The Mind-Body Problem

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My Abstract

A process GRW universe composed solely of agents possessing free will

The Ghirardi, Rimini, Weber (GRW) interpretation of quantum mechanics naturalises measurement, unifies the macroscopic and microscopic, and explains why macroscopic objects have well-defined trajectories. A fault of GRW is that it proposes random (causeless) localisation events; because absolutely causeless events are metaphysically dubious. This presentation instead proposes that the universe consists of nothing other than agents possessing free-will in the (alternate-possibilities) sense of Conway and Kochen’s Free Will Theorem. Localisations depend on the choices of agents, whose propensities to act are given by the GRW statistical rules. The model: (1) specifies the agents in explicit physical terms (by maximally factorising the total wave function at that moment in history into factors that are mutually unentangled); explains (2) how inconsistencies among agents’ choices are resolved; (3) how the universe’s fixed past develops over time by adding single layers of space-like separated localisation events; (4) how agents come into being, combine and die: when another layer of localisations is added, the total wave function is changed slightly. Despite philosophical differences this model is empirically identical to the original GRW model. But, in contrast to the original, it is easy to demonstrate that this model satisfies the Free Will Theorem.

NOTES: With hindsight I would, (a) focus on Robert Kane’s theory of free will, rather than on the Free Will Theorem; (b) apply the theory to any Objective Reduction interpretation of quantum mechanics – not only to GRW.

My Poster

A process GRW universe composed solely of agents possessing free will

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INTRODUCTION

The GRW interpretation of QM is a spontaneous collapse theory with a physicalist ontology. This poster proposes that our universe (mathematically identical to GRW) is metaphysically different. It consists of nothing other than agents possessing free-will in the limited (Alternative Possibilities) sense of Robert Kane. Localisations depend on the choices of agents, whose propensities to act are given by the GRW statistical rules. The model: (1) specifies the agents in physical terms; and explains (2) how inconsistencies among agents’ choices are resolved; (3) the process by which the universe develops over time; (4) how agents come into being, combine and die.

Keywords: Agency, Combination problem, Causation, Entanglement, Free will, GRW, Idealism, Panpsychism, Process ontology

GRW in brief

The Ghirardi, Rimini, Weber (GRW) interpretation of quantum mechanics supposes that the wave function of the universe usually evolves according to the Schrödinger equation. But this is occasionally interrupted by a flash which localises the position of a given particle to within about 10^-5 cm of a particular place. The law about where flashes occur is defined so as to satisfy Born’s Rule. On average a given particle will undergo a flash once in every 10⁸ years. Flashes are measurement-like events, but they are defined objectively, without reference to observers. GWR naturalises measurement, unifies the macroscopic and microscopic, and explains why large objects have well-defined trajectories. The GRW theory is physicalist, with the flashes happening to particles spontaneously – at random and without any cause.

The theory outlined here is mathematically identical to GRW, but has an idealist ontology in which flashes are not random but are instead caused by agents.

Agents, Idealism and Realism

A given wavefunction is of the form ψ(some arguments; t), where t denotes the temporal evolution of the Schrödinger equation. But, according to GRW, this evolution is occasionally interrupted by flashes, which change the wavefunction to another. We will introduce a superscript T to denote different wavefunctions brought about by flashes. We will say that ψ^T is the wave function of the universe at cosmic time T. This can be expressed uniquely as a product:

Ψ^T = α₁^T α₂^T α₃^T α₄^T …

such that each α_i^T describes the state of a collection of entangled particles that cannot be factorised further.

Agents and their properties

• The α_i^T are precisely the agents that exist at cosmic time T. Every agent has a qualitative percept of at least some other agents.
• Agents behave lawfully, with a certain degree of freedom, according to their percepts.
• An agent’s freedom lies in its ability to cause its own particles to flash in any way that is consistent with: the GRW rules; its state of entanglement; and also the choices of other agents.
• Agents can consist of many entangled particles, thus forming macroscopic objects ranging in complexity from rocks to organisms.
• The set of agents existing at cosmic T+1 will be somewhat different from those at time T, but often the latter will be recognisable as descendants of the former. This gives a complete solution to what is known as the combination problem of panpsychism.

Idealism and Realism

Agents are omnipresent in this idealist scheme and, because of this, all physical facts can in principle be reduced to correspondences between structural facts that exist within the percepts of these agents (Ells, 2018). It is also realist, because the catalogue of agents listed by the idealist is essentially the same as the inventory of existents that would be given by a physicalist. The difference being that the physicalist only describes the mathematical structure of existents, and gives mathematical laws stating how they relate to each other; the idealist does all this, but also gives an account of the intrinsic character of the entities that possess this structure.

