Abstract. The recent controversy of applicability of quantum formalism to brain dynamics has been critically analyzed. PELLIONISZ and LLINÁS (1982) proposed a functional geometry to understand the internal representation of the events associated to the space-timing of moving objects in the external world. The joint representation of space and time associated to an event as understood by the brain is shown to be different from that understood in modern physics. This indicates that the four-dimensional geometry i.e. Minkowski geometry is not an appropriate description for the internal world. If it is to be the case, the applicability of any kind of quantum field theory in modeling brain function has to be analyzed with great care. Here, the issue of applicability of quantum mechanics to brain function has been discussed in general, from an anatomical perspective and then particular emphasis has been given to the applicability of quantum field theory. 1.
Abstract. The recent controversy of applicability of quantum formalism to brain dynamics has been critically analyzed. PELLIONISZ and LLINÁS (1982) proposed a functional geometry to understand the internal representation of the events associated to the space-timing of moving objects in the external world. The joint representation of space and time associated to an event as understood by the brain is shown to be different from that understood in modern physics. This indicates that the four-dimensional geometry i.e. Minkowski geometry is not an appropriate description for the internal world. If it is to be the case, the applicability of any kind of quantum field theory in modeling brain function has to be analyzed with great care. Here, the issue of applicability of quantum mechanics to brain function has been discussed in general, from an anatomical perspective and then particular emphasis has been given to the applicability of quantum field theory. 1.
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of brain permits any kind of smooth geometric notion like Hilbert structure or four dimensional Minkowskian structure for quantum field theory. The present understanding of brain function clearly denies any kind of space-time representation in Minkowskian sense. However, three dimensional space and one time can be assigned to the neuromanifold and the concept of probabilistic geometry is shown to be appropriate framework to understand the brain dynamics. The possibility of quantum structure is also discussed in this framework.
The question of whether quantum mechanical phenomena play a functional role in brain activity and the emergence of consciousness remains one of the most controversial yet intellectually stimulating debates at the intersection of physics, neuroscience, and philosophy of mind. This review systematically examines the principal theoretical frameworks proposing quantum-level mechanisms in neural computation, including the Orchestrated Objective Reduction (Orch OR) hypothesis by Penrose and Hameroff, the quantum brain hypothesis of Stapp, quantum coherence models in microtubules, and quantum field theories of consciousness. We critically evaluate the current state of empirical evidence—including recent quantum biology findings, the challenge of decoherence in warm, biological systems, and experimental observations of quantum effects in biological systems—alongside computational models that bridge quantum formalism and neural network dynamics. Furthermore, we discuss the implications of quantum cognition models for understanding perception, decision-making, and memory. Despite significant scientific skepticism, emerging evidence from quantum biology and advanced neuroimaging technologies provides tentative support for quantum processes in neural substrates. We conclude by identifying critical gaps in current knowledge and outlining future research directions that may resolve the debate, including proposals for experimental paradigms using quantum sensing technologies applied to neural tissue. This review aims to serve as a foundational reference for researchers across disciplines approaching the quantum mind hypothesis with scientific rigor.
Our research forms two directions, the first considers two approaches to the brain, one based on classical mechanics, the second using quantum physics, the second direction of research refers to the dynamics of0 information as an interaction between differential geometry, mathematical statistics, probability theory. and quantum mechanics which led to the construction of classical and quantum information geometry. Financial entanglement is multidimensiona in time and space, dynamic, less understood and interesting because it functions in real life, like the brain. Neuroscientists who focus on mathematical frameworks for how the brain’s shape affects its activity—an area of mathematical neuroscience called neural field theory will begin to understand the relationship between brain shape, structure, and function in yet another way. Analysis of research into the geometry of the brain’s contours, that is, the way in which brain activity resonates over and through its architecture, is perhaps more significant than the connections between neurons. Research by scientists from the University of Sydney and Monash University showed that the overall shape and geometry of the human brain – its contours and curvature – has a greater influence on brain dynamics than the internal connectivity of brain cells (Our brain shape influences how it works, 2023) in short, Australian scientists indicate the possibility of predicting brain function directly from its shape. “We have long thought that specific thoughts or sensations elicit activity in specific parts of the brain, but this study reveals that structured patterns of activity are excited across nearly the entire brain, just like the way in which a musical note arises from vibrations occurring along the entire length of a violin string, and not just an isolated segment,” (Dr J. Pang,2023).”We found that eigenmodes defined by brain geometry – its contours and curvature – represented the strongest anatomical constraint on brain function, much like the shape of a drum influences the sounds it can make” (A. Fornito, 2023). “Using mathematical models, we confirmed theoretical predictions that the close link between geometry and function is driven by wave-like activity propagating throughout the brain, just as the shape of a pond influences the wave ripples that are formed by a falling pebble” (A. Fornito, 2023).
