J. Di Rienzi

College of Notre Dame of Maryland, Baltimore, Maryland


C. A. Hilgartner

Hilgartner & Associates, 254 Kensington Place, Marion, Ohio


The aim of physics is to understand phenomena in the physical universe. For physicists, this has come to mean the development of a quantifiable theory whose predictions can survive testing. But physicists also hold an unstated additional condition for an acceptable theory, that it be satisfying to them on aesthetic and intuitive grounds. In other words, they want it to make sense.


Against this premise we examine the great achievement of contemporary physics, quantum theory. In the sixty or so years since its development, quantum theory has become an important tool in the investigation of the structure of matter, the development of transistors, the understanding of superconducting materials, etc.


Quantum theory has however troubled proponents and opponents, both in and out of physics, for its entire history. Though experimentally confirmable, it rubs harshly against our "common sense" notions of reality. It uses mathematical constructs to predict observable quantities that have no associated physical reality. Its probabilistic nature seems to undermine the traditional thrust of science in seeking to "know" the physical universe. The participation of the observer in the event, while crucial and fundamental, is not understood in any rational sense.


A familiar way to illustrate these problems is to consider a double-slit experiment in which a stream of electrons from a single source passes through a barrier that has two small openings on the way to a distant fluorescent screen which can detect their positions. Looking at the flashes on the screen we see a pattern identical to a two-slit interference effect produced by monochromatic light -- a continuous distribution of intensity, featuring a progression of bright and dark areas. The interference pattern would still be observed even if the stream of electrons could be slowed to one electron at a time.


In quantum theory an electron is represented by a mathematical expression called a wavefunction. The evolution of the wavefunction represents the probabilities of the future positions of the electron. In the double-slit experiment the superposition of the probability of an electron passing through one hole with the probability of it passing through the other hole produces the observed interference pattern.

The effect is altered when detectors are placed at each hole to try to determine which one the electron actually passed through. In the physical act of making such a determination the interference pattern on the screen disappears, and is replaced by a pattern indicative of the electron either passing through one hole or the other. Once definite knowledge has been gained as to which hole the electron passed through, the wavefunction corresponding to the probability of passing through the other hole must be set equal to zero. Therefore, there is no longer a superposition effect, hence no interference pattern. Now the difficulty arises in that if we conclude that the wavefunction followed by the electron was real, the other must have no physical reality, but was retained as long as we did not know which wavefunction the electron would follow. If this is so, how can the wave interfere? How can a real wave interfere with an "illusion" to produce a real interference pattern?


Unable to resolve these difficulties, physicists have come to regard quantum theory as a formal set of operations, which when performed make predictions on the outcome of measurements. This "cookbook," with its inherent probabilistic nature, distressed Albert Einstein. He reluctantly granted that the theory was consistent, but never admitted that it was complete. Einstein, with the assistance of Boris Podolsky and Nathan Rosen (1935), searched for a "thought experiment" that, using additional conditions -- the so-called hidden parameters -- would enable them to make experimental predictions that would differ from those of quantum theory (and would survive testing), thus providing evidence of the incompleteness or inaccuracy of quantum theory.


John S. Bell (1964) devised such a test using correlations of spin components involving elementary particles. The "Bell inequality," which embodies local realistic theories of physics, can be proved through a straightforward argument in the mathematical theory of sets using, according to Bernard d'Espagnat (1979), three assumptions: (1) the existence of a physical reality independent of human observers; (2) the free use of mathematical inference in reasoning; and (3) Einstein separability, the premise that no influence can propagate faster than the speed of light. These assumptions are regarded by d'espagnat as local realistic theories of nature.


The Bell inequality leads to explicit predictions concerning the properties of elementary particles (and photons) that disagree with quantum theoretic predictions. Thus Bell's inequality provides the basis for a critical test: an experiment whose results would select between local realistic and quantum theories. In the last ten years real experiments of this nature have been performed and, although not all experiments have been in agreement, the most careful have cast doubt upon the Bell inequality and supported the quantum correlations. (Abner Shimony, 1988).


If we accept these results, where does that leave us in terms of the assumptions on which the Bell inequality is based? Clearly, they seem to invalidate at least one of the local realistic theories. But choosing among them is difficult, for each holds a cherished place in the constructs of science. The first assumption, which implies an objective reality apart from our minds, is difficult to deny and still do science; the second, which allows all the reasoning tools available in mathematics, is essential to any formal study; the third, Einstein separability, although a cornerstone of the theory of relativity, seems currently the most suspect. The decision among them is not that clear, however; there has been no direct experimental test for Einstein separability. Physicists may have cited it as the invalidating assumption in Bell's inequality mainly because they are less willing to give up the other two assumptions, the notion of objective reality and the use of mathematical inference.


Hilgartner & Di Rienzi (1988) suggest that there may be another assumption, a "classical" one related to the logical axiom of identity, but not previously recognized, that leads to the disagreement of Bell's inequality with experimental results. They posit a cognate, "deviant" assumption, which the early quantum theorists tacitly included among the foundations of quantum theory and which leads to its theoretical and experimental success, but whose consequences violate our "common sense".


