It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.
It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.
Signal-tuned Gabor functions — Gaussian-modulated sinusoids whose parameters are determined by a spatial or spectral “tuning signal” — have previously been shown to provide a plausible model for the stimulus-dependent receptive fields and responses of the simple and complex cells of the primary visual cortex (V1). The signal-tuned responses obey Schrödinger equations, which has led to the proposal of a quantum-like model for V1 cells: by considering the squared magnitude of a particular signal-tuned wave function as a probability density, one arrives at a Poisson spiking process which appears consistent with the neurophysiological findings. Here, by incorporating Hermite-polynomial factors to the signal-tuned Gabor functions, we obtain a generalized quantum-like signal-tuned model for which further relevant properties are demonstrated, such as receptive-field coding of the stimulus and its derivatives, saturating spatial summation curves and half-wave rectification of the simple cell responses. Although only a one-dimensional approach is considered here, such properties will carry over to a two-dimensional model, in which case, as our preliminary analysis indicates, end-stopping — another important feature of cortical cells — can also be accommodated.
Quantum Mechanics is appropriately named because it is mostly about the mechanics of working out probability problems as they apply to the mysterious effect of measurement that makes energy present as quantum particle-waves. It is easy to visualize a quantum particle but there seems to be no way to visualize a “probability wave” so there has never been a clear interpretation of what quantum physics tells us – or should tell us – about the underlying essence of reality. Fortunately, a new approach was discovered and proven to work in biology that treats the mystery of life like a locking system and provides not only the key, but also the keyhole and the direction in which to turn it. In this paper the systems approach is introduced, including some background information on the history of how the systems approach has integrated elements of substance philosophy with process philosophy and has become a powerful tool for use in science. Here, it is applied to physics and used to represent the transformation of implicit energy into an explicit space-time quantum domain superimposed on a relativistic time-space background. These two “products” are then correlated with two of four blocks in a basic control-system diagram (input and output) commonly used in control-systems engineering. (The four blocks are input, transfer function, output and feedback function) Because they are explicit, they can be drawn explicitly on the space versus time plot as a map of motion. We emphasize that this is a map – an explicit projection of an implicit function (in this case, a plot of space versus time is a projection of the variance we call motion) represented as an implicit domain (a perpendicular dimension). We recognizing that a feedback function is equivalent to and therefore implies a back-projection or reflection back “up” into that “implicate order.” These two implicit functions (projection and reflection) are then correlated with the transfer function and feedback function in the control system. The motion function is related to the probability wave by the name used in statistics – the “variance” of a statistical distribution – and we point out that each axis of the space-time domain is scaled by standard “deviations,” which define the explicit scales. Because a standard deviation is the square root of a variance, the square space that maps as a relativistic scalar plot (a standard Cartesian coordinate system) of space versus time or “space-time” actually represents one of two square roots of the implicit variance we call motion. In essence, our measurements of this domain keep us rooted in physical reality. However, this coordinate system is shown to be just the root – one part of a “whole system” that includes a non-physical implicit feedback function. The feedback function is correlated with the “reflection” of the explicit domain, i.e. inverse-space and inverse-time, presented as a phase space called time-space and represented as a unit of spatial frequency versus temporal frequency. These frequency representations are shown to be the two well-known equations for quantum energy from quantum mechanics and they are used to identify energy-space as “the quantum domain” inside of, or superimposed on the background “relativistic domain,” which is a scalar space. These two domains are then shown to be coupled at the point where both scales are equal to “1”. As a whole, and in the language of quantum field theory, this model is a graphical representation of an energy-momentum tensor and as a visual model, it provides a clear conceptual interpretation of complexity theory, in which reality is expressed as the superposition of a self-organizing control system that convolves with a dissipative open system or “sea of disorder” and transforms it into physical units of order. This “holomorphic systems approach” is similar to, but much simpler and visually illustrative than the mathematically rigorous discussion On Symmetry and the Reality of Holomorphic Hartree–Fock Wavefunctions [1] or the Kohn-Sham Density Functional Theory [2]. Furthermore, it reveals that the question about the beginning of time is a question fallacy, by representing the equivalence of space and time as S=Tc2, and presents it geometrically to be the exact same relation as the mass-energy equivalence equation E=mc2. The model also reveals that quantized energy (which Huynh and Thom refer to as self-consistent fields or SCF) projects as a characteristic and allows one to visualize the solution to the particle-wave duality “problem” as being a change in perspective. It’s the change in perspective that makes the particle-like property and wave-like property appear as “emergent” – analogous to what would appear when one visualizes an object from two different perspectives – at rest with respect to one’s own body yet in motion relative to some other “moving” body. The approach also reveals how the transfer function and feedback function act to transform matter, adding the fourth component (the Controller) and making it a complete control system: a self-organizing, self-sensing system that can see itself explicitly and reflect upon itself implicitly. How that correlates with living systems becomes obvious.
