In contrast with classical physics, in which the results of an observation are implicit in the theory itself, quantum theory requires an interpretation to relate the theory to an observation.
6.1.1. Interpretation in terms of an external, objective reality
Most physicists think that quantum mechanics is not complete without an interpretation in terms of an external, objective reality. There are at least three general categories of objective interpretation:
a) Quantum theory is either incorrect or incomplete as it stands because it must be modified to describe the process of observation or it must be supplemented to include the phenomenon of wavefunction collapse. The "orthodox" interpretation belongs to the latter category.
b) Quantum theory is correct but incomplete as it stands. It must be supplemented by the addition of "hidden-variables", i.e., the positions and velocities of all of the particles at all times. In this interpretation, the particles are always present. The wavefunction is no longer interpreted as a probability, but is the source of a quantum force (also a hidden variable) which acts on the particles in addition to all of the classical forces like the electromagnetic and gravitational forces.
c) Quantum theory is as correct and as complete as possible. This leads to the "many-worlds" interpretation.
6.1.2. Interpretation in terms of subjective knowledge
On the other hand, some physicists assert that, if there is an objective reality, it is not described by quantum theory. They think the theory can be used only to calculate the probabilities for the different possible outcomes of any given observation. To them, this is the only interpretation that quantum theory has. This can be called a subjective interpretation because the wavefunction reflects only our knowledge of a situation rather than describing an objective reality.
In this interpretation, before an observation there are no particles, only a wavefunction that is a complete description of the system, i.e., no other information about the system is possible. At the moment of observation, the wavefunction must change from a probability wave that includes all of the possibilities that existed before the observation to one that describes only the possibility that is observed. This is called reduction, or collapse, which is not explained by the theory. In this interpretation, the wavefunction is the only external, objective reality that exists prior to a observation.
The orthodox interpretation is also called the Copenhagen interpretation because it was formulated at Niels Bohr's Copenhagen institute in the 1920s. The absence of an objective reality is summed up in Bohr's statement, "There is no quantum world. There is only an abstract quantum description" (quoted in Nick Herbert's book, Quantum Reality (1985) p. 17), and in the statement of John Archibald Wheeler (1911- 2008, brilliant American theoretical physicist and cosmologist who coined the term "black holes"): "No elementary phenomenon is a real phenomenon until it is an observed phenomenon" (quoted in Herbert's book, p. 18).
(In this and the following two sections, we draw heavily on Chapter 11 of the 1990 book by Euan Squires, Conscious Mind in the Physical World.) We will first show that any system that is completely described by quantum theory cannot exhibit wavefunction reduction.
In order to do this in the most efficient manner, we will use a current symbolic notation that makes the description concise and precise. Do not let this frighten you--it is simply a notation, not higher mathematics. The notation will refer to a particular type of experiment with particles that have spin. The spin of a particle is related to its rotation. A macroscopic analog is a spinning top. We can say that if the top is spinning normally on a flat, smooth surface, the spin (like the top) is pointing down. If for some reason, the top flips so that it spins upside down (there are tops that do this), we can say the spin is pointing up. Particles with spin (like the electron) can have their spins pointing either up or down.
We start with an experiment in which an incoming electron is in a superposition of spin-up (+) states and spin-down (-) states. By superposition, we mean that the wavefunction is a sum of two terms, one describing the + state, and one describing the - state. The superposition sums all of the possible states of the system. This is an example of what is called a "pure" state. The notation we now introduce is called the Dirac "ket" notation. Instead of writing the wavefunction simply as y as we did before, we enclose it in ket brackets and write çy>. We use the same kind of notation for the + and the - states, and obtain
çy> = aç+> + b ç->
All this equation says is that the electron is a wavefunction consisting of a superposition of a spin-up component and a spin-down component. Here, çaç2 is the probability that an observation would see a spin-up particle, and çbç2 is the probability that it would see a spin-down particle. (These are written with absolute value signs because a and b are in general complex quantities. However, this detail need not concern us here.)
