arXiv subjects

Mark D. Roberts

Publications and source records attributed to Mark D. Roberts.

44 records · Page 3Linked to original sources

arXiv1999

The Physical Interpretation of the Lanczos Tensor

The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamically significant, even when the electro-magnetic field tensor $F_{ab}$ vanishes. Here it is assumed that in the quantum realm the Lanczos tensor is dynamically significant, and this leads to an attempt to quantize the gravitational field by pursuing the analogy between the vector field and the Lanczos tensor.

gr-qc↗

arXiv1999

Exact Nonnull Wavelike Solutions to Gravity with Quadratic Lagrangians

Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse $N$ and the Riemann tensor takes the form $R^{t}_{.itj}=-k_{i}k_{j}, i,j=1,2,3$; thus these solutions depend on cross terms in the Riemann tensor and therefore complement the linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitaional energy Poynting vectors are construcetd for the solutions and one of these, based on the Lanczos tensor, supports the indication in the linearized theory that nonnull gravitational radiation can occur.

gr-qc↗

arXiv1999

The Quantization of Geodesic Deviation

There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations which generalize the Klein-Gordon equation. The resulting equations might have applications, and also show that entirely unexpected systems can be quantized. The possible applications of quantized geodesic deviation are to: i)the spreading wave packet in quantum theory, ii)and also to the one particle to many particle problem in second quantized quantum field theory.

gr-qc↗

arXiv1999

Autocatalytic Theory of Meaning

Recently it has been argued that autocatalytic theory could be applied to the origin of culture. Here possible application to a theory of meaning in the philosophy of language, called radical interpretation, is commented upon and compared to previous applications.

cs.CL↗

arXiv1999

An Expansion Term In Hamilton's Equations

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (δH_{c})/(δq)=\dotπ+Θπ, $+ (δH_{c})/(δπ)=\dot{q}$, where $Θ= V^{a}_{.;a}$ is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vector. As measured by this absolute time the expansion term is present. Similarly in cosmology, each observer has a co-moving vector and Hamilton's equations again have an expansion term. It is necessary to include the expansion term to quantize systems such as the above by the canonical method of replacing Dirac brackets by commutators. Hamilton's equations in this form do not have a corresponding sympletic form. Replacing the expansion by a particle number $N\equiv exp(-\intΘd \ta)$ and introducing the particle numbers conjugate momentum $π^{N}$ the standard sympletic form can be recovered with two extra fields N and $π^N$. Briefly the possibility of a non-standard sympletic form and the further possibility of there being a non-zero Finsler curvature corresponding to this are looked at.

gr-qc↗

arXiv1998

Non Metric Mass

In general relativity g_ab;c=0 implies that the wave equation (\Box^2-M)g_ab=0 always has M=0. If the underlying geometry is generalized to include non-metricity this incurs M \neq 0, and the above wave equation can be rewritten as M(x)+\td{\na}_a Q_.^a+(\ep+\fr{d}{2}-2)Q_a Q_.^a=0, where \ep=0, 1, 2, or 3, d is the dimension of the spacetime, and Q is the object of non-metricity. The consequences of this equation and the properties of M are investigated.

gr-qc↗

arXiv1998

Name Strategy: Its Existence and Implications

It is argued that colour name strategy, object name strategy, and chunking strategy in memory are all aspects of the same general phenomena, called stereotyping. It is pointed out that the Berlin-Kay universal partial ordering of colours and the frequency of traffic accidents classified by colour are surprisingly similar. Some consequences of the existence of a name strategy for the philosophy of language and mathematics are discussed. It is argued that real valued quantities occur {\it ab initio}. The implication of real valued truth quantities is that the {\bf Continuum Hypothesis} of pure mathematics is side-stepped. The existence of name strategy shows that thought/sememes and talk/phonemes can be separate, and this vindicates the assumption of thought occurring before talk used in psycholinguistic speech production models.

cs.CL↗

arXiv1998

The Quantum Commutator of a Perfect Fluid

A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum operator in the denominator of some coordinate quantum commutators. It is shown that it is possible to multiply throughout by this momentum operator. Factor ordering differences can result in a viscosity term. The resulting quantum commutator algebra is \vspace{1.0truein} \bc$v_{4}(v_{3}v_{2}-v_{2}v_{3})=-i,$\ec \bc$v_{4}(v_{1}v_{3}-v_{3}v_{1})=-iv_{3},$\ec \bc$v_{4}v_{1}-v_{1}v_{4}=-i,$\ec \bc$v_{5}v_{2}-v_{2}v_{5}=-i$.\ec

gr-qc↗