Quantum Mechanics is appropriately named because it is mostly about the mechanics of working out probability problems as they apply to the mysterious effect of measurement that makes energy present as quantum particle-waves. It is easy to visualize a quantum particle but there seems to be no way to visualize a “probability wave” so there has never been a clear interpretation of what quantum physics tells us – or should tell us – about the underlying essence of reality. Fortunately, a new approach was discovered and proven to work in biology that treats the mystery of life like a locking system and provides not only the key, but also the keyhole and the direction in which to turn it. In this paper the systems approach is introduced, including some background information on the history of how the systems approach has integrated elements of substance philosophy with process philosophy and has become a powerful tool for use in science. Here, it is applied to physics and used to represent the transformation of implicit energy into an explicit space-time quantum domain superimposed on a relativistic time-space background. These two “products” are then correlated with two of four blocks in a basic control-system diagram (input and output) commonly used in control-systems engineering. (The four blocks are input, transfer function, output and feedback function) Because they are explicit, they can be drawn explicitly on the space versus time plot as a map of motion. We emphasize that this is a map – an explicit projection of an implicit function (in this case, a plot of space versus time is a projection of the variance we call motion) represented as an implicit domain (a perpendicular dimension). We recognizing that a feedback function is equivalent to and therefore implies a back-projection or reflection back “up” into that “implicate order.” These two implicit functions (projection and reflection) are then correlated with the transfer function and feedback function in the control system. The motion function is related to the probability wave by the name used in statistics – the “variance” of a statistical distribution – and we point out that each axis of the space-time domain is scaled by standard “deviations,” which define the explicit scales. Because a standard deviation is the square root of a variance, the square space that maps as a relativistic scalar plot (a standard Cartesian coordinate system) of space versus time or “space-time” actually represents one of two square roots of the implicit variance we call motion. In essence, our measurements of this domain keep us rooted in physical reality. However, this coordinate system is shown to be just the root – one part of a “whole system” that includes a non-physical implicit feedback function. The feedback function is correlated with the “reflection” of the explicit domain, i.e. inverse-space and inverse-time, presented as a phase space called time-space and represented as a unit of spatial frequency versus temporal frequency. These frequency representations are shown to be the two well-known equations for quantum energy from quantum mechanics and they are used to identify energy-space as “the quantum domain” inside of, or superimposed on the background “relativistic domain,” which is a scalar space. These two domains are then shown to be coupled at the point where both scales are equal to “1”. As a whole, and in the language of quantum field theory, this model is a graphical representation of an energy-momentum tensor and as a visual model, it provides a clear conceptual interpretation of complexity theory, in which reality is expressed as the superposition of a self-organizing control system that convolves with a dissipative open system or “sea of disorder” and transforms it into physical units of order. This “holomorphic systems approach” is similar to, but much simpler and visually illustrative than the mathematically rigorous discussion On Symmetry and the Reality of Holomorphic Hartree–Fock Wavefunctions [1] or the Kohn-Sham Density Functional Theory [2]. Furthermore, it reveals that the question about the beginning of time is a question fallacy, by representing the equivalence of space and time as S=Tc2, and presents it geometrically to be the exact same relation as the mass-energy equivalence equation E=mc2. The model also reveals that quantized energy (which Huynh and Thom refer to as self-consistent fields or SCF) projects as a characteristic and allows one to visualize the solution to the particle-wave duality “problem” as being a change in perspective. It’s the change in perspective that makes the particle-like property and wave-like property appear as “emergent” – analogous to what would appear when one visualizes an object from two different perspectives – at rest with respect to one’s own body yet in motion relative to some other “moving” body. The approach also reveals how the transfer function and feedback function act to transform matter, adding the fourth component (the Controller) and making it a complete control system: a self-organizing, self-sensing system that can see itself explicitly and reflect upon itself implicitly. How that correlates with living systems becomes obvious.
