arXiv subjects

Ronald J. Adler

Publications and source records attributed to Ronald J. Adler.

17 recordsLinked to original sources

arXiv2026

Temperature of a spinning black hole via a simple derivation

According to current theory a black hole has a nonzero temperature and thus radiates like any black body. This remarkable result was first shown by Hawking for a non-spinning black hole using general relativity to describe the black hole gravitational field and quantum field theory to describe the radiation. Since then the temperature of a spinning Kerr black hole has been calculated. There have also been many heuristic derivations for the temperature. In this work we derive the temperature of a Kerr spinning black hole using only classical general relativity and thermodynamics. It is very similar to Ref. 11 but is mathematically simpler and more self-contained. Our purpose is mainly pedagogical, to be more accessible to students and non-specialists with a knowledge of general relativity. We also call further attention to the expected explosive evaporation of small black holes, not yet observed, which would be an almost unique window into Planck scale physics. Finally, we discuss the idea that the cosmological dark matter, whose nature is currently unknown, may be composed of small primordial black hole remnants.

gr-qc↗

arXiv2014

The three-fold theoretical basis of the Gravity Probe B gyro precession calculation

The Gravity Probe B (GP-B) experiment is complete and the results are in agreement with the predictions of general relativity (GR) for both the geodetic precession, 6.6 arcsec/yr to about 0.3%, and the Lense-Thirring precession, 39 marcsec to about 19%. This note is concerned with the theoretical basis for the predictions. The predictions depend on three elements of gravity theory, firstly that macroscopic gravity is described by a metric theory such as general relativity, secondly that the Lense-Thirring metric provides an approximate description of the gravitational field of the spinning earth, and thirdly that the spin axis of a gyroscope is parallel displaced in spacetime, which gives its equation of motion. We look at each of these three elements to show how each is solidly based on previous experiments and well-tested theory. The agreement of GP-B with theory strengthens our belief that all three elements are correct and increases our confidence in applying GR to astrophysical phenomena. Conversely, if GP-B had not verified the predictions a major theoretical quandary would have occurred.

gr-qc↗

arXiv2014

A quantum theory of distance along a curve

We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it according to the rules of quantum mechanics and interpret its eigenvalues as physically observable distances; the distance eigenvalues are naturally quantized. There are both positive and negative eigenvalues, which requires interpretation. Multi-element curves are defined as direct sums of line elements, and behave much like systems of spin half electrons in a magnetic field. For a curve of many elements an entropy and energy and temperature are quite naturally defined, leading via standard statistical thermodynamics to a relation between the most probable curve length and temperature. That relation may be viewed as a universal heat-shrinking property of curves. At this stage of the theory we do not include bodies or particles in the mix, do not suggest field equations for the quantum geometry, and questions of interpretation remain. The theory might conceivably be testable using observations of the early Universe, when the temperature of space was presumably quite high. In particular cosmogenesis may be thought of as time stopping at an infinite temperature as we go backwards in time to the beginning.

gr-qc↗

arXiv2014

On a digital quantum description of physical space versus the continuum description

The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum effects forces us to re-evaluate the concept of space (and time), and some sort of discreteness or granularity is expected. Here we study a cubic grid of points representing fundamental volumes of space and derive the spectra of momenta and wave number, which are not generally proportional to each other. The momentum is bounded and discrete for a finite grid. The uncertainty principle must be modified to reflect small scale spatial non-locality but it is consistent with the standard uncertainty principle in the continuum limit. We only consider kinematics in this work, and do not discuss time or energy or dynamical evolution.

