QUANTUM MECHANICS IS a procedure. It is a specific way of looking at a specific part of reality. The only people who use it are physicists. The advantage of following the procedure of quantum mechanics is that it allows us to predict the probabilities of certain results provided our experiment is performed in a certain way. The purpose of quantum mechanics is not to predict what actually will happen, but only to predict the probabilities of various possible results. Physicists would like to be able to predict subatomic events more accurately, but, at present, quantum mechanics is the only workable theory of subatomic phenomena that they have been able to construct.
Probabilities follow deterministic laws in the same way that macroscopic events follow deterministic laws. There is a direct parallel. If we know enough about the initial conditions of an experiment, we can calculate, using rigid laws of development, exactly what the probability is for a certain result to occur.
For example, there is no way that we can calculate where a single photon in a double-slit experiment will strike the photographic plate (see here). However, we can calculate with precision the probability that it will strike it at a certain place, provided that the experiment has been prepared properly and that the results are measured properly.
Suppose that we calculate a 60 percent probability for the photon to land in area A. Does that mean that it can land somewhere else? Yes. In fact, there is a 40 percent probability that it will.
In that case (asking the question for Jim de Wit), what determines where the photon will land? The answer given by quantum theory: pure chance.
This pure-chance aspect was another objection that Einstein had about quantum mechanics. It is one of the reasons that he never accepted it as the fundamental physical theory. “Quantum mechanics is very impressive,” he wrote in a letter to Max Born, “. . . but I am convinced that God does not play dice.”1
Two generations later, J. S. Bell, an Irish physicist, proved that he may have been right, but that is another story, which we will come to later.
The first step in the procedure of quantum mechanics is to prepare a physical system (the experimental apparatus) according to certain specifications, in an area called the region of preparation.
The second step in the procedure of quantum mechanics is to prepare another physical system to measure the results of the experiment. This measuring system is located in an area called the region of measurement. Ideally, the region of measurement is far away from the region of preparation. Of course, to a subatomic particle, even a small macroscopic distance is a long way.
Now let us perform the double-slit experiment using this procedure. First, we set a light source on a table, and then, a short distance away, we place a screen with two vertical slits in it. The area where these apparatuses are located is the region of preparation. Next we fix an unexposed photographic plate on the opposite side of the screen from the light source. This area is the region of measurement.
The third step in the procedure of quantum mechanics is to translate what we know about the apparatus in the region of preparation (the light and the screen) into mathematical terms which represent it, and to do likewise for the apparatus that is located in the region of measurement (the photographic plate).
To do this we need to know the specifications of the apparatus. In practice, this means that we give the technician who sets up the equipment precise instructions. We tell him, for example, the exact distance to place the double-slit screen from the light source, the frequency and intensity of the light that we will use, the dimensions of the two slits and their position relative to each other and to the light source, etc. We also give him equally explicit instructions concerning the measuring apparatus, such as where to put it, the type of photographic film that we will use, how to develop it, etc.
After we translate these specifications of the experimental arrangement into the mathematical language of quantum theory, we feed these mathematical quantities into an equation that expresses the form of natural causal development. Notice that this last sentence doesn’t say anything about what is developing. That is because nobody knows. The Copenhagen Interpretation of Quantum Mechanics (see here) says that quantum theory is a complete theory because it works (correlates experience), in every possible experimental situation not because it explains in detail what is going on.fn1 (Einstein’s complaint was that quantum theory doesn’t fully explain things because it deals with group behaviour and not with individual events).
However, when it comes to predicting group behavior, quantum theory works as advertised. In a double-slit experiment, for example, it can predict exactly the probabilities of a photon being recorded in region A, in region B, in region C, and so forth.
Of course, the last step in the procedure of quantum mechanics is actually to do the experiment and get a result.
To apply quantum theory, the physical world must be divided into two parts. These parts are the observed system and the observing system. The observed system and the observing system are not the same as the region of preparation and the region of measurement. “Region of preparation” and “region of measurement” are terms which describe the physical organization of the experimental apparatus. “Observed system” and “observing system” are terms which pertain to the way that physicists analyze the experiment. (The “observed” system, by the way, cannot be observed until it interacts with the observing system, and even then all that we can observe are its effects on a measuring device).
