arXiv subjects

Don N. Page

Publications and source records attributed to Don N. Page.

At least 127 records · Page 7Linked to original sources

arXiv2002

Exact Quantum-Statistical Dynamics of Time-Dependent Generalized Oscillators

Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum.

quant-ph↗

arXiv2002

Phase Transitions for Gauge Theories on Tori from the AdS/CFT Correspondence

The vacuum of a large-N gauge field on a p-torus has a spatial stress tensor with tension along the direction of smallest periodicity and equal pressures (but p times smaller in magnitude) along the other directions, assuming an AdS/CFT correspondence and a refined form of the Horowitz-Myers positive-energy conjecture. For infinite N, the vacuum exhibits a phase transition when the lengths of the two shortest periodicities cross. A comparison is made with the Surya-Schleich-Witt phase transition at finite temperature. A zero-loop approximation is also given for large but finite N.

hep-th↗

arXiv2002

Quantum Mechanics as a Simple Generalization of Classical Mechanics

A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices with suitable Hermitian matrices.

quant-ph↗

arXiv2002

Schwinger Pair Production via Instantons in Strong Electric Fields

In the space-dependent gauge, each mode of the Klein-Gordon equation in a strong electric field takes the form of a time-independent Schrödinger equation with a potential barrier. We propose that the single- and multi-instantons of quantum tunneling may be related with the single- and multi-pair production of bosons and the relative probability for the no-pair production is determined by the total tunneling probability via instantons. In the case of a uniform electric field, the instanton interpretation recovers exactly the well-known pair production rate for bosons and when the Pauli blocking is taken into account, it gives the correct fermion production rate. The instanton is used to calculate the pair production rate even in an inhomogeneous electric field. Furthermore, the instanton interpretation confirms the fact that bosons and fermions can not be produced by a static magnetic field only.

hep-th↗

arXiv2001

Mindless Sensationalism: A Quantum Framework for Consciousness

The ideas of Sensible Quantum Mechanics are expressed in lay terms for philosophers of consciousness and others. A framework is proposed and explained for the `psycho-physical-parallelism' between conscious experiences and the mathematical structures of quantum physics (e.g., a set of quantum operators obeying some algebra, and a quantum state giving the expectation value of each operator). In particular, it is proposed that each set of possible conscious experiences has a measure given by the expectation value of a corresponding operator (a positive-operator-valued measure). Then one has a generalization of the Weak Anthropic Principle named the Conditional Aesthemic Principle: given that we are conscious beings, our conscious experiences are likely to be typical experiences in the set of all conscious experiences with its measure.

quant-ph↗

arXiv2001

Classical and Quantum Action-Phase Variables for Time-Dependent Oscillators

For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to the invariant space, in which the action-phase variables are defined. We find the action operator for the time-dependent oscillator via the classical-quantum correspondence. Candidate phase operators conjugate to the action operator are discussed, but no satisfactory ones are found.

quant-ph↗

arXiv2001

Black Hole Configurations with Total Entropy Less than A/4

If one surrounds a black hole with a perfectly reflecting shell and adiabatically squeezes the shell inward, one can increase the black hole area A to exceed four times the total entropy S, which stays fixed during the process. A can be made to exceed 4S by a factor of order unity before the one enters the Planck regime where the semiclassical approximation breaks down. One interpretation is that the black hole entropy resides in its thermal atmosphere, and the shell restricts the atmosphere so that its entropy is less than A/4.

gr-qc↗

arXiv2000

Thermodynamics of Near-Extreme Black Holes

The thermodynamics of nearly-extreme charged black holes depends upon the number of ground states at fixed large charge and upon the distribution of excited energy states. Here three possibilities are examined: (1) Ground state highly degenerate (as suggested by the large semiclassical Hawking entropy of an extreme Reissner-Nordstrom black hole), excited states not. (2) All energy levels highly degenerate, with macroscopic energy gaps between them. (3) All states nondegenerate (or with low degeneracy), separated by exponentially tiny energy gaps. I suggest that in our world with broken supersymmetry, this last possibility seems most plausible. An experiment is proposed to distinguish between these possibilities, but it would take a time that is here calculated to be more than about 10^837 years.