We present the quantum-like model of information processing by the brain’s neural networks. The model does not refer to genuine quantum processes in the brain. In this model, uncertainty generated by the action potential of a neuron is represented as quantum-like superposition of the basic mental states corresponding to a neural code. Neuron’s state space is described as complex Hilbert space (quantum information representation). The brain’s psychological functions perform self-measurements by extracting concrete answers to questions (solutions of problems) from quantum information states. This extraction is modeled in the framework of open quantum systems theory. In this way, it is possible to proceed without appealing to the state’s collapse. Dynamics of the state of psychological function F is described by the quantum master equation. Its stationary states represent classical statistical mixtures of possible outputs of F (decisions). This model can be used for justification of quantum-like modeling cognition and decision-making. The latter is supported by plenty of statistical data collected in cognitive psychology.
Abstract Interactions of a non-holonomic type are fundamentally different from interactions which can be treated as part of the Hamiltonian of a system. They usually lead to constraints which do not commute with the Hamiltonian, and cause important alterations in the development of a state vector. This paper deals with the Heisenberg equations of motion by analogy with classical dynamics using the Poisson bracket formalism of a previous paper (Eden 1951). The Schrödinger equation is investigated in co-ordinate representation, and it is shown that the wave function will have a non-integrabie phase factor or quasi phase. The quasi phase leads to an indefiniteness in the wave function, but does not violate the fundamental laws of quantum mechanics nor lead to any ambiguity in the physical interpretation of the theory. The relation between the Schrödinger and the Heisenberg equations shows that the Schrödinger treatment is also consistent with the classical analogue. If there is a given initial probability that the non-holonomic system has co-ordinates q(0)r, then there will be the same probability that the wave function in the subsequent motion will be zero except in a certain region of co-ordinate space. This region is the part of co-ordinate space which is accessible in the classical theory from the point q(0)r.
Quantum-like modeling (QLM) – quantum theory applications outside of physics – are intensively developed with applications in biology, cognition, psychology, and decision-making. For cognition, QLM should be distinguished from quantum reductionist models in the spirit of Hameroff and Penrose and well as Umezawa and Vitiello. QLM is not concerned with just quantum physical processes in the brain but also QL information processing by macroscopic neuronal structures. Although QLM of cognition and decision-making has seen some success, it suffers from a knowledge gap that exists between oscillatory neuronal network functioning in the brain and QL behavioral patterns. Recently, steps toward closing this gap have been taken using the generalized probability theory and prequantum classical statistical field theory (PCSFT) – a random field model beyond the complex Hilbert space formalism. PCSFT is used to move from the classical ``oscillatory cognition'' of the neuronal networks to QLM for decision-making. In this study, we addressed the most difficult problem within this construction: QLM for entanglement generation by classical networks, i.e., “mental entanglement.” We started with the observational approach to entanglement based on operator algebras describing “local observables” and bringing into being the tensor product structure in the space of QL states. Moreover, we applied the standard states entanglement approach: entanglement generation by spatially separated networks in the brain. Finally, we discussed possible future experiments on “mental entanglement” detection using the EEG/MEG technique.