There are various ways in which the neural processes underlying cognition could be quantum-like. The strongest possibility is that they literally involve subtle quantum effects. For example, following Niels Bohr, David Bohm speculated about this possibility already in 1951 in his textbook Quantum theory [6]. Anticipating the current research on quantum cognition [1, 15], he drew attention to what he considered to be remarkable point-by-point analogies between quantum processes and thought. He added that it would provide a natural explanation of these analogies if it turned out that some key neural processes (e.g. in synapses) were subject to quantum-theoretical limitations (for a discussion of Bohm’s analogies see Pylkkänen 2014 [17]).

Harald Atmanspacher (2011) has provided a useful overview of various programs of what I have above call “strong quantum cognition” [2]. First of all, there are approaches that stay within the usual interpretation of the quantum theory. There is the von Neumann-Wigner line of thought that assumes that consciousness plays a role in quantum state reductions; in Stapp’s later development of this approach the neural correlates of conscious intentional acts are assumed to involve quantum state reductions. There is the Ricciardi-Umezawa-Vitiello approach that sees mental states, particularly memory states, as vacuum states of quantum fields (this approach has been given an imaginative philosophical interpretation by Globus 2003 [10]). Finally, there is the Beck-Eccles approach, where it is assumed that due to quantum mechanical processes the frequency of exocytosis at a synaptic cleft can be controlled by mental intentions, without violating the conservation of energy (for a discussion of this last approach see also Hiley and Pylkkänen 2005 [13]).

Atmanspacher also draws attention to programs of strong quantum cognition that involve further extensions or generalizations of present-day quantum theory. Most notably, there is Penrose’s proposal that human (say mathematical) insight is non-computable and that the physiological correlates of such insight thus need to involve non-computable physical processes. He thinks that such process might well be related to quantum state reduction. However, Penrose is not satisfied with quantum state reduction as this is characterized in the usual interpretation of quantum theory. Instead, he proposes that gravity brings about the reduction under certain circumstances, which allows the possibility of an orchestrated objective reduction (Orch-OR) – the idea being that the reduction can take place without the activity of a human conscious observer, and in an orchestrated way. This involves an extension of current quantum theory, in which latter the state reductions obey the usual laws of quantum probability. Together with Hameroff, Penrose proposed that neural microtubules might provide a site where Orch-ORs could take place. Their assumption is that Orch-ORs in neural microtubules, when suitably integrated, constitute conscious moments. (So it is not that consciousness collapses the wave function but rather that the collapses constitute consciousness.) The idea is similar to Stapp’s later ideas, but one difference is that while Stapp stays within the usual interpretation of quantum theory, Penrose’s approach involves going beyond it (in that the reductions can be objective and orchestrated, and need not obey the usual quantum laws). Hameroff and Penrose (2014) have recently published an extensive review of their approach, with new features and, in the same journal, a reply to various criticisms [12].

Those who advocate strong quantum cognition typically encounter the criticism that quantum effects are washed out in the “warm, wet and noisy” conditions of the macroscopic world and brains in particular (the “decoherence problem”). It is thus concluded that quantum theory is only relevant to physical processes in the (sub)atomic domain and should be ignored in other physical domains. However, there are many recent research developments suggesting that biological organisms at ordinary temperatures exploit subtle quantum effects, and biological evolution would thus have been able to solve the decoherence problem at least in some biological contexts (e.g. the studies on energy-harvesting in photosynthesis and avian magnetoreception; for a short review, see Ball, P. (2011) [4]). As Atmanspacher points out, it is however still a controversial issue whether subtle quantum processes play a significant role in the neural correlates of cognition and consciousness.