Interpretation Of Quantum Mechanics

Type of physical science: Atomic physics

Field of study: Nonrelativistic quantum mechanics

Quantum mechanics is one of the most successful theories in the history of science. Fundamental questions regarding its interpretation remain open, and their investigation casts new light on some of science's most basic presuppositions.

Overview

Quantum mechanics is undoubtedly one of the most successful theories in the history of science. Its predictions have been confirmed for a wide range of phenomena, from the level of the most fundamental elementary particles to that of molecules and further. The enormously successful theories of quantum electrodynamics, quantum chromodynamics, and quantum field theory in general have all been developed within its theoretical framework. In spite of its successes, however, profound questions arise regarding the nature of the reality that the theory describes. This is the problem of interpretation.

Consider the electron, for example. When a stream of electrons is sent through two narrow slits placed closely parallel to each other, a pattern of bands of minimum and maximum intensity can be seen. Such an "interference pattern" is generally associated with wavelike phenomena, such as light, and is typically explained in terms of wave-trains passing through each slit and producing dark and light fringes by mutual reinforcement and cancellation. As generally understood, the formalism of quantum mechanics explains these results by associating with each particle a wave function that describes the state of the particle. These wave functions can be superposed, just as classical waves can. Yet, the squares of the amplitudes of the waves in quantum mechanics give, not the energy as in the classical view, but the "probabilities" that the electron will be found in a certain state. When an observation is made, the superposition is said to collapse and a determinate result is obtained, with a probability given by the mathematical formalism. Thus, in the above two-slit situation, where the amplitude of the resultant wave function is large, there is a higher probability that the electron will be localized and thus more electrons will be detected at that spot; where the amplitude is small, the probability and number observed are correspondingly small. Furthermore, it follows from this formalism that certain properties, such as position and momentum, cannot be simultaneously measured to an arbitrary precision. If an electron is localized at a certain spot, so that it can be said to have a well-determined position, for example, then its momentum is completely indeterminable.

Likewise, if a precise measurement of the momentum is made, then its position is indeterminable, and the electron can be thought of as revealing its wavelike aspect. This, in essence, is the famous uncertainty principle. It is important to realize that this is not the expression of some experimental limitation but follows from the mathematical formalism of quantum mechanics itself.

How are these formal results to be interpreted? How can an electron behave like a particle and like a wave? According to the standard view of quantum mechanics, these descriptions should be viewed as "complementary," in the sense that any experiment designed to reveal particle-like characteristics will, by necessity, preclude the simultaneous experimental detection of the wavelike ones. This notion of complementarity finds its mathematical expression in the uncertainty principle. The emphasis here is on the experiment and what can be observed.

On this view, it simply makes no sense to ask what the electrons are doing when they are not being observed--that is, when they are in a superposition of states.

This came to be known as the Copenhagen interpretation. Most of the physicists who work with quantum mechanics and have played a part in its experimental successes have adopted this interpretation. Nevertheless, there are some who are uncomfortable with its restriction to talking about what can be observed only. Scientists point out, for example, that the Moon is generally regarded as being in a certain location and following a certain path around the earth, even when it is not being observed. If the job of a theory is to say how the world is, both at the observable level and beyond, then quantum mechanics, understood in terms of the Copenhagen interpretation, is not being effective. This is the "realist" view. Thus, it has been claimed by those who hold this latter position that quantum theory is fundamentally "incomplete," in the sense that there are certain properties that exist in physical reality but that are not taken into account in the theory. This is the conclusion of the Einstein-Podolsky-Rosen argument (named for Albert Einstein, B. Podolsky, and N. Rosen).

According to the realist interpretation, a property possessed by a particle, such as an electron, is said to be real, in the sense of actually existing in the physical world, if its values can be predicted without disturbing the particle. Now suppose that there are two electrons that briefly interact before flying apart. There is nothing in quantum theory that prohibits the precise measurement of their total momentum and their distance apart at the time they interacted.

Knowing the total momentum, if the momentum of one electron is then measured, that of the other electron can be predicted on the basis of the principle of conservation of momentum.