gr-qc↗

arXiv2011

Comment on the cosmological constant and a gravitational alpha

We call attention to a simple analogy between atomic physics and cosmology. Both have two characteristic length scales. In atomic physics the lengths are the Compton wavelength of the electron and the Bohr radius; the ratio of these two lengths is the fine structure constant, $α=7.30\times10^{-3}$. In cosmology we take the lengths to be the Planck length and the de Sitter radius divided by $\sqrt 3$; the ratio of these two lengths is about $α_g=1.91\times10^{-61}$, which we suggest should be called the gravitational fine structure constant. There is also a basic energy ratio in atomic physics, the ratio of the hydrogen atom binding energy to the electron rest energy, which is equal to ${α^2}/2$. The analogous energy ratio in cosmology is the ratio of the dark energy density (described in terms of the cosmological constant) to the Planck energy density, which is equal to $(1/8π)α_g^2$. The long-standing problem of the nature of the dark energy and its small density is obviously equivalent to understanding the extraordinarily small value of $α_g$. We further emphasize that our observational knowledge of dark energy, which is consistent with the cosmological constant interpretation, is entirely on the cosmological scale, so we know essentially nothing about the nature of dark energy on a smaller and presumably more fundamental scale.

gr-qc↗

arXiv2011

Gravitomagnetism and spinor quantum mechanics

We give a systematic treatment of a spin 1/2 particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it is largely self-contained and may serve as an introduction to spinors in a Riemann space. The analysis is based on the Dirac equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The restriction to a slowly moving matter source, such as the earth, allows us to describe the gravitational field by a gravitoelectric (Newtonian) potential and a gravitomagnetic (frame-dragging) vector potential, the existence of which has recently been experimentally verified. Our main interest is the coupling of the orbital and spin angular momenta of the particle to the gravitomagnetic field. Specifically we calculate the gravitational gyromagnetic ratio as gsubg=1 ; this is to be compared with the electromagnetic gyromagnetic ratio of gsube=2 for a Dirac electron.

gr-qc↗

arXiv2011

Genesis and the tipping pencil; why the Universe is flat

In a room with five cosmologists there there may easily be ten theories of cosmogenesis. Cosmogenesis is a popular topic for speculation because it is philosophically deep and because such speculations are unlikely to be proven wrong in the near future. The scenario we present here was intended mainly as a pedagogical illustration or toy model, but it turns out to possibly have a more serious and interesting result - a rationale for the spatial flatness of the Universe. Our basic assumptions are that the cosmological scale factor obeys the standard Friedman equation of general relativistic cosmology and that the equation is dominated by a cosmological constant term and a curvature term; the dynamics of the Universe is then (approximately) the same as that of a tipping pencil. The scale factor cannot remain at an unstable initial value of zero and must increase (i.e. the Universe must come into existence) according to the uncertainty principle, that is due to quantum fluctuations; in other words we propose in a precise but limited context an answer to Heidegger's famous question "Why is there something rather than nothing." The mechanism is the same as that whereby an idealized pencil balanced on its point cannot remain so and must tip over. If it is moreover assumed that the Universe expands at the minimum asymptotic rate consistent with the uncertainty principle then the result is spatial flatness.

gr-qc↗

arXiv2011

A terrestrial search for dark contents of the vacuum, such as dark energy, using atom interferometry

We describe the theory and first experimental work on our concept for searching on earth for the presence of dark content of the vacuum (DCV) using atom interferometry. Specifically, we have in mind any DCV that has not yet been detected on a laboratory scale, but might manifest itself as dark energy on the cosmological scale. The experimental method uses two atom interferometers to cancel the effect of earth's gravity and diverse noise sources. It depends upon two assumptions: first, that the DCV possesses some space inhomogeneity in density, and second that it exerts a sufficiently strong non-gravitational force on matter. The motion of the apparatus through the DCV should then lead to an irregular variation in the detected matter-wave phase shift. We discuss the nature of this signal and note the problem of distinguishing it from instrumental noise. We also discuss the relation of our experiment to what might be learned by studying the noise in gravitational wave detectors such as LIGO.The paper concludes with a projection that a future search of this nature might be carried out using an atom interferometer in an orbiting satellite. The apparatus is now being constructed.

astro-ph.CO↗

arXiv2010

Gravitomagnetism in Quantum Mechanics

We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field, which is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form (SEF), which we then analyze in the non-relativistic limit. We include a discussion of some rather general observable physical effects implied by the SEF, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.

