Some further comments on special relativity and dark energy
Date
2019
Authors
Hill, J.M.
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Zeitschrift fur Angewandte Mathematik und Physik, 2019; 70(1, article no. 5):1-9
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Abstract
In this note, we provide some new derivations and further elaboration on a recent proposal by the author Hill (Zeitschrift fur angewandte Mathematik und Physik 69: 133–145, 2018. https://doi.org/10.1007/s00033-018-1028-4) regarding the formal origins of dark energy. Using the framework of special relativity and validation through Lorentz invariance,Hill (2018) develops the usual relations of special relativity, but makes a distinction between particle energy e = mc2 and the actual work done by the particle E , and adopts the perspective that both the momentum vector p = mu and the intrinsic particle energy e itself contribute to the work done E . The alternative formulation provides an extension of Newton’s second law that is properly invariant under the Lorentz group and yields new expressions for the work done involving the log function. The log terms can generate extremely large energies and may represent the first formal indication of the origin of dark energy. The new approach suggests that large energies might be generated for slowly moving systems and that dark energy might arise in consequence of conventional mechanical theory neglecting both the de Broglie wave energy and the work done in the direction of time. In these notes, a number of alternative derivations and connections relating to Hill (2018) are presented that were not made explicit in Hill (2018), including new derivations from the wave equation, a generalised approach and relating the solutions of Hill (2018) to a known result for uniform acceleration and to Hubble’s law for receding galaxies.
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Copyright 2018 Springer Nature