University of Cambridge > Talks.cam > DAMTP Friday GR Seminar > A theory of what Background Independence is, with GR and Kendall's Shape Theory as examples

A theory of what Background Independence is, with GR and Kendall's Shape Theory as examples

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A theory of what Background Independence is will be presented. According to this theory, General Relativity is an implementation of Background Independence, whereas Shape Theory (in David Kendall’s sense, mostly used hitherto in Shape Statistics) can be set up to provide a simpler implementation. Conceptual incompatibilities between Background Independent Theories and background-dependent branches of Physics – such as classical Newtonian Physics, Special Relativity and their quantum counterparts - will furthermore be argued to manifest themselves as Isham and Kuchar’s multi-faceted formulation of the Problem of Time. (Or, more precisely, as a conceptually clearer and more general version of multi-faceted formulation due to the author).

The Problem of Time has hitherto been notorious for resolutions of one facet being extended to resolve another facet ceasing to resolve the first facet… The Author has resolved this at the classical and semi-classical levels locally (and without claim of uniqueness in the latter case). The number of moves this requires is much too sizeable to fit into a seminar, and yet a partial jist can be offered. I will sketch how dealing with just one aspect – Temporal Relationalism, which lies behind the Frozen Formalism facet – in a consistent manner requires re-inventing around half of the habitual basic portions of the Principles of Dynamics. This amounts to treating the Jacobi Principle as not just an alternative to the Euler-Lagrange principle, but as a fundamental principle that all of the rest of the Principles of Dynamics is to be derived from (at least in this application!) In so doing, one finds that many of what become the key players in quantum theory – momenta, Hamiltonian, Poisson brackets, constraints, observables – are in already-Temporally Relational form and so do not require modification. But many other objects – velocities, Lagrangians, total Hamiltonians, the Dirac Algorithm… need to be replaced. The Author replaces all such used in assembling a local resolution of the Problem of Time, and (in the Author’s book) then does the same for foliation kinematics, canonical quantization and path integral formulation. This extensive reformulation combines with ‘group averaging’, the new variant of the Dirac Algorithm, and an emergent rigidity of GR to give the local resolution. The Minisuperspace and Shape Theory versions of this are easier – by which they offer useful conceptual guidance - and yet the approach presented remains technically tractable for perturbative classical and semiclassical-quantum cosmological modelling.

References: K.V. Kuchar, ” Time and Interpretations of Quantum Gravity” Int. J. Mod. Phys. D 20 , Suppl. 1 p.3 (2011): reprint of 1992 book article.

C.J. Isham, “Canonical Quantum Gravity and the Problem of Time”, arXiv:gr-qc/9210011

D. G. Kendall, D. Barden, T. K. Carne and H. Le, "Shape and Shape Theory" (Wiley, 1999).

E. Anderson “The Problem of Time. Quantum Mechanics versus General Relativity” (Springer, 2017), Ebook link: https://link.springer.com/book/10.1007%2F978-3-319-58848-3 (the Preface, Abstracts of each chapter and 200-page “Mathematical Methods for Basic and Foundational Quantum Gravity”Appendix part of this book are freely available online from this link).

This talk is part of the DAMTP Friday GR Seminar series.

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