We now send this electron into a "Stern-Gerlach" apparatus, which is also represented by a Schrödinger wavefunction. This contains a nonuniform magnetic field which causes the ç+> component of the wavefunction to go upward and the ç-> component to go downward. Therefore, after the electron passes through the apparatus, the Schrödinger equation tells us that it is described by the pure state wavefunction
çy> = a ç+,up> + b ç-,down>
where it is obvious that ç+,up> goes up and ç-,down> goes down. This wavefunction is not arbitrary--given the initial state wavefunction and the characteristics of the Stern-Gerlach apparatus, the Schrödinger equation dictates this form. We now send the electron into a detector, which records "on" if the ç+> component is detected and "off" if the ç-> component is detected. (The labels "on" and "off" are purely arbitrary. They could also be called, e.g., "1" and "2".) To make this clear, a diagram is shown below.
We assume that the detector, like the rest of the system, is described by the Schrödinger equation. We must then include the states of the detector in the wavefunction, and the pure state becomes
çy> = a ç+,up,on> + b ç-,down,off>
This leads to a very important conclusion. Any object in the system that can be described by the Schrödinger equation must be included in the superposition of terms describing the system. The Schrödinger equation always converts a pure state into a pure state. A pure state wavefunction will always be a superposition, which means that there is a probability of finding the system in either state.
Reduction, or collapse, of the wavefunction requires going from a pure state consisting of a superposition to a final state consisting of only one term because the reduced wavefunction must describe the detector being in either one state or the other, but not both. Therefore, no object that can be described by the Schrödinger equation can reduce the wavefunction, i.e., make an observation.
Now suppose that I look at the detector and that I also can be described by the Schrödinger equation. Two components are needed to describe me, which we will call me+ and me-, with the obvious connotations. The final wavefunction will be the pure state,
çy> = a ç+,up,on,me+> + b ç-,down,off,me->
However, if I am aware of the final state of the detector, this wavefunction cannot describe the combined system since I know that the detector is either in the "on" state or the "off" state. Something that cannot be described by quantum mechanics has reduced the wavefunction to the observed state only. If we assume that any physical system can be described by quantum mechanics, then reduction must have been caused by something nonphysical. The obvious nonphysical attribute that I possess is consciousness.
In the Schrödinger cat paradox of Section 4.2, I observe the cat in either the live state or the dead state, not both. If consciousness reduces the wavefunction, it is either my consciousness or the cat’s that does it. It is a metaphysical question which of the two consciousnesses it is because what I see when I open the box will be exactly the same in both cases.
Because most physicists are materialists and believe that consciousness is at most an epiphenomenon, they do not like to admit that consciousness is needed to reduce the wavefunction. Rather, they prefer to think that it is some physical property of macroscopic devices that causes reduction. Of course, if that is the case, that property at present cannot be described by quantum theory, so to them, quantum theory is presently incorrect. (However, inconsistently, most do not believe that to be true, either.)
In the orthodox interpretation, wavefunction reduction defines the forward direction of time because the reduced state is irreversible. This is true for both microscopic and macroscopic systems. Recall from Section 2.3 that, in classical physics, the second law of thermodynamics determined the forward direction of time because macroscopic natural processes are statistically irreversible. In classical physics, irreversibility is a property of a system whether or not it is observed, while in the orthodox interpretation, irreversibility is a result of observation itself.
In this section, we shall assume the orthodox interpretation. We suppose that we have a Stern-Gerlach experiment with two detectors instead of one, as shown in the figure below. One detector is set up to record the ç+,up> part of of the wavefunction, and the other is set up to record the ç-,down> part. The detectors may be arbitrarily far apart. At the instant of wavefunction collapse, what prevents both detectors from simultaneously recording the electron? This example shows that no local process can collapse the wavefunction because such processes cannot prevent simultaneous coincidences between the detectors. Hence, we must conclude that wavefunction collapse cannot be produced by any known physical process (which are all local). (This result also can be inferred from the Bell-Aspect experiments, see Section 4.3.) Since the wavefunction collapses over all parts of space simultaneously, it is an intrinsically nonlocal phenomenon. Thus, any interpretation of quantum theory requiring wavefunction collapse is not consistent with a local theory of reality, such as the philosophies of materialism or scientism (see Section 1.2).
