Science in Christian Perspective

Reality According to Quantum Mechanics
Richard H. Bube
Department of Materials Science and Engineering
Stanford University
Stanford, California 94305

From: JASA 36 (March 1984): 37-39.

"Local hidden variables theory is dead." These are the first words of an article by theoretical physicist Fritz Rohrlich of Syracuse University.¹ In this article he takes a look at the current state of quantum mechanics, some of the philosophical interpretations that have been spun off, and the current thinking of physicists themselves that gives no support for some of the bizarre quasi-religious implications so frequently claimed, In this communication, I summarize in a brief way some of the more significant of these inputs.

Although public recognition of the fact is low, the philosophical implications of quantum mechanics have often been perceived at a similar level of significance for theology as the much more popularly aired debate between creation and evolution. The reason for this is that the implications of quantum mechanics suggest a basic stratum of chance events underlying all of reality, a situation that may be conceived of as the antithesis of divine control and sovereign action This is certainly a much more basic ground of possible conflict between science and religion than creation and evolution, which at least may be cast into a disagreement about mechanisms and processes rather than about the fundamental nature of physical reality. This so offended the religious sensitivity of Albert Einstein that he never did accept quantum mechanics as complete,"^2,3 and his summary statement that "God does not play dice" has become famous. When several attempts on the part of Einstein to point out errors in Niels Bohr's interpretation of quantum mechanics failed, Einstein retreated from the position that the theory was in error, to the position that the theory was incomplete: i.e., that there were "hidden variables" underlying the apparently chance phenomena, which if known, would convert the theory into a deterministic one once again.

Two kinds of hidden variable theories have been proposed. The first of these can be called a "local hidden variables theory," so-called "Einstein locality," which holds that if two particles are spatially separated, then a measurement on one of these particles in no way affects the other. Since signals cannot travel faster than the speed of light, if the two particles are sufficiently separated in space, there will be no possibility of communication between them. This form of local hidden variables theory can be experimentally tested against quantum mechanics, since they predict different outcomes for a suitable experiment. A suitably defined correlation S between the two particles has been shown to be less than or equal to 2 if hidden variables theory is adopted (the so-called "Bell's inequality"⁴), whereas values of this correlation larger than 2 are possible according to quantum mechanics. In 1982 experiments were carried out in Paris using the polarization of two photons as the experimental parameter.^5,6 The results appear to have unambiguously refuted the hidden variables theory satisfying Einstein locality. Hence the opening words of this communication.

"Nonlocal hidden variables" theories have also been proposed, first by Bohm^7-9 and then by others."^10,11 They have been constructed to give the same results as quantum mechanics, and at the present time there is no way to distinguish between nonlocal hidden variables theories and quantum mechanics itself. As long as the nonlocal hidden variables theories remain untestable, they do not really enter into the meaningful realm of scientific theories. For them to achieve this status, it must be demonstrated that they are able to account for some experimental result that quantum mechanics is unable to deal with. Present trends do not suggest that this deterministic nonlocal hidden variables theory is likely to gain the advantage over the probabilistic quantum mechanics. Indeed, quantum field theory, a generalization of quantum mechanics developed to be consistent with special relativity, is even more probabilistic than quantum mechanics; e.g., in quantum mechanics one can speak of measurements at a precise time, whereas in quantum field theory one can speak only of measurements made in finite time intervals.¹²

Claims have been made that the new understanding of reality afforded us by quantum mechanics either without or with nonlocal hidden variables provides us with philosophical (and even theological) insights that we have not previously had. A number of books have appeared proposing that the new physics provides the basis for correlation with Eastern philosophy^13,14 and with a holistic metaphysics that sees the universe as a single giant organism.¹⁵ Nobel Laureate Eugene Wigner has sought to relate physical reality to human consciousness.¹⁶ it is appropriate that we stop and ask for the best assessment of these claims at the present time.