The observed system in the double-slit experiment is a photon. It is pictured as traveling between the region of preparation and the region of measurement. The observing system in all quantum mechanical experiments is the environment which surrounds the observed system—including the physicists who are studying the experiment. While the observed system is traveling undisturbed (“propagating in isolation”), it develops according to a natural causal law. This law of causal development is called the Schrödinger wave equation. The information that we put into the Schrödinger wave equation is the data about the experimental apparatuses that we have transcribed into the mathematical language of quantum theory.
Each set of these experimental specifications that we transcribed into the mathematical language of quantum theory corresponds to what physicists call an “observable”. Observables are the features of the experiment and nature that are considered to be fixed, or determined, when and if the experimental specifications that we have transcribed actually are met. We may have transcribed into mathematical language several experimental specifications for the region of measurement, each one corresponding to a different possible result (the possibility that the photon will land in region A, the possibility that the photon will land in region B, the possibility that the photon will land in region C, etc.).
In the world of mathematics, the experimental specifications of each of these possible situations in the region of measurement and in the region of preparation corresponds to an observable.fn2 In the world of experience, an observable is the possible occurrence (coming into our experience) of one of these sets of specifications.
In other words, what happens to the observed system between the region of preparation and the region of measurement is expressed mathematically as a correlation between two observables (production and detection). Yet we know that the observed system is a particle—a photon. Said another way, the photon is a relationship between two observables. This is a long, long way from the building-brick concept of elementary particles. For centuries scientists have tried to reduce reality to indivisible entities. Imagine how surprising and frustrating it is for them to come so close (a photon is very “elementary”), only to discover that elementary particles don’t have an existence of their own!
As Stapp wrote for the Atomic Energy Commission:
. . . an elementary particle is not an independently existing, unanalyzable entity. It is, in essence, a set of relationships that reach outward to other things.2
Furthermore, the mathematical picture which physicists have constructed of this “set of relationships” is very similar to the mathematical picture of a real (physical) moving particle.fn3 The motion of such a set of relationships is governed by exactly the same equation which governs the motion of a real moving particle.
Wrote Stapp:
A long-range correlation between observables has the interesting property that the equation of motion which governs the propagation of this effect is precisely the equation of motion of a freely moving particle.3
Things are not “correlated” in nature. In nature, things are as they are. Period. “Correlation” is a concept which we use to describe connections which we perceive. There is no word, “correlation”, apart from people. There is no concept, “correlation”, apart from people. This is because only people use words and concepts.
“Correlation” is a concept. Subatomic particles are correlations. If we weren’t here to make them, there would not be any concepts, including the concept of “correlation”. In short, if we weren’t here to make them, there wouldn’t be any particles!fn4
Quantum mechanics is based on the development in isolation of an observed system. “Development in isolation” refers to the isolation that we create by separating the region of preparation from the region of measurement. We call this situation “isolation”, but in reality, nothing is completely isolated, except, perhaps, the universe as a whole. (What would it be isolated from?)
The “isolation” that we create is an idealization, and one point of view is that quantum mechanics allows us to idealize a photon from the fundamental unbroken unity so that we can study it. In fact, a “photon” seems to become isolated from the fundamental unbroken unity because we are studying it.
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.fn5 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!fn6
This is impossible to visualize since our experience is limited to three dimensions. Nonetheless, 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 multi-dimensional 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.fn7
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”).fn8 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 probabilities. 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.fn9 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 our 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.fn10
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.
However, when the observed system as represented by the wave function interacts with the observing system (when we make a measurement), it abruptly leaps to a new state. These “Quantum Leap” type transitions are idea-like characteristics. Ideas (like our knowledge about something) can and do change discontinuously. Therefore, whatever the wave function represents, that something also has an idea-like aspect.
The wave function, strictly speaking, represents an observed system in a quantum mechanical experiment. In more general terms, it describes physical reality at the most fundamental level (the subatomic) that physicists have been able to probe. In fact, according to quantum mechanics, the wave function is a complete description of physical reality at that level. Most physicists believe that a description of the substructure underlying experience more complete than the wave function is not possible.
