5,619 research outputs found
Interacting vector fields in Relativity without Relativity
Barbour, Foster and \'{O} Murchadha have recently developed a new framework,
called here {\it{the 3-space approach}}, for the formulation of classical
bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime
are presupposed. Both arise as emergent features of the world from
geodesic-type dynamics on a space of 3-dimensional metric--matter
configurations. In fact gravity, the universal light cone and Abelian gauge
theory minimally coupled to gravity all arise naturally through a single common
mechanism. It yields relativity -- and more -- without presupposing relativity.
This paper completes the recovery of the presently known bosonic sector within
the 3-space approach. We show, for a rather general ansatz, that 3-vector
fields can interact among themselves only as Yang--Mills fields minimally
coupled to gravity.Comment: Replaced with final version accepted by Classical and Quantum Gravity
(14 pages, no figures
Central limit approximations for Markov population processes with countably many types
When modelling metapopulation dynamics, the influence of a single patch on
the metapopulation depends on the number of individuals in the patch. Since
there is usually no obvious natural upper limit on the number of individuals in
a patch, this leads to systems in which there are countably infinitely many
possible types of entity. Analogous considerations apply in the transmission of
parasitic diseases. In this paper, we prove central limit theorems for quite
general systems of this kind, together with bounds on the rate of convergence
in an appropriately chosen weighted norm.Comment: 24 page
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
The geometry of the Barbour-Bertotti theories I. The reduction process
The dynamics of interacting particles is investigated in the
non-relativistic context of the Barbour-Bertotti theories. The reduction
process on this constrained system yields a Lagrangian in the form of a
Riemannian line element. The involved metric, degenerate in the flat
configuration space, is the first fundamental form of the space of orbits of
translations and rotations (the Leibniz group). The Riemann tensor and the
scalar curvature are computed by a generalized Gauss formula in terms of the
vorticity tensors of generators of the rotations. The curvature scalar is
further given in terms of the principal moments of inertia of the system. Line
configurations are singular for . A comparison with similar methods in
molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit
Leptons, quarks, and their antiparticles from a phase-space perspective
It is argued that antiparticles may be interpreted in macroscopic terms
without explicitly using the concept of time and its reversal. The appropriate
framework is that of nonrelativistic phase space. It is recalled that a quantum
version of this approach leads also, alongside the appearance of antiparticles,
to the emergence of `internal' quantum numbers identifiable with weak isospin,
weak hypercharge and colour, and to the derivation of the Gell-Mann-Nishijima
relation, while simultaneously offering a preonless interpretation of the
Harari-Shupe rishon model. Furthermore, it is shown that - under the assumption
of the additivity of canonical momenta - the approach entails the emergence of
string-like structures resembling mesons and baryons, thus providing a
different starting point for the discussion of quark unobservability.Comment: Talk given at Fifth Int. Workshop DICE2010 Space-Time-Matter,
Castiglioncello, Italy, September 13-17, 201
Scale-Invariant Gravity: Geometrodynamics
We present a scale-invariant theory, conformal gravity, which closely
resembles the geometrodynamical formulation of general relativity (GR). While
previous attempts to create scale-invariant theories of gravity have been based
on Weyl's idea of a compensating field, our direct approach dispenses with this
and is built by extension of the method of best matching w.r.t scaling
developed in the parallel particle dynamics paper by one of the authors. In
spatially-compact GR, there is an infinity of degrees of freedom that describe
the shape of 3-space which interact with a single volume degree of freedom. In
conformal gravity, the shape degrees of freedom remain, but the volume is no
longer a dynamical variable. Further theories and formulations related to GR
and conformal gravity are presented.
Conformal gravity is successfully coupled to scalars and the gauge fields of
nature. It should describe the solar system observations as well as GR does,
but its cosmology and quantization will be completely different.Comment: 33 pages. Published version (has very minor style changes due to
changes in companion paper
A law of large numbers approximation for Markov population processes with countably many types
When modelling metapopulation dynamics, the influence of a single patch on
the metapopulation depends on the number of individuals in the patch. Since the
population size has no natural upper limit, this leads to systems in which
there are countably infinitely many possible types of individual. Analogous
considerations apply in the transmission of parasitic diseases. In this paper,
we prove a law of large numbers for rather general systems of this kind,
together with a rather sharp bound on the rate of convergence in an
appropriately chosen weighted norm.Comment: revised version in response to referee comments, 34 page
Scale-invariant gravity: Spacetime recovered
The configuration space of general relativity is superspace - the space of
all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued
that the configuration space for gravity should be conformal superspace - the
space of all Riemannian 3-metrics modulo diffeomorphisms and conformal
transformations. Recently a manifestly 3-dimensional theory was constructed
with conformal superspace as the configuration space. Here a fully
4-dimensional action is constructed so as to be invariant under conformal
transformations of the 4-metric using general relativity as a guide. This
action is then decomposed to a (3+1)-dimensional form and from this to its
Jacobi form. The surprising thing is that the new theory turns out to be
precisely the original 3-dimensional theory. The physical data is identified
and used to find the physical representation of the theory. In this
representation the theory is extremely similar to general relativity. The
clarity of the 4-dimensional picture should prove very useful for comparing the
theory with those aspects of general relativity which are usually treated in
the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex
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