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TEMPORAL PROCESS in a FREE WILL GRW UNIVERSE

Definitions: flashes are GRW localisation events that have already occurred. Function Ψ⁰ is the initial wavefunction for the universe. The cosmic past is the union of the past light cones (including interiors) of all the flashes. The past is unalterable and is given uniquely by Ψ⁰ and the flashes. The cosmic present, or “now”, is the upper boundary of the cosmic past, shown by the zig-zag lines, which mark past-directed light cones.

Ψ^T is the current wave function of the universe, which is determined by Ψ⁰, and the flashes. It can be expressed uniquely as a product:

Ψ^T = α₁^T α₂^T α₃^T α₄^T … , where each α is an agent.

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STEP 1: At cosmic time T, independently of one another, each agent attempts to land all of its constituent particles at specific locations of its own choosing – subject to agreement with GRW & entanglement rules – in the future. (Attempts are shown as open circles.)The agents shown here are: six free particles; three entangled pairs; an entangled triplet; and an entangled quartet.

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STEP 2: Attempted flashes that lie within the future light-cone of other attempts are deleted (shown crossed out). The remainder are accepted (shown as a black dot), producing a new “now.”  We arrive at cosmic time T+1. Note the similarities between this, and the sketch for cosmic time T.

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ABOUT THE PROCESS

This two-step process is natural, and is perhaps the only possible one.

1. Each agent freely selects where it will attempt to flash. Its propensities for making these choices are in accordance with the GRW statistical rules, and its own state of entanglement; but the agent still retains true agency in Kane’s sense of Alternative Possibilities (1998, 33).
2. Inconsistencies between agents’ attempted choices are resolved by deleting all attempted flashes that lie in the future light-cones of other attempted choices.

Because idealism holds, the choices made by agents, which are the only true causes, are more fundamental than ‘randomness’, which is no more than a mathematical description of the propensities of agents to make these choices. Such choices are a primitive form of freedom, which every entity possesses, in a manner that is consistent with quantum mechanics. Kane rejects similar (what he calls) ‘agent-causation’ (hyphenated), but his rejection is not valid because he assumes physicalism (Kane, 1998, 187-95). With this reservation, Kane (1998) gives an excellent account of human libertarian free will.

Because, for each particle, flashes occur with a Poisson distribution according to GRW, the rejection of some attempted flashes is of no consequence.

Cosmic time T gives a foliation of the cosmos into spacelike slices of finite thickness. This foliation is not arbitrary, but arises as a natural consequence of the choices made by agents. If we take a process view of the evolution of the cosmos – in which, at cosmic time T: some events exist in the past; some events exist in the present; and future events merely exist as potentialities – then the two-step process seems inevitable. (The usual way to describe Aspect-type experiments, in the context of GRW, is to assume that the flashes at spacelike separated locations A and B occur either at A first, or at B first, but this is not relativistically valid, even though these distinct assumptions yield empirically indistinguishable results. The account given here is therefore preferable.) Looking at this idealist GRW ontology in terms of John Bell’s ‘beables’ (1976), we find that flashes are the local beables, agents are non-local beables, and Ψ is a global beable.

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CONCLUDING REMARKS

The poster describes an idealist GRW ontology in which the universe is comprised solely of agents possessing primitive free will. This can be extended, as detailed by Kane (1998), to a theory in which humans possess libertarian free will.

Idealist GRW gives a complete and precise solution to the well-known combination problem.

As developed so far, the theory lacks any description of the percepts of agents. The best one might expect in the future is a mathematical description of the structures that exist within the percepts of agents.

No account is given of qualia within this theory and none is expected in the foreseeable future. This is not a fatal flaw because the ontology is idealist: qualia can be taken as fundamental – and hence they require no explanation. What we can say is that experienced qualitative differences define the just-mentioned structures within percepts – rather in the manner that patches of contrasting colour bring into being the structures seen within a Mark Rothko painting.

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REFERENCES

Bell, J. (1976), ‘The theory of Local Beables’ Epistemelogical Letters 9; Dialectica 39, pp. 86-96.

Ells, P. (2011), Panpsychism: the philosophy of the sensuous cosmos (Winchester: John Hunt Publishing).

Ells, P. (2018), ‘Alternatives to physicalism’ in Castro, J., Fowler, B. & Gomes, L. (Eds.), Time, science and the critique of technological reason: essays in honour of Hermínio Martins (Switzerland: Palgrave Macmillan).

Ghirardi, G., Rimini, A., & Weber, T. (1986), ‘Unified dynamics for microscopic and macroscopic systems’ Phys. Rev. D 34, pp. 471-91.

Kane, R. (1998), The significance of free will (Oxford: Oxford University Press).