hep-th↗

arXiv2000

Subsystem Entropy Exceeding Bekenstein's Bound

If Bekenstein's conjectured bound on the microcanonical entropy, S < 2 pi E R, is applied to a closed subsystem of maximal linear size R and excitation energy up through E, it can be violated by an arbitrarily large factor by a scalar field having a symmetric potential allowing domain walls, and by the electromagnetic field modes in a coaxial cable.

hep-th↗

arXiv2000

Huge Violations of Bekenstein's Entropy Bound

Bekenstein's conjectured entropy bound for a system of linear size R and energy E, S < 2 pi E R, can be violated by an arbitrarily large factor, among other ways, by a scalar field having a symmetric potential allowing domain walls, and by the electromagnetic field modes between an arbitrarily large number of conducting plates.

gr-qc↗

arXiv2000

Can Quantum Cosmology Give Observational Consequences of Many-Worlds Quantum Theory?

Although many people have thought that the difference between the Copenhagen and many-worlds versions of quantum theory was merely metaphysical, quantum cosmology may allow us to make a physical test to distinguish between them empirically. The difference between the two versions shows up when the various components of the wavefunction have different numbers of observers and observations. In the Copenhagen version, a random observation is selected from the sample within the component that is selected by wavefunction collapse, but in the many-worlds version, a random observation is selected from those in all components. Because of the difference in the samples, probable observations in one version can be very improbable in the other version.

gr-qc↗

arXiv1999

Observational Consequences of Many-Worlds Quantum Theory

Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur when the number of observers is not uniquely predicted by the theory. In single-history theories, each history is weighted simply by its quantum-mechanical probability, but in many-worlds theories in which random observations are considered, there should also be the weighting by the numbers or amounts of observations occurring in each history.

quant-ph↗

arXiv1999

Low Velocity Gravitational Capture by Long Cosmic Strings

Coupled ordinary differential equations are derived for the distant gravitational interaction of a compact object of mass M and charge Q with an initially straight, infinitely long, cosmic string of tension mu << 1/G = 1, when the relative velocities are very low compared to the speed of light c = 1. (An intermediate result of this derivation is that any localized force F(t) on the string that is confined to a single plane perpendicular to the initial string configuration gives the intersection of the string with this plane -- the point where the force is applied -- the velocity F(t)/(2 mu).) The coupled equations are then used to calculate the critical impact parameter b for marginal gravitational capture as a function of the incident velocity v. For v<<(1-Q^2/M^2)^(1/3) mu^(2/3), so that the string acts relatively stiffly, b = (pi/4)[12 mu^3 (1-Q^2/M^2)^4]^(1/5) M v^(-7/5) + O(M v^(-1/5)). For (1-Q^2/M^2)^(1/3) mu^(2/3) << v << 1 - Q^2/M^2$, so that the string acts essentially as a test string that stays nearly straight, b = [(pi/2)(1-Q^2/M^2)]^(1/2) M v^(-1/2) + O(M v^(-2)). Between these two limits the critical impact parameter is found numerically to fit a simple algebraic combination of these two formulas to better than 99.5% accuracy.

gr-qc↗

arXiv1998

Gravitational Capture and Scattering of Straight Test Strings with Large Impact Parameters

The capture or scattering of an initially straight infinite test cosmic string by a Kerr-Newman black hole, or by any other small source of an electrovac gravitational field, is analyzed analytically when the string moves with initial velocity v and large impact parameter b >> M so that the string stays very nearly straight (except during the final capture process, if that occurs, or except far behind the gravitating object, if b is not much greater than the energy of the object in the frame of the string). The critical impact parameter for capture at low velocities is shown to be [(pi/2)(M^2-Q^2)/v]^{1/2}. For all larger b, the displacement of the string from the plane of the gravitating object after the scattering approaches the final value [b^2 - (pi/2)(M^2-Q^2)/v]^{1/2} - 2 pi M v/(1-v^2)^{1/2}, for any v, so long as b >> M.

