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Kevin Lambert - One of the best experts on this subject based on the ideXlab platform.

  • The uses of analogy: James Clerk Maxwell's ‘On Faraday's Lines of Force’ and early Victorian analogical argument
    The British Journal for the History of Science, 2010
    Co-Authors: Kevin Lambert
    Abstract:

    AbstractEarly Victorian analogical arguments were used to order the natural and the social world by maintaining a coherent collective experience across cultural oppositions such as the ideal and material, the sacred and profane, theory and fact. Maxwell's use of analogical argument in ‘On Faraday's Lines of Force’ was a contribution to that broad nineteenth-century discussion which overlapped theology and natural philosophy. I argue here that Maxwell understood his theoretical work as both a technical and a socially meaningful practice and that embedding his use of analogy in the social and intellectual context of Victorian Britain provides a means of telling a sociocultural history of Maxwell's development of a new cognitive tool: a way of thinking on paper analogous to thinking with objects in the laboratory.And analogy can do no more, immediately or directly, than shew such and such things to be true or credible considered only as matters of fact.Bishop Butler, 17361

  • The uses of analogy: James Clerk Maxwell's ' On Faraday's Lines of Force' and early Victorian analogical argument
    The British Journal for the History of Science, 2010
    Co-Authors: Kevin Lambert
    Abstract:

    Early Victorian analogical arguments were used to order the natural and the social world by maintaining a coherent collective experience across cultural oppositions such as the ideal and material, the sacred and profane, theory and fact. Maxwell's use of analogical argument in ‘On Faraday's Lines of Force’ was a contribution to that broad nineteenth-century discussion which overlapped theology and natural philosophy. I argue here that Maxwell understood his theoretical work as both a technical and a socially meaningful practice and that embedding his use of analogy in the social and intellectual context of Victorian Britain provides a means of telling a sociocultural history of Maxwell's development of a new cognitive tool: a way of thinking on paper analogous to thinking with objects in the laboratory. And analogy can do no more, immediately or directly, than shew such and such things to be true or credible considered only as matters of fact. Bishop Butler, 1736 1

Carlo Rovelli - One of the best experts on this subject based on the ideXlab platform.

  • Classical and quantum dynamics of the Faraday Lines of Force.
    Physical review. D Particles and fields, 1994
    Co-Authors: Simonetta Frittelli, Sucheta Koshti, Ezra T. Newman, Carlo Rovelli
    Abstract:

    We study the vacuum Maxwell theory by expressing the electric field in terms of its Faraday Lines of Force. This representation allows us to capture the two physical degrees of freedom of the electric field by means of two scalar fields. The corresponding classical canonical theory is constructed in terms of four scalar fields, is fully gauge invariant, has an attractive kinematics, but a rather complicated dynamics. The corresponding quantum theory can be constructed in a well-defined functional representation, which we refer to as the Euler representation. This representation turns out to be related to the loop representation. The resulting quantization scheme is, perhaps, of relevance for non-Abelian theories and for gravity.

  • generalized Lines of Force as the gauge invariant degrees of freedom for general relativity and yang mills theory
    Physical Review Letters, 1992
    Co-Authors: Ezra T. Newman, Carlo Rovelli
    Abstract:

    We present a set of equations that determine (with certain qualifications) what is (i) a complete canonical set of gauge-invariant variables for Yang-Mills (YM) theory that generalize Faraday's electric Lines of Force and (ii) a complete canonical set of the diffeomorphism- and gauge-invariant observables for general relativity (GR). Both results come from solving the Hamilton-Jacobi version of the constraint equations: the Gauss law constraints of YM theory and the Gauss law and diffeomorphism constraint of GR in the Ashtekar formalism

  • Generalized Lines of Force as the gauge invariant degrees of freedom for general relativity and Yang-Mills theory
    Physical review letters, 1992
    Co-Authors: Ezra T. Newman, Carlo Rovelli
    Abstract:

    We present a set of equations that determine (with certain qualifications) what is (i) a complete canonical set of gauge-invariant variables for Yang-Mills (YM) theory that generalize Faraday's electric Lines of Force and (ii) a complete canonical set of the diffeomorphism and gauge invariant observables for general relativity (GR). Both results come from solving the Hamilton-Jacobi version of the constraint equations: the Gauss law constraints of YM theory and the Gauss law and diffeomorphism constraint of GR in the Ashtekar formalism. These results are local in physical space as well as in phase space.

Ezra T. Newman - One of the best experts on this subject based on the ideXlab platform.

  • Classical and quantum dynamics of the Faraday Lines of Force.
    Physical review. D Particles and fields, 1994
    Co-Authors: Simonetta Frittelli, Sucheta Koshti, Ezra T. Newman, Carlo Rovelli
    Abstract:

    We study the vacuum Maxwell theory by expressing the electric field in terms of its Faraday Lines of Force. This representation allows us to capture the two physical degrees of freedom of the electric field by means of two scalar fields. The corresponding classical canonical theory is constructed in terms of four scalar fields, is fully gauge invariant, has an attractive kinematics, but a rather complicated dynamics. The corresponding quantum theory can be constructed in a well-defined functional representation, which we refer to as the Euler representation. This representation turns out to be related to the loop representation. The resulting quantization scheme is, perhaps, of relevance for non-Abelian theories and for gravity.

