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Don N. Page

Publications and source records attributed to Don N. Page.

At least 37 records · Page 2Linked to original sources
arXiv2019

Equivalence between the phase-integral and worldline-instanton methods

The phase-integral and worldline-instanton methods are two widely used methods to calculate Schwinger pair-production densities in electric fields of fixed direction that depend on just one time or space coordinate in the same fixed plane of the electromagnetic field tensor. We show that for charged spinless bosons the leading results of the phase-integral method integrated up through quadratic momenta are equivalent to those of the worldline-instanton method including prefactors. We further apply the phase-integral method to fermion production and time-dependent electric fields parallel to a constant magnetic field.

hep-th↗
arXiv2018

Relativity and quantum optics: accelerated atoms in optical cavities

We analyze the physics of accelerated particle detectors (such as atoms) crossing optical cavities. In particular we focus on the detector response as well as on the energy signature that the detectors imprint in the cavities. In doing so, we examine to what extent the usual approximations made in quantum optics in cavities (such as the single-mode approximation, or the dimensional reduction of 3+1D cavities to simplified 1+1D setups) are acceptable when the atoms move in relativistic trajectories. We also study the dependence of these approximations on the state of the atoms and the relativistic nature of the trajectory. We find that, on very general grounds, and already in the weak coupling limit, single- and few-mode approximations, as well as 1+1D dimensional reductions, yield incorrect results when relativistic scenarios are considered.

quant-ph↗
arXiv2018

The Bekenstein Bound

Bekenstein's conjectured entropy bound for a system of linear size $R$ and energy $E$, namely $S \leq 2 πE R$, has counterexamples for many of the ways in which the "system," $R$, $E$, and $S$ may be defined. One consistent set of definitions for these quantities in flat Minkowski spacetime is that $S$ is the total von Neumann entropy and $E$ is the expectation value of the energy in a "vacuum-outside-$R$" quantum state that has the the vacuum expectation values for all operators entirely outside a sphere of radius $R$. However, there are counterexamples to the Bekenstein bound for this set of definitions. Nevertheless, an alternative formulation ten years ago by Horacio Casini for the definitions of $S$ and of $2 πE R$ have finally enabled a proof for this particular formulation of the Bekenstein bound.

hep-th↗
arXiv2018

Qubit Transport Model for Unitary Black Hole Evaporation without Firewalls

We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon, and it avoids a counterargument that has been raised for subsystem transfer models as resolutions of the firewall paradox. Furthermore, it fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector. Although the qubit model is too crude to be quantitively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.

hep-th↗
arXiv2017

Radiation from Atoms Falling into a Black Hole

We show that atoms falling from outside through a cavity into a black hole (BH) emit acceleration radiation which to a distant observer looks much like Hawking BH radiation. In particular, we find the entropy of the acceleration radiation via a simple laser-like analysis. We call this entropy Horizon Brightened Acceleration Radiation (HBAR) entropy to distinguish it from the BH entropy of Bekenstein and Hawking.

quant-ph↗
arXiv2017

Approximations for the Lowest Energy Eigenstates in a Double Square Well Potential

Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between (so that the potential is a sequence of five constant pieces that alternate in value from being above and below the ground state and first excited state energies), under the assumption that the barrier is sufficiently wide that the tunneling across it is very small.

quant-ph↗
arXiv2017

Bayes Keeps Boltzmann Brains at Bay

Sean Carroll has recently argued that theories predicting that observations are dominated by Boltzmann Brains should be rejected because they are cognitively unstable: "they cannot simultaneously be true and justifiably believed." While such Boltzmann Brain theories are indeed cognitively unstable, one does not need to appeal to this argumentation to reject them. Instead, they may be ruled out by conventional Bayesian reasoning, which is sufficient to keep Boltzmann Brains at bay.

hep-th↗
arXiv2017

Anthropic Estimates for Many Parameters of Physics and Astronomy

Anthropic arguments of Carter, Carr, and Rees give two approximate power-law relations between the elementary charge e, the mass of the proton m_p, and the mass of the electron m_e in Planck units: m_p ~ e^{18}, m_e ~ e^{21}. A renormalization group argument of mine gives e^{-2} ~ -(10/pi)ln{m_p}. Combining this with the Carter-Carr-Rees relations gives e^2 ln{e} ~ -pi/180. Taking the exact solutions of these approximate equations gives values for e, m_p, and m_e whose logarithms have relative errors only 0.7%, 1.3%, and 1.0% respectively, without using as input the observed values of any parameters with potentially continuous ranges. One can then get anthropic estimates for the masses, sizes, luminosities, times, velocities, etc. for many other structures in physics and astronomy, from atoms to giraffes to the universe, as simple powers of the anthropic estimate for the elementary charge. For example, one gets an anthropic estimate for the real part of the logarithm of the dark energy density with a relative error of only 0.2%.

hep-th↗
arXiv2016

Are Most Particles Gravitons?

