78 research outputs found
Observing Shape in Spacetime
The notion of "reference frame" is a central theoretical construct for
interpreting the physical implications of spacetime diffeomorphism invariance
in General Relativity. However, the alternative formulation of classical
General Relativity known as Shape Dynamics suggest that a subset of spacetime
diffeomorphisms - namely hypersurface deformations - are, in a certain sense,
dual to spatial conformal (or Weyl) invariance. Moreover, holographic
gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance
can be replaced by the properties of boundary CFTs. How can these new
frameworks be compatible with the traditional notion of reference frame so
fundamental to our interpretation of General Relativity? In this paper, we
address this question by investigating the classical case of maximally
symmetric spacetimes with a positive cosmological constant. We find that it is
possible to define a notion of "Shape Observer" that represents a conformal
reference frame that is dual to the notion of inertial reference frame in
spacetime. We then provide a precise dictionary relating the two notions. These
Shape Observers are holographic in the sense that they are defined on the
asymptotic conformal boundaries of spacetime but know about bulk physics. This
leads to a first principles derivation of an exact classical holographic
correspondence that can easily be generalized to more complicated situations
and may lead to insights regarding the interpretation of the conformal
invariance manifest in Shape Dynamics.Comment: 23 pages including 3 figures + title pages, references and appendice
Schrodinger Evolution for the Universe: Reparametrization
Starting from a generalized Hamilton-Jacobi formalism, we develop a new
framework for constructing observables and their evolution in theories
invariant under global time reparametrizations. Our proposal relaxes the usual
Dirac prescription for the observables of a totally constrained system
(`perennials') and allows one to recover the influential partial and complete
observables approach in a particular limit. Difficulties such as the
non-unitary evolution of the complete observables in terms of certain partial
observables are explained as a breakdown of this limit. Identification of our
observables (`mutables') relies upon a physical distinction between gauge
symmetries that exist at the level of histories and states (`Type 1'), and
those that exist at the level of histories and not states (`Type 2'). This
distinction resolves a tension in the literature concerning the physical
interpretation of the partial observables and allows for a richer class of
observables in the quantum theory. There is the potential for the application
of our proposal to the quantization of gravity when understood in terms of the
Shape Dynamics formalism.Comment: 25 pages (including title page and references), 1 figur
Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics
In this PhD thesis, we develop a new approach to classical gravity starting
from Mach's principles and the idea that the local shape of spatial
configurations is fundamental. This new theory, "shape dynamics", is equivalent
to general relativity but differs in an important respect: shape dynamics is a
theory of dynamic conformal 3-geometry, not a theory of spacetime. Equivalence
is achieved by trading foliation invariance for local conformal invariance (up
to a global scale). After the trading, what is left is a gauge theory invariant
under 3d diffeomorphisms and conformal transformations that preserve the volume
of space. The local canonical constraints are linear and the constraint algebra
closes with structure constants. Shape dynamics, thus, provides a novel new
starting point for quantum gravity.
The procedure for the trading of symmetries was inspired by a technique
called "best matching". We explain best matching and its relation to Mach's
principles. The key features of best matching are illustrated through finite
dimensional toy models. A general picture is then established where relational
theories are treated as gauge theories on configuration space. Shape dynamics
is then constructed by applying best matching to conformal geometry. We then
study shape dynamics in more detail by computing its Hamiltonian and
Hamilton-Jacobi functional perturbatively.
This thesis is intended as a pedagogical but complete introduction to shape
dynamics and the Machian ideas that led to its discovery. The reader is
encouraged to start with the introduction, which gives a conceptual outline and
links to the relevant sections in the text for a more rigorous exposition. When
full rigor is lacking, references to the literature are given. It is hoped that
this thesis may provide a starting point for anyone interested in learning
about shape dynamics.Comment: 117 pages, 2 tables, 10 figures, PhD thesi
New Difficulties for the Past Hypothesis
Many macroscopic physical processes are known to occur in a time-directed way despite the apparent time-symmetry of the known fundamental laws. A popular explanation is to postulate an unimaginably atypical state for the early universe --- a `Past Hypothesis' (PH) --- that seeds the time-asymmetry from which all others follow. I will argue that such a PH faces serious new difficulties. First I strengthen the grounds for existing criticism by providing a systematic analytic framework for assessing the status of the PH. I outline three broad categories of criticism that put into question a list of essential requirements of the proposal. The resulting analysis paints a grim picture for the prospects of providing an adequate formulation for an explicit PH. I then provide a new argument that substantively extends this criticism by showing that any time-independent measure on the space of models of the universe must necessarily break one of its gauge symmetries. The PH then faces a new dilemma: reject a gauge symmetry of the universe and introduce a distinction without difference or reject the time-independence of the measure and lose explanatory power
New Difficulties for the Past Hypothesis
Many macroscopic physical processes are known to occur in a time-directed way despite the apparent time-symmetry of the known fundamental laws. A popular explanation is to postulate an unimaginably atypical state for the early universe --- a `Past Hypothesis' (PH) --- that seeds the time-asymmetry from which all others follow. I will argue that such a PH faces serious new difficulties. First I strengthen the grounds for existing criticism by providing a systematic analytic framework for assessing the status of the PH. I outline three broad categories of criticism that put into question a list of essential requirements of the proposal. The resulting analysis paints a grim picture for the prospects of providing an adequate formulation for an explicit PH. I then provide a new argument that substantively extends this criticism by showing that any time-independent measure on the space of models of the universe must necessarily break one of its gauge symmetries. The PH then faces a new dilemma: reject a gauge symmetry of the universe and introduce a distinction without difference or reject the time-independence of the measure and lose explanatory power
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