In support of this supposition, Hilgartner (1978) argues that we have built up what we call "the scientific world-view" -- including our traditional logics, mathematics and sciences -- by specializing the grammar common to the Western Indo-European (WIE) (or generically aristotelian) languages. Classical scientists unavoidably subscribe to the implicit and unstated assumptions encoded there. Alfred Korzybski (1933) first disclosed the most important of those implicit assumptions, replaced it, and so developed a general semantics, the first non-aristotelian system. There he focussed on the construct of identity, (defined as "absolute sameness in all respects or negation of difference"). This construct rests upon and conceals the unsupportable presupposition that the non-verbal structure of ourselves-and-the-world-we-inhabit matches point for point the linguistic structure common to the spoken and written, discursive and notational WIE languages. We call this presupposition tacit identity, and treat it as NEVER valid (cf. Hilgartner, 1978; Hilgartner & Di Rienzi, 1988).


Ten years later Korzybski (1943) explicitly states the premises of his non-aristotelian system. These include three undefined terms (structure, order and relation) and three postulates:


Non-identity: Presume that no structure, order, or relation qualifies as identical with any structure, order or relation (including itself).


Non-allness: Presume that no structure, order or relation can represent all the aspects of any structure, order or relation.


Self-reflexiveness: Presume that no structure, order or relation exists free of aspects which refer to itself and/or the organism which elaborates it.


These postulates explicitly forbid (disallow) identity (or the binary relation of identical with) in any guise or form, explicit or tacit. However, the construct of identity proves intrinsic to the WIE grammar as well as to the modern logical axiom of identity. Thus when we explicitly replace the assumption of tacit identity with the postulate of non-identity, the language structure itself gets altered, and the constructs built up from language require re-working.


The authors hypothesize that the "deviant" assumptions which the quantum theorists included among the foundations of quantum theory amounts to a special case of the postulate of non-identity (Hilgartner & Di Rienzi, 1988). For example, Werner Heisenberg (1925) represents the canonical coordinates that denote position, velocity, energy and time in terms of the constructs of matrix algebra. Since matrices are non-commutative to multiplication, he thereby represents quantum "events" in terms of an algebra that does not satisfy the logical axiom of identity (and so violates the concealed premise of tacit identity).


If this reasoning is correct, then the quantum theorists have already found ways to perform their studies using an (inconsistent) frame of reference which (in part) relies on the negation of identity. Further, our reasoning suggests that the chronic difficulties in "understanding" quantum theory follow from this inconsistency, e.g. the fact that both proponents and opponents talk about the non-identity-based constructs of quantum theory in the identity-based terms of WIE logic, mathematics, science, etc. To facilitate the study of the quantum domain, we shall require a new kind of mathematics, one not based on the logical axiom of identity and the concealed assumption of tacit identity, but rather on the Postulate of Non-identity.


It is difficult at this writing to foresee what using the non-aristotelian assumptions of Korzybski in quantum theory might lead to. It is clear, however, that the resulting re-formulation would free the theory of any further reliance on tacit identity. If there is a hidden assumption of tacit identity in the Bell inequality, perhaps this would account for the discrepancies with the quantum theoretical predictions. It remains the task to derive a cognate of the Bell theorem with the postulate of non-identity to see what predictions result. Success in deriving such a cognate might open the way to a critical test designed to select between these various theories.


If an approach based on Non-identity turns out to be valid, using it might free quantum theory of the conceptual difficulties that have troubled it, and make it more "intelligible" to its users. Then this investigation will have uncovered a larger issue: Perhaps, contrary to the claims of critics, we should not regard quantum theory as non-intuitive; perhaps it simply belongs to an unfamiliar domain, such as that of the Postulate of Non-identity, and proves non-intuitive only when we try to "intuit" about it from within a foreign domain, such as that of the logical axiom of identity. In that case, the traditional difficulties in "understanding" quantum theory may resemble the tip of an iceberg and expose much that we now consider intuitive as faulty.




Bell, J. S. (1964). "On the Einstein Podolsky Rosen Paradox", Physics, vol 1, no. 3, November/December 1964, pp. 195-200.


d'Espagnat, B. (1979). "Quantum Theory and Reality", Scientific American, vol. 241, no. 5, November 1979, pp. 158-180.


Einstein, A., Boris Podolsky and Nathan Rosen (1935). "Can Quantum- Mechanical Descriptions of Physical Reality be Considered Complete?", Physical Review, vol. 47, 1935, pp. 777-780. Reprinted in Physical Reality, S. Toulmin (ed.), Harper & Row, New York, 1970.


Heisenberg, W. (1925). "Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations", Zs Physics, 33, 1925, pp. 879-893. Reprinted as Ch. 12 in Sources of Quantum Physics, B. L. Van Waerden (ed.), Dover Publications, New York, 1967.


Hilgartner, C. A. (1978). "Some Traditional Assumings Underlying Indo- European Languages: Unstated, Unexamined, and Untenable." General Semantics Bulletin nos. 44/45, 1977/78, pp. 132-154.


Hilgartner, C. A. & Joseph Di Rienzi (1988). "Using the Non-aristotelian Assumptions in Contemporary Physics", presented at the International Conference on General Semantics, Yale University, New Haven CT, July 1988.


Korzybski, A. (1933). Science and Sanity: An Introduction to Non-aristotelian Systems and General Semantics, Non-aristotelian Library Publishing Co., Chicago, 1933.


Korzybski, A. (1943). "General Semantics, Psychiatry, Psychotherapy, and Prevention", Papers from the Second American Congress on General Semantics, M. Kendig (ed.), Institute of General Semantics, Chicago, 1943.


Shimony, A. (1988). "The Reality of the Quantum World", Scientific American, vol. 258, no. 1, January 1988, pp. 46-53.