1. Quantum mechanics applies to aspects of reality that are not part of our everyday experience. Although most of this experience deals with the microscopic atomic and nuclear aspects of reality, it is not limited to these aspects: phenomena in superconductivity and superfluidity, as well as the quantum phenomena measured in the Paris experiments, can be observed in the macroscopic world. Just as the realization of the finiteness of the speed of light, c, caused us to make major changes in our everyday thinking about reality (such concepts as simultaneity and addition of velocities), the realization of the finite value of Planck's constant, h > 0, causes us to make major changes in our everyday thinking about quantum reality.

2. Physical theories are approximate descriptions of reality with limited validity. Sometimes this range of validity appears to encompass most of our macroscopic experience, and it is hard to accept the fact that it does not also encompass areas beyond our macroscopic experience. We must be prepared to accept the fact, however, that pictures and descriptions adequate for everyday experience may well not be adequate at all for areas of reality beyond everyday experience.

3. The quantum world differs from the everyday world (commonly called "the classical world") qualitatively as well as quantitatively. The basic particles of the quantum world, such as electrons, protons, photons etc., cannot be distinguished one from another. There is no way that we can label a particular electron and follow it; all electrons look alike-they are indistinguishable. Common language derived from our everyday experience often fails us in the quantum realm; classically we know what "particles" are and what "waves" are, but we do not know what an "electron" is, which sometimes behaves "just like a particle" and sometimes "just like a wave" depending on the experimental situation.

4. In order for us to measure the quantum world effects we must use a "classical" apparatus. We arrive at a measurement of quantum effects only after the quantum effects have left a permanent record in our classical measuring apparatus, e.g., a visible track on a photographic plate due to the passage of an electron. Human evaluation of this observation through the human consciousness occurs last of all and totally within the classical domain. It does not seem possible, therefore, for the human consciousness to play any role in determining the behavior of the electron itself.

5. The measuring apparatus plays a significant role in the total experimental system. Unlike the classical situation, where the measuring apparatus can be considered almost totally independent of the effect being measured, in the quantum realm the system apparatus interaction can play an important role.

6. Unlike the classical system for which all observables can be known at the same time with arbitrary precision (in principle), each quantum system is characterized by a set of observables that can be known with arbitrary precision and another set of observables that cannot. The latter can occur with various different values; which of these values will occur in a measurement is precisely given by a probability distribution. An imperfect analogy is given by the sum of the faces of two dice; this sum can take on a variety of different values and the probability of a given value for the sum can be precisely given by a probability distribution (we know, for example, that the sum "T' will occur six times more often than the sum "T' or " 12"). If we consider two observables, one from the set that can be known (e.g., momentum if the system is in a given energy state), and one from the set that cannot be known (e.g., position), it follows that both momentum and position cannot be precisely known-leading to the well known Heisenberg Indeterminacy Principle. An analogy is given by our inspection of a famous masterwork painting: if we use a high power magnifying glass to look at the details of the brush strokes, or if we use our eyes when standing back a distance of 10 feet, we get different information in the two cases, which cannot be obtained simultaneously. Both pieces of information are necessary to describe the painting totally; they are said to be "complementary." ¹⁷

7. Changes in the state of a quantum system are not described in a probabilistic mode: the state of the system changes according to the deterministic Schroedinger equation and is uniquely given by the knowledge of its initial state. If interactions occur between this system and another system, then of course changes occur that can be calculated only by taking into account both systems and their mutual interaction. When a system changes, then in general so do the set of observables that can be determined with arbitrary precision. A measurement constitutes such an interaction.

8. Our inability to know precisely is not the consequence of our inability or imperfection, but rather simply because the requested information is not present in the particular state of the system. This occurs when the observable has a distribution of values in that state of the system, rather than being capable of precise determination. This distribution can indeed be known precisely.

9. The major difference between a quantum probability distribution and a classical probability distribution is that the quantum distribution is the square of a sum of probability amplitudes (coherent superposition of states) whereas the classical distribution is a sum of the squares of probability amplitudes (incoherent superposition), i.e., quantum: (A + B + C)' vs classical: (A 2 + B 2 + C'). This fact means that in the quantum case it is possible that the probability for two different values of an observable to occur can interfere with one another, something that is impossible in the classical case. It is this interference that accounts for the difference between the local hidden variables interpretation and the quantum mechanical interpretation of the Paris experiments.

