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European journal of applied sciences

A Dual Hilbert-space Formalism for Consciousness; Memory Experiments

R. Englman, Asher Yahalom A

Published Mar 25, 2024• 1 citation
Publisher

Abstract

Inspired by works of W. H. Zurek and others, a mathematical, physical theory, entirely within a quantum mechanical formalism, is proposed for cognitive processes in terms of an abstract Hilbert-space for the conscious state that is an exact replica of the Hilbert-space for the neuronic physical state. Thus, any actual state of consciousness arises by its formal alignment (identification) with some-one in the set of the neuronic states, with the latter undergoing perpetual changes in the wake of life-long experiences. It is posited that these changes become expressed by an increase in the number of ordered, coherent neuronic states at the expense of the pre-ordinal random neuronic states. Changes, transitions between states are induced by a Gorini-Kossakowski-Sudarshan-Lindblad formalism, which is also instrumental in the effect of the conscious state on bodily actions. The paradigmatic findings of R.N. Shepard (1958 - 2011) and of S. Sternberg (1966 - 2016) for long- and short-term recalls are interpreted within the model.

DOI
10.14738/aivp.123.16966

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Inspired by works of W. H. Zurek and others, a mathematical, physical theory, entirely within a quantum mechanical formalism, is proposed for cognitive processes in terms of an abstract Hilbert-space for the conscious state that is an exact replica of the Hilbert-space for the neuronic physical state. Thus, any actual state of consciousness arises by its formal alignment (identification) with some-one in the set of the neuronic states, with the latter undergoing perpetual changes in the wake of life-long experiences. It is posited that these changes become expressed by an increase in the number of ordered, coherent neuronic states at the expense of the pre-ordinal random neuronic states. Changes, transitions between states are induced by a Gorini-Kossakowski-Sudarshan-Lindblad formalism, which is also instrumental in the effect of the conscious state on bodily actions. The paradigmatic findings of R.N. Shepard (1958 - 2011) and of S. Sternberg (1966 - 2016) for long- and short-term recalls are interpreted within the model.
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states, which are pairwise orthogonal. In this formalism, I prove that a conscious observer is necessarily a physical object that can memorize local events by setting one of its parts in an exactly specified constant quantum state (hypotheses H1, H2 and H3). Then I define the probability of a future event as the proportion of initial observers, all identical, who will actually experience that event. It then becomes possible to establish the usual results of quantum mechanics. Furthermore, I detail the link between probabilities and relative frequencies. Additionally, I study the biological feasibility of this modelling of observer's mind. The second part of this paper completes the neuronal description of the mind functions, based on current neuroscientific knowledge. It provides a model that is compatible with the assumptions of the first part and consistent with our daily conscious experience. In particular, it develops a model of self-consciousness based on an explicit use of the random component of neuron behaviour; according to the first part, that random is in fact the coexistence of a multiplicity of possibilities. So, when the mind measures the random part of certain neurons in the brain, he goes himself within each of these possibilities. The mind has a decision-making component that is active in this situation, appearing then as the cause of the choice of this possibility among all the others. This models the self-consciousness which then ensures the unity of our conscious experience by equating this experience with ``what the ego is conscious about''. The conclusion details the points that remain to be developed.
A model of consciousness is proposed, in which the experience attributable to a single neuron is related to its instantaneous firing rate. In that the experience afforded by a sensory neuron can only be quantified within statistical limits from the incidence of spikes across multiple presentations of a stimulus, consciousness remains inaccessible to direct measurement on a single trial. In this way, the model disambiguates subjective experience from objective neural properties. The model adopts a quantum mechanical formalism, in which the state of the neuron is represented as a vector in \nA complex vector space, or as a projector from the space onto that vector. Extension of this formalism to more realistic neural systems merely requires the assimilation of the quantum mechanical principles applicable in this broader context. \nInitially, a mathematical expression for the smooth evolution of a single dimension of perceptual experience will be derived for the single neuron case. \n \nThere follows a description of how the neural state itself might evolve in this \nprocess, utilising the