The Hard Problem and the Measurement Problem: a No-Go Theorem and Potential Consequences

The hard problem and the measurement problem: a no-go theorem and potential consequences Igor Salom Institute of Physics, Belgrade University, Pregrevica 118, Zemun, Serbia The \measurement problem" of quantum mechanics, and the \hard problem" of cognitive science are the most profound open problems of the two research fields, and certainly among the deepest of all unsettled conundrums in contemporary science in general. Occasionally, scientists from both fields have suggested some sort of interconnectedness of the two problems. Here we revisit the main motives behind such expectations and try to put them on more formal grounds. We argue not only that such a relation exists, but that it also bears strong implications both for the interpretations of quantum mechanics and for our understanding of consciousness. The paper consists of three parts. In the first part, we formulate a \no-go-theorem" stating that a brain, functioning solely on the principles of classical physics, cannot have any greater ability to induce subjective experience than a process of writing (printing) a certain sequence of digits. The goal is to show, with an attempt to mathematical rigor, why the physicalist standpoint based on classical physics is not likely to ever explain the phenomenon of consciousness { justifying the tendency to look beyond the physics of the 19th century. In the second part, we aim to establish a clear relation, with a sort of correspondence mapping, between attitudes towards the hard problem and interpretations of quantum mechanics. Then we discuss these connections in the light of the no-go theorem, pointing out that the existence of subjective experience might differentiate between otherwise experimentally indistinguishable interpretations. Finally, the third part is an attempt to illustrate how quantum mechanics could take us closer to the solution of the hard problem and break the constraints set by the no-go theorem. INTRODUCTION statement. This cannot be easily brushed aside as he then completely relies on this assumption to infer, as he writes a bit later, that the wavefunction collapse thus appears Some critics rightfully argue that majority of attempts merely as a sort of illusion in the subjective experience of to relate the quantum measurement problem with the the observer. hard problem of consciousness follow a pretty shallow reasoning pattern: both problems are difficult and open, We will return to this aspect of the many-worlds in- so thus they must be somehow related. Indeed, we are not terpretation (MWI) when dealing more comprehensively aware of many serious scientific papers (clearly set apart with the relation between the hard problem and the inter- from pseudoscience) which discuss the precise connection pretations of quantum mechanics (QM). Of course, it is of the two problems. And yet, the existence of this con- not only the many-worlds interpretation that takes sides nection is nevertheless beyond any dispute, at least for- in the cognitive science debate, nor it is only the hard-line mally. As this might sound to some as a (slightly at least) physicalist views that enjoy the support of the physicists. controversial statement, we will right away mention an Quantum mechanics has been notorious for flirting with example that clearly proves the assertion. In Everett's ideas on consciousness that were not generally considered seminal paper [1, 2] (doctorate thesis, to be more pre- as mainstream in the western school of thought. Since the cise) where he introduces the \relative state formalism" advent of quantum mechanics, scientists were perplexed { the basis of now quite popular many world's interpre- by the new role that the act of observation had seem- tation { he explicitly writes: \As models for observers ingly gained in physics. Basic (Copenhagen) formulation we can, if we wish, consider automatically functioning of QM carried an inherent, though maybe unspoken, sub- machines, possessing sensory apparata and coupled to jective character that was hard to avoid in the measure- recording devices capable of registering past sensory data ment postulate, palpable in the vagueness of (or lack of) and machine configurations”. Therefore, by equating ob- the definitions of the \measurement apparatus" and the server with an automaton, he decisively takes a very defi- \moment of measurement". The formalism allowed the nite side in the ongoing debate in the contemporary cog- Heisenberg cut { that was dividing the objective realm nitive science and also in AI research (presuming such of superpositions governed by deterministic Schrodinger automaton would possess \strong AI"1), seemingly not equation and the subjective perception of a single well- even noticing that he is introducing a highly nontrivial defined stochastic measurement outcome { to be posi- tioned fluidly and arbitrarily along the von Neuman's chain. This prompted some of the founding fathers of QM to assume crucial interconnection between the phe- 1 Term coined by J. Searle for a machine with mind, i.e. conscious- nomenon of subjective experience and the basic laws of