1. Introduction

The relationship between quantum measurement and consciousness has been studied since the founding of quantum mechanics (von Neumann 1932/1955; London and Bauer 1939; Wigner 1967; Stapp 1993, 2007; Penrose 1989, 1994; Hameroff and Penrose 1996; Hameroff 1998, 2007; Gao 2004, 2006b, 2008b). Quantum measurement problem is generally acknowledged as one of the hardest problems in modern physics, and the transition from quantum to classical is still a deep mystery. On the other hand, consciousness remains another deep mystery for both philosophy and science, and it is still unknown whether consciousness is emergent or fundamental. It has been conjectured that these two mysteries may have some intimate connections, and finding them may help to solve both problems (Chalmers 1996).

There are two main viewpoints claiming that quantum measurement and consciousness are intimately connected. The first one holds that the consciousness of an observer causes the collapse of the wave function and helps to complete the quantum measurement or quantum-to-classical transition in general (von Neumann 1932/1955; London and Bauer 1939; Wigner 1967; Stapp 1993, 2007). This view seems understandable. Though what physics commonly studies are insensible objects, the consciousness of observer must take part in the last phase of measurement. The observer is introspectively aware of his perception of the measurement results, and consciousness is used to end the infinite chains of measurement here. The second view holds that consciousness arises from objective wavefunction collapse (Penrose 1989, 1994; Hameroff and Penrose 1996; Hameroff 1998, 2007). One argument is that consciousness is a process that cannot be described algorithmically, and the gravitation-induced wavefunction collapse seems non-computable as a fundamental physical process, and thus the elementary acts of consciousness must be realized as objective wavefunction collapse, e.g., collapse of coherent superposition states in brain microtubules. Though these two views are obviously contrary, they both insist that a conscious perception is always definite and classical, and there are no quantum superpositions of definite conscious perceptions.

Different from these seemingly extreme views, it is widely thought that the quantum-to-classical transition and consciousness are essentially independent with each other (see, e.g. Nauenberg (2007) for a recent review). At first sight, this common-sense view seems too plain to be intriguing. However, it has been argued that, by permitting the existence of quantum superpositions of different conscious perceptions, this view will lead to an unexpected new result, a quantum physical effect of consciousness (Gao 2004, 2006b, 2008b). In this article, we will introduce this interesting result and discuss its possible implications.

2. The Effect

Quantum mechanics is the most fundamental theory of the physical world. Yet as to the measurement process or quantum-to-classical transition process, the standard quantum mechanics provides by no means a complete description, and the collapse postulate is just a makeshift (Bell 1987). Dynamical collapse theories (Ghirardi 2008), many-worlds theory (Everett 1957) and de Broglie-Bohm theory (Bohm 1952) are the main alternatives to a complete quantum theory. The latter two replace the collapse postulate with some new structures, such as branching worlds and Bohmian trajectories, while the former integrate the collapse postulate with the normal Schrödinger evolution into a unified dynamics. It has been recently shown that the dynamical collapse theories are probably in the right direction by admitting wavefunction collapse (Gao 2011). Here we will mainly discuss the possible quantum effects of consciousness in the framework of dynamical collapse theories, though the conclusion also applies to the other alternatives. Our analysis only relies on one common character of the theories, i.e., that the collapse of the wave function (or the quantum-to-classical transition in general) is one kind of objective dynamical process, essentially independent of the consciousness of observer, and it takes a finite time to finish.

It is a well-known result that nonorthogonal quantum states cannot be distinguished (by physical measuring device) in both standard quantum mechanics and dynamical collapse theories (see, e.g. Wootters and Zurek 1982; Ghirardi et al 1993; Nielsen and Chuang 2000). However, it has been argued that a conscious being can distinguish his definite perception states and the quantum superpositions of these states, and thus when the physical measuring device is replaced by a conscious observer, the nonorthogonal states can be distinguished in principle in dynamical collapse theories (Gao 2004, 2006b, 2008b). The distinguishability of nonorthogonal states will reveal a distinct quantum physical effect of consciousness, which is lacking for physical measuring systems without consciousness. In the following, we will give a full exposition of this result.

Let v1 and v2 be two definite perception states of a conscious being, and v1 + v2 is the quantum superposition of these two definite perception states. For example, v1 and v2 are triggered respectively by a small number of photons with a certain frequency entering into the eyes of the conscious being from two directions, and v1 + v2 is triggered by the superposition of these two input states. Assume that the conscious being satisfies the following slow collapse condition, i.e., that the collapse time of the superposition state v1 + v2, denoted by tc, is longer than the normal conscious time tp of the conscious being for definite states, and the time difference is large enough for him to identify. This condition ensures that consciousness can take part in the process of wavefunction collapse; otherwise consciousness can only appear after the collapse and will surely have no influence upon the collapse process. Now we will explain why the conscious being can distinguish the definite perception states v1 or v2 and the superposition state v1 + v2.

