DO WE NEED QUANTUM MECHANICS TO EXPLAIN HOW THE BRAIN WORKS?

Roger Penrose

COSMAS K. ZACHOS

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides — coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.

Herbert S. Green, T. Triffet

Patrick Suppes, J. Acácio de Barros

Saul Youssef

We show that the phenomena explained by quantum mechanics can alternatively be explained as a breakdown of probability theory without the need for wave-particle duality or the idea that a particle does not have a unique path in space. The single-particle Lagrangian consistent with the reformulated quantum mechanics is derived and specialized to the Schrödinger and Klein-Gordon theories. The usual paradoxes of quantum mechanics are explained. A connection to gravity is proposed. Probability theory is restored in the classical limit.

To study brain impulses, we adopted the Schrodinger picture from Quantum Mechanics.We began by examining the time-dependent Schrodinger equation and solving it, which led to the derivation of the Schrödinger picture.In this framework, the state vector evolves over time while the operators remain fixed.By drawing an analogy between the state vector and brain impulses, we proposed that brain activity can be modeled and analyzed within this mathematical framework.This approach provides a novel perspective on understanding brain impulses through the principles of quantum mechanics.