Likewise, if the position of the same electron is measured precisely, then, knowing the momentum of the other electron and their original separation, the precise position of this second electron can also be predicted. In other words, assuming that the measurements made on one electron do not disturb the other--a condition known as "locality"--then the exact position and momentum of the distant electron can be predicted. Therefore, these quantities must exist in the physical world. According to quantum theory, however, an electron cannot simultaneously possess a precise position and a precise momentum; there is no counterpart to these quantities in the theory. Hence, the theory must be incomplete.

Various suggestions have been made as to how the theory could be completed. The most common suggestion is that quantum mechanics should be regarded in the same terms as classical statistical mechanics, that is, as giving nothing more than a statistical approximation of the particles' behavior. At a deeper level, however, this behavior is not statistical at all, or so it is claimed, but is governed by nonprobabilistic laws relating certain factors that operate at this more fundamental level of reality. These factors are then mathematically expressed in terms of so-called hidden variables that would effectively complete the theory.

Supporters of the Copenhagen interpretation claim that it is not completeness that should be given up but the basic understanding of reality that underlies the Einstein-Podolsky-Rosen argument. In terms of this understanding, the two electrons, after the interaction, can be regarded as two separate physical systems, and a measurement made on one allows the prediction of the values of certain quantities possessed by the other. Nevertheless, quantum mechanics implies that the two electrons cannot be regarded as separate in this manner; they are, in a fundamental sense, entangled. This results from the fact that they are in a superposition of states and until an observation is actually made, it is impossible to decompose this superposition into the individual components corresponding to the states of each electron.

Since the position and momentum of each electron are measured through a particular experimental set-up, it is the entire experimental arrangement that must be considered in the Einstein-Podolsky-Rosen argument. This arrangement represents the very conditions that define what predictions are possible, and it is simply illegitimate to talk about, or predict, measurements that can be achieved only through another, essentially different, experimental arrangement. Thus, on the Copenhagen view, the position and momentum of the second electron simply have no objective meaning until they are measured, no matter what is done to the first electron.

The disagreement, then, is essentially metaphysical, in the sense that it involves a fundamental difference in the conception of reality that is held. Nevertheless, a profoundly important mathematical result, known as Bell's inequality (named for John Bell), has effectively shifted the debate from the level of the metaphysical to that of the experimental. According to this result, on the basis of any plausible attempt to complete quantum theory in terms of introducing hidden variables, the values of certain properties, such as the spin, of two interacting particles should be statistically correlated in a definite way. The quantum mechanical formalism, on the other hand, predicts that the correlation will be completely different. Moreover, these correlations can be experimentally measured, and the results unambiguously favor quantum mechanics.

These experimental results have been taken to rule out any plausible hidden variables interpretation, and the supporters of the Copenhagen approach claim that their view has been vindicated. In response to such claims, however, it can be argued that what these observations actually reveal is the truly bizarre nature of quantum reality. Bell's inequality also assumes the locality condition--which states that measurements made on one particle cannot affect those made on another, separated from the first. The peculiar quantum mechanical entanglement, expressed through the superposition of states, clearly violates this condition, since the measurements made on one particle determine what measurements can be made on the other particle. The experimental violation of Bell's inequality demonstrates that the quantum world is nonlocal, in a fundamental and nonclassical sense. Therefore, it is claimed, what is required is a conceptual framework, or interpretation, that can accommodate this nonlocality without restricting discussion of what the world is like to the level of the observable only.

Applications

The bizarre nature of the view of reality offered by quantum mechanics is fully revealed through an interesting "thought-experiment" known as Schrodinger's cat (named for physicist Erwin Schrodinger). Imagine a cat placed in a box that contains a radioactive source, a Geiger counter, and a glass bottle containing cyanide, arranged in such a way that if the Geiger counter detects a radioactive decay, the bottle is broken and the cat dies. If no decay is detected, the cat lives. The counter is switched on only long enough for there to be a 50-50 chance that one of the atoms in the radioactive material will decay. The question is: Before the box is opened, and an observation made, is the cat alive or dead?

According to the quantum mechanical formalism, the atoms of the radioactive source, the counter, the bottle containing cyanide, and the cat are all in a superposition of states.

