A Comment on Background Independence in Quantum Theory
2016 (English)In: Journal of the Chinese Chemical Society (Taipei), ISSN 0009-4536, E-ISSN 2192-6549, Vol. 63, no 1, 11-19 p.Article in journal (Refereed) PublishedText
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.
Place, publisher, year, edition, pages
2016. Vol. 63, no 1, 11-19 p.
General relativity, Quantum theory, Conjugate operators, Non-positive metrics
IdentifiersURN: urn:nbn:se:uu:diva-280106DOI: 10.1002/jccs.201500067ISI: 000369014800001OAI: oai:DiVA.org:uu-280106DiVA: diva2:910115
FunderSwedish Research CouncilSwedish Foundation for Strategic Research EU, European Research Council