In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly.
The name is an initialism for Wentzel–Kramers–Brillouin. It is also known as the LG or Liouville–Green method. Other often-used letter combinations include JWKB and WKBJ, where the "J" stands for Jeffreys.
https://en.wikipedia.org/wiki/WKB_approximation
The diffusion of plasma across a magnetic field was conjectured to follow the Bohm diffusion scaling as indicated from the early plasma experiments of very lossy machines. This predicted that the rate of diffusion was linear with temperature and inversely linear with the strength of the confining magnetic field.
The rate predicted by Bohm diffusion is much higher than the rate predicted by classical diffusion, which develops from a random walk within the plasma. The classical model scaled inversely with the square of the magnetic field. If the classical model is correct, small increases in the field lead to much longer confinement times. If the Bohm model is correct, magnetically confined fusion would not be practical.
Early fusion energy machines appeared to behave according to Bohm's model, and by the 1960s there was a significant stagnation within the field. The introduction of the tokamak in 1968 was the first evidence that the Bohm model did not hold for all machines. Bohm predicts rates that are too fast for these machines, and classical too slow; studying these machines has led to the neoclassical diffusion concept.
https://en.wikipedia.org/wiki/Bohm_diffusion
In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of unobservable hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts at a deterministic description of quantum mechanics, to avoid quantum indeterminacy, but at the expense of requiring the existence of nonlocal interactions.
Albert Einstein objected to the fundamentally probabilistic nature of quantum mechanics,[1] and famously declared "I am convinced God does not play dice".[2][3] Einstein, Podolsky, and Rosen argued that quantum mechanics is an incomplete description of reality.[4][5] Bell's theorem would later suggest that local hidden variables (a way for finding a complete description of reality) of certain types are impossible. A famous non-local theory is the De Broglie–Bohm theory.
https://en.wikipedia.org/wiki/Hidden-variable_theory
In theoretical physics, the pilot wave theory, also known as Bohmian mechanics, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave–particle duality, instantaneous wave function collapse, and the paradox of Schrödinger's cat. To solve these problems, the theory is inherently nonlocal.
The de Broglie–Bohm pilot wave theory is one of several interpretations of (non-relativistic) quantum mechanics. An extension to the relativistic case has been developed since the 1990s.[3][4][5][6]
https://en.wikipedia.org/wiki/Pilot_wave_theory
Holonomic brain theory, also known as The Holographic Brain, is a branch of neuroscience investigating the idea that human consciousness is formed by quantum effects in or between brain cells. This is opposed by traditional neuroscience, which investigates the brain's behavior by looking at patterns of neurons and the surrounding chemistry, and which assumes that any quantum effects will not be significant at this scale. The entire field of quantum consciousness is often criticized as pseudoscience, as detailed on the main article thereof.
This specific theory of quantum consciousness was developed by neuroscientist Karl Pribram initially in collaboration with physicist David Bohm building on the initial theories of holograms originally formulated by Dennis Gabor. It describes human cognition by modeling the brain as a holographic storage network.[1][2] Pribram suggests these processes involve electric oscillations in the brain's fine-fibered dendritic webs, which are different from the more commonly known action potentials involving axons and synapses.[3][4][5] These oscillations are waves and create wave interference patterns in which memory is encoded naturally, and the wave functionmay be analyzed by a Fourier transform.[3][4][5][6][7] Gabor, Pribram and others noted the similarities between these brain processes and the storage of information in a hologram, which can also be analyzed with a Fourier transform.[1][8] In a hologram, any part of the hologram with sufficient size contains the whole of the stored information. In this theory, a piece of a long-term memory is similarly distributed over a dendritic arbor so that each part of the dendritic network contains all the information stored over the entire network.[1][8][9] This model allows for important aspects of human consciousness, including the fast associative memory that allows for connections between different pieces of stored information and the non-locality of memory storage (a specific memory is not stored in a specific location, i.e. a certain cluster of neurons).[1][10][11]
https://en.wikipedia.org/wiki/Holonomic_brain_theory
Challenges to some generally prevailing views[edit]
In proposing this new notion of order, Bohm explicitly challenged a number of tenets that he believed are fundamental to much scientific work:
- that phenomena are reducible to fundamental particles and laws describing the behaviour of particles, or more generally to any static (i.e., unchanging) entities, whether separate events in spacetime, quantum states, or static entities of some other nature;
- related to (1), that human knowledge is most fundamentally concerned with mathematical prediction of statistical aggregates of particles;
- that an analysis or description of any aspect of reality (e.g., quantum theory, the speed of light) can be unlimited in its domain of relevance;
- that the Cartesian coordinate system, or its extension to a curvilinear system, is the deepest conception of underlying order as a basis for analysis and description of the world;
- that there is ultimately a sustainable distinction between reality and thought, and that there is a corresponding distinction between the observer and observed in an experiment or any other situation (other than a distinction between relatively separate entities valid in the sense of explicate order); and
- that it is, in principle, possible to formulate a final notion concerning the nature of reality, i.e., a Theory of Everything.