Now suppose there are two observers, you and I (see figure below), so that you observe the ç-,down> state while I observe the ç+,up> state. Then when I observe my detector to record "on", you must observe your detector to record "off" because there is only one electron. Thus, if consciousness collapses the wavefunction, your consciousness cannot be different from my consciousness. Therefore, there can be only one consciousness, so consciousness must be nonlocal.
This conclusion can be illustrated in a much simpler example than the experiment described above. We still assume that an object is represented by a wavefunction prior to an observation. Now suppose two observers make simultaneous observations of the same object whose color is unknown before the observation. In this case all possible colors must be represented in the wavefunction of the object before it is observed. Then why do both observers observe the same color rather than one observer observing, for example, a red object and the other observing a blue object? If consciousness collapses the wavefunction, the answer must be that the consciousness of both observers is the same consciousness. Thus, the consciousness of all sentient observers is the same nonlocal universal consciousness.
Now let us consider the same example without reference to quantum theory. As before, let us assume that all objects are observer-created rather than existing in an objective sense, but now there are no wavefunctions before observation. It is easy to see that the consciousness of the observers must be universal consciousness if both observers are to see the same object. Thus, whenever we assume that objects appear only as mental images, not as independently existing objects, the consciousness of the individual observers must be universal consciousness. Of course, in this example, even the observers themselves must be mental images.
In everyday life, we think that different observers see the same object because the objects are objectively present. Thus, we are unaware that universal consciousness is the only consciousness that is operating.
| Question: Assume there is no objective reality. You see
a red object and I see a green object. What is a possible resolution of this conflict? |
One reason we abandoned classical particles was because we showed they could not go through two slits at once and produce interference, whereas waves could (see Section 4.1). But interference is possible with classical particles if there is also a wave present. A theory that includes both is the hidden variable theory developed by David Bohm (1917 - 1992) [brilliant, unconventional American-Brazilian physicist who left the U.S. never to return after being blacklisted in 1949 by Senator Joe McCarthy during the anticommunist hysteria, was arrested and charged with contempt of Congress after pleading the Fifth Amendment and refusing to recant his Marxism, was fired by Princeton University, was later acquitted by the court but lost his American citizenship]. This is the best developed and best known of the hidden variable models. This model is fully deterministic and assumes that the particles are classical and are subject to classical forces (which are all local). However, they are also subject to a quantum force that is derived from a wavefunction. [To be more accurate, there is a quantum potential that is derived from the wavefunction, and the quantum force is derived from the quantum potential.] The wavefunction is now not a probability wave. Since the particles are assumed to be classical, their positions and velocities are always definite, even before an observation. Contrary to the orthodox interpretation, the wavefunction in the hidden-variables interpretation is not a complete description of the system because the particle positions are also required. In the initial state, the wavefunction specifies the actual distribution of particles in space, not just a probability. The time development of the wavefunction is then described by Schrödinger’s equation, as in ordinary quantum theory.
Although the wavefunction now has a different interpretation, it is mathematically identical with that in orthodox quantum theory and contains all parts of the waves, e.g., reflected and transmitted parts, or the parts going through different slits, even if none of the particles follow those paths. (A peculiarity of the quantum force is that it can be very large even where the wavefunction is very small.) Since the wavefunction, and therefore the quantum force, depends on all parts of the experimental apparatus (e.g., in a two-slit experiment), so do the particle trajectories, even though trajectories and apparatus may be quite distant from each other. The result is that the quantum force from all parts of the apparatus acts simultaneously on all of the particles--hence, it is nonlocal.
Since classical particles exist in a hidden-variables interpretation, there is no wavefunction collapse, and therefore it is not necessary to introduce consciousness into the interpretation. Hence, hidden-variables theories are consistent with scientific materialism (see Section 1.2). They are examples of "realist" theories because they assume that the particles are real particles, not just quantum waves.
