In collaboration with David Chalmers (NYU), we are working on formulating mathematically precise and experimentally verifiable formulations of the hypothesis that consciousness causes the collapse of the wave-function.

I recently presented this research at the 2016 Science of Consciousness conference. A video clip of the talk can be found here.

A follow-up interview for Consciousness TV can be found here.

A presentation of an earlier stage of this research by David Chalmers, from 2014, can be found here.

A pop science article, aimed at a general audience, can be found here.

—–

The textbook formulation of quantum mechanics (John von Neumann, 1932) describes physical systems by a wave-function. The wave-function evolves deterministically when no measurements occur. But when measurements occur the wave-function undergoes a sudden indeterministic evolution called wave-function collapse. This theory is inadequate because it does not specify what measurement is, and consequently, why or when collapse occurs.

The most common reactions to this problem involve modifying the textbook theory significantly. The three most common approaches involve (i) removing the collapse postulate [many worlds interpretation]; (ii) removing the collapse postulate and introducing additional variables [Bohmian mechanics etc.]; and (iii) attributing to particles a probability per unit time for spontaneous collapse [GRW, Pearle, etc.].

There is an alternative, largely unexplored way of proceeding, which attempts to stay as close to the textbook framework as much as possible. The motivation for doing so is the success of the textbook theory, which suggests that we should not give up on it too easily. The basic idea involves interpreting the textbook theory as endowing certain physical entities with a special property – a “measurement property” – which is responsible for collapse. To remove reliance on “measurement”, we call these “m-properties”. We refer to this framework as “m-property theory”. M-properties are precisely definable properties that refuse superposition and respond with collapse. An existing example of this general idea is the Penrose-Diosi theory, which treats spacetime curvature as an m-property. But m-property theory is more general, in principle allowing any number of properties to be the m-property. Different hypotheses for the m-property will require different fundamental laws that govern the candidate m-property’s behaviour.

To make the consciousness causes collapse hypothesis precise we consider neuroscientific proposals for the physical correlate of consciousness and whether they can be treated as m-properties. Our first two hypotheses come from considering the integrated information theory (IIT) of consciousness.

The first hypothesis uses the property that IIT treats as the physical correlate to a system’s consciousness: the system’s maximally irreducible conceptual structure (MICS). The fundamental law describing how a system’s MICS can act as its m-property is best formulated analogously to the Penrose-Diosi model of collapse. On their view, spacetime curvature is the m-property, and as the difference in the curvature between two components of a curvature superposition rises, the probability of collapse to one of those curvatures rises. Analogously, we can say that as the difference in the MICS between two components of a MICS superposition rises, the probability of collapse to one of those MICSs rises. The difference between two MICSs can arguably be defined in terms of distance in IIT qualia space.

The second hypothesis uses the property that IIT treats as the physical correlate to a system’s *amount* of consciousness: the system’s amount of integrated information (*phi*). The fundamental law describing how a system’s *phi *can act as its m-property is best formulated analogously to the GRW-Pearle model of collapse. On their view, the probability per unit time for spontaneous collapse (to position) is a function of the system’s particle number. Analogously, we can say that the probability per unit time for spontaneous collapse (either to *phi* or to position) is a function of the system’s *phi*. Recently, a version of this hypothesis has been explored by Kobi Kremnizer and André Ranchin. On their model, the probability per unit time for spontaneous collapse (to position) is a function of the system’s *quantum integrated information*.

As well as spelling out these and other m-property theories in detail, we aim to draw out philosophical implications for the mind-body problem. A draft paper will be uploaded here within the coming months. So watch this space!