First, we assume that a definite perception can appear only after the collapse of the superposition state v1 + v2. This assumption seems plausible. Then the conscious being can have a definite perception after the conscious time tp for the states v1 and v2, but only after the collapse time tc can the conscious being have a definite perception for the superposition state v1 + v2. Since the conscious being satisfies the slow collapse condition and can distinguish the times tp and tc, he can distinguish the definite perception state v1 or v2 and the superposition state v1 + v2. Note that a similar argument was first given by Squires (1992).

Next, we assume that the above assumption is not true, i.e., that the conscious being in a superposition state can have a definite perception before the collapse has completed. We will show that the conscious being can also distinguish the states v1 + v2 and v1 or v2 with non-zero probability.

(1). If the definite perception of the conscious being in the superposed state v1 + v2 is neither v1 nor v2 (e.g. the perception is some sort of mixture of the perceptions v1 and v2), then obviously the conscious being can directly distinguish the states v1 + v2 and v1 or v2.

(2). If the definite perception of the conscious being in the superposed state v1+v2 is always v1, then the conscious being can directly distinguish the states v1+v2 and v2. Besides, the conscious being can also distinguish the states v1 + v2 and v1 with probability 1/2. The superposition state v1 + v2 will become v2 with probability 1/2 after the collapse, and the definite perception of the conscious being will change from v1 to v2 accordingly. But for the state v1, the perception of the conscious being has no such change.

(3). If the definite perception of the conscious being in the superposed state v1 + v2 is always v2, the proof is similar to (2).

(4). If the definite perception of the conscious being in the superposed state v1 + v2 is random, i.e., that one time it is v1, and another time it is v2, then the conscious being can still distinguish the states v1 + v2 and v1 or v2 with non-zero probability. For the definite perception states v1 or v2, the perception of the conscious being does not change. For the superposition state v1 + v2, the perception of the conscious being will change from v1 to v2 or from v2 to v1 with non-zero probability during the collapse process.

In fact, we can also give a compact proof by reduction to absurdity. Assume that a conscious being cannot distinguish the definite perception states v1 or v2 and the superposition state v1 + v2. This requires that for the superposition state v1 + v2 the conscious being must have the perception v1 or v2 immediately after the conscious time tp, and moreover, the perception must be exactly the same as his perception after the collapse of the superposition state v1 + v2. Otherwise he will be able to distinguish the superposition state v1 + v2 from the definite state v1 or v2. Since the conscious time tp is shorter than the collapse time tc, the requirement means that the conscious being knows the collapse result beforehand. This is impossible due to the essential randomness of the collapse process. Note that even if this is possible, the conscious being also has a distinct quantum physical effect, i.e., that he can know the random collapse result beforehand.

To sum up, we have shown that if a conscious being satisfies the slow collapse condition, he can readily distinguish the nonorthogonal states v1 + v2 (or v1 - v2) and v1 or v2, which is an impossible task for a physical measuring system without consciousness.

3. The Condition

The above quantum physical effect of consciousness depends on the slow collapse condition, namely that for a conscious being the collapse time of a superposition of his conscious perceptions is longer than his normal conscious time. Whether this condition is available for human brains depends on concrete models of consciousness and wavefunction collapse. For example, if a definite conscious perception involves less neurons such as several thousand neurons, then the collapse time of the superposition of such perceptions will be readily in the same level as the normal conscious time (several hundred milliseconds) according to some dynamical collapse models (Gao 2006a, 2006b, 2008a, 2008b). This result is also supported by the Penrose-Hameroff orchestrated objective reduction model (Hameroff and Penrose 1996; Hagan, Hameroff and Tuszynski 2002). In the model, if a conscious perception involves about 109 participating tubulin, then the collapse time will be several hundred milliseconds and in the order of normal conscious time. When assuming that 10% of the tubulin contained becomes involved, the conscious perception also involves about one thousand neurons (there are roughly 107 tubulin per neuron). In addition, even though the slow collapse condition is unavailable for human brains, it cannot be in principle excluded that there exist some small brain creatures in the universe who satisfy the slow collapse condition (see also Squires 1992).

A more important point needs to be stressed here. The collapse time estimated above is only the average collapse time for an ensemble composed of identical superposition states. The collapse time of a single superposition state is an essentially stochastic variable, which value can range between zero and infinity. As a result, the slow collapse condition can always be satisfied for some collapse events with a certain probability. For these random collapse processes, the collapse time of the single superposition state is much longer than the average collapse time and the normal conscious time, and thus the conscious being can distinguish the nonorthogonal states and have the distinct quantum physical effect. As we will see, this ultimate possibility will have important implications for the nature of consciousness.

