Derivation of a Schr\"{o}dinger Equation for Single Neurons Through Stochastic Neural Dynamics

TL;DR

This paper proposes that electrical noise in neuron membranes can lead to an emergent Schrödinger equation, suggesting a quantum-like behavior in neurons that challenges traditional neuroscience and quantum physics views.

Contribution

It introduces a novel derivation of a Schrödinger equation from neuronal stochastic dynamics, implying quantum effects may play a role in brain function.

Findings

Electrical noise induces an emergent Schrödinger equation in neurons

A new neuronal constant e4hbarf is proposed

Potential empirical test involves quantum fluctuations in neural oscillations

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' Schr\"{o}dinger 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.