Abstract
The idea of complementarity is one of the key concepts of quantum mechanics. Yet, the idea was originally developed in William James’ psychology of consciousness. Recently, it was re-applied to the humanities and forms one of the pillars of modern quantum cognition. I will explain two different concepts of complementarity: Niels Bohr’s ontic conception and Werner Heisenberg’s epistemic conception. Furthermore, I will give an independent motivation of the epistemic conception based on the so-called operational interpretation of quantum theory, which has powerfully been applied in the domain of quantum cognition. Finally, I will give examples illustrating the potency of complementarity in the domains of bounded rationality and survey research. Concerning the broad topic of consciousness, I will focus on the psychological aspects of awareness. This closes the circle spanning complementarity, quantum cognition, the operational interpretation, and consciousness.
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Notes
- 1.
An almost complete realization of such misunderstandings is accomplished in Hümmler (2017).
- 2.
See also the impressive overview provided by Walach (2019) concerning the topic of health.
- 3.
- 4.
The term uncertainty principle is a translation of the German term Unschärfeprinzip or Unbestimmtheitsprinzip.
- 5.
A classic observation is that the set of projections is naturally a complete orthomodular lattice.
- 6.
Obviously, this operation does not correspond to the intersection A ∩ B of two vector spaces. We rename it by “A & then B”.
- 7.
Note that in a real-valued vector space the states 𝑩𝑨(𝑆) and 𝑩\( \overline{A} \)(𝑆) are both subspaces of B and cosΔ is either 0 or 1. Hence only by making use of Hilbert spaces the term can vary between −1 and + 1.
- 8.
Mathematically, an orthomodular lattice has to satisfy the following axioms (the complement operation is indicated by′, conjunction by ∧, and disjunction by ∨): (i) x′′ = x; (ii) if x ≤ y then y′ ≤ x′; (iii) x ∧ x′ = 0; (iv) if x ≤ y then y = x ∨ (x′ ∧ y) (orthomodular law). The main difference between an orthomodular lattice and a Boolean lattice is that for the latter the law of distributivity is valid but not for the former. Hence, the law of total probability can be derived for Boolean lattices only.
- 9.
In the original example, the firefly can be flashing or not (the latter is indicated by being in world 5). We simplify a bit and ignore the world number 5. For a more detailed discussion, cf. Blutner and beim Graben (2016).
- 10.
- 11.
At least, this is true if a theory of resources is assumed as proposed by Halford et al. (1998).
- 12.
In case of analysing the phenomenon of ‘tonal attraction’, a number of different empirical observations can be introduced in terms of a musical gauge field based on the internal symmetry group SU(2) (beim Graben and Blutner 2019).
- 13.
Also, the notion of spiritual consciousness including the experience of meditation deserves attention. However, even in this case, I see the notion of psychological consciousness in the foreground, and the topic of investigation is its correlation with certain physiological parameters. In the sense of Planck (1947), I consider the mind-mind problem and the hard mind-body problem as Schein problems of science. However, this does not have any visible consequences because the “real” scientific problems can be solved based on the psychological conception of mind.
- 14.
Recently, several models with network-like abilities have been proposed for the modelling of conscious and subconscious processes (Anderson 1990; Blutner 2004; Grossberg 2021). In contrast with Görnitz (2018), I cannot see that these ideas give an explication of consciousness in terms of quantum theory. I know a handful of papers only that directly connect neural networks with quantum effects (e.g. Acacio de Barros and Suppes 2009). These papers, however, do not refer to awareness or consciousness. Hence, the present ideas do not contain a novel (quantum) mechanism for handling consciousness. Rather, they provide some constraints for the route to this goal.
- 15.
In the field of music, Mannone (2018) refers to another aspect of the mind-body problem referring to musical gestures that connect the cognitive-symbolic layer of music to the physical layer of sound.
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Acknowledgement
My thanks go to Anand Srivastav for inviting me to contribute to this issue and for directing my research in a certain direction – trying to connect the field of quantum cognition with the work of Thomas Görnitz. Further, I would like to thank Peter beim Graben for his vital and critical comments and Stefan Blutner-Montaño for feedback on an earlier draft of this chapter.
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Blutner, R. (2024). Complementarity and Quantum Cognition. In: Satsangi, P.S., Horatschek, A.M., Srivastav, A. (eds) Consciousness Studies in Sciences and Humanities: Eastern and Western Perspectives. Studies in Neuroscience, Consciousness and Spirituality, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-031-13920-8_19
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