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SUMMARY:A theory of what Background Independence is\, with GR and Kendall'
 s Shape Theory as examples - Edward Anderson\, Paris 7 - Denis Diderot
DTSTART:20171201T130000Z
DTEND:20171201T140000Z
UID:TALK96343@talks.cam.ac.uk
CONTACT:Michalis Agathos
DESCRIPTION:A theory of what Background Independence is will be presented.
   \nAccording to this theory\, General Relativity is an implementation of 
 Background Independence\,\nwhereas Shape Theory (in David Kendall's sense\
 , mostly used hitherto in Shape Statistics) can be set up to provide a sim
 pler implementation.\nConceptual incompatibilities between Background Inde
 pendent Theories\nand background-dependent branches of Physics - such as c
 lassical Newtonian Physics\, Special Relativity and their quantum counterp
 arts -\nwill furthermore be argued to manifest themselves as Isham and Kuc
 har's multi-faceted formulation of the Problem of Time.  \n(Or\, more prec
 isely\, as a conceptually clearer and more general version of multi-facete
 d formulation due to the author).\n\nThe Problem of Time has hitherto been
  notorious for resolutions of one facet being extended to resolve another 
 facet ceasing to resolve the first facet...\nThe Author has resolved this 
 at the classical and semi-classical levels locally (and without claim of u
 niqueness in the latter case). \nThe number of moves this requires is much
  too sizeable to fit into a seminar\, and yet a partial jist can be offere
 d.  \nI will sketch how dealing with just one aspect - Temporal Relational
 ism\, which lies behind the Frozen Formalism facet - in a consistent manne
 r \nrequires re-inventing around half of the habitual basic portions of th
 e Principles of Dynamics. \nThis amounts to treating the Jacobi Principle 
 as not just an alternative to the Euler-Lagrange principle\,\nbut as a fun
 damental principle that all of the rest of the Principles of Dynamics is t
 o be derived from (at least in this application!) \nIn so doing\, one find
 s that many of what become the key players in quantum theory - momenta\, H
 amiltonian\, Poisson brackets\, constraints\, observables - \nare in alrea
 dy-Temporally Relational form and so do not require modification. But many
  other objects - velocities\, Lagrangians\, total Hamiltonians\, the Dirac
  Algorithm... need to be replaced.\nThe Author replaces all such used in a
 ssembling a local resolution of the Problem of Time\, and (in the Author's
  book) then does the same for foliation kinematics\, canonical quantizatio
 n and path integral formulation.  \nThis extensive reformulation combines 
 with 'group averaging'\, the new variant of the Dirac Algorithm\, and an e
 mergent rigidity of GR to give the local resolution.  \nThe Minisuperspace
  and Shape Theory versions of this are easier - by which they offer useful
  conceptual guidance -\nand yet the approach presented remains technically
  tractable for perturbative classical and semiclassical-quantum cosmologic
 al modelling.\n\nReferences: K.V. Kuchar\, " Time and Interpretations of Q
 uantum Gravity" Int. J. Mod. Phys. D 20\, Suppl. 1 p.3 (2011): reprint of 
 1992 book article.\n\nC.J. Isham\, "Canonical Quantum Gravity and the Prob
 lem of Time"\, arXiv:gr-qc/9210011\n\n D. G. Kendall\, D. Barden\, T. K. C
 arne and H. Le\, "Shape and Shape Theory" (Wiley\, 1999).\n\nE. Anderson "
 The Problem of Time. Quantum Mechanics versus General Relativity" (Springe
 r\, 2017)\,  \nEbook link: https://link.springer.com/book/10.1007%2F978-3-
 319-58848-3 (the Preface\, Abstracts of each chapter and 200-page "Mathema
 tical Methods for Basic and Foundational Quantum Gravity"Appendix part of 
 this book are freely available online from this link). 
LOCATION:Pavilion B Potter Room (B1.19)
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