Since the early days of quantum mechanics, physicists and philosophers argued that resolving the measurement problem requires an appeal to the minds of conscious observers. That is still the case today, argues Shan Gao.

Quantum mechanics is a very successful physical theory due to its accurate empirical predictions. But a key puzzle remains at its core: the measurement problem. There seems to be a conflict between what Schrödinger’s equation tells us, namely that a system described by the wave function can be in a state of superposition, instantiating apparently conflicting properties, and what experience tells us, namely that when we take a measurement of such a system, we get one, definite result, not a superposition. To use Schrödinger’s thought experiment, quantum mechanics would seem to imply that a cat can be both alive and dead at the same time, but we only ever experience cats that are either alive or dead. 

There are a number of proposed solutions to the measurement problem, including what has come to be known as the hidden variables theory, which suggests that the wavefunction isn’t a full description of a system and does away with states of superposition, and the many-worlds interpretation, that suggests the superpositions are expressed across different universes, each with one definite result. But ever since the early days of quantum mechanics, physicists and philosophers have argued that the human mind is needed to resolve the measurement problem. In order to understand why that’s still the case, we need to look at the measurement problem and the proposed solutions more closely.

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Formalizing the measurement problem

In 1995, Tim Maudlin gave a precise formulation of the measurement problem. According to this formulation, the measurement problem originates from the incompatibility of the following three claims:

(C1) The wave function of a physical system is a complete description of the system;

(C2) the wave function always evolves in accord with a linear dynamical equation, such as the Schrödinger equation;

(C3) a measurement yields a single definite result.

There are three main approaches to solving the measurement problem thus formulated. The first approach is to deny the claim (C1) and add certain hidden variables and corresponding dynamics to explain the definite measurement results. A well-known example is the pilot-wave theory of de Broglie and Bohm, or Bohmian mechanics. The second approach is to deny the claim (C2) and revise the linear and deterministic Schrödinger equation by adding certain nonlinear and stochastic evolution terms, which describe the dynamical collapse of the wave function, to explain the definite measurement results. Such theories are called collapse theories. The third approach is to deny the claim (C3) and assume the existence of many equally real worlds to accommodate all possible results of measurements. In this way, it may also explain the definite measurement results in each world including our world. This approach is called Everett’s theory or the many-worlds interpretation of quantum mechanics.

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When you observe that the pointer of a measuring device points to a definite position after a measurement, are you really sure that the pointer indeed points to a definite position as a matter of fact?

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Where does the mind come into quantum mechanics?

So far we have not talked about observers and their minds. And it seems that quantum mechanics has nothing to do with consciousness. However, there are two well-known and intriguing conjectures which say that quantum mechanics and consciousness have intimate connections. These two conjectures are both related to the collapse theories. The first one suggests that consciousness causes the collapse of the wave function. This conjecture has a long history, and it can be traced back to von Neumann (1932), London and Bauer (1939), Wigner (1961), and Stapp (1993). Recently Chalmers and McQueen (2022) give a more rigorous and complete formulation of the conjecture based on the Integrated Information Theory (IIT) of consciousness. The other one argues that the collapse of the wave function creates consciousness. This conjecture is proposed by Penrose and Hameroff (1996, 2014), and it has been called the Orchestrated Objective Reduction model. Admittedly, many researchers in this field think that these two conjectures are too radical to be true, although experiments have not yet given us a final answer either way.

So, does mind really matter in quantum mechanics? My answer is yes, at least for now. Let me ask you a simple question. When you observe that the pointer of a measuring device points to a definite position after a measurement, are you really sure that the pointer indeed points to a definite position as a matter of fact? Unfortunately, I must say that physicists still don’t know whether the pointer points to a definite position in this case. In fact, what we know with certainty, by experience, is only that we as observers obtain a definite record after a measurement by having a definite mental state of that record. But we don’t know with certainty whether a measuring device really obtains a definite result after a measurement. For example, if the mental state is determined randomly by one result branch of the post-measurement superposition as in the single-mind theory (Albert and Loewer, 1988), then the pointer of a measuring device does not indicate a definite position after a measurement, but an observer will obtain a definite record after an observation of the position of the pointer.