quantum operations formalism of amplitude damping. This approach reveals how smooth evolution of conscious experience might arise from discrete spikes and discontinuous synaptic interaction between neurons. A tensor product formalism will be used to describe the combination of state spaces of individual neurons to form a composite neural space, in which a pure 'mental state' would represent unified conscious experience. The binding of elementary features in this non-local mental state would be reflected in specific patterns of correlated neural firing between remote brain regions. In contrast, the conventional neuron doctrine is classical and local realistic. Local realistic constraints, expressed as Bell Inequalities, limit potential correlations in firing between remote neurons, presenting an opportunity for the experimental test of the scheme in a neurophysiologic thought experiment.
This paper proposes a "Consciousness Decoherence Model" grounded in a structured metaphor drawn from quantum decoherence theory. The model frames pre-conscious states as a superposition of multiple possible contents, and characterizes the formation of conscious awareness as a process of decoherence—triggered by internal and external "environments" (including sensory input, interoception, and attention)—that stabilizes one specific classical state into reportable awareness. Through systematic conceptual mapping and comparative analysis with Global Neuronal Workspace Theory, Integrated Information Theory, and other recent decoherence-inspired frameworks, the model unifies diverse cognitive phenomena such as creative insight, decision paralysis, and psychopathological states under a single dynamical logic.
Quantum consciousness concerns both the possible role that quantum mechanics has for understanding consciousness as well as the role that consciousness has for interpreting quantum physics. Quantum brain theories hypothesize that quantum physical processes occur within and between the neurons of the brain and have important effects on cognition as well as consciousness. Quantum cognition is a growing new field in cognitive science concerned with the application of the mathematical principles of quantum theory to human judgment and decision-making behaviour. What do all these theories have to do with each other? Quantum theories of consciousness have more to say about quantum physics than cognitive psychology and conscious experiences. Quantum brain theories have not been sufficiently ‘scaled up’ to provide clear implications for how quantum physical processes generate more complex cognition. Quantum cognition theories have avoided addressing fundamental issues about consciousness and have remained agnostic with respect to the quantum brain hypothesis. This article will address the problem of connecting these ideas together by connecting quantum cognition to the other two topics.
We develop the mathematical and physical formulation of cognitive cost optimization that underlies the path-integral model of consciousness. The goal-directed cognitive process is modeled as imaginary-time evolution (ITE) under a projector Hamiltonian that rewards configurations consistent with a target concept. We establish three results. First, this ITE coincides with a double-bracket flow and is therefore the Riemannian gradient flow of a Hilbert--Schmidt cost whose unique minimum is the solution. Second, a Wick rotation re-expresses this non-unitary descent as an equivalent unitary evolution on the same Hilbert space, which admits an exact discrete path-integral representation in which the oracle and the initial-state diffusion projector play the roles of potential and kinetic energy. Third, we identify the continuum from unconscious to conscious processing with the strength of the unitary interaction between the cognitive system and a neural-environment probe, recovering the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) decoherence model of Asano \textit{et al.} in the Markovian weak-coupling limit, and the projective, reportable fixation of an optimized state in the strong-coupling limit, an insight-like ``Aha'' endpoint. Both regimes share the same ITE and path-integral structure, and only the measurement-interaction strength varies. The Wick rotation is therefore a technique of re-description, not a physical regime change.
The ideas of Sensible Quantum Mechanics are expressed in lay terms for philosophers of consciousness and others. A framework is proposed and explained for the `psycho-physical-parallelism' between conscious experiences and the mathematical structures of quantum physics (e.g., a set of quantum operators obeying some algebra, and a quantum state giving the expectation value of each operator). In particular, it is proposed that each set of possible conscious experiences has a measure given by the expectation value of a corresponding operator (a positive-operator-valued measure). Then one has a generalization of the Weak Anthropic Principle named the Conditional Aesthemic Principle: given that we are conscious beings, our conscious experiences are likely to be typical experiences in the set of all conscious experiences with its measure.