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Entropy

Complementarity as Relativity: Bohr’s Relativistic Analogy

Gregg S. Jaeger

Published Sep 27, 2026• 0 citations
Publisher

Abstract

Niels Bohr asserted both that (i) the properties of quantum systems are specifiable, in general, only in relation to mutually exclusive experimental arrangements which may be freely chosen by experimenters, and that (ii) observed physical behavior is objective. In a move that reduces the apparent tension between those two assertions, Bohr put forward an analogy between quantum complementarity (in effect, the dependence of property values on measurement apparatus configuration in quantum mechanics) and the principle of relativity (in effect, the dependence of property values on the inertial reference frame in special relativity). Here, Bohr's analogy is considered in a theoretical context. The elements of quantum mechanics and special relativity involved are set side by side, the analogous elements are identified with their roles in the analogy spelled out, and a number of dissimilarities that impact the force of the analogy are indicated-for example, quantum value determination, in general, requires an uncontrollable interaction during measurement, whereas non-quantum relativistic value determination does not. These dissimilarities point to weaknesses in the analogy, which he did not highly develop, and suggest that any stronger such analogy involving the two theories must take these differences more fully into account.

DOI
10.3390/e28101064

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Niels Bohr asserted both that (i) the properties of quantum systems are specifiable, in general, only in relation to mutually exclusive experimental arrangements which may be freely chosen by experimenters, and that (ii) observed physical behavior is objective. In a move that reduces the apparent tension between those two assertions, Bohr put forward an analogy between quantum complementarity (in effect, the dependence of property values on measurement apparatus configuration in quantum mechanics) and the principle of relativity (in effect, the dependence of property values on the inertial reference frame in special relativity). Here, Bohr's analogy is considered in a theoretical context. The elements of quantum mechanics and special relativity involved are set side by side, the analogous elements are identified with their roles in the analogy spelled out, and a number of dissimilarities that impact the force of the analogy are indicated-for example, quantum value determination, in general, requires an uncontrollable interaction during measurement, whereas non-quantum relativistic value determination does not. These dissimilarities point to weaknesses in the analogy, which he did not highly develop, and suggest that any stronger such analogy involving the two theories must take these differences more fully into account.
Having discussed the meaning of complementarity in general and wave particle complementarity in particular, I wish now to explicate Bohr's subtle argument for the thesis that certain pairs of classical concepts which are mutually compatible in classical physics are mutually exclusive in quantum physics, i.e. the thesis of kinematic–dynamic complementarity. It is generally held that Bohr regarded the mutual exclusiveness in question as being not only epistemic but also ontic or semantic, in the sense that the uncertainty principle expresses a restriction not only on the joint measurability of canonically conjugate observables but also on the joint instantiation of the properties corresponding to these observables. I shall consider the question of the ontic or semantic construal of kinematic–dynamic complementarity in Chapter 7. Bohr's argument for complementarity in the epistemic sense is, however, more fundamental: it goes to the heart of his theory of observation and measurement in quantum physics. What, then, is Bohr's argument? The mutual exclusiveness of kinematic and dynamic properties Kinematic and dynamic attributes in quantum mechanics are mutually exclusive in the sense that they cannot be simultaneously measured; they are, in this sense, epistemically incompatible. Why did Bohr think this? His reasons may seem intricate, but they are basically quite simple. Two main factors, he maintains, account for the epistemic incompatibility: ( a ) measurements of these two different sorts of properties require mutually exclusive experimental arrangements, incompatible measurement procedures; ( b ) the indeterminability of the interaction between the object and the instrument of measurement precludes extrapolation of the different measurement results to one and the same time.
Introduction In order to develop the insight that is worked out by Brock (Niels Bohr's Philosophy of Quantum Mechanics, Logos, 2003), that the philosophy of quantum mechanics should parallel Kant's philosophy of natural science, some preliminary analyses of key concepts need to be done. Initiated by Niels Bohr (Atomic Physics and Human Knowledge, John Wiley and Sons, 1958), the concept of ‘complementarity’ has played a major role in the interpretation of quantum theory. However, the exact place it occupies in respect of the logical form of the relation of complementarity between descriptive predicates has not been spelled out in detail to my knowledge. Complementary predicates exclude one another as simultaneous attributions to the same subject. Exactly what form does this exclusion take? How is it related to the basic exclusion-of-predicates principle, the logical law of non-contradiction?
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. The complementary descriptions approach is a framework for the interpretation of quantum mechanics, more specifically, it focuses in the development of the idea of complementarity and the concept of potentiality in the orthodox quantum formulation. In PART I of this article, we analyze the ideas of Bohr and present the principle of complementary description which takes into account Einstein's ontological position. We argue, in PART II, that this development allows a better understanding of some of the paradigmatic interpretational problems in quantum mechanics, such as the measurement problem and the quantum to classical limit. We conclude that one should further develop complementarity in order to elaborate a consistent worldview.
SUMMARYThe article contains the result of an attempt to examine analytically and critically the usefulness in psychology of Niels Bohr's concept of complementarity.In the first section it is shown through quotations (from (1) and (2)) that Bohr actually applies “complementarity” with two meanings in physics: 1. Special complementarity: The relation between two sets of concepts which supplement each other but mutually exclude each other.2. General complementarity: A description that includes the conditions of observation under which a phenomenon has been produced.In the second section it is shown through quotations how Bohr through the use of the concept of complementarity forms four analogies between atomic physics and psychology, namely: 1) the subject-object relation, 2) the determinism-indeterminism relation, 3) the thought-emotion relation, and 4) the instinct-reason relation. The first two relations are examples of general complementarity, the two last ones are examples of special complementarity.In ...
Quantum mechanics challenges classical intuitions of space, time, and causality via the superposition principle, which allows systems to exist in multiple states simultaneously. Niels Bohr addressed these paradoxes through his Complementarity Principle, asserting that mutually exclusive properties-such as wave and particle behaviour-are jointly necessary for a complete description of quantum systems. Bohr also emphasized contextuality, the idea that measurement outcomes depend on the broader experimental setup. Despite his profound insights, Bohr did not offer a formal logical framework for these concepts. We address this gap by generalizing Reichenbach's three-valued logic into a seven-valued, formally contextual system, where contextuality is explicitly encoded via existential quantifiers. This logic retains Reichenbach's indeterminate value while modelling conditional truths across incompatible measurements, resolving key quantum paradoxes without logical inconsistency or nonlocality. Our approach draws inspiration from Jain logic which embraces multiple, context-dependent truths. Beyond quantum theory, this framework has potential applications in perceptual psychology and cognitive science, where context and contradiction also play central roles. The aim is to extend Bohr's legacy by equipping his epistemological vision with rigorous, many-valued logical tools.
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. The complementary descriptions approach is a framework for the interpretation of quantum mechanics, more specifically, it focuses in the development of the idea of complementarity and the concept of potentiality in the orthodox quantum formulation. In PART I of this article, we analyze the ideas of Bohr and present the principle of complementary description which takes into account Einstein's ontological position. We argue, in PART II, that this development allows a better understanding of some of the paradigmatic interpretational problems in quantum mechanics, such as the measurement problem and the quantum to classical limit. We conclude that one should further develop complementarity in order to elaborate a consistent worldview.