The number of baryons in the observable universe is of the order of $10^{80}$, as is the number of electrons. The number of photons is about nine orders of magnitude greater, $10^{89}$, as is the estimated number of neutrinos. However, the number of gravitons could be more than twenty orders of magnitude larger yet, of the order of $10^{113} r$, where $r$ is the tensor-to-scalar ratio for quantum fluctuations produced by inflation, which could be as high as $0.1$.

hep-th↗
arXiv2016

Naked Black Hole Firewalls

In the firewall proposal, it is assumed that the firewall lies near the event horizon and should not be observable except by infalling observers, who are presumably terminated at the firewall. However, if the firewall is located near where the horizon would have been, based on the spacetime evolution up to that time, later quantum fluctuations of the Hawking emission rate can cause the "teleological" event horizon to have migrated to the inside of the firewall location, rendering the firewall naked. In principle, the firewall can be arbitrarily far outside the horizon. This casts doubt about the notion that firewalls are the "most conservative" solution to the information loss paradox.

hep-th↗
arXiv2016

A New Way to Derive the Taub-NUT Metric with Positive Cosmological Constant

We investigate a biaxial Bianchi IX model with positive cosmological constant, which is sometimes called the Lambda-Taub-NUT spacetime, whose exact solution is well known. The minisuperspace of biaxial Bianchi IX models admits two non-trivial Killing tensors that play an important role for deriving the Taub-NUT metric. We also give a brief discussion about the asymptotic behaviour of Bianchi IX models.

gr-qc↗
arXiv2015

Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole

Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.

hep-th↗
arXiv2015

The Universal Area Product: An Heuristic Argument

We present an heuristic argument for the universal area product: A_{+}A_{-}=(8πJ)^{2}+(4πQ^{2})^{2} for a four-dimensional, stationary, axisymmetric, electrically charged black hole with an arbitrary stationary axisymmetric distribution of external matter (possibly charged), derived by Marcus Ansorg and Jorg Hennig. Here A_{+} and A_{-} are the areas of the event and Cauchy horizons, and J and Q are the angular momentum and electric charge. Based on this argument, we conjecture that a universal area product holds for higher-dimensional, stationary, multi-horizon black objects in the presence of an external stationary charged distribution of matter.

hep-th↗
arXiv2015

Finite Upper Bound for the Hawking Decay Time of an Arbitrarily Large Black Hole in Anti-de Sitter Spacetime

In an asymptotically flat spacetime of dimension d > 3 and with the Newtonian gravitational constant G, a spherical black hole of initial horizon radius r_h and mass M ~ r_h^{d-3}/G has a total decay time to Hawking emission of t_d ~ r_h^{d-1}/G ~ G^{2/(d-3)}M^{(d-1)/(d-3)} which grows without bound as the radius r_h and mass M are taken to infinity. However, in asymptotically anti-de Sitter spacetime with a length scale l and with absorbing boundary conditions at infinity, the total Hawking decay time does not diverge as the mass and radius go to infinity but instead remains bounded by a time of the order of l^{d-1}/G.

hep-th↗
arXiv2015

Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes

Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime.

gr-qc↗
arXiv2014

Cosmological Ontology and Epistemology

In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and relationships are. One must also make epistemological assumptions or metatheories of how one can test cosmological theories. Here I shall propose a Bayesian analysis in which the likelihood of a complete theory is given by the normalized measure it assigns to the observation used to test the theory. In this context, a discussion is given of the trade-off between prior probabilities and likelihoods, of the measure problem of cosmology, of the death of Born's rule, of the Boltzmann brain problem, of whether there is a better principle for prior probabilities than mathematical simplicity, and of an Optimal Argument for the Existence of God.

physics.hist-ph↗
arXiv2014

Spacetime Average Density (SAD) Cosmological Measures

The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also the danger of domination by Boltzmann Brains. Here two new Spacetime Average Density (SAD) measures are proposed, Maximal Average Density (MAD) and Biased Average Density (BAD), for getting a finite number of observation occurrences by using properties of the Spacetime Average Density (SAD) of observation occurrences to restrict to finite regions of spacetimes that have a preferred beginning or bounce hypersurface. These measures avoid Boltzmann brain domination and appear to give results consistent with other observations that are problematic for other widely used measures, such as the observation of a positive cosmological constant.

hep-th↗