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Thus we must ASSUME a certain form of psychophysical connection in quantum theories for now. Without an assumption about the connection between mind and quantum mechanics, we cannot even test the predictions of a quantum theory, since measurements are made by an observer in the final analysis, and a measurement finishes only when the result is consciously perceived by an observer. This motivates a more fundamental formulation of the measurement problem for observers (Gao, 2019), which states the incompatibility of the following three assumptions:

(A1) The mental state of an observer is determined by her wave function;

(A2) the wave function always evolves in accord with a linear dynamical equation, such as the Schrödinger equation;

(A3) a measurement by an observer yields a single mental state with a definite record.

This formulation of the measurement problem highlights the important role of psychophysical connection in causing the problem. With this new formulation, we can look at the solutions to the measurement problem from a new angle. In particular, the three main realist quantum theories, namely Bohmian mechanics, Everett’s theory, and collapse theories, correspond to three different forms of psychophysical connection. In fact, there are only three types of physical states that may determine the mental state of an observer, which are (1) the wave function in collapse theories, (2) certain branches of the wave function in Everett’s theory, and (3) other hidden variables such as particle configuration in Bohmian mechanics.

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Notwithstanding the big progress in neuroscience and quantum technologies, quantum mechanics and consciousness remain two mysteries in our times

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As an optimist, I believe that we will eventually know which form of psychophysical connection and which quantum theory is true. That’s one basic reason I qualify the claim that mind matters in quantum mechanics for now. Another deeper reason is that the form of psychophysical connection assumed by a quantum theory has to be consistent with our current scientific and philosophical understandings of the conscious mind. In other words, an analysis of the minds of observers may help determine which quantum theory is false.

Take Bohmian mechanics as an example. In Bohmian mechanics, the physical state, which determines the result of a measuring device and the mental state of an observer, is not the wave function but the configuration of the Bohmian particles. These particles have only positions and velocities in three-dimensional space, have no mass or charge, and they have no interactions with each other either (when their wave function is not an entangled state). An interesting question then arises: can these Bohmian particles compose brains that create conscious minds? Or, to put it otherwise, do observers have conscious minds in Bohmian mechanics?

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It is a fundamental postulate in neuroscience and philosophy of mind that the parts of a system must be strongly connected to each other so that it can generate the conscious mind. A typical example is the Integrated Information Theory of consciousness, which is one of the leading theories of consciousness. According to that theory, consciousness requires a grouping of elements within a system that have physical cause-effect power upon one another, and the level of consciousness of a system is described by the integrated information of the system, which can be represented by a precise mathematical quantity Φ. A system whose elements have strong connections will have high Φ, while a system whose elements have weak connections will have low Φ. Our brain has very high Φ, and it is therefore highly conscious. By contrast, if the components of a system have no connections, the system will have zero Φ, which means that it is not conscious at all.

Now let's turn to the key issue: what if our brain is composed only of the Bohmian particles? Could this Bohmian brain generate the conscious mind? We need a common assumption in neuroscience and philosophy of mind to answer this question. It is that our conscious mind is generated by the activities of some quasi-classical systems such as neurons in our brain without involving quantum entanglement. In this case, the effective wave function of these quasi-classical systems is a product state, or in other words, each system has its own effective wave function or wavepacket, and the motion of its Bohmian particles is guided only by its wavepacket.

Then, we can argue that such a Bohmian brain cannot generate the conscious mind. For example, according to the Integrated Information Theory of consciousness, a Bohmian brain will have zero Φ and thus have no conscious experiences, since there are no connections between the Bohmian particles of the nonentangled quasi-classical systems in the brain, and the whole system does not integrate information.

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Without an assumption about the connection between mind and quantum mechanics, we cannot even test the predictions of a quantum theory

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The above example of Bohmian mechanics demonstrates that mind indeed matters in quantum mechanics for now. According to our current understandings of the conscious mind, our bains cannot be composed only of Bohmian particles since they cannot create the conscious minds we have, and thus certain versions of Bohmian mechanics (whose ontology consists only of particles) are probably false.

Notwithstanding the big progress in neuroscience and quantum technologies, quantum mechanics and consciousness remain two mysteries in our times. In my view, a careful and thorough examination of possible connections between them is not only necessary but also even pressing in order to unravel these two mysteries. I really hope this article will inspire more people to join the search for the ultimate reality of the universe.