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CATEGORIES:DAMTP Friday GR Seminar
SUMMARY:A theory of what Background Independence is\, with
GR and Kendall's Shape Theory as examples - Edwar
d Anderson\, Paris 7 - Denis Diderot
DTSTART;TZID=Europe/London:20171201T130000
DTEND;TZID=Europe/London:20171201T140000
UID:TALK96343AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/96343
DESCRIPTION:A theory of what Background Independence is will b
e presented. \nAccording to this theory\, General
Relativity is an implementation of Background Ind
ependence\,\nwhereas Shape Theory (in David Kendal
l's sense\, mostly used hitherto in Shape Statisti
cs) can be set up to provide a simpler implementat
ion.\nConceptual incompatibilities between Backgro
und Independent Theories\nand background-dependent
branches of Physics - such as classical Newtonian
Physics\, Special Relativity and their quantum co
unterparts -\nwill furthermore be argued to manife
st themselves as Isham and Kuchar's multi-faceted
formulation of the Problem of Time. \n(Or\, more
precisely\, as a conceptually clearer and more gen
eral version of multi-faceted formulation due to t
he author).\n\nThe Problem of Time has hitherto be
en notorious for resolutions of one facet being ex
tended 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 uniqueness in the latter ca
se). \nThe number of moves this requires is much t
oo sizeable to fit into a seminar\, and yet a part
ial jist can be offered. \nI will sketch how deal
ing with just one aspect - Temporal Relationalism\
, which lies behind the Frozen Formalism facet - i
n a consistent manner \nrequires re-inventing arou
nd half of the habitual basic portions of the Prin
ciples of Dynamics. \nThis amounts to treating the
Jacobi Principle as not just an alternative to th
e Euler-Lagrange principle\,\nbut as a fundamental
principle that all of the rest of the Principles
of Dynamics is to be derived from (at least in thi
s application!) \nIn so doing\, one finds that man
y of what become the key players in quantum theory
- momenta\, Hamiltonian\, Poisson brackets\, cons
traints\, observables - \nare in already-Temporall
y Relational form and so do not require modificati
on. But many other objects - velocities\, Lagrangi
ans\, total Hamiltonians\, the Dirac Algorithm...
need to be replaced.\nThe Author replaces all such
used in assembling a local resolution of the Prob
lem of Time\, and (in the Author's book) then does
the same for foliation kinematics\, canonical qua
ntization and path integral formulation. \nThis e
xtensive reformulation combines with 'group averag
ing'\, the new variant of the Dirac Algorithm\, an
d an emergent rigidity of GR to give the local res
olution. \nThe Minisuperspace and Shape Theory ve
rsions of this are easier - by which they offer us
eful conceptual guidance -\nand yet the approach p
resented remains technically tractable for perturb
ative classical and semiclassical-quantum cosmolog
ical modelling.\n\nReferences: K.V. Kuchar\, " Tim
e and Interpretations of Quantum Gravity" Int. J.
Mod. Phys. D 20\, Suppl. 1 p.3 (2011): reprint of
1992 book article.\n\nC.J. Isham\, "Canonical Quan
tum Gravity and the Problem of Time"\, arXiv:gr-qc
/9210011\n\n D. G. Kendall\, D. Barden\, T. K. Car
ne and H. Le\, "Shape and Shape Theory" (Wiley\, 1
999).\n\nE. Anderson "The Problem of Time. Quantum
Mechanics versus General Relativity" (Springer\,
2017)\, \nEbook link: https://link.springer.com/b
ook/10.1007%2F978-3-319-58848-3 (the Preface\, Abs
tracts of each chapter and 200-page "Mathematical
Methods for Basic and Foundational Quantum Gravity
"Appendix part of this book are freely available o
nline from this link).
LOCATION:Pavilion B Potter Room (B1.19)
CONTACT:Michalis Agathos
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