when the observed system as represented by the wave function propagates in isolation between the region of preparation and the region of measurement, it develops according to a strictly deterministic law (the Schrödinger wave equation). Temporal development in accordance with a causal law is a matter-like characteristic. Therefore, whatever the wave function represents, that something has a matter-like aspect.