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Charles T. Sebens - One of the best experts on this subject based on the ideXlab platform.
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Electromagnetism as quantum physics
Foundations of Physics, 2019Co-Authors: Charles T. SebensAbstract:One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell’s equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon’s quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good in Phys Rev 105(6):1914–1919, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell’s equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.
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Electromagnetism as quantum physics
arXiv: Quantum Physics, 2019Co-Authors: Charles T. SebensAbstract:One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.
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The Mass of the Gravitational Field
The British Journal for the Philosophy of Science, 2019Co-Authors: Charles T. SebensAbstract:By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and Electromagnetism by way of gravitoElectromagnetism, an intermediate theory of gravity that resembles Electromagnetism.
Daigo Oue - One of the best experts on this subject based on the ideXlab platform.
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Electromagnetism at finite temperature: a density operator approach
Journal of Modern Optics, 2019Co-Authors: Daigo OueAbstract:ABSTRACTIn order to analyse classical Electromagnetism in a medium at finite temperature we introduce ‘an optical density operator’, and reformulate Maxwell's equations with the operator, starting ...
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Electromagnetism at finite temperature a density operator approach
arXiv: Optics, 2019Co-Authors: Daigo OueAbstract:In order to analyse classical Electromagnetism in a medium at finite temperature we introduce `an optical density operator', and reformulate Maxwell's equations with the operator, starting from the Dirac-equation-like formulation of Electromagnetism. We find the thermal state of electromagnetic field in the medium from the `optical Dirac Hamiltonian', which is the effective Hamiltonian in the Dirac-like formulation. In the thermal state, the two transverse modes (left-handed and right-handed circular polarisation) of electromagnetic fields exist at the same ratio. We also analyse the asymptotics of the thermal state. At the low temperature limit, there is correlation between the electric field and the magnetic field. This means that there exists an electromagnetic wave at the thermal equilibrium, and this recovers Maxwell's classical Electromagnetism. In contrast, the correlation vanishes at the high temperature limit. This means that electromagnetic waves are unsustainable and only independent electric fields and magnetic fields exist at the high temperature limit.
Franco Nori - One of the best experts on this subject based on the ideXlab platform.
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dual Electromagnetism helicity spin momentum and angular momentum
New Journal of Physics, 2013Co-Authors: Konstantin Y Bliokh, Aleksandr Bekshaev, Franco NoriAbstract:The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of Electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical Electromagnetism. This dual Electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincare symmetries, examine both local and integral conserved quantities and show that only the dual Electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.
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dual Electromagnetism helicity spin momentum and angular momentum
arXiv: Optics, 2012Co-Authors: Konstantin Y Bliokh, Aleksandr Bekshaev, Franco NoriAbstract:The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity, and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of Electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy-momentum, spin, and orbital angular momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical Electromagnetism. This dual Electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy-momentum and angular momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides rigorous derivation of results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincar\'e symmetries, examine both local and integral conserved quantities, and show that only the dual Electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.
Germain Rousseaux - One of the best experts on this subject based on the ideXlab platform.
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Galilean Covariance versus Gauge Invariance
2009Co-Authors: Germain RousseauxAbstract:We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the ”gauge conditions” in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known ”gauge conditions” of the literature are interpreted physically as electromagnetic continuity equations hence the ”gauge fields”. The existence of a Galilean Electromagnetism with TWO dual limits (”electric” and ”magnetic”) is the crux of the problem [1]. A phase-space with the domains of validity of the various ”gauge conditions” is provided and is shown to depend on three characteristic times : the magnetic diffusion time, the charge relaxation time and the transit time of electromagnetic waves in a continuous medium [2].
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On some applications of Galilean electrodynamics of moving bodies
2006Co-Authors: Marc De Montigny, Germain RousseauxAbstract:We discuss the seminal article in which Le Bellac and Lévy-Leblond have identified two Galilean limits of Electromagnetism [1], and its modern implications. Recent works have shed a new light on the choice of gauge conditions in classical Electromagnetism. We discuss various applications and experiments, such as in quantum mechanics, superconductivity, electrodynamics of continuous media, etc. Much of the current technology, where waves are not taken into account, is actually based on Galilean Electromagnetism
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On the electrodynamics of moving bodies at low velocities
European Journal of Physics, 2006Co-Authors: Marc De Montigny, Germain RousseauxAbstract:We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of Electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and Electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical Electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean Electromagnetism.
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On the physical meaning of the gauge conditions of Classical Electromagnetism : the hydrodynamics analogue viewpoint
Annales de la Fondation Louis de Broglie, 2003Co-Authors: Germain RousseauxAbstract:Based on an analogy between Fluid Mechanics and Electromagnetism, we claim that the gauge conditions of Classical Electromagnetism are not equivalent contrary to the common belief. These "gauges" are usually considered as mathematical conditions that one must specify in order to solve any electromagnetic problem. Here, the author shows that these conditions are physical constraints which can be interpreted as electromagnetic continuity equations. As a consequence, light cannot be considered as a pure transverse wave in vacuum from the point of view of the potentials. We discuss the (lack of) meaning of gauge transformations.
J. Brian Pitts - One of the best experts on this subject based on the ideXlab platform.
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What Are Observables in Hamiltonian Einstein–Maxwell Theory?
Foundations of Physics, 2019Co-Authors: J. Brian PittsAbstract:Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive Electromagnetism with gauge freedom (‘Stueckelberg’) are inequivalent to those of massive Electromagnetism without gauge freedom (‘Proca’). The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G , a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive Electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both $$F_{\mu \nu }$$ F μ ν and $$g_{\mu \nu }$$ g μ ν are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.
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What Are Observables in Hamiltonian Einstein–Maxwell Theory?
Foundations of Physics, 2019Co-Authors: J. Brian PittsAbstract:Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive Electromagnetism with gauge freedom (‘Stueckelberg’) are inequivalent to those of massive Electromagnetism without gauge freedom (‘Proca’). The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G , a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive Electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both $$F_{\mu \nu }$$ F μ ν and $$g_{\mu \nu }$$ g μ ν are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.