According to the Copenhagen interpretation, it is only when the box is opened and an act of observation takes place that the cat can be said to be either alive or dead. Yet surely, it may be objected, it is one thing to say that microscopic entities, such as electrons, are in peculiar, entangled superpositions, but quite another to say the same of familiar macroscopic things such as cats.

Nevertheless, experiments with macroscopically sized rings of superconducting material (about half a centimeter across) have provided evidence of these nonclassical superpositions. A circulating electric current in such a ring generates a magnetic flux. Under normal circumstances, this flux would be trapped within the superconducting ring and would have only one value. Yet, if the ring is interrupted by a thin slice of insulating material through which the electrons can "tunnel" (another quantum mechanical effect), the flux can change from one value to another. By measuring the magnetic flux extremely accurately, it can be shown that states of the ring can be prepared in which the flux is in a superposition of states and does not have a definite value, just as the cat is in a superposition of the states "dead" and "alive."

These quantum mechanical effects have suggested a number of practical applications, particularly in the fields of computer and laser technology. Clearly, as the field of microelectronics moves down to even smaller dimensions and pushes into the quantum domain, the interpretation of these effects assumes an ever greater importance. Progressing in the other direction, from the very small to the very large, quantum mechanics has come to play an important role in cosmological speculations about the origin of the universe. Here again, questions of interpretation arise.

Thus, for example, there is a view that states that in the case of Schrodinger's cat, there are, in fact, two cats in this situation, one alive and one dead, occupying different worlds. When the box is opened, one of the alternative worlds is effectively selected and becomes part of what is taken to be the "real" world. There is then no collapse of the superposition but rather a "splitting" of reality into alternative worlds every time an observation is made. Furthermore, it can be shown, on the basis of the quantum mechanical formalism itself, that these worlds must be inaccessible to each other, so that an observer never perceives the splitting. This "many worlds" interpretation sounds like something from a science-fiction novel, yet it is being seriously entertained by some cosmologists who see it as offering a way of understanding the early development of the universe immediately after the big bang. Another suggestion is that the big bang itself was nothing but a quantum fluctuation, created in accordance with the uncertainty principle, which subsequently "inflated" into the observable universe.

These are, admittedly, speculations, yet it may fairly be claimed that if quantum mechanics is going to be invoked to explain the origin of the universe and why it appears the way it does, then there is even more reason to come up with an interpretation of the theory that goes beyond the level of the observable to describing "how the world is."

Context

Philosophical problems arose at the very birth of the quantum theory and were a continuing source of concern as it grew and developed. Although many people contributed to this development, two physicists were key players: Erwin Schrodinger and Werner Heisenberg. In 1925, by explicitly following the empiricist line that a theory should be concerned only with what can be observed, Heisenberg laid down the basis of what came to be known as "matrix mechanics," in which the states of an atom, for example, are represented in terms of arrays of numbers standing for quantities that could be measured experimentally. This work was further extended in collaboration with Ernst Pascual Jordan and Max Born and, through the work of Niels Bohr (for whom Heisenberg worked as an assistant at the time of his discovery), became an integral part of the Copenhagen interpretation.

At the same time, Louis de Broglie suggested that electrons possessed a wavelike aspect. This idea was brought to Schrodinger's attention through a paper by Albert Einstein, and Schrodinger subsequently elaborated upon it in a series of papers published in 1926.

Schrodinger's wave mechanics soon ran into interpretational difficulties, however, as it was pointed out that the waves not only contained an imaginary component but also were multidimensional. Following Born's suggestion that the square of the amplitude of these waves at a given point was a measure of the probability of finding the article at that point, many physicists took up the Copenhagen point of view.

It was later shown by Paul Adrien Maurice Dirac, Carl Eckart, and Schrodinger himself that the formal structures of matrix mechanics and wave mechanics are, in fact, mathematically equivalent. Indeed, Dirac's quantum algebra contains both as special cases. Nevertheless, Schrodinger and Einstein continued to favor a more classical interpretation of the formalism, and together they insisted that, given their understanding of reality, the theory had to be incomplete in the sense of not being able to capture all aspects of that reality. This was the motivation behind Schrodinger's cat and the Einstein-Podolsky-Rosen arguments. The latter, in particular, arose as the result of an extended debate between Einstein and Bohr.