gr-qc↗

arXiv1998

Maximal Acceleration Is Nonrotating

In a stationary axisymmetric spacetime, the angular velocity of a stationary observer that Fermi-Walker transports its acceleration vector is also the angular velocity that locally extremizes the magnitude of the acceleration of such an observer, and conversely if the spacetime is also symmetric under reversing both t and phi together. Thus a congruence of Nonrotating Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence Accelerating Locally Extremely (SCALE). These congruences are defined completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs), which requires knowledge around a symmetry axis. The SCALE subcase of a Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary worldlines that may be considered to be locally most nearly at rest in a stationary axisymmetric gravitational field. Formulas for the angular velocity and other properties of the SCALEs are given explicitly on a generalization of an equatorial plane, infinitesimally near a symmetry axis, and in a slowly rotating gravitational field, including the weak-field limit, where the SCAM is shown to be counter-rotating relative to infinity. These formulas are evaluated in particular detail for the Kerr-Newman metric. Various other congruences are also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which coincide with a SCAM on an equatorial plane of reflection symmetry. Applications are also made to the gravitational fields of maximally rotating stars, the Sun, and the Solar System.

gr-qc↗

arXiv1997

Sensible Quantum Mechanics: Are Only Perceptions Probabilistic?

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators in a quantum state of the universe which never jumps or collapses. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets rather than as propensities for potentialities to be actualized, so there is nothing indeterministic in SQM. These frequency-type probabilities generally cannot be given by the ordinary quantum "probabilities" for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth. No fundamental correlation or equivalence is postulated between different perceptions (each being the entirety of a single conscious experience and thus not in direct contact with any other), so SQM, a variant of Everett's "many-worlds" framework, is a "many-perceptions" framework but not a "many-minds" framework. Different detailed SQM theories may be tested against experienced perceptions by the typicalities (defined herein) they predict for these perceptions. One may adopt the Conditional Aesthemic Principle: among the set of all conscious perceptions, our perceptions are likely to be typical. An experimental test is proposed to compare SQM with a variant, SQMn.

quant-ph↗

arXiv1997

Stress Tensors for Instantaneous Vacua in 1+1 Dimensions

The regularized expectation value of the stress-energy tensor for a massless bosonic or fermionic field in 1+1 dimensions is calculated explicitly for the instantaneous vacuum relative to any Cauchy surface (here a spacelike curve) in terms of the length L of the curve (if closed), the local extrinsic curvature K of the curve, its derivative K' with respect to proper distance x along the curve, and the scalar curvature R of the spacetime: T_{00} = - epsilon pi/(6L^2) - K^2/(24 pi), T_{01} = - K'/(12 pi), T_{11} = - epsilon pi/(6L^2) - K^2/(24 pi) + R/(24 pi), in an orthonormal frame with the spatial vector parallel to the curve. Here epsilon = 1 for an untwisted (i.e., periodic in x) one-component massless bosonic field or for a twisted (i.e., antiperiodic in x) two-component massless fermionic field, epsilon = -1/2 for a twisted one-component massless bosonic field, and epsilon = - 2 for an untwisted two-component massless fermionic field. The calculation uses merely the energy-momentum conservation law and the trace anomaly (for which a very simple derivation is also given herein, as well as the expression for the Casimir energy of bosonic and fermionic fields twisted by an arbitrary amount in R^{D-1} x S^1). The two coordinate and conformal invariants of a quantum state that are (nonlocally) determined by the stress-energy tensor are given. Applications to topologically modified deSitter spacetimes, to a flat cylinder, and to Minkowski spacetime are discussed.

gr-qc↗

arXiv1997

Space for Both No-Boundary and Tunneling Quantum States of the Universe

At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the `tunneling' wavefunction. If the probability distribution is cut off at the Planck density (say), this suggests that the former quantum state is inconsistent with our observations. For inhomogeneous models in which stochastic inflation can occur, it is known that the idea of including a volume factor in the observational probability distribution can lead to arbitrarily large universes' being likely. Here this idea is shown to be sufficient to save the Hartle-Hawking proposal even at the minisuperspace level (for suitable inflaton potentials), by giving it enough space to be consistent with observations.

gr-qc↗