gr-qc↗

arXiv2010

Six easy roads to the Planck scale

We give six arguments that the Planck scale should be viewed as a fundamental minimum or boundary for the classical concept of spacetime, beyond which quantum effects cannot be neglected and the basic nature of spacetime must be reconsidered. The arguments are elementary, heuristic, and plausible, and as much as possible rely on only general principles of quantum theory and gravity theory. The paper is primarily pedagogical, and its main goal is to give physics students, non-specialists, engineers etc. an awareness and appreciation of the Planck scale and the role it should play in present and future theories of quantum spacetime and quantum gravity.

gr-qc↗

arXiv2002

Black Hole Remnants and Dark Matter

We argue that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse. Specifically we invoke the GUP to obtain a modified Hawking temperature, which indicates that there should exist non-radiating remnants (BHR) of about Planck mass. BHRs are an attractive candidate for cold dark matter. We investigate an alternative cosmology in which primordial BHRs are the primary source of dark matter.

gr-qc↗

arXiv2001

The Generalized Uncertainty Principle and Black Hole Remnants

In the current standard viewpoint small black holes are believed to emit radiation as black bodies at the Hawking temperature, at least until they reach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system. Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse: the collapse is prevented, not by symmetry, but by dynamics, as a minimum size and mass are approached.

gr-qc↗

arXiv1999

On the detectability of quantum spacetime foam with gravitational-wave interferometers

We discuss a recent provocative suggestion by Amelino-Camelia and others that classical spacetime may break down into ``quantum foam'' on distance scales many orders of magnitude larger than the Planck length, leading to effects which could be detected using large gravitational wave interferometers. This suggestion is based on a quantum uncertainty limit obtained by Wigner using a quantum clock in a gedanken timing experiment. Wigner's limit, however, is based on two unrealistic and unneccessary assumptions: that the clock is free to move, and that it does not interact with the environment. Removing either of these assumptions makes the uncertainty limit invalid, and removes the basis for Amelino-Camelia's suggestion.

gr-qc↗

arXiv1999

On a Generalization in Quantum Theory: Is $\hbar$ Constant?

We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a constant. The generalized theory is most easily viewed in the wave vector space analog of the Lagrangian. We need no reference to spacetime. In the generalized theory the de Broglie relation between wave vector and momentum is generalized, as are the canonical commutation relations and the uncertainty principle. The generalized uncertainty principle obtained is the same as has been derived from string theory, or by a general consideration of gravitational effects during the quantum measurement process. The propagator of the scalar field is also generalized, and an illustrative example is given in which it factors into the usual propagator times a "propagator form factor."

hep-th↗

arXiv1999

On Gravity and the Uncertainty Principle

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.

gr-qc↗

arXiv1995

Null Surfaces, Initial Values and Evolution Operators for Scalar Fields

We analyze the initial value problem for scalar fields obeying the Klein-Gordon equation. The standard Cauchy initial value problem for second order differential equation is to construct a solution function in a neighborhood of space and time form values of the function and its time derivative on a selected initial value surface. On the characteristic surfaces the time derivative of the solution function may be discontinuous, so the standard Cauchy construction breaks down. For the Klein-Gordon equation the characteristic surfaces are null surfaces. An alternative version of the initial data needed differs from that of the standard Cauchy problem, and in the case we discuss here the values of the function on an intersecting pair of null surfaces comprise the necessary initial value data. We also present an expression for the construction of a solution from null surface data; two analogues of the quantum mechanical Hamiltonian operator determine the evolution of the system.

hep-th↗

arXiv1995

Null Surfaces, Initial Values and Evolution Operators for Spinor Fields

We analyze the initial value problem for spinor fields obeying the Dirac equation, with particular attention to the characteristic surfaces. The standard Cauchy initial value problem for first order differential equations is to construct a solution function in a neighborhood of space and time from the values of the function on a selected initial value surface. On the characteristic surfaces the solution function may be discontinuous, so the standard Cauchy construction breaks down. For the Dirac equation the characteristic surfaces are null surfaces. An alternative version of the initial value problem may be formulated using null surfaces; the initial value data needed differs from that of the standard Cauchy problem, and in the case we here discuss the values of separate components of the spinor function on an intersecting pair of null surfaces comprise the necessary initial value data. We present an expression for the construction of a solution from null surface data; two analogues of the quantum mechanical Hamiltonian operator determine the evolution of the system.

hep-th↗