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 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.
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.
Hilbert space structure is assumed as a valid geometric description for neurodynamics, i.e., for applying any kind of quantum formalism in brain dynamics. The orientation selectivity of the neurons is used as a justification to construct a type of statistical distance function which is proportional to the usual distance (or angle) between orientations of the neurons. The equivalence between the statistical distance and the Hilbert-space distance is discussed within this framework. It gives rise to the possibility of reanalysing the issue of measurement and information processing in the brain function
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.
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.
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).
The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.