 likely that mental states and observables show features that resemble quantum behavior although the correlated brain activity may be entirely classical: quantum mind without quantum brain.
Intuitively, it is not difficult to understand why non-commuting operations or non-Boolean logic should be relevant, even inevitable, for mental systems that have nothing to do with quantum physics. Simply speaking, the non-commutativity of operations means nothing else than that the sequence, in which operations are applied, matters for the final result. And non-Boolean logic refers to propositions that may have unsharp truth values beyond yes or no, shades of plausibility or credibility as it were. Both versions obviously abound in psychology and cognitive science (and in everyday life). Pylkkänen (2015) has even suggested to use this intuitive accessibility of mental quantum features for a better conceptual grasp of quantum physics.
The particular strength of the idea of generalizing quantum theory beyond quantum physics is that it provides a formal framework which both yields a transparent well-defined link to conventional quantum physics and has been used to describe a number of concrete psychological applications with surprisingly detailed theoretical and empirical results. Corresponding approaches fall under the third category of Section 4.1: further developments or generalizations of quantum theory.
One rationale for the focus on psychological phenomena is that their detailed study is a necessary precondition for further questions as to their neural correlates. Therefore, the investigation of mental quantum features resists the temptation to reduce them (within scenario A) all-too quickly to neural activity. There are several kinds of psychological phenomena which have been addressed in the spirit of mental quantum features so far: (i) decision processes, (ii) order effects, (iii) bistable perception, (iv) learning, (v) agency, (vi) semantic networks, and (vii) super-quantum entanglement correlations.
An early precursor of work on decision processes is due to Aerts and Aerts (1994). However, the first detailed account appeared in a comprehensive publication by Busemeyer et al.(2006). The key idea is to define probabilities for decision outcomes and decision times in terms of quantum probability amplitudes. Busemeyer et al. found agreement of a suitable Hilbert space model (and disagreement of a classical alternative) with empirical data. Moreover, they were able to clarify the long-standing riddle of the so-called conjunction and disjunction effects (Tversky and Shafir 1992) in decision making (Pothos and Busemeyer 2009). Another application refers to the asymmetry of similarity judgments (Tversky 1977), which can be adequately understood by quantum approaches (see Aerts et al. 2011, Pothos et al. 2013).
Order effects in polls, surveys, and questionnaires, recognized for a long time (Schwarz and Sudman 1992), are still insufficiently understood today. Their study as contextual quantum features (Aerts and Aerts 1994, Busemeyer et al. 2011) offers the potential to unveil a lot more about such effects than the well-known fact that responses can drastically alter if questions are swapped. Atmanspacher and Römer (2012) proposed a complete classification of possible order effects (including uncertainty relations, and independent of Hilbert space representations), and Wang et al. (2014) discovered a fundamental covariance condition (called the QQ equation) for a wide class of order effects.
The perception of a stimulus is bistable if the stimulus is ambiguous, such as the Necker cube. Atmanspacher and colleagues developed a detailed model predicting a quantitative relation between basic psychophysical time scales in bistable perception that has been confirmed experimentally (Atmanspacher and Filk 2013). Moreover, Atmanspacher and Filk (2010) conjectured that particular distinguished states in bistable perception may violate temporal Bell inqualitities—a litmus test for quantum behavior. See also Mahler (2015) for an informed overview of temporal Bell inequalities and their consequences.
Another quite obvious arena for non-commutative behavior is learning behavior. In theoretical studies, Atmanspacher and Filk (2006) showed that in simple supervised learning tasks small recurrent networks not only learn the prescribed input-output relation but also the sequence in which inputs have been presented. This entails that the recognition of inputs is impaired if the sequence of presentation is changed. In very few exceptional cases, with special characteristics that remain to be explored, this impairment is avoided.
A quantum approach for understanding issues related to agency, intention, and other controversial topics in the philosophy of mind has been proposed by Briegel and Müller (2014, in Other Internet Resources). This proposal is based on work on quantum algorithms for reinforcement learning in neural networks (“projective simulation”, Paparo et al. 2012), which can be regarded as a variant of quantum machine learning (Wittek 2014). The gist of the idea is how agents can develop agency as a kind of independence from their environment and the deterministic laws governing it (Briegel 2012). The behavior of the agent itself is simulated as a non-deterministic quantum random walk in its memory space.
