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  • 1.
    Brändas, Erkki J.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    A Comment on Background Independence in Quantum Theory2016In: Journal of the Chinese Chemical Society (Taipei), ISSN 0009-4536, E-ISSN 2192-6549, Vol. 63, no 1, p. 11-19Article in journal (Refereed)
    Abstract [en]

    In this communication we take up the significance and purpose of selecting the proper coordinate system from the flat space-time of non-relativistic theories to the quantum theoretic formulation of general relativity. The universal background problem is straight forwardly framed as a momentum-energy portrait in nexus with its space-time conjugates. The description is based on operator matrix algebra, where the related analogue of the secular equation yields a Klein-Gordon type equation and the associated Minkowski eigentime element. The energy-momentum and their conjugate partners are represented by spaces that have (+,-) signatures. The general theory implicates both non-zero- and zero rest-mass entities, and it is proved that the conjugate relationship between energy and time provide a simple derivation of the Schwarzschild line element for the case of a gravitational field outside a spherical non-rotational uncharged mass. This result, indicating the appearance of a black hole as a true singularity in the energy-time formulation, and obtained as a direct consequence of their conjugate relationship, manifests background independence in concert with Einstein's equivalence principle. Inducing a reformulation of the Lorentz Transformation respecting the indefinite Minkowski metric, displays an interesting relation between complex dilations and indefinite metric spaces, validating the complex symmetric ansatz.

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