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Scale invariance, killing vectors, and the size of the fifth dimension

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Abstract

An analysis is made of the classical five-dimensional sourceless Kaluza-Klein equations with the existence of the usual∂/∂ψ Killing vector not assumed, whereψ is the coordinate of the fifth dimension. The physical distance around the fifth dimensionD 5, needed for the calculation of the fine structure constantα, is not calculable in the usual theory because the equations have a global scale invariance. In the present case, the Killing vector and the global scale invariance are not present, but it is found rather generally thatD 5=0. This indicates that quantum gravity is a necessary ingredient ifα is to be calculated. It also provides an alternate explanation of why the universe appears four-dimensional.

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Authors and Affiliations

  1. Physics Department, Iowa State University Ames, 50011, Iowe

    D. K. Ross

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  1. D. K. Ross
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Ross, D.K. Scale invariance, killing vectors, and the size of the fifth dimension. Int J Theor Phys 25, 663–670 (1986). https://doi.org/10.1007/BF00668712

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  • DOI: https://doi.org/10.1007/BF00668712

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