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arXiv:2406.16991

Derivation of a Schrödinger Equation for Single Neurons Through Stochastic Neural Dynamics

Partha Ghose

Published Jun 24, 2024• 0 citations
arXivHTMLPDF

Abstract

Despite the prevalent view that quantum mechanics is irrelevant to macroscopic biological systems because of inherent noise and decoherence, this paper demonstrates that the electrical noise (Brownian motion) in neuron membranes gives rise to an `emergent' Schrödinger equation involving a new neuronal constant $\hat{\hbar}$, fundamentally challenging the standard view of neuronal behaviour. This result could provide new insights into the underlying mechanisms of brain function, thus challenging existing paradigms in both quantum physics and neuroscience. A possible empirical test of this emergent quantum behaviour would be to look for quantum fluctuations in subthreshold neural oscillations.

DOI
10.48550/arxiv.2406.16991

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Despite the prevalent view that quantum mechanics is irrelevant to macroscopic biological systems because of inherent noise and decoherence, this paper demonstrates that the electrical noise (Brownian motion) in neuron membranes gives rise to an `emergent' Schrödinger equation involving a new neuronal constant ℏ^\hat{\hbar}ℏ^, fundamentally challenging the standard view of neuronal behaviour. This result could provide new insights into the underlying mechanisms of brain function, thus challenging existing paradigms in both quantum physics and neuroscience. A possible empirical test of this emergent quantum behaviour would be to look for quantum fluctuations in subthreshold neural oscillations.
It is unclear whether quantum phenomena can be observed in brain recordings because of thermal noise causing decoherence, that is, quantum superpositions and entanglement quickly collapsing into classical, i.e. non-quantum states. This paper first demonstrates that neuronal noise of the Brownian motion type is mathematically equivalent to a wave-particle description of the kind predicted by a fundamental equation in quantum mechanics known as the Schrödinger equation. It then extends the considerations to the more realistic FitzHugh-Nagumo model which has been widely used to describe neuronal dynamics. This approach could provide new insights into the underlying mechanisms of brain function.
Artificial intelligence (AI) has drawn significant inspiration from neuroscience to develop artificial neural network (ANN) models. However, these models remain constrained by the Von Neumann architecture and struggle to capture the complexity of the biological brain. Quantum computing, with its foundational principles of superposition, entanglement, and unitary evolution, offers a promising alternative approach to modeling neural dynamics. This paper explores the possibility of a neuro-quantum model of the brain by introducing a stochastic quantum approach that incorporates random fluctuations of neuronal processing within a quantum framework. We propose a mathematical formalization of stochastic quantum neural networks (QNNS), where qubits evolve according to stochastic differential equations inspired by biological neuronal processes. We also discuss challenges related to decoherence, qubit stability, and implications for AI and computational neuroscience.
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Abstract The nervous system probably cannot display macroscopic quantum (i.e. classically impossible) behaviours such as quantum entanglement, superposition or tunnelling (Koch and Hepp, Nature 440:611, 2006). However, in contrast to this quantum ‘mysticism’ there is an alternative way in which quantum events might influence the brain activity. The nervous system is a nonlinear system with many feedback loops at every level of its structural hierarchy. A conventional wisdom is that in macroscopic objects the quantum fluctuations are self-averaging and thus not important. Nevertheless this intuition might be misleading in the case of nonlinear complex systems. Because of a high sensitivity to initial conditions, in chaotic systems the microscopic fluctuations may be amplified upward and thereby affect the system's output. In this way stochastic quantum dynamics might sometimes alter the outcome of neuronal computations, not by generating classically impossible solutions, but by influencing the selection of many possible solutions (Satinover, Quantum Brain, Wiley & Sons, 2001). I am going to discuss recent theoretical proposals and experimental findings in quantum mechanics, complexity theory and computational neuroscience suggesting that biological evolution is able to take advantage of quantum-computational speed-up. I predict that the future research on quantum complex systems will provide us with novel interesting insights that might be relevant also for neurobiology and neurophilosophy.
The nervous system probably cannot display macroscopic quantum (i.e. classically impossible) behaviours such as quantum entanglement, superposition or tunnelling (Koch and Hepp, Nature 440:611, 2006). However, in contrast to this quantum ‘mysticism’ there is an alternative way in which quantum events might influence the brain activity. The nervous system is a nonlinear system with many feedback loops at every level of its structural hierarchy. A conventional wisdom is that in macroscopic objects the quantum fluctuations are self-averaging and thus not important. Nevertheless this intuition might be misleading in the case of nonlinear complex systems. Because of a high sensitivity to initial conditions, in chaotic systems the microscopic fluctuations may be amplified upward and thereby affect the system's output. In this way stochastic quantum dynamics might sometimes alter the outcome of neuronal computations, not by generating classically impossible solutions, but by influencing the selection of many possible solutions (Satinover, Quantum Brain, Wiley & Sons, 2001). I am going to discuss recent theoretical proposals and experimental findings in quantum mechanics, complexity theory and computational neuroscience suggesting that biological evolution is able to take advantage of quantum-computational speed-up. I predict that the future research on quantum complex systems will provide us with novel interesting insights that might be relevant also for neurobiology and neurophilosophy.
The nervous system is a non-linear dynamical complex system with many feedback loops. A conventional wisdom is that in the brain the quantum fluctuations are self-averaging and thus functionally negligible. However, this intuition might be misleading in the case of non-linear complex systems. Because of an extreme sensitivity to initial conditions, in complex systems the microscopic fluctuations may be amplified and thereby affect the system's behavior. In this way quantum dynamics might influence neuronal computations. Accumulating evidence in non-neuronal systems indicates that biological evolution is able to exploit quantum stochasticity. The recent rise of quantum biology as an emerging field at the border between quantum physics and the life sciences suggests that quantum events could play a non-trivial role also in neuronal cells. Direct experimental evidence for this is still missing but future research should address the possibility that quantum events contribute to an extremely high complexity, variability and computational power of neuronal dynamics.