Lastly, we note that the slow collapse condition is also available in the many-worlds theory and de Broglie-Bohm theory (Gao 2004). For these two theories, the collapse time will be replaced by the decoherence time. First, since a conscious being is able to be conscious of its own state, he can always be taken as a closed self-measuring system in theory. In both many-worlds theory and de Broglie-Bohm theory, the state of a closed system satisfies the linear Schrödinger equation, and thus no apparent collapse happens or the decoherence time is infinite for the superposition state of a closed conscious system. Therefore, the slow collapse condition can be more readily satisfied in these theories when a conscious system has only a very weak interaction with environment. By comparison, in most dynamical collapse theories, the superposition state of a closed system also collapses by itself. Secondly, a conscious system (e.g. a human brain or neuron groups in the brain) often has a very strong interaction with environment in practical situations. As a result, the decoherence time is usually much shorter than the collapse time, and the slow collapse condition will be less readily satisfied in many-worlds theory and de Broglie-Bohm theory than in the dynamical collapse theories. This difference can be used to test these different quantum theories.

4. Implications

Consciousness is the most familiar phenomenon. Yet it is also the hardest to explain. The relationship between objective physical process and subjective conscious experience presents a well-known hard problem for science (Chalmers 1996). It retriggers the recent debate about the long-standing dilemma of panpsychism versus emergentism (Strawson et al 2006; Seager and Allen-Hermanson 2010). Though emergentism is currently the most popular solution to the hard problem of consciousness, many doubt that it can bridge the explanation gap ultimately. By comparison, panpsychism may provide an attractive and promising way to solve the hard problem, though it also encounters some serious problems (Seager and Allen-Hermanson 2010). It is widely believed that the physical world is causally closed, i.e., that there is a purely physical explanation for the occurrence of every physical event and the explanation does not refer to any consciousness property (see, e.g. McGinn 1999). But if panpsychism is true, the fundamental consciousness property should take part in the causal chains of the physical world and should present itself in our investigation of the physical world. Then does consciousness have any causal efficacy in the physical world?

As we have argued above, a conscious observer can distinguish two nonorthogonal states, while the physical measuring system without consciousness cannot. Accordingly, consciousness does have a causal efficacy in the physical world when considering the fundamental quantum processes. This will provide a strong support for panpsychism. In fact, we can argue that if consciousness has a distinct quantum physical effect, then it cannot be emergent but be a fundamental property of substance. Here is the argument.

If consciousness is emergent, then the conscious beings should also follow the fundamental physical principles such as the principle of energy conservation etc, though they may have some distinct high-level functions. According to the principles of quantum mechanics, two nonorthogonal states cannot be distinguished. However, a conscious being can distinguish the nonorthogonal states in principle. This clearly indicates that consciousness violates the quantum principles, which are the most fundamental physical principles. Therefore, the consciousness property cannot be reducible or emergent but be a fundamental property of substance. It should be not only possessed by the conscious beings, but also possessed by atoms as well as physical measuring devices. The difference only lies in the conscious content. The conscious content of a human being can be very complex, while the conscious content of a physical measuring device is probably very simple. In order to distinguish two nonorthogonal states, the conscious content of a measuring system must at least contain the perceptions of the nonorthogonal states. It might be also possible that the conscious content of a physical measuring device can be complex enough to distinguish two nonorthogonal states, but the effect is too weak to be detected by present experiments.

On the other hand, if consciousness is a fundamental property of substance, then it is quite natural that it violates the existing fundamental physical principles, which do not include it at all. It is expected that a complete theory of nature must describe all properties of substance, thus consciousness, the new fundamental property, must enter the theory from the start. Since the distinguishability of nonorthogonal states violates the linear superposition principle, consciousness will introduce a nonlinear element to the complete evolution equation of the wave function. The nonlinearity is not stochastic but definite. It has been argued that the nonlinear quantum evolution introduced by consciousness has no usual problems of nonlinear quantum mechanics (Gao 2006b).

Lastly, it should be noted that the above argument for panpsychism depends on the assumption that the wavefunction collapse or the quantum-to-classical transition in general is an objective physical process. However, the conclusion is actually independent of the origin of the wavefunction collapse. If the wavefunction collapse results from the consciousness of observer, then consciousness will also have the distinct quantum effect of collapsing the wave function, and thus consciousness should be a fundamental property of substance too. In addition, we stress that this conclusion is also independent of the interpretations of quantum mechanics. It only depends on two firm facts: one is the existence of indefinite quantum superpositions, and the other is the existence of definite conscious perceptions.

5. Conclusions

It is widely thought that the quantum-to-classical transition and consciousness are two essentially independent processes. But this does not mean that the result of their combination must be plain. In this article, we have shown that a conscious being can have a distinct quantum physical effect during the quantum-to-classical transition. A conscious system can measure whether he is in a definite perception state or in a quantum superposition of definite perception states, while a system without consciousness cannot distinguish such nonorthogonal states. This new result may have some important implications for quantum theory and the science of consciousness. In particular, it may provide a quantum basis for panpsychism.