The Bohm theory is not the only possible hidden-variables theory. However, we have already seen that the Aspect experiments excluded all local hidden-variables theories, while the Gröblacher experiments excluded most hidden variables theories whether they are local or not (Section 4.3). Because of these experiments, we shall conclude that it is not likely that hidden-variables theories describe reality.
This interpretation was invented by Hugh Everett (1930-1982) in 1957 so that cosmologists could apply quantum theory to the entire universe at the time of its origin. According to accepted cosmology, the universe exploded from a point at the time of the big bang, approximately 14 billion years ago. Early on, the universe was so tiny and its density was so high that its gravitational forces were enormously high. In such conditions, gravity cannot be treated classically so it must be described quantum mechanically. Even though as yet we have no quantum theory of gravity, we do think that the initial universe must be described by a wavefunction. The universe by definition includes everything, so there can be no outside observers. However, without observers, there can be no wavefunction collapse, so quantum theory is assumed to be correct without any corrections or additions.
Let us now look at the Stern-Gerlach experiment in the light of the many-worlds interpretation. We return to the wavefunction that describes my observation of the detector:
çy> = a ç+,up,on,me+> + b ç-,down,off,me->
There can be no reduction of the wavefunction now. Both terms must describe reality. The many-worlds interpretation says that at the moment of an observation, the world splits, or branches, and that both branches continue after the observation. There is a me in both branches. This interpretation maintains that in each branch, the me in that branch is aware of only the observation that it made. Since in my world, I am aware of only one result, I exist only in my branch. In the other branch, the other me is aware of the other result. The two branches do not communicate with each other, so the two mes are unaware of each other.
[Technical note: Assuming all of this to be true, what then is the interpretation of a and b? The probabilistic interpretation of quantum theory says that çaç2 and çbç2 are the statistical probabilities of each outcome. These probabilities can be measured only by making many observations on identical systems. What can they mean here when we have only one system (the universe)? Bryce S. de Witt in 1970 proposed the following interpretation. In the first trial of such an experiment, both branches result from the observation. If I now make many observations with my apparatus in my branch, I will measure probabilities that agree with çaç2 and çbç2. At each observation, there will be another branching, which will result in this me being in my branch, and another me being in another branch. If each of these other mes continues the observations, he will also measure probabilities which agree with çaç2 and çbç2.]
It is easy to see that the number of branches rapidly proliferates as the observations continue. In addition, most observations on most types of systems will result in not just two branches, but many more, as many as are allowed by Schrödinger’s equation. In fact, the number of branches at each observation is usually infinite. Also, like orthodox theory, many-worlds theory is nonlocal because all parts of an entire branch (world) are materialized simultaneously.
While the many-worlds interpretation is very economical in terms of the number of concepts required in the theory, it is grossly extravagant in terms of the complexity of the world it describes. Furthermore, the existence of the other branches is intrinsically unverifiable--they are hypothesized merely to preserve the mathematics of quantum theory. It is these features that most physicists find hard to accept.
In the many-worlds interpretation, after a branching, I am in only my branch, and I observe only my branch. As far as I am concerned, the other branches are not materialized. The advantage of many-worlds is that the unobserved branches can still be described by wavefunctions even though they are not observed. Thus, quantum theory does not require any mysterious reduction mechanism to get rid of the unobserved wavefunctions, even though some mysterious mechanism is required to materialize my branch. Cosmologists think this mysterious mechanism could be epiphenomenal consciousness that arose after the wavefunction evolved into enough complexity (this assumes that space-time is objectively real). If we stipulate that the unobserved branches remain unmaterialized, the many-worlds and orthodox interpretations are very similar, and for our purposes can be considered to be equivalent.
In Section 6.5, we saw that all quantum systems are nonlocal, not just those of the Aspect and Gröblacher experiments that were described in Section 4.3. Because orthodox quantum theory cannot explain nonlocality, we see that it is either incorrect or incomplete, as was mentioned in Section 6.1. Furthermore, since both hidden-variables and many-worlds theory also are nonlocal, and neither can explain nonlocality, physics has no explanation whatsoever for it. (This is reminiscent of Gödel’s theorem, which we discussed in Section 5.6.) Thus, we must now begin to question our assumptions about the reality of space and time. We shall say more about this in Section 7.1 and Chapter 12.
