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Louis Crane

Publications and source records attributed to Louis Crane.

At least 19 recordsLinked to original sources
arXiv2019

Tetrahedral Geometry from Areas

We solve a very classical problem motivated by considerations in quantum gravity: providing a description of the geometry of a Euclidean tetrahedron from the initial data of the areas of the faces and the areas of the medial parallelograms of Yetter or equivalently of the pseudofaces of McConnell. In particular, we derive expressions for the dihedral angles, face angles and (an) edge length, the remaining parts being derivable by symmetry or by identities in the classic 1902 compendium of results on tetrahedral geometry of Richardson. We also provide an alternative proof using (bi)vectors of the result of Yetter that four times the sum of the squared areas of the medial parallelograms is equal to the sum of the squared areas of the faces. The updated version corrects several errors and provides better historical context for the result.

gr-qc↗
arXiv2014

Moves on Filtered PL Manifolds and Stratified PL Spaces

We extend results of Pachner and Casali to give finite sets of moves relating triangulations of PL manifolds respecting filtrations by locally flat manifolds and stratifications in which a finite family of simple local models exists for neighborhoods of strata.

math.GT↗
arXiv2012

String Field Theory from Quantum Gravity

Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group $E_6$, as explained by the quantum Mckay correspondence of Frenkel Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.

gr-qc↗
arXiv2011

Discrete Symmetry in the EPRL Model and Neutrino Physics

In \cite{C1}, we proposed a new interpretation of the EPRL quantization of the BC model for quantum general relativity using a monoidal functor we call the time functor. In this preliminary draft we apply the theory of modules over monoidal functors \cite{Y1} to the time functor, to propose an extension of the EPRL model which would include the standard model. This is motivated by recent advances in neutrino Physics.

math-ph↗
arXiv2010

Holography in the EPRL Model

In this research announcement, we propose a new interpretation of the EPR quantization of the BC model using a functor we call the time functor, which is the first example of a CLa-ren functor. Under the hypothesis that the universe is in the Kodama state, we construct a holographic version of the model. Generalisations to other CLa-ren functors and connections to model category theory are considered.

gr-qc↗
arXiv2010

Starships and Spinoza

We discuss a proposal to make small artificial black holes (ABH's) using a huge laser. Because of Hawking radiation, they would be extremely powerful energy sources. We investigate the technical problems of using them to make power plants and starships. The first suggestion is due to Hawking. Next, we consider what challenges the ABH proposal would pose for a future quantum theory of gravity. The form of a theory which would allow us to compute the necessary corrections to classical theory is considered. It is widely believed that every black hole produces a new baby universe on the other side of its singularity. If this is true, ABH technology will involve future humanity in the creation process of universes. Finally, we ponder the effects that the ABH proposal would have on the culture of a future society, particularly if the baby universe theory is correct. The changes in our economic life and understanding of our role in the cosmos would be so profound as to have a "spiritual" aspect.

gr-qc↗
arXiv2010

The Evolution and Development of the Universe

This document is the Special Issue of the First International Conference on the Evolution and Development of the Universe (EDU 2008). Please refer to the preface and introduction for more details on the contributions. Keywords: acceleration, artificial cosmogenesis, artificial life, Big Bang, Big History, biological evolution, biological universe, biology, causality, classical vacuum energy, complex systems, complexity, computational universe, conscious evolution, cosmological artificial selection, cosmological natural selection, cosmology, critique, cultural evolution, dark energy, dark matter, development of the universe, development, emergence, evolution of the universe evolution, exobiology, extinction, fine-tuning, fractal space-time, fractal, information, initial conditions, intentional evolution, linear expansion of the universe, log-periodic laws, macroevolution, materialism, meduso-anthropic principle, multiple worlds, natural sciences, Nature, ontology, order, origin of the universe, particle hierarchy, philosophy, physical constants, quantum darwinism, reduction, role of intelligent life, scale relativity, scientific evolution, self-organization, speciation, specification hierarchy, thermodynamics, time, universe, vagueness.

physics.gen-ph↗
arXiv2009

Are Black Hole Starships Possible

We investigate whether it is physically possible to build starships or power sources using the Hawking radiation of an artificial black hole as a power source. The proposal seems to be at the edge of possibility, but quantum gravity effects could change the picture.

gr-qc↗
arXiv2008

Model Categories and Quantum Gravity

We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as an object in a model category. One of the versions of our models appears as a thickening of spacetime, which we interpret as a formulation of relational geometry. Avenues toward constructing an actual quantum theory of gravity on our models are given a preliminary exploration.

gr-qc↗
arXiv2008

A Pointless Model for the Continuum as the Foundation for Quantum Gravity

In this paper, we outline a new approach to quantum gravity; describing states for a bounded region of spacetime as eigenstates for two classes of physically plausible gedanken experiments. We end up with two complementary descriptions in which the point set continuum disappears. The first replaces the continuum of events with a handlebody decomposition of loop space. We conjecture that techniques fron algebraic topology will allow us to extend state sum models on spacetime to loop space. The second picture replaces the continuum with a nondistributive lattice; the classical limit seems more tractible in this picture.

gr-qc↗
arXiv2007

What is the Mathematical Structure of Quantum Spacetime?

We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In the process of constructing a quantum topos for quantum gravity, we propose a new, operational approach to the problem of the obervables in quantum gravity, which leads to a new mathematical point of view on the state sum models.

gr-qc↗
arXiv2005

Causal sites as quantum geometry

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relativity. We propose an approach to quantization of causal sites as well.

gr-qc↗
arXiv2003

A More Sensitive Lorentzian State Sum

We give the construction modulo normalization of a new state sum model for lorentzian quantum general relativity, using the construction of Dirac's expansors to include quantum operators corresponding to edge lengths as well as the quantum bivectors of the Barrett-Crane model, and discuss the problem of its normalization. The new model gives rise to a new picture of quantum geometry in which lengths come in a discrete spectrum, while areas have a continuum of values.

gr-qc↗
arXiv2001

A New Approach to the Geometrization of Matter

We show that the sum over geometries in the Lorentzian 4-D state sum model for quantum GR in [1] includes terms which correspond to geometries on manifolds with conical singularities. Natural approximations suggest that they can be interpreted as gauge bosond for the standard model, plus fermions plus matter.

gr-qc↗