“Wait a minute!” says Jim de Wit (jumping out of the blue). “The description contained in the wave function consists of coordinates (three, six, nine, etc.) and a time (see here). How can that be a complete description of reality? Imagine how I felt when my girl friend ran off to Mexico with a gypsy. Where does that show up in a wave function?”
It doesn’t. The “complete description” that quantum theory claims the wave function to be is a description of physical reality (as in physics). No matter what we are feeling, or thinking about, or looking at, the wave function describes as completely as possible where and when we are doing it.
Since the wave function is thought to be a complete description of physical reality and since that which the wave function describes is idea-like as well as matter-like, then physical reality must be both idea-like and matter-like. In other words, the world cannot be as it appears. Incredible as it sounds, this is the conclusion of the orthodox view of quantum mechanics. The physical world appears to be completely substantive (made of “stuff”). Nonetheless, if it has an idea-like aspect, the physical world is not substantive in the usual sense of the word (one hundred percent matter, zero percent idea).
According to Stapp:
If the attitude of quantum mechanics is correct, in the strong sense that a description of the substructure underlying experience more complete than the one it provides is not possible, then there is no substantive physical world, in the usual sense of this term. The conclusion here is not the weak conclusion that there may not be a substantive physical world but rather that there definitely is not a substantive physical world.6
This does not mean that the world is completely idea-like. The Copenhagen Interpretation of Quantum Mechanics does not go so far as to say what reality is “really like behind the scenes”, but it does say that it is not like it appears. It says that what we perceive to be physical reality is actually our cognitive construction of it. This cognitive construction may appear to be substantive, but the Copenhagen Interpretation of Quantum Mechanics leads directly to the conclusion that the physical world itself is not.
This claim at first appears so preposterous and remote from experience that our inclination is to discard it as the foolish product of cloistered intellectuals. However, there are several good reasons why we should not be so hasty. The first reason is that quantum mechanics is a logically consistent system. It is self-consistent and it also is consistent with all known experiments.
Second, the experimental evidence itself is incompatible with our ordinary ideas about reality.
Third, physicists are not the only people who view the world this way. They are only the newest members of a sizable group; most Hindus and Buddhists also hold similar views.
Therefore, it is evident that even physicists who disclaim metaphysics have difficulty avoiding it. Now we come to those physicists who have jumped feet first into describing “reality”.
So far our discussions have been based on the Copenhagen Interpretation of Quantum Mechanics. The unavoidable flaw in this interpretation is the Problem of Measurement. Some type of detection by an observing system is required to collapse the wave function of the observed system into a physical reality, otherwise the “observed system” does not physically exist except as an endlessly proliferating number of possibilities generated in accordance with the Schrödinger wave equation.
The theory proposed by Hugh Everett, John Wheeler, and Neill Graham solves this problem in the simplest way possible.7 It claims that the wave function is a real thing, all of the possibilities that it represents are real, and they all happen. The orthodox interpretation of quantum mechanics is that only one of the possibilities contained in the wave function of an observed system actualizes, and the rest vanish. The Everett-Wheeler-Graham theory says that they all actualize, but in different worlds that coexist with ours!
Let’s go back to the double-slit experiment again. A light source emits a photon. The photon can pass through slit one or through slit two. A detector is placed at slit one and at slit two. Now we add a new experimental procedure. If the photon goes through slit one, I run upstairs. If the photon goes through slit two, I run downstairs. Therefore, one possible occurrence is that the photon goes through slit one, detector one fires, and I run up the stairs. The second possible occurrence is that the photon goes through slit two, detector two fires, and I run down the stairs.
According to the Copenhagen Interpretation, these two possibilities are mutually exclusive because it is not possible for me to run upstairs and to run downstairs at the same time.
According to the Everett-Wheeler-Graham theory, at the moment the wave function “collapses”, the universe splits into two worlds. In one of them I run up the stairs and in the other I run down the stairs. There are two distinct editions of me. Each one of them is doing something different, and each one of them is unaware of the other. Nor will their (our) paths ever cross since the two worlds into which the original one split are forever separate branches of reality.