10. The situation that an observable has a distribution of values will be encountered whenever we measure an observable that does not have precise values in a particular system. The system and the measuring equipment enter into interaction according to the quantum mechanical treatment until finally one of the states of the system being measured leaves a permanent record in the measuring equipment," e.g., a photographic track or a needle position. This position cannot be predicted for a single experiment, but the precise relative probabilities for all pointer positions can be calculated from quantum mechanics and can therefore be checked experimentally in a large number of measurements. Our imperfect analogy of throwing dice can again be invoked; before the dice are thrown the probability of obtaining a "T' is 6/36, but after the dice are thrown the probability reduces to either I (a "T' is thrown) or 0 (a "T' is not thrown).

11. Reality is not created by the measurement. A quantum mechanical system exists in a real state before the interaction with the measuring equipment. Two dice are real before they hit the table. Reality is not created by the observation; the system is present all the time. The claim that quantum mechanics requires us to believe that the universe does not actually exist "out there" independent of the observer, but rather is created by the observer, has no necessary support from quantum mechanics.

12. There are certain questions about quantum mechanical systems that have no answers. We can be seriously misled by our efforts to describe quantum mechanical effects using words from common experience that do not apply. The question of where the photon comes from when a electron drops from an excited state to the ground state of the hydrogen atom, for example, has no answer. An analogy would be the calculation of reflection from a highly absorbing medium using the classical wave model for light; the model gives accurate values for the reflection but is totally incapable of answering questions about what happens in the material to cause reflection. To get meaningful answers of a scientific model, one must ask questions consistent with the nature of that model. If we insist that quantum mechanics must supply the same kind of answers as classical physics, we have made the decision that classical question answering must be normative.

13. Physical reality on the quantum level cannot be defined in classical terms. The world of electrons, protons, photons etc. exists "out there" quite independent of us, and behaves (as far as we know today) exactly the way that quantum mechanics describes. The addition of probability amplitudes characteristic of quantum mechanics, rather than the addition of probabilities characteristic of classical physics, constitutes a qualitative difference between the classical and quantum worlds. This difference must be accepted as indicative of the actual properties of the natural world at the quantum level, just as the universal constancy of the speed of light is accepted as indicative of the actual properties of the natural world at the relativistic level. There is no known scientific reason today that would cause one to deviate from this position.

¹Fritz Rohrlich, "Facing Quantum Mechanical Reality," Science 221, No. 4617, 1Z51 (1983).

⁶A. Aspect, J. Delibard, and G. Roger, Phys. Rev. Lett. 49,1804 (1982). 

⁷D. Bohm, Phys. Rev. 85, 166, 180 (1982).

⁸D. Bohm, Causality and Chance in Modern Physics, Van Nostrand, Princeton, N.J. (1957).

⁹D. Bohm, Wholeness and the Implicate Order, Routledge and Kegan Paul, London(1980).

¹⁰For a review see F.J. Belinfante, A Survey of Hidden Variables Theories, Pergamon, N.Y. (1973)~

¹¹For a review see M.Jammer, The Philosophy of Quanturn Mechanics, John Wiley & Sons, N.Y. (1974).

¹⁴ G. Zukav, The Dancing Wu-Li Masters: An Overview of the New Physics, Morrow, New York (1979).

¹⁵V.S. Owen, And the Trees Clap Their Hands, Eerdmans, Grand Rapids, Michigan (1983).

¹⁶E.P. Wigner, Symmetries and Reflections, Indiana Univ. Press, Bloomington, (1967).

¹⁷JW. Haas, Jr., "Complementarity and Christian Thought-Xn Assessment," journal ASA 35,145, 203 (1983); R.H. Babe, "The Appeal (the Necessity?) of Complementarity," journal ASA 35, 240 (1983).