Topological Approaches to Electromagnetism

Barrett, T. W.

doi:10.1002/0471231495.ch14

Cited by 5 publications

(4 citation statements)

References 21 publications

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“…The energy values that characterize the spatial patterns are bivalent; low or zero values are just as important as high values for identification and classification, because patterns require black and gray as well as white. This contrast in 21 st century neuroscience resembles that in 19 th century physics between Newtonian interpretations of electric and magnetic forces in terms of point charges vs. the fields of Faraday and Maxwell Walter J Freeman [Barrett, 2000[Barrett, , 2001Arianrhod, 2005]. Then and now the contrasting views are polar opposites; neither view can be used to critique the other, because the divergence begins with the design of the experiments that are needed to collect the raw data to test them [Kuhn, 1962].…”

Section: Comparison Of the Reflex Arc And The Action-perception Cyclementioning

confidence: 99%

Indirect biological measures of consciousness from field studies of brains as dynamical systems

Freeman

2007

Neural Networks

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Consciousness fully supervenes when the 1.5 kgm mass of protoplasm in the head directs the body into material and social environments and engages in reciprocity. While consciousness is not susceptible to direct measurement, a limited form exercised in animals and pre-lingual children can be measured indirectly with biological assays of arousal, intention and attention. In this essay consciousness is viewed as operating simultaneously in a field at all levels ranging from subatomic to social. The relations and transpositions between levels require sophisticated mathematical treatments that are largely still to be devised. In anticipation of those developments the available experimental data are reviewed concerning the state variables in several levels that collectively constitute the substrate of biological consciousness. The basic metaphors are described that represent the neural machinery of transposition in consciousness. The processes are sketched by which spatiotemporal neural activity patterns emerge as fields that may represent the contents of consciousness. The results of dynamical analysis are discussed in terms serving to distinguish between the neural point processes dictated by the neuron doctrine vs. continuously variable neural fields generated by neural masses in cortex.

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Section: Comparison Of the Reflex Arc And The Action-perception Cyclementioning

confidence: 99%

Indirect biological measures of consciousness from field studies of brains as dynamical systems

Freeman

2007

Neural Networks

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“…Neuropercolation [Kozma et al, 2005] is based in random graph theory extended to include small world effects and scale-free networks [Wang and Chen, 2003]. Another route may be to exploit electric and magnetic field theory [Barrett, 1993[Barrett, , 2000[Barrett, , 2001. A third may be explore quantum field theory as distinct from quantum mechanics [Pessa, 2000;Vitiello, 2001;Potapov and Ali, 2001].…”

Section: Modeling Neocortical Dynamics With the Kv Setmentioning

confidence: 99%

A field-theoretic approach to understanding scale-free neocortical dynamics

Freeman

2005

Biol Cybern

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Special Issue "Nonlinear spatio-temporal neural dynamics -experiments and theoretical models" AbstractA mesoscopic field-theoretic approach is compared with neural network and brain imaging approaches to understanding brain dynamics. Analysis of high spatiotemporal resolution rabbit EEG reveals neural fields in the form of spatial patterns in amplitude (AM) and phase (PM) modulation of gamma and beta carrier waves that serve to classify EEGs from trials with differing conditioned stimuli (CS+/-). Paleocortex exemplified by olfactory EEG has one AM-PM pattern at a time that forms by an input-dependent phase transition. Neocortex shows multiple overlapping AM-PM patterns before and during presentation of CSs. Modeling suggests that neocortex is stabilized in a scale-free state of self-organized criticality, enabling cooperative domains to form virtually instantaneously by phase transitions ranging in size from a few hypercolumns to an entire hemisphere. Self-organized local domains precede formation of global domains that supervene and contribute global modulations to local domains. This mechanism is proposed to explain Gestalt formation in perception.

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“…[27][28][29][30][31][32][33][34]). The physicality of the vector potential is now well proven experimentally [35] and it was shown that in certain well-defined situations are measurable and possess a topology transforming according to the SU(2) group [36].…”

Section: The Electromagnetic Origin Of Inertiamentioning

confidence: 99%

On the Electromagnetic Origin of Inertia and Inertial Mass

Martins¹,

Pinheiro

2008

Int J Theor Phys

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We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton's second law) taking due account of the vector potential and its convective derivative. We obtain a development in terms of retarded potentials allowing an intuitive physical interpretation of its main terms. The inertial property of matter is then discussed in terms of a kind of induction law related to the extended charged particle's own vector potential. Moreover, it is obtained a force term that represents a drag force acting on the charged particle when in motion relatively to its own vector potential field lines. The time rate of variation of the particle's vector potential leads to the acceleration inertia reaction force, equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle's vector potential is connected with the relativistic increase of mass with velocity and generates a longitudinal stress force that is the source of electric field lines deformation. In the framework of classical electrodynamics, we have shown that the electron mass has possibly a complete electromagnetic origin and the obtained covariant equation solves the "4/3 mass paradox" for a spherical charge distribution.

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Topological Approaches to Electromagnetism

Cited by 5 publications

References 21 publications

Indirect biological measures of consciousness from field studies of brains as dynamical systems

Indirect biological measures of consciousness from field studies of brains as dynamical systems

A field-theoretic approach to understanding scale-free neocortical dynamics

On the Electromagnetic Origin of Inertia and Inertial Mass

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