In other words, according to the Copenhagen Interpretation of Quantum Mechanics, the development of the Schrödinger wave equation generates an endlessly proliferating number of possibilities. According to the Everett-Wheeler-Graham theory, the development of the Schrödinger wave equation generates an endlessly proliferating number of different branches of reality! This theory is called, appropriately, the Many Worlds Interpretation of Quantum Mechanics.
The theoretical advantage of the Many Worlds Interpretation is that it does not require an “external observer” to “collapse” one of the possibilities contained in a wave function into physical reality. According to the Many Worlds theory, wave functions do not collapse, they just keep splitting as they develop according to the Schrödinger wave equation. When a consciousness happens to be present at such a split, it splits also, one part of it associating with one branch of reality and the other part(s) of it associating with the other branch(es) of reality. However, each branch of reality is experientially inaccessable to the other(s), and a consciousness in any one branch will consider that branch to be the entirety of reality. Therefore, the role of consciousness, which was central to the Copenhagen Interpretation (if consciousness is associated with an act of measurement), is incidental to the Many Worlds theory.
However, the Many Worlds description of the structure of the relationship between the various branches of physical reality sounds like a quantitative version of a mystical vision of unity. Every state of a subsystem of a composite system is uniquely correlated to the states of the remaining subsystems which constitute the whole of which it is a part. A “composite system”, in this case, means a combination of both the observed system and the observing system. In other words, every state of the observing system is correlated to a particular state of the observed system.
Said another way, the Many Worlds theory defines any particular branch of reality which might “actualize” to us as a result of an interaction of an observed system and an observing system as merely one way of decomposing the wave function which represents them both. According to this theory, all of the other states which “could have” resulted from the same interaction did happen, but in other branches of reality. Each of these branches of reality are real, and, together, they constitute all the different ways in which we can decompose the universal wave function.
In this way, the Problem of Measurement is no longer a problem. The problem of measurement, ultimately, was, “Who is looking at the universe?” The Many Worlds theory says that it is not necessary to collapse a wave function to actualize the universe. All of the mutually exclusive possibilities contained within the wave function of an observed system that (according to the Copenhagen Interpretation) do not actualize when the wave function “collapses” actually do actualize, but not in this branch of the universe. In our experiment, for example, one of the possibilities contained in the wave function actualizes in this branch of the universe (I run up the stairs). The other possibility contained in the wave function (I run down the stairs) also actualizes, but in a different branch of reality. In this branch of reality I run up the stairs. In another branch of reality I run down the stairs. Neither “I” knows the other. Both “I”s believe that their branch of the universe is the entirety of reality.
The Many Worlds theory says that there is one universe and that its wave function represents all of the ways that it can be decomposed into different possible realities. We are all together here in a big box and it is not necessary to look at the box from the outside to actualize it.
In this regard, the Many Worlds theory is especially interesting because Einstein’s general theory of relativity shows that our universe might be something like a large closed box and, if this is so, it is never possible to get “outside” of it.fn11
“Schrödinger’s Cat” sums up the differences between classical physics, the Copenhagen Interpretation of Quantum Mechanics, and the Many Worlds Interpretation of Quantum Mechanics. “Schrödinger’s Cat” is a dilemma posed long ago by the famous discoverer of the Schrödinger wave equation:
A cat is placed inside a box. Inside the box is a device which can release a gas, instantly killing the cat. A random event (the radioactive decay of an atom) determines whether the gas is released or not. There is no way of knowing, outside of looking into the box, what happens inside it. The box is sealed and the experiment is activated. A moment later, the gas either has been released or has not been released. The question is, without looking, what has happened inside the box. (This is reminiscent of Einstein’s unopenable watch).
According to classical physics, the cat is either dead or it is not dead. All that we have to do is to open the box and see which is the case. According to quantum mechanics, the situation is not so simple.
