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Temporal Relationalism (TR)

  • Edward Anderson
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 190)

Abstract

We develop here a detailed theory of Temporal Relationalism, consisting of the following.
  1. A)

    The Leibnizian ‘there is no time for the universe as a whole at the primary level’.

     
  2. B)

    This is then resolved by an emergent time arising at the secondary level, along the lines of Mach’s ‘time is to be abstracted from change’. This chapter clarifies furthermore that this is an ephemeris-type time emergent from a sufficient totality of locally relevant change.

     

A) is implemented by reformulating a fair portion of the principles of dynamics for use at the primary level. There being no time at the primary level means that change supplants velocity. Now, on the one hand, Jacobi arc elements, Jacobi’s principle and consequent ‘Jacobi–Mach’ equations of motion supplant Lagrangians, Euler–Lagrange’s principle and Euler–Lagrange equations respectively. On the other hand, the standard notions of momentum and action survive this transition to a Temporal Relationalism implementing principles of dynamics (TRiPoD: see also the freely available online Appendix L). This program can moreover be viewed as taking Jacobi’s principle seriously enough for all of its logical conclusions to supplant those of the Euler–Lagrange action principle wherever the two are formulaically distinct.

TRiPoD gives some indication that it can take a lot of work to remain inside one of the Problem of Time facet ‘gates’ during subsequent attempts to pass through further gates.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Edward Anderson
    • 1
  1. 1.DAMTPCentre for Mathematical SciencesCambridgeUK

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