Bohm's proposals have at times been dismissed largely on the basis of such tenets. His paradigm is generally opposed to reductionism, and some view it as a form of ontological holism. On this, Bohm noted of prevailing views among physicists that "the world is assumed to be constituted of a set of separately existent, indivisible, and unchangeable 'elementary particles', which are the fundamental 'building blocks' of the entire universe ... there seems to be an unshakable faith among physicists that either such particles, or some other kind yet to be discovered, will eventually make possible a complete and coherent explanation of everything" (Bohm 1980, p. 173).
In Bohm's conception of order, primacy is given to the undivided whole, and the implicate order inherent within the whole, rather than to parts of the whole, such as particles, quantum states, and continua. This whole encompasses all things, structures, abstractions, and processes, including processes that result in (relatively) stable structures as well as those that involve a metamorphosis of structures or things. In this view, parts may be entities normally regarded as physical, such as atoms or subatomic particles, but they may also be abstract entities, such as quantum states. Whatever their nature and character, according to Bohm, these parts are considered in terms of the whole, and in such terms, they constitute relatively separate and independent "sub-totalities." The implication of the view is, therefore, that nothing is fundamentally separate or independent.
Bohm 1980, p. 11, said: "The new form of insight can perhaps best be called Undivided Wholeness in Flowing Movement. This view implies that flow is in some sense prior to that of the ‘things’ that can be seen to form and dissolve in this flow." According to Bohm, a vivid image of this sense of analysis of the whole is afforded by vortex structures in a flowing stream. Such vortices can be relatively stable patterns within a continuous flow, but such an analysis does not imply that the flow patterns have any sharp division, or that they are literally separate and independently existent entities; rather, they are most fundamentally undivided. Thus, according to Bohm’s view, the whole is in continuous flux, and hence is referred to as the holomovement (movement of the whole).
https://en.wikipedia.org/wiki/Implicate_and_explicate_order#Challenges_to_some_generally_prevailing_views
Classical nonradiation conditions define the conditions according to classical electromagnetism under which a distribution of accelerating charges will not emit electromagnetic radiation. According to the Larmor formula in classical electromagnetism, a single point charge under acceleration will emit electromagnetic radiation, i.e. light. In some classical electron models a distribution of charges can however be accelerated so that no radiation is emitted.[1] The modern derivation of these nonradiation conditions by Hermann A. Haus is based on the Fourier components of the current produced by a moving point charge. It states that a distribution of accelerated charges will radiate if and only if it has Fourier components synchronous with waves traveling at the speed of light.[2]
https://en.wikipedia.org/wiki/Nonradiation_condition
In theoretical physics, the pilot wave theory, also known as Bohmian mechanics, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave–particle duality, instantaneous wave function collapse, and the paradox of Schrödinger's cat. To solve these problems, the theory is inherently nonlocal.
The de Broglie–Bohm pilot wave theory is one of several interpretations of (non-relativistic) quantum mechanics. An extension to the relativistic case has been developed since the 1990s.[3][4][5][6]
https://en.wikipedia.org/wiki/Pilot_wave_theory
In physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quantization of plasma oscillations, just like phonons are quantizations of mechanical vibrations. Thus, plasmons are collective (a discrete number) oscillations of the free electron gas density. For example, at optical frequencies, plasmons can couple with a photon to create another quasiparticle called a plasmon polariton.
https://en.wikipedia.org/wiki/Plasmon
Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s. They are used to describe two different frameworks for understanding the same phenomenon or aspect of reality. In particular, the concepts were developed in order to explain the bizarre behavior of subatomic particles which quantum physics struggles to explain.
In Bohm's Wholeness and the Implicate Order, he used these notions to describe how the appearance of such phenomena might appear differently, or might be characterized by, varying principal factors, depending on contexts such as scales.[1] The implicate (also referred to as the "enfolded") order is seen as a deeper and more fundamental order of reality. In contrast, the explicate or "unfolded" order includes the abstractions that humans normally perceive. As he wrote:
- In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders (Bohm 1980, p. xv).
https://en.wikipedia.org/wiki/Implicate_and_explicate_order
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.
https://en.wikipedia.org/wiki/Quantum_decoherence
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