arXiv subjects

Lawrence R. Mead

Publications and source records attributed to Lawrence R. Mead.

14 recordsLinked to original sources

arXiv2020

Reaffirmation of Cosmological Oscillations in the Scale Factor from the Pantheon Compilation of 1048 Type Ia Supernovae

We observe damped temporal oscillations in the scale factor at a dominant frequency of ~ 7 cycles/Hubble-time in the Pantheon Compilation of 1048 type Ia supernovae (SNe). The residual oscillations observed in the Pantheon data closely matches and reaffirms our initial observation of oscillations from earlier SNe data (primarily SNLS3, 2011) at 2-sigma confidence. The nearly identical shapes in amplitude, frequency, phase and damping constant makes it highly likely the signal is real. Furthermore, 2/3 of the Pantheon SNe cover different portions of the sky compared with SNLS3 strengthening this conclusion. Our model describing the oscillation, presented in an earlier paper, is a simple scalar field harmonic oscillator coupled to the LCDM Friedmann eqn, but carried into the present epoch. The scalar field energy density plays the role of the dark matter energy density in LCDM cosmology, fits well as an average, and closely matches the present dark matter density parameter, suggesting the oscillation play a role in the dark matter sector. Temporal oscillations in the scale factor and its derivative, as described in the present work, would also induce temporal oscillations of the Hubble parameter.

astro-ph.CO↗

arXiv2018

The shape of the orbit in FLRW spacetimes

The shape of the orbit of a free particle is examined in FLRW cosmologies. The spatial projection of the orbit is time-independent and has a simple geometric description. We relate this description to the expression in terms of standard FLRW coordinates.

gr-qc↗

arXiv2016

A selection rule for transitions in PT-symmetric quantum theory

Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrodinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum.

hep-th↗

arXiv2015

Model-Independent Plotting of the Cosmological Scale Factor as a Function of Lookback Time

In the present work we describe a model-independent method of developing a plot of scale factor versus lookback time from the usual Hubble diagram of modulus data against redshift. This is the first plot of this type. We follow the model-independent methodology of Daly and Djorgovski (2004) used for their radio-galaxy data. Once the data plot is completed, any model can be applied and will display accordingly as described in standard literature. We then compile an extensive data set to z = 1.8 by combining SNe Ia data from SNLS3 of Conley et al. (2011), High-z SNe data of Riess et al. (2004) and radio-galaxy data of Daly & Djorgovski (2004) to be used to validate the new plot. We first display these data on a standard Hubble diagram to confirm the best fit for LCDM cosmology and thus validate the joined data set. The scale factor plot is then developed from the data and the LCDM model is again displayed from a least-squares fit. The fit parameters are in agreement with the Hubble diagram fit confirming the validity of the new plot. Of special interest is the transition-time of the universe which in the scale factor plot will appear as an inflection point in the data set. Noise is more visible on this presentation which is particularly sensitive to inflection points of any model displayed on the plot unlike on a modulus-z diagram where there are no inflection points and the transition-z is not at all obvious by inspection. We obtain a lower limit of z >0.6. It is evident from this presentation that there is a dearth of SNe data in the range, z = 1-2, exactly the range necessary to confirm a LCDM transition-z in the neighborhood of z = 0.76.

astro-ph.CO↗

arXiv2014

Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum Theory?

Update: A time-independent $n\times n$ PT-symmetric (and symmetric) Hamiltonian is diagonalizable since it has all distinct real eigenvalues and the resulting diagonal matrix is a real symmetric matrix. The diagonalization results an isometry so there shouldn't be any issue with unitarity and unfortunately this very elementary mathematical fact somehow did not draw the authors' attention. However, PT-symmetric quantum mechanics is not out of trouble. For time-dependent PT-symmetric (and symmetric) Hamiltonians (even $2\times 2$ ones) the authors observed that there is a violation of unitarity. Moreover, the first named author showed in his recent article arXiv:1312.7738 that PT-symmetric quantum mechanics is indeed a certain kind of Hermitian quantum mechanics and that in order for time-evolution to be unitary with respect to $J$-inner product (one that gives rise to a Hilbert space structure on the space of state functions), the potential energy operator $V(x)$ must be real. This means that those complex PT-symmetric Hamiltonians that have been studied by physicists are unfortunately unphysical. The first named author discussed in a subsequent article arXiv:1401.5149 that while finite-state PT-symmetric quantum mechanics with time-independent Hamiltonians is not physically any different from Hermitian quantum mechanics, PT-symmetric quantum mechanics exhibits a distinctive symmetry from that of Hermitian quantum mechanics.

quant-ph↗

arXiv2012

On a Bipolar Model of Hyperbolic Geometry and its Relation to Hyperbolic Robertson-Walker Space

Negatively curved, or hyperbolic, regions of space in an FRW universe are a realistic possibility. These regions might occur in voids where there is no dark matter with only dark energy present. Hyperbolic space is strange and various "models" of hyperbolic space have been introduced, each offering some enlightened view. In the present work we develop a new bipolar model of hyperbolic geometry, closely related to an existing model - the band model - and show that it provides new insights toward an understanding of hyperbolic as well as elliptic Robertson-Walker space and the meaning of its isometries. In particular, we show that the circular geodesics of a hyperbolic Robertson-Walker space can be referenced to two real centers - a Euclidean center and an offset hyperbolic center. These are not the Euclidean center or poles of the bipolar coordinate system but rather refer to two distinct centers for circular orbits of particles in such systems. Considering the physics of elliptic RW space is so well confirmed in the Lambda-CDM model with respect to Euclidean coordinates from a Euclidean center, it is likely that the hyperbolic center plays a physical role in regions of hyperbolic space.