In 1964, John Bell published the theorem that bears his name, and almost twenty years later, in 1982, Alain Aspect and his coworkers performed the now classic experiment that demonstrated the inadequacy of any attempt to complete the quantum mechanical formalism in a physically plausible way. In the years following the publication of Bell's theorem, much interesting technical and philosophical work has been done. It has been shown, for example, that quantum mechanical nonlocality does not allow messages to be sent faster than the speed of light and hence that there is a peaceful coexistence between the theory and special relativity.

Philosophers characterize this nonlocality as "passion-at-a-distance." Clearly, for those who refuse to accept the Copenhagen interpretation and its injunction against talking of that which cannot be observed, the strange world of quantum mechanics remains open to future exploration.

Principal terms

COPENHAGEN INTERPRETATION: the standard interpretation of quantum mechanics, which claims that it makes no sense to ask what a particle is doing or what properties it has when it is not being measured or observed

LOCALITY: no influence can propagate faster than the speed of light

REALISM: the view that the aim of science is to describe how the world is in both its observable and nonobservable aspects

SUPERPOSITION OF STATES: prior to a measurement being performed, a quantum mechanical particle may be described as being in a wavelike superposition of its possible states

UNCERTAINTY PRINCIPLE: it is impossible, in principle, to measure precisely certain pairs of properties, such as position and momentum, simultaneously

WAVE FUNCTION: the square of the amplitude of a particle's wave function gives the probability of finding a particle in a particular state

Bibliography

D'Espagnat, Bernard. "Quantum Theory and Reality." SCIENTIFIC AMERICAN 241 (November, 1979): 158-181. Contains a detailed description of Bell's work and some of the early experiments that tested his results. D'Espagnat's discussion of the assumptions underlying the realist interpretation is particularly noteworthy.

Gribbin, John R. IN SEARCH OF SCHRODINGER'S CAT. New York: Bantam Books, 1984. An informal account of almost all aspects of quantum physics.

Covers the history of the subject and also some of its practical applications, from superconductivity to genetic engineering. Toward the end, Gribbin reveals his preference for the many worlds interpretation.

Herbert, Nick. QUANTUM REALITY. Garden City, N.Y.: Doubleday, 1985. Presents eight different models of quantum reality, or interpretations, that the mathematical formalism can support. There is also an amusing discussion, in baseball terms, of the Einstein-Podolsky-Rosen argument, together with a fictional conversation between Bohr and Einstein. Somewhat technical.

Jammer, Max. THE CONCEPTUAL DEVELOPMENT OF QUANTUM MECHANICS. New York: McGraw-Hill, 1966. A difficult work but one from which much worthwhile information can be gleaned, even if the mathematics is skipped. Jammer concentrates on the historical development of quantum physics but also emphasizes the accompanying philosophical difficulties.

Pagels, Heinz R. THE COSMIC CODE. New York: Simon & Schuster, 1982. Written by a theoretical physicist, this is a very readable account, not only of quantum theory but also of some of the more important theories involved in its development, such as statistical mechanics. There is a useful section, "The Reality Marketplace," and chapters on quarks, quantum field theory, and cosmology.

Powers, Jonathan. PHILOSOPHY AND THE NEW PHYSICS. New York: Methuen, 1982. This is a general introduction to some of the philosophical problems generated by the "new physics" of quantum mechanics and the theory of relativity. Although the discussion of the technical details is rather superficial, this is one of the few works accessible to the general reader that takes the philosophical issues involved seriously.

Shimony, Abner. "The Reality of the Quantum World." SCIENTIFIC AMERICAN 258 (January, 1988): 46-53. A philosopher with a background in physics, Shimony was a member of the group that proposed one of the first tests of Bell's theorem. This paper outlines the various tests that have been performed, including Aspect's, and the magnetic flux experiments. The results are discussed and the philosophical implications are clearly drawn.