Quantum mechanics, interference, and the brain
Introduction
The human brain is arguably the most powerful computational device known. The underlying mechanisms behind it are not yet revealed, though progress has been made in recent years toward their understanding. One of the mysteries is how fast the brain processes information, given that neurons are relatively slow. In recent years, there has been an increasing number of researchers speculating that the high processing speed of the brain and the emergence of consciousness are due to quantum processes, perhaps even quantum computations (Beck and Eccles, 1992, Eccles, 1986, Eccles, 1990, Freeman and Vitiello, 2006, Hameroff, 1998, Jahn and Dunne, 1986, Khrennikov, 2006, Kurita, 2005, Ricciardi and Umezawa, 1967, Schwartz et al., 2005, Thaheld, 2003, Vitiello, 1995).
Richard Feynman was one of the first persons to discuss quantum computers. In Feynman (1996), he asked whether there were any advantages if the bits of information were treated as quantum mechanical superpositions. Some years after Feynman’s remarks, Shor (1999) found a quantum algorithm that could factor a prime number in polynomial time. Since no known classical algorithms factor prime numbers that quickly, Shor’s work brought quantum computers to the fore.
Quantum algorithms differ from classical ones because a single quantum system can be represented by the linear superposition of possible orthogonal states. If a particular state is not realized by the system, i.e., the system does not collapse onto it, this state can interfere with other possible states. This interference allows for multiple computations via different paths without the system actually collapsing through those paths. In other words, a quantum computer can work on potential realizations of computations. This should be contrasted with a classical computer, which needs to step through each individual computational path. The consequence is that quantum computers can perform massively parallel “virtual” computations (Steane, 1998).
If the brain uses quantum computations, this could explain why it is so fast. However, quantum computation has a difficulty. Despite a strong push to build complex quantum computers, up until now none have been built. This is due to a phenomenon called environmental decoherence (Omnes, 1994). When a quantum system interacts with the environment, the phase of the state vector changes stochastically. Since interference between different states depends on phase relations, the more environmentally induced the phase changes, the less visible the interference. At some point, if decoherence is too strong, interference disappears (Omnes, 1994). For quantum computers, the loss of coherence increases exponentially with the number of digits. Consequently, experimental realizations of quantum computers have, thus far, involved only a very small number of bits.
Notwithstanding, the perspective of quantum computation in the brain, a device that operates at relatively high temperatures, is tantalizing. For instance, Penrose and Hameroff (Hameroff, 1998, Penrose, 1989, Penrose, 1994) proposed that quantum computations might be feasible in protected environments of microtubules in the neurons. In a detailed analysis of different environmental sources of decoherence in the brain, Tegmark (2000) pointed out that the time scale for decoherence is orders of magnitude faster than those calculated by Penrose and Hameroff. Hagan, Hameroff and Tuszyński (2002) claimed that Tegmark’s work did not address correctly the model proposed by Penrose and Hameroff, and if you took into account the correct dimensions at play, the decoherence time computed by Tegmark could be of a bigger order of magnitude. However, Rosa and Faber (2004) showed that Hagan et al. (2002) did not use Tegmark’s equations under the correct assumptions, and thus the decoherence time would indeed be smaller than estimated by Hameroff (1998). In any case, as Davies (2004) points out, there seems to be a lot of wishful thinking on both sides of this discussion, and quantum processing in the brain will not be widely accepted until quantum superpositions are shown to exist in some special cases in the brain. As it stands, it seems that even for microtubules, environmental decoherence would happen so quickly as to render it improbable, though not impossible, that the brain uses any quantum computations. It is hard to imagine any protected region of the brain where quantum interference could occur without fast decoherence. Despite this, there is a large volume of research on quantum aspects of the brain.
In this paper we show that quantum-like effects can be present in the brain without an underlying quantum process. Our argument will be presented in the following way. In Section 2 we briefly describe the characteristics of quantum mechanics that are considered non-classical. In Section 2.4, we discuss the main empirical arguments in favor of quantum effects in the brain, and we stress that their main characteristic is the contextuality of observables. In Section 3, we argue that the contextual outcomes of experiments of Section 2.4 can be modeled by classical interference. We end with some remarks on what might be the origin of interference in the brain.
Section snippets
Quantum mechanics and the nature of reality
Quantum mechanics is extremely successful in describing nature. But, more than a century after its initial formulation, the meaning of this description is still a matter of intense debate. The main points of discussion are the following. (i) Nondeterminism; (ii) contextuality; and (iii) nonlocality. In this section we will analyze each point, and bring out the features that we deem relevant to quantum mechanical models of the brain.
Fields, oscillators, and the brain
Though quantum mechanics received a lot of attention with Penrose’s proposal that quantum computation is related to consciousness, other researchers see quantum mechanics as a possible mechanism for other cognitive processes. For example, Khrennikov and Haven (2007) claim that quantum probability interference is present in social phenomena as well as in cognition. In a more detailed and, in our opinion, interesting paper, Busemeyer, Wang, and Townsend (2006) analyzed the dynamics of human
Final remarks
In a previous paper (Suppes & de Barros, 2007), we analyzed quantum effects in the brain from a different perspective, as a consequence of an eye photodetector being able to measure single photon states. In this paper we continued the analysis by making a distinction between nonlocality and contextuality, and asking if quantum effects are really necessary beyond the ones presented in (Suppes & de Barros, 2007). In some sense, nonlocality and contextuality are intimately related, since the
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2018, Journal of Mathematical PsychologyCitation Excerpt :Quantum-like models have to be sharply distinguished from genuinely quantum physical models of cognition which are based on consideration of quantum physical processes in the brain, cf. with Hameroff (1994) and Penrose (1989). Although the quantum physical models have been criticized for mismatching between the temperature and space–times scales of the quantum physical processes and neuronal processing in the brain, see especially Tegmark (2000), they cannot be rejected completely and one may expect that quantum-like models of cognition will be (soon or later) coupled with real physical processes in the brain, see Busemeyer, Fakhari, and Kvam (in press), de Barros (2012), de Barros and Suppes (2009), Khrennikov (2011), Melkikh (2013, 2014) and Takahashi (2014) for some steps in this direction. We remark that the open quantum systems approach to decision making can be considered as a possible realization of the contextual treatment of cognition, cf. Dzhafarov (2014), Dzhafarov and Kujala (2012) and Khrennikov (2004a, 2010).