Neuropsychological research on the neural basis of behavior generally posits that brain mechanisms will ultimately suffice to explain all psychologically described phenomena. This assumption stems from the idea that the brain is made up entirely of material particles and fields, and that all causal mechanisms relevant to neuroscience can therefore be formulated solely in terms of properties of these elements. Thus terms having intrinsic mentalistic and/or experiential content (e.g., ''feeling,'' ''knowing,'' and ''effort'') are not included as primary causal factors. This theoretical restriction is motivated primarily by ideas about the natural world that have been known to be fundamentally incorrect for more than three quarters of a century. Contemporary basic physical theory differs profoundly from classical physics on the important matter of how the consciousness of human agents enters into the structure of empirical phenomena. The new principles contradict the older idea that local mechanical processes alone can account for the structure of all observed empirical data. Contemporary physical theory brings directly and irreducibly into the overall causal structure certain psychologically described choices made by human agents about how they will act. This key development in basic physical theory is applicable to neuroscience, and it provides neuroscientists and psychologists with an alternative conceptual framework for describing neural processes. Indeed, due to certain structural features of ion channels critical to synaptic function, contemporary physical theory must in principle be used when analyzing human brain dynamics. The new framework, unlike its classical-physics-based predecessor is erected directly upon, and is compatible with, the prevailing principles of physics, and is able to represent more adequately than classical concepts the neuroplastic mechanisms relevant to the growing number of empirical studies of the capacity of directed attention and mental effort to systematically alter brain function.
In this paper we shall re-visit the well-known Schrödinger and Lindblad dynamics of quantum mechanics. However, these equations may be realized as the consequence of a more general, underlying dynamical process. In both cases we shall see that the evolution of a quantum state Pψ=ϱ(0) has the not so well-known pseudo-quadratic form ∂tϱ(t)=V⋆ϱ(t)V where V is a vector operator in a complex Minkowski space and the pseudo-adjoint V⋆ is induced by the Minkowski metric η. The interesting thing about this formalism is that its derivation has very deep roots in a new understanding of the differential calculus of time. This Minkowski-Hilbert representation of quantum dynamics is called the \emph{Belavkin Formalism}; a beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be `unraveled' in a second-quantized Minkowski space. Working in such a space provided the author with the means to construct a QS (quantum stochastic) Duhamel principle and known applications to a Schrödinger dynamics perturbed by a continual measurement process are considered. What is not known, but presented here, is the role of the Lorentz transform in quantum measurement, and the appearance of Riemannian geometry in quantum measurement is also discussed.
The article aims to discuss the problem of applicability of quantum-mechanical concepts to the analysis of the mechanisms of brain and the nature of consciousness. Are these tools sufficient and adequate to solve this problem? We claim that despite numerous attempts made in this direction it is difficult to speak about any significant progress. Although the intersection and active interaction between quantum theory and neuroscience forms a kind of “zone of exchange”, allowing us to claim the formation of “quantum neurophysics”, physicalism and reductionism, actually imposed by quantum mechanics, allow us to discuss the nonlocality of neural networks only by analogy with quantum nonlocality. This discussion actually do not touch the underlying machinery of the functionality of these networks, including the processes of their synchronization. Although J. Fodor’s concept of modularity in the context of holism philosophy and ideas of biocultural co-constructivism lead to the idea that it is possible to apply N. Bohr’s complementarity to comprehension of brain functions, but in reality the presence of quantum effects at the level of brain as an integral system is not so obvious. The expression of thought in a word, which means the transformation of a continuous spectrum into a discrete one, only superficially resembles the process of wave function reduction. We can conclude that the boundaries of applicability of quantum-mechanical representations pass through the conceptual space, which does not capture to advance extent the essential features of neither brain, nor consciousness.