The Copenhagen Interpretation of Quantum Mechanics says that the cat is in a kind of limbo represented by a wave function which contains the possibility that the cat is dead and also the possibility that the cat is alive.fn12 When we look in the box, and not before, one of these possibilities actualizes and the other vanishes. This is known as the collapse of the wave function because the hump in the wave function representing the possibility that did not occur, collapses. It is necessary to look into the box before either possibility can occur. Until then, there is only a wave function.
Of course, this does not make sense. Experience tells us that a cat is what we put into the box and a cat is still what is inside the box, not a wave function. The only question is whether the cat is a live cat or a dead cat. But a cat is there whether we look at it or not. If we take a vacation before we look inside the box, it makes no difference as far as the cat is concerned. Its fate was decided at the beginning of the experiment.
This commonsense view is also the view of classical physics. According to classical physics, we get to know something by observing it. According to quantum mechanics, it isn’t there until we do observe it! Therefore, the fate of the cat is not determined until we look inside the box.
The Many Worlds Interpretation of Quantum Mechanics and the Copenhagen Interpretation of Quantum Mechanics agree that the fate of the cat is not determined for us until we look inside the box. What happens after we look inside the box, however, depends upon which interpretation we choose to follow. According to the Copenhagen Interpretation, at the instant that we look inside the box, one of the possibilities contained in the wave function representing the cat actualizes and the other possibility vanishes. The cat is either dead or alive.
According to the Many Worlds Interpretation, at the instant that the atom decays (or doesn’t decay, depending upon which branch of reality we are talking about), the world splits into two branches, each with a different edition of the cat. The wave function representing the cat does not collapse. The cat is both dead and alive. At the instant that we look into the box, our wave function also splits into two branches, one associated with the branch of reality in which the cat is dead and one associated with the branch of reality in which the cat is alive. Neither consciousness is aware of the other.
In short, classical physics says that there is one world, it is as it appears, and this is it. Quantum physics allows us to entertain the possibility that this is not so. The Copenhagen Interpretation of Quantum Mechanics eschews a description of what the world is “really like”, but concludes that whatever it is like, it is not substantive in the usual sense. The Many Worlds Interpretation of Quantum Mechanics says that different editions of us live in many worlds simultaneously, an uncountable number of them, and all of them are real. There are even more interpretations of quantum mechanics, but all of them are weird in some way.
Quantum physics is stranger than science fiction.
Quantum mechanics is a theory and a procedure dealing with subatomic phenomena. Subatomic phenomena, in general, are inaccessible to all but those with access to elaborate (and expensive) facilities. Even at the most expensive and elaborate facilities, however, we can see only the effects of subatomic phenomena. The subatomic realm is beyond the limits of sensory perception.fn13 It is also beyond the limits of rational understanding. Of course, we have rational theories about it, but “rational” has been stretched to include what formerly was nonsense, or, at best, paradox.
The world that we live in, the world of freeways, bathtubs, and other people, seems as remote as it can be from wave functions and interference. In short, the metaphysics of quantum mechanics is based upon an unsubstantiated leap from the microscopic to the macroscopic. Can we apply these implications of subatomic research to the world at large?
No, not if we have to provide a mathematical proof in each instance. But what is a proof? A proof only proves that we are playing by the rules. (We make the rules, anyway). The rules, in this case, are that what we propose about the nature of physical reality (1) be logically consistent, and (2) that it correspond to experience. There is nothing in the rules that says that what we propose has to be anything like “reality”. Physics is a self-consistent explanation of experience. It is in order to satisfy the self-consistency requirement of physics that proofs become important.
The New Testament presents a different point of view. Christ, following His resurrection, proved to Thomas (who became the proverbial “Doubting Thomas”) that He really was He, risen from the dead, by showing Thomas His wounds. At the same time, however, Christ bestowed His special favor on those who believed Him without proof.
Acceptance without proof is the fundamental characteristic of western religion. Rejection without proof is the fundamental characteristic of western science. In other words, religion has become a matter of the heart and science has become a matter of the mind. This regrettable state of affairs does not reflect the fact that, physiologically, one cannot exist without the other. Everybody needs both. Mind and heart are only different aspects of us.
Who, then, is right? Should disciples believe without proof? Should scientists insist on it? Is the world without substance? Is it real, but divided and dividing into countless branches?