As we have seen in Sections 6.4 and 6.5, if it is consciousness that collapses the wavefunction (or that materializes a branch as in Section 6.7), then consciousness must be nonphysical. If it is nonlocal universal consciousness, we are faced with some other far-reaching conclusions. What two individual observers see is determined by universal consciousness, not by any kind of individual consciousness that might exist. This applies to all of our sensory perceptions without exception. Since everything we perceive is determined by universal consciousness, it makes no sense to say that there is a material world independent of consciousness. Thus the dualism of mind and matter is excluded.
It is only a small step now to suppose that, if all of our sensory perceptions are determined by universal consciousness, then so also are all of our thoughts and feelings because there is no intrinsic difference between them (as we shall see in Chapters 9 and 23). If all experiences are determined by universal consciousness, then we must conclude that nothing in our lives that we consider to be "ours" as individuals is truly ours. If everything flows from universal consciousness, "our" lives are not our lives at all but are lives of universal consciousness. "My" consciousness cannot really be mine, nor can there be any free will if none of "my" thoughts is mine. Even the thought that I exist is not mine. With these astounding conclusions, we are forced to ask the questions, "Do I really exist?", and, "What am I, really?" We shall consider these questions later in the course.
| Question: If you really knew that you are universal, nonlocal consciousness, could you still suffer? |
As we saw in Section 4.1, interference suggests that physical waves are interfering, whether or not they are identified with the wavefunction. Identifying them with the wavefunction is tempting because they produce the same kind of interference pattern that the wavefunction would produce were it a physical object. Yet, this leads to the nonphysicality of nonlocality. Perhaps this dilemma is Nature’s way of hinting to us that there is no such thing as external, physical reality.
In Section 6.1.2, we mentioned the possibility that the wavefunction is not a physical wave but is merely a tool for calculating the probabilities for certain specified events to occur. If this is so, there is no external quantum wave either before or after an observation. Since the wavefunction reflects only our knowledge of a situation and nothing more, we can call this a subjective interpretation.
A few physicists hold this viewpoint because it avoids all of the problems of nonlocality. [Note to physicists: For a discussion of this, see the article by Christopher Fuchs and Asher Peres, "Quantum Theory Needs No 'Interpretation'", in Physics Today, March 2000, pp.70, and "Letters" in Physics Today, September 2000, pp. 11.] These physicists do not deny the possibility of the existence of an external reality independent of what observers perceive, but they do not state what its significance would be.
Assuming there is no external reality, our concepts of nature are limited by the kinds of experiments we do and by the type of theory that we use to interpret them. Our present picture of the microscopic world as consisting of atoms, molecules, and elementary particles is determined in an essential way by these limits. Radically different kinds of experiments and theories might produce a radically different kind of picture.
As we discussed in Section 1.1, it is clear that the existence of an external reality can never be proved nor disproved, and thus can only be a metaphysical assumption. If it makes no difference whether or not an external reality exists, it can have no effect on any observation. Thus, the concept of an external reality is superfluous. However, even though an external reality can itself have no effects, the concept of one certainly can. In fact, in Chapter 9 we shall see that it is this concept that causes all of the suffering there is.
It is ironic to think that the careful, painstaking, empirical and theoretical study of external physical reality, which is what we call physics, could lead to the conclusion that there is no such reality! It appears that the hypothesis of external reality contains the seeds of its own destruction! What physicists really do is to study their own minds because that is the only place where objects are present. Perhaps the domain of physics will some day shift from objectivity to subjectivity, and physicists will begin to welcome the sages as friends rather than viewing them with suspicion.
| Question: Assuming that there is no consciousness but nonlocal universal consciousness,can there still be more than one mind? How would we know? (See the discussion of solipsism and nonsolipsism in the questions at the end of Section 4.3.) |