gr-qc↗

arXiv2009

A New Formula Describing the Scaffold Structure of Spiral Galaxies

We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inward and outward arms are also described by the analytic continuation of the same formula. The formula is r(phi) = A/log[B tan(phi/2N)]. This function intrinsically generates a bar in a continuous, fixed relationship relative to an arm of arbitrary winding sweep. A is simply a scale parameter while B, together with N, determine the spiral pitch. Roughly, greater N results in tighter winding. Greater B results in greater arm sweep and smaller bar/bulge while smaller B fits larger bar/bulge with a sharper bar/arm junction. Thus B controls the "bar/bulge-to-arm" size, while N controls the tightness much like the Hubble scheme. The formula can be recast in a form dependent only on a unique point of turnover angle of pitch - essentially a 1-parameter fit, aside from a scale factor. The recast formula is remarkable and unique in that a single parameter can define a spiral shape with either constant or variable pitch capable of tightly fitting Hubble types from grand design spirals to late type large-barred galaxies. We compare the correlation of our pitch parameter to Hubble type with that of the traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our formula produces a very tight correlation with ideal Hubble type suggesting it is a good discriminator compared to logarithmic pitch, which shows poor correlation here similar to previous works. Representative examples of fitted galaxies are shown.

astro-ph.GA↗

arXiv2009

Almost rolling motion: An investigation of rolling grooved cylinders

We examine the dynamics of cylinders that are grooved to form N teeth for rolling motion down an inclined plane. The grooved cylinders are experimentally found to reach a terminal velocity. This result can be explained by the inclusion of inelastic processes which occur whenever a tooth hits the surface. The fraction of the angular velocity that is lost during an inelastic collision is phenomenologically found to be proportional to (2*sin^2*pi/N)-(alpha*sin^3*pi/N), and the method of least squares is used to find the constant alpha=0.98. The adjusted theoretical results for the time of rolling as well as for terminal velocity are found to be in good agreement with the experimental results.

physics.class-ph↗

arXiv2009

Simple Fit of Data Relating Supermassive Black Hole Mass to Galaxy Pitch Angle

Seigar, et al, have recently demonstrated a new, tight correlation between galactic central supermassive black hole (BH) mass and the pitch angle of the spiral arm in disc galaxies which they attribute to other indirect correlations. They fit a double power law, governed by five parameters, to the BH mass as a function of pitch. Noting the features of their fitted curve, we show that a simple linear proportion of the BH mass to the cotangent of the pitch angle can obtain the same fit, within error. Such a direct, elegant fit may help shed light on the nature of the correlation.

astro-ph.GA↗

arXiv2006

Are Dark Matter and Dark Energy the Residue of the Expansion-Reaction to the Big Bang ?

We derive the phenomenological Milgrom square-law acceleration, describing the apparent behavior of dark matter, as the reaction to the Big Bang from a model based on the Lorentz-Dirac equation of motion traditionally describing radiation reaction in electromagnetism but proven applicable to expansion reaction in cosmology. The model is applied within the Robertson-Walker hypersphere, and suggests that the Hubble expansion exactly cancels the classical reaction imparted to matter following the Big Bang, leaving behind a residue proportional to the square of the acceleration. The model further suggests that the energy density associated with the reaction acceleration is precisely the critical density for flattening the universe thus providing a potential explanation of dark energy as well. A test of this model is proposed.

gr-qc↗

arXiv2005

Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space

Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1-dimensional Riemann flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to "induce matter" in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space.

gr-qc↗

arXiv2002

Comment on "Gain-assisted Superluminal Light Propagation"

Wang, Kuzmich and Dogariu, in their 20 July, 2000, Nature article, describe an experiment ostensibly measuring superluminal speeds of 310c via a few percent shift in time of an optical pulse undergoing anomalous dispersion in a pumped medium. This paper seems to have become part of the superluminal lore and is often referenced as a profound example of superluminality. We have closely examined the article and find serious flaws that need to be addressed.

physics.optics↗

arXiv1993

Random Walks in Noninteger Dimension

One can define a random walk on a hypercubic lattice in a space of integer dimension $D$. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given number of time steps. These formulas are physically meaningful for integer values of $D$. However, these formulas are unacceptable as probabilities when continued to noninteger $D$ because they give values that can be greater than $1$ or less than $0$. In this paper we propose a random walk which gives acceptable probabilities for all real values of $D$. This $D$-dimensional random walk is defined on a rotationally-symmetric geometry consisting of concentric spheres. We give the exact result for the probability of returning to the origin for all values of $D$ in terms of the Riemann zeta function. This result has a number-theoretic interpretation.

hep-lat↗

arXiv1993

Discrete Time Quantum Mechanics

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy based on the method of finite elements. We are able to formulate fully consistent quantum-mechanical systems directly on a lattice in terms of operator difference equations. One advantage of this discretized formulation of quantum mechanics is that the ambiguities associated with operator ordering are eliminated. Furthermore, the scheme provides an easy way in which to obtain the energy levels of the theory numerically. A generalized version of this discretization scheme can be applied to quantum field theory problems. The difficulties normally associated with fermion doubling are eliminated. Also, one can incorporate local gauge invariance in the finite-element formulation. Results for some field theory models are summarized. In particular, we review the calculation of the anomaly in two-dimensional quantum electrodynamics (the Schwinger model). Finally, we discuss nonabelian gauge theories.

hep-ph↗