The Wu Li Masters know that “science” and “religion” are only dances, and that those who follow them are dancers. The dancers may claim to follow “truth” or claim to seek “reality”, but the Wu Li Masters know better. They know that the true love of all dancers is dancing.
fn1 According to the complementarity argument, which is at the heart of the Copenhagen Interpretation, the latitude in the choice of possible wave functions exactly corresponds to (or at least includes) the latitude in the set of possible experimental arrangements, so that every possible experimental situation or arrangement is covered by quantum theory.
fn2 Each set of experimental specifications A or B, that can be transcribed into a corresponding theoretical description S A or S B, corresponds to an observable. In the mathematical theory the observable is S A or S B; in the world of our experience the observable is the possible occurrence (coming into our experience) of the satisfied specifications.
fn3 The particle is represented by a wave function which has almost all of the characteristics (when properly squared, to get a probability function) of a probability density function. However, it lacks the crucial feature of a probability density function, namely the property of being positive.
fn4 From the pragmatic point of view, nothing can be said about the world “out there” except via our concepts. However, even within the world of our concepts particles do not seem to have an independent existence. They are represented in theory only by wave functions and the meaning of the wave function lies only in correlations of other (macroscopic) things.
Macroscopic objects, like a “table” or a “chair”, have certain direct experiential meanings, that is, we organize our sensory experiences directly in terms of them. These experiences are such that we can believe that these objects have a persisting existence and well-defined location in space-time that is logically independent of other things. Nonetheless, the concept of independent existence evaporates when we go down to the level of particles. This limitation of the concept of independent entity at the level of particles emphasizes, according to the pragmatic view, that even tables and chairs are, for us, tools for correlating experience.
fn5 What we can predict is the probability corresponding to any specification that can be mapped into a density function. Accurately speaking, we do not calculate probabilities at points, but rather transition probabilities between two states (initial preparation, final detection), each of which is represented by a continuous function of x and p (position and momentum).
fn6 The state of a system containing n particles is represented at each time by a wave function in a 3n dimensional space. If we make an observation on each of the n particles the wave function is reduced to a special form—to a product of n wave functions each of which is in a three-dimensional space. Thus the number of dimensions in the wave function is determined by the number of particles in the system.
fn7 To see the conciseness of mathematical expression, consider that the entire process described in the Theory of Measurement, from photon (system, S) to detectors (measuring device, M) to technician (observer, O) can be represented mathematically by one “sentence”:
fn8 The Theory of Measurement presented here is essentially from John von Neumann’s 1932 discussion.
fn9 The wave function is the physicist’s description of reality. At issue is the interpretation of the wave function and whether it is the best possible description (or simply the only one that fits the language used by physicists).
fn10 The wave function, since it is a tool for our understanding of nature, is something in our thoughts. It represents certain specifications of certain physical systems. Specifications are objective in the sense that scientists and technicians can agree on them. However, specifications do not exist apart from thought. Also, any given physical system satisfies many sets of specifications, and many physical systems can satisfy one set of specifications. All of these characteristics are idea-like and, to that extent, that which is represented by the wave function is idea-like, even though it is objective.
However, these specifications are transcribed into wave functions that develop according to a determined law (the Schrödinger wave equation). This is a matter-like aspect. The thing that develops describes only probabilities. Probabilities can be thought to describe either things that exist apart from thought, or things that exist only within thought. Thus that which the wave function represents has both idea-like and matter-like characteristics.
fn11 “How is one to apply the conventional formulation of quantum mechanics to the space time geometry itself? The issue becomes especially acute in the case of a closed universe. There is no place to stand outside the system to observe it.”—Hugh Everett III (Reviews of Modern Physics, 29. 3. 1957, 455).
fn12 In practice, it is not clear that a macroscopic object such as a cat actually can be represented by a wave function due to the dominating influence of thermodynamically irreversible processes. Even so, Schrödinger’s cat long has illustrated to physics students the psychedelic aspects of quantum mechanics.
fn13 The dark-adapted eye can detect single photons. All of the other subatomic particles must be detected indirectly.