  • generalized Lines of Force as the gauge invariant degrees of freedom for general relativity and yang mills theory
    Physical Review Letters, 1992
    Co-Authors: Ezra T. Newman, Carlo Rovelli
    Abstract:

    We present a set of equations that determine (with certain qualifications) what is (i) a complete canonical set of gauge-invariant variables for Yang-Mills (YM) theory that generalize Faraday's electric Lines of Force and (ii) a complete canonical set of the diffeomorphism- and gauge-invariant observables for general relativity (GR). Both results come from solving the Hamilton-Jacobi version of the constraint equations: the Gauss law constraints of YM theory and the Gauss law and diffeomorphism constraint of GR in the Ashtekar formalism

  • Generalized Lines of Force as the gauge invariant degrees of freedom for general relativity and Yang-Mills theory
    Physical review letters, 1992
    Co-Authors: Ezra T. Newman, Carlo Rovelli
    Abstract:

    We present a set of equations that determine (with certain qualifications) what is (i) a complete canonical set of gauge-invariant variables for Yang-Mills (YM) theory that generalize Faraday's electric Lines of Force and (ii) a complete canonical set of the diffeomorphism and gauge invariant observables for general relativity (GR). Both results come from solving the Hamilton-Jacobi version of the constraint equations: the Gauss law constraints of YM theory and the Gauss law and diffeomorphism constraint of GR in the Ashtekar formalism. These results are local in physical space as well as in phase space.

Paul Mansfield - One of the best experts on this subject based on the ideXlab platform.

Frederick David Tombe - One of the best experts on this subject based on the ideXlab platform.

  • Physical Lines of Force in the Aether
    2011
    Co-Authors: Frederick David Tombe
    Abstract:

    al Lines of Force are actually Lines of tension, and that Maxwell’s molecular vortices are dielectric in nature. The linear polarization of these dipolar vortices, caused by the gravitational field, will increase the centrifugal pressure which is exerted laterally, and this pressure will result in a repulsive Force in competition with the attractive Force. The attractive Force, being a monopole field, will obey the inverse square law, whereas the repulsive Force, being a dipole field, will obey the inverse cube law. Hence if the charge of an object increases, the inverse cube law relationship for the surrounding repulsive Force field will lead to a reversal threshold, where it will dominate over the attractive Force. The charge can increase electrostatically or because of inertia. In the latter case, the repulsive Force field is the large scale centrifugal Force.

  • A Solenoidal Double Helix of Sinks and Sources (Faraday's Lines of Force)
    2008
    Co-Authors: Frederick David Tombe
    Abstract:

    The magnetic field is solenoidal, yet the equation for the magnetic field indicates the existence of singularities. This paper shows how a double helix arrangement of sinks and sources can resolve this dilemma. Faraday's Lines of Force, while being solenoidal on one scale, contain within them a double helix array of electrons and positrons. This accounts for the Coulomb Force of attraction between two unlike magnetic poles, and the centrifugal Force of repulsion between two like magnetic poles.

  • The Double Helix Theory of the Magnetic Field (An Interpretation of Maxwell's 1861 Paper 'On Physical Lines of Force')
    2008
    Co-Authors: Frederick David Tombe
    Abstract:

    Maxwell's 1861 paper 'On Physical Lines of Force' is interpreted. An improvement is proposed that involves replacing his molecular vortices with rotating electron-positron dipoles. These dipoles will each comprise of an electron and a positron undergoing a mutual orbit. Electromagnetism is then explained in terms of an electric sea in which magnetic Lines of Force are physically comprised of helical springs created out of rotating electron-positron dipoles. The electron- positron dipoles are bonded together in a double helix pattern and the resulting helical springs form elliptical or circular solenoidal hoops around an electric current circuit or a bar magnet.

  • The Coriolis Force in Maxwell's Equations (A comparative study of Maxwell's 1865 paper 'A Dynamical Theory of the Electromagnetic Field' and his 1861 paper 'On Physical Lines of Force')
    2007
    Co-Authors: Frederick David Tombe
    Abstract:

    Maxwell's 1865 paper 'A Dynamical Theory of the Electromagnetic Field' appears to abandon the theory of molecular vortices that was a central feature of his 1861 paper 'On Physical Lines of Force'. After writing part I of his 1861 paper, Maxwell realized that a purely hydrodynamical approach to electromagnetic theory was insufficient and so he introduced electrical particles as idle wheels rolling around the outside of his molecular vortices. Maxwell was never clear about the details of the connecting mechanism between the electrical particles and the vortices and he gradually shifted towards a more elasticity based approach in which he emphasized the dielectric nature of the aether as opposed to the vortex nature. This article investigates whether or not any physics was lost as a result of Maxwell apparently having abandoned his theory of molecular vortices by 1864. The focus of attention is centred on equation (5) of his 1861 paper as this equation contains the Coriolis Force. Maxwell used the mathematical form of the Coriolis Force to derive Ampere's Circuital Law and this paper will demonstrate that the Coriolis Force can also be used to derive the vXB component of the Lorentz Force. Since a rotating frame of reference is needed for a Coriolis Force, it follows therefore that Ampere's Circuital Law and the vXB component of the Lorentz Force must depend entirely on the fine-grain rotating aethereal substance within Maxwell's molecular vortices. The conclusion is that Maxwell need not have had any hesitation at all regarding his theory of molecular vortices, and that the result of playing it down was that the physical explanation for vXB and Ampere's Circuital Law was lost to future generations.