arXiv subjects

Robert C. Hilborn

Publications and source records attributed to Robert C. Hilborn.

9 recordsLinked to original sources

arXiv2019

Gravitational waves without general relativity: A tutorial

This tutorial leads the reader through the details of calculating the properties of gravitational waves from orbiting binaries, such as two orbiting black holes. Using analogies with electromagnetic radiation, the tutorial presents a calculation that produces the same dependence on the masses of the orbiting objects, the orbital frequency, and the mass separation as does the linear version of General Relativity (GR). However, the calculation yields polarization, angular distributions, and overall power results that differ from those of GR. Nevertheless, the calculation produces waveforms that are nearly identical to the pre-binary-merger portions of the signals observed by the Laser Interferometer Gravitational-Wave Observatory (LIGO-Virgo) collaboration. The tutorial should be easily understandable by students who have taken a standard upper-level undergraduate course in electromagnetism.

physics.ed-ph↗

arXiv2019

GW170817 event rules out general relativity in favor of vector gravity

The observation of gravitational waves by the three LIGO-Virgo interferometers allows the examination of the polarization of gravitational waves. Here we analyze the binary neutron star event GW170817, whose source location and distance are determined precisely by concurrent electromagnetic observations. Applying a signal accumulation procedure to the LIGO-Virgo strain data, we find ratios of the signals detected by the three interferometers. We conclude that the signal ratios are inconsistent with the predictions of general relativity, but consistent with the recently proposed vector theory of gravity [Phys. Scr. 92, 125001 (2017)]. Moreover, we find that vector gravity yields a distance to the source in agreement with the astronomical observations. If our analysis is correct, Einstein's general theory of relativity is ruled out in favor of vector gravity at 99% confidence level and future gravitational wave detections by three or more observatories should confirm this conclusion with higher precision.

physics.gen-ph↗

arXiv2019

GW170814: Gravitational wave polarization analysis

To determine the polarization character of gravitational waves, we use strain data from the GW170814 binary black hole coalescence event detected by the three LIGO-Virgo observatories, extracting the gravitational wave strain signal amplitude ratios directly from those data. Employing a geometric approach that links those ratios to the gravitational wave polarization properties, we find that there is a range of source sky locations, partially overlapping the LIGI-Virgo 90% credible range of GW170814 source locations, for which vector polarization is consistent with the observed amplitude ratios. A Bayesian inference analysis indicates that the GW170814 data cannot rule out vector polarization for gravitational waves. Confirmation of a vector polarization component of gravitational waves would be a sign of post-general relativity physics.

gr-qc↗

arXiv2012

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.

q-bio.MN↗

arXiv2009

Stochastic Coherence in an Oscillatory Gene Circuit Model

We show that noise-induced oscillations in a gene circuit model display stochastic coherence, that is, a maximum in the regularity of the oscillations as a function of noise amplitude. The effect is manifest as a system-size effect in a purely stochastic molecular reaction description of the circuit dynamics. We compare the molecular reaction model behavior with that predicted by a rate equation version of the same system. In addition, we show that commonly used reduced models that ignore fast operator reactions do not capture the full stochastic behavior of the gene circuit. Stochastic coherence occurs under conditions that may be physiologically relevant.

q-bio.MN↗

arXiv2003

Coherence resonance in models of an excitable neuron with both fast and slow dynamics

We demonstrate the existence of noise-induced periodicity (coherence resonance) in both a discrete-time model and a continuous-time model of an excitable neuron. In particular, we show that the effects of noise added to the fast and slow dynamics of the models are dramatically different. A Fokker-Planck analysis gives a quantitative explanation of the effects.

q-bio.NC↗

arXiv2002

Einstein coefficients, cross sections, f values, dipole moments, and all that

The relationships among various parameters describing the strength of optical transitions in atoms and molecules are reviewed. The application of these parameters to the description of the interaction between nearly monochromatic, directional light beams and atoms and molecules is given careful attention. Common pitfalls in relating these parameters are pointed out. This is a revised (February, 2002) version of a paper that originally appeared in Am. J. Phys. 50, 982-986 (1982).

physics.atom-ph↗

arXiv1999

Quon Statistics for Composite Systems and a Limit on the Violation of the Pauli Principle for Nucleons and Quarks

The quon algebra gives a description of particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons, for which $q = +1$, and fermions, for which $q = -1$. Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. Here we generalize this result to composite systems of identical quons. We find $q_{composite}=q_{constituent}^{n^2}$ for a system of $n$ identical quons. This result reduces to the earlier result for bosons and fermions. Using this generalization we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.

quant-ph↗

arXiv1998

The Relation of Constraints on Particle Statistics for Different Species of Particles

Quons are particles characterized by the parameter $q$, which permits smooth interpolation between Bose and Fermi statistics; $q=1$ gives bosons, $q=-1$ gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form $\bar{f}fb$, where $f$ is fermion-like and $b$ is boson-like. We show that $q_f^2=q_b$. In particular, we relate the bound on $q_γ$ for photons to the bound on $q_e$ for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to high precision.

hep-th↗