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arXiv:quant-ph/0309166

"Measurement" as a neurophysical process: a hypothetical linear and deterministic scenario

L. Polley

Published Sep 23, 2003• 1 citation
arXivHTMLPDF

Abstract

Tunnel amplitudes of molecular configurations (like neuronal channel pores) may be very sensitive to thermal vibrations of the barrier width (vibration-assisted tunneling) resulting in pseudo-random spikes of widely varying sizes. An observer who ``lives'' behind the barrier would experience as an ``event'' an accidental minimum of the barrier width, the timing being determined by the microstate of the neuron's heat bath. In two neurons, set to detect a ``left'' or ``right'' state of an object, firing amplitudes typically differ so much as to produce a quasi-selection of one option.

DOI
10.48550/arxiv.quant-ph/0309166

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Tunnel amplitudes of molecular configurations (like neuronal channel pores) may be very sensitive to thermal vibrations of the barrier width (vibration-assisted tunneling) resulting in pseudo-random spikes of widely varying sizes. An observer who lives'' behind the barrier would experience as an event'' an accidental minimum of the barrier width, the timing being determined by the microstate of the neuron's heat bath. In two neurons, set to detect a left'' or right'' state of an object, firing amplitudes typically differ so much as to produce a quasi-selection of one option.
A non-collapse scenario for ``conscious'' selection of a term from a superposition was proposed in quant-ph/0309166: thermally assisted tunneling of neuronal pore molecules. But ``observers'' consisting of only two neurons appear to be at odds with Born's rule. In the present paper, an observer is assumed to possess a large number of auxilliary properties irrelevant for the result of the measurement. Born's rule then reduces to postulating that, prior to the result becoming conscious, irrelevant properties are in an entangled state with maximum likelihood, in the sense that phase-equivalent entanglements cover a maximal fraction of the unit sphere (leading to equal-amplitude superpositions).
In cortical neurons, spontaneous membrane potential fluctuations affect the likelihood of firing an action potential. Yet despite retaining sensitivity to random electrical noise in gating signaling outcomes, these cells achieve highly accurate computations with extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron firing as a thermodynamic process of non-deterministic computation. Typically, the cortical neuron is modeled as a binary computational unit, in either an off-state or an on-state, but here, the cortical neuron is modeled as a two-state quantum system, with some probability of switching from an off-state to an on-state. This approach explicitly takes into account the contribution of random electrical noise in gating signaling outcomes, particularly during cortical up-states. In this model, the membrane potential is described as the mixed sum of all component microstates, or the quantity of von Neumann entropy encoded by the computational unit. This distribution of macrostates is given by a density matrix, which undergoes a unitary change of basis as each unit, ‘System A’, interacts with its surrounding environment, ‘System B’. Any linear correlations reduce the number of distinguishable pure states, leading to the selection of an optimal system state in the present context. This process of information compression is shown to be equivalent to the extraction of predictive value from a thermodynamic quantity of information. Calculations demonstrate that estimated coulomb scattering profiles and decoherence timescales in cortical neurons are consistent with a quantum system, with random electrical noise driving signaling outcomes.
The dynamics of resonant tunneling via a spatially oscillating narrow well is investigated. The well generates a quasiresonance state, which can trap the incoming particles. Four spectral regimes are found: (1) the adiabatic regime, when the vibrations' frequency is lower than the spectral width of the resonance. In this regime, the mean current is independent of the vibration's frequency, and the current decreases as a function of the vibration's amplitude. (2) When the frequency of the vibration is higher than the spectral width of the resonance, the particle is partially trapped to the moving well and the dependence of the current on the vibrations' amplitude is more moderate. (3) However, and this is the main result of this paper, beyond a certain frequency the kinetic energy of the trapped particle exceeds the spectral width of the resonance, in which case particles cannot be trapped in the moving well and the current is abruptly suppressed. (4) When the energy quanta of the vibrations are higher than the energy gap between the resonance energy and the barrier's potential height, a single phonon can be absorbed by the particle only when the final energy agrees with the resonances of the barrier, in which case current suppression is selective and occurs only for specifics frequencies. The model is solved exactly numerically, and analytical approximations are presented for the different regimes. The analytical solutions show high agreement with the numerical ones. This effect can be implemented in extremely sensitive accelerometers. Moreover, it may explain the odor receptor's sensitivity to molecular vibrations.