ness. nature: from Heisenberg's \the concept of the objective 2 reality of the elementary particles has thus evaporated..." tion is applicable from the \third-person view". Apart [3], via Planck's \I regard consciousness as fundamen- from the explicitly \subjectivist" reading of Copenhagen tal, I regard matter as derivative from consciousness" [4], interpretation, but similar to it, in the group of interpre- to Schrödinger's\mind has erected the objective outside tations that fully acknowledge both postulates at the ex- world...out of its own stuff (from his book of an appro- pense of introducing observer-dependent elements (such priate title \Mind and Matter" [5]) and all the way to as subject/observer/system relative collapse) are also the most radical Wigner's stance that \consciousness" e.g. Wheeler's \participatory universe" concept [9, 10], objectively causes reduction of the wavepacket [6]. QBism [11], relational interpretation [12] and Brukner's The dilemma of whether the wavefunction collapse is variant of the latter [13, 14]. Some of these views ad- objective or subjective (if existent at all) still lingers, be- vocate a relatively radical denial of the existence of ob- ing a divergence point of many interpretations of QM. jective (non-observer-relative) facts in general (Brukner's The views that hold the collapse to be truly objective, \no facts of the world" doctrine), but this is not a neces- in some experimentally measurable way, actually should sity [15]. While all these views see collapse to some extent not be seen as interpretations of QM, but as scientific as subjective only, the collapse nevertheless does happen, proposals which predict new physics (we prefer to de- and a subject exists always in a single well-defined state note this type of ideas as \mechanical collapse" models). of reality (from his reference point at least). This is to Namely, in whichever way the objective collapse is there be contrasted with the many-world interpretations (or, envisioned, such a collapse event can be in principle en- somewhat more generally, Everett's relative state inter- closed in an isolated box and the following noted: the pretation) where the subject himself keeps being in a Schrödingerequation dictates that the evolution within superposition and subjective perception of a single real- the box must be linear and unitary, while the proposed ity is a sort of illusion itself (the result of a certain brain objective wave-packet reduction demands the opposite. state being correlated with only the corresponding state The expected violation of unitarity is, in principle, a of the environment). measurable effect and thus requires both experimental Therefore, from the speculations of the fathers of QM confirmation (so far in all cases lacking) and a mathe- to the present-day debates on the enduring issues, at- matical modification of the QM formalism that would tempts to understand quantum mechanics have often replace and extend Schrodinger's equation in a consis- led out of the boundaries of the purely objective realm, tent way. Very diverse ideas belong to this same cat- touching upon the problems of cognition and subjective egory of objective (mechanical) collapse, some of them perception. proposing certain relations to \consciousness" and some More recently, in a last few decades, we have witnessed not at all: from purely physicalist GRW collapse models a push from the opposite direction: researchers dealing [7], over Penrose-Hameroff orchestrated objective reduc- with the \hard problem of consciousness" are increas- tion hypothesis [8], to Wigner's expectation that \con- ingly looking in direction of quantum mechanics, feeling sciousness" should somehow cause this objective collapse that some extension of the classical physics paradigm (ei- [6]. While all suffer from the same lack of a slightest ex- ther into quantum mechanics or into something else) is a perimental indication in their favor, those attempting to prerequisite for further progress in their field. Namely, in relate collapse with mental phenomena in an experimen- spite of the advances in the understanding of brain func- tally confirmable way are further hampered by difficulties tions and of the neural correlates of consciousness { and to construct a consistent underlying mathematical theory maybe even more so due to these advances { many scien- (most evident in the Wigner's case: whose conscious- tists and philosophers find that there is an \explanatory ness is entitled to cause collapse, would a mouse, or an gap" between understanding of how the brain functions amoeba, or single neuron suffice, and how to write down and why does that functioning produce any subjective, an analogon of the Schrödingerequation which would first-person experience. Most notably, this problem with break down unitarity only for complex enough systems a long philosophical history has been, some 20 years ago, representing conscious observers?) rephrased by David Chalmers as the \hard problem of There is a fairly common misconception that relat- consciousness": even if we understand all brain functions ing QM with subjective, i.e.

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