The difficult issue of meaning in natural languages is often explored in terms of semantic networks. Gabora and Aerts (2002) described the way in which concepts are evoked, used, and combined to generate meaning depending on contexts. Their ideas about concept association in evolution were further developed by Gabora and Aerts (2009). Bruza et al.(2009) referred to meaning relations in terms of entanglement-style features in quantum representations of the human mental lexicon and propose experimental work capable of testing this approach. See Bruza et al. (2013, in Other Internet Resources) for first empirical results in this direction.
Quantum entanglement implies correlations exceeding standard classical correlations (by violating Bell-type inequalitites) but obeying the so-called Tsirelson bound. However, this bound does not exhaust the range by which Bell-type correlations can be violated in principle. Popescu and Rohrlich (1994) found such correlations for particular quantum measurements, and Dzhafarov and Kujala (2013) derived a compact way to distinguish the different types of correlations theoretically. Super-quantum correlations may arise due to priming or other context effects in mental systems. Possible examples are non-separable concept combinations a la Bruza et al. (2013, in Other Internet Resources).
It is a distinguishing aspect of the approaches listed above that they have led to well-defined and specific theoretical models with empirical consequences and novel predictions. A second point worth mentioning is that the approaches have formed a scientific community—there are several groups worldwide (rather than solitary actors) studying quantum ideas in cognition, partly even in collaborative efforts. For about a decade there have been regular international conferences with proceedings for the exchange of new results and ideas, and target articles and special issues of well established journals have been devoted to basic frameworks and new developments (Busemeyer and Bruza 2013, Pothos and Busemeyer 2013, Haven and Khrennikov 2013, Wang et al. 2013), Wendt (2015).
The historical motivation for exploring quantum theory in trying to understand consciousness derived from the realization that collapse-type quantum events introduce an element of randomness, which is primary (ontic) rather than merely due to ignorance or missing information (epistemic). Approaches such as those of Wigner, of Stapp, and of Beck and Eccles emphasize this (in different ways), insofar as the ontic randomness of quantum events is regarded to provide room for mental causation, i.e., the possibility that conscious mental acts can influence brain behavior. The approach by Penrose and Hameroff also focuses on state collapse, but with a significant move from mental causation to the non-computability of (particular) conscious acts.
Any discussion of state collapse or state reduction (e.g. by measurement) refers, at least implicitly, to superposition states since those are the states that are reduced. Insofar as entangled systems remain in a quantum superposition as long as no measurement has occurred, entanglement is always co-addressed when state reduction is discussed. By contrast, some of the dual-aspect quantum approaches utilize the topic of entanglement differently, and independently of state reduction in the first place. Inspired by the entanglement-induced nonlocal correlations of quantum physics, mind-matter entanglement is conceived as the hypothetical origin of mind-matter correlations. This reflects the highly speculative picture of a fundamentally holistic, psychophysically neutral level of reality from which correlated mental and material domains emerge.
Each of the examples discussed in this overview has both promising and problematic aspects. The approach by Beck and Eccles is most detailed and concrete with respect to the application of standard quantum mechanics to the process of exocytosis. However, it does not solve the problem of how the activity of single synapses enters the dynamics of neural assemblies, and it leaves mental causation of quantum processes as a mere claim. Stapp’s approach suggests a radically expanded ontological basis for both the mental domain and status-quo quantum theory as a theory of matter without essentially changing the formalism of quantum theory. Although related to inspiring philosophical and some psychological background, it still lacks empirical confirmation. The proposal by Penrose and Hameroff exceeds the domain of present-day quantum theory by far and is the most speculative example among those discussed. It is not easy to see how the picture as a whole can be formally worked out and put to empirical test.
The approach initiated by Umezawa is embedded in the framework of quantum field theory, more broadly applicable and formally more sophisticated than standard quantum mechanics. It is used to describe the emergence of classical activity in neuronal assemblies on the basis of symmetry breakings in a quantum field theoretical framework. A clear conceptual distinction between brain states and mental states has often been missing, but this ambiguity has recently been resolved in favor of brain states. Their relation to mental states is ultimately left open; some of Vitiello’s accounts suggest