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Note on the natural system of units

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Abstract

We propose to substitute Newton’s constant G N for another constant G 2, as if the gravitational force would fall off with the 1/r law, instead of the 1/r 2; so we describe a system of natural units with G 2, c and ℏ. We adjust the value of G 2 so that the fundamental length L = L Pl is still the Planck’s length and so G N = L × G 2. We argue for this system as (1) it would express longitude, time and mass without square roots; (2) G 2 is in principle disentangled from gravitation, as in (2 + 1) dimensions there is no field outside the sources. So G 2 would be truly universal; (3) modern physics is not necessarily tied up to (3 + 1)-dim. scenarios and (4) extended objects with p = 2 (membranes) play an important role both in M-theory and in F-theory, which distinguishes three (2, 1) dimensions.

As an alternative we consider also the clash between gravitation and quantum theory; the suggestion is that non-commutative geometry [x i , x j ] = Λ2 θ ij would cure some infinities and improve black hole evaporation. Then the new length Λ shall determine, among other things, the gravitational constant G N.

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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad de Zaragoza, E-50009, Zaragoza, Spain

    Luis J. Boya & Cristian Rivera

  2. Physics Department, University of Texas, Austin, 78712, USA

    E. C. G. Sudarshan

Authors
  1. Luis J. Boya
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  2. Cristian Rivera
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  3. E. C. G. Sudarshan
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Correspondence to Luis J. Boya.

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Boya, L.J., Rivera, C. & Sudarshan, E.C.G. Note on the natural system of units. Pramana - J Phys 73, 961–968 (2009). https://doi.org/10.1007/s12043-009-0172-y

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  • DOI: https://doi.org/10.1007/s12043-009-0172-y

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