7 research outputs found
Tachyonic media in analogue models of special relativity
In sonic models of special relativity, the fact that the sonic medium
violates (ordinary) Lorentz symmetry is apparent to observers external to the
sonic medium but not to a class of observers existing within the medium itself.
We show that the situation is symmetric: internal observers will judge physics
in the external laboratory to violate their own sonic Lorentz symmetries. We
therefore treat all observers on an equal footing such that each is able to
retain a commitment to their own Lorentz symmetries. We then generalize beyond
the case of subsystem-environment decompositions to situations in which there
exist multiple phonon fields, all obeying Lorentz symmetries but with different
invariant speeds. In such cases, we argue that all observers have freedom to
choose which field is symmetry preserving, and so -- in a certain precise sense
-- which other fields are perceived as having an 'ether.' This choice is
influenced -- but not determined -- by a desire for simplicity in the
description of physical laws. Sending information faster than sound serves as a
model of tachyonic signalling to a distant receiver. Immutable causality of the
laboratory setup when perceived externally to a sonic medium manifests
internally through the confinement of the tachyons to an apparent ether (with a
rest frame), which we call a 'tachyonic medium,' thereby preventing tachyonic
exchange from emulating the scenario of a round-trip signal travelling into an
observer's past causal cone. The assignment of sonic-Lorentz-violating effects
to fields that obey 'photonic' Lorentz symmetries thus ensures that causality
associated with the 'sonic' Lorentz symmetries is preserved.Comment: (v2) minor changes after peer review; (v1) 13 pages, 4 figure
Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus
It is known that exactly self-dual gauge-field configurations with
topological charge |Q|=1 cannot exist on the untwisted continuum 4-torus. We
explore the manifestation of this remarkable fact on the lattice 4-torus for
SU(3) using advanced techniques for controlling lattice discretization errors,
extending earlier work of De Forcrand et. al. for SU(2). We identify three
distinct signals for the instability of |Q|=1 configurations, and show that
these manifest themselves early in the cooling process, long before the
would-be instanton has shrunk to a size comparable to the lattice
discretization threshold. These signals do not appear for our |Q|=2
configurations. This indicates that these signals reflect the truly global
nature of the instability, rather than local discretization effects.
Monte-Carlo generated SU(3) gauge field configurations are cooled to the
self-dual limit using an O(a^4)-improved gauge action chosen to have small but
positive O(a^6) errors. This choice prevents lattice discretization errors from
destroying instantons provided their size exceeds the dislocation threshold of
the cooling algorithm. Lattice discretization errors are evaluated by comparing
the O(a^4)-improved gauge-field action with an O(a^4)-improved action
constructed from the square of an O(a^4)-improved lattice field-strength
tensor, thus having different O(a^6) discretization errors. The number of
action-density peaks, the instanton size and the topological charge of
configurations is monitored. We observe a fluctuation in the total topological
charge of |Q|=1 configurations, and demonstrate that the onset of this unusual
behavior corresponds with the disappearance of multiple-peaks in the action
density. At the same time discretization errors are minimal.Comment: 12 pages, 9 figures, submitted to Phys. Rev.
Quantum gravity and the standard model
We show that a class of background independent models of quantum spacetime
have local excitations that can be mapped to the first generation fermions of
the standard model of particle physics. These states propagate coherently as
they can be shown to be noiseless subsystems of the microscopic quantum
dynamics. These are identified in terms of certain patterns of braiding of
graphs, thus giving a quantum gravitational foundation for the topological
preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space
has a basis of states given by ribbon graphs embedded in a three-dimensional
manifold up to diffeomorphisms, and the dynamics is given by local moves on the
graphs, such as arise in the representation theory of quantum groups. For such
models, matter appears to be already included in the microscopic kinematics and
dynamics.Comment: 12 pages, 21 figures, improved presentation, results unchange