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Don N. Page

Publications and source records attributed to Don N. Page.

At least 55 records · Page 3Linked to original sources
arXiv2014

Excluding Black Hole Firewalls with Extreme Cosmic Censorship

The AMPS argument for black hole firewalls seems to arise not only from the assumption of local effective field theory outside the stretched horizon but also from an overcounting of internal black hole states that include states that are singular in the past. Here I propose to exclude such singular states by Extreme Cosmic Censorship (the conjectured principle that the universe is entirely nonsingular, except for transient singularities inside black and/or white holes). I argue that the remaining set of nonsingular realistic states do not have firewalls but yet preserve information in Hawking radiation from black holes that form from nonsingular initial states.

hep-th↗
arXiv2013

Cosmic Mnemonics

Our current description of the large-scale Universe is now known with a precision undreamt of a generation ago. Within the simple standard cosmological model only six basic parameters are required. The usual parameter set includes quantities most directly probed by the cosmic microwave background, but the nature of these quantities is somewhat esoteric. However, many more numbers can be derived that quantify various aspects of our Universe. Using constraints from the Planck satellite, in combination with other data sets, we explore several such quantities, highlighting some specific examples.

astro-ph.CO↗
arXiv2013

Time Dependence of Hawking Radiation Entropy

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4 pi M_0^2, or about 7.509 M_0^2 \approx 6.268 x 10^{76}(M_0/M_sun)^2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018 M_0^2 \approx 1.254 x 10^{77}(M_0/M_sun)^2, and then decreases back down to 4 pi M_0^2 = 1.049 x 10^{77}(M_0/M_sun)^2.

hep-th↗
arXiv2013

Hyper-Entropic Gravitational Fireballs (Grireballs) with Firewalls

Recently there has been much discussion as to whether old black holes have firewalls at their surfaces that would destroy infalling observers. Though I suspect that a proper handling of nonlocality in quantum gravity may show that firewalls do not exist, it is interesting to consider an extension of the firewall idea to what seems to be the logically possible concept of hyper-entropic gravitational hot objects (gravitational fireballs or grireballs for short) that have more entropy than ordinary black holes of the same mass. Here some properties of such grireballs are discussed under various assumptions, such as assuming that their radii and entropies both go as powers of their masses as the one independent parameter, or assuming that their radii depend on both their masses and their entropies as two independent parameters.

hep-th↗
arXiv2012

A Theological Argument for an Everett Multiverse

Science looks for the simplest hypotheses to explain observations. Starting with the simple assumption that {\em the actual world is the best possible world}, I sketch an {\it Optimal Argument for the Existence of God}, that the sufferings in our universe would not be consistent with its being alone the best possible world, but the total world could be the best possible if it includes an omnipotent, omniscient, omnibenevolent God who experiences great value in creating and knowing a universe with great mathematical elegance, even though such a universe has suffering. God seems loathe to violate elegant laws of physics that He has chosen to use in His creation, such as Maxwell's equations for electromagnetism or Einstein's equations of general relativity for gravity within their classical domains of applicability, even if their violation could greatly reduce human suffering (e.g., from falls). If indeed God is similarly loathe to violate quantum unitarity (though such violations by judicious collapses of the wavefunction could greatly reduce human suffering by always choosing only favorable outcomes), the resulting unitary evolution would lead to an Everett multiverse of `many worlds', meaning many different quasiclassical histories beyond the quasiclassical history that each of us can observe over his or her lifetime. This is a theological argument for one reason why God might prefer to create a multiverse much broader than what one normally thinks of for a history of the universe.

physics.gen-ph↗
arXiv2012

Too Soon for Doom Gloom?

The observation that we are among the first 10^{11} or so humans reduces the prior probability that we find ourselves in a species whose total lifetime number of individuals is much higher, according to arguments of Carter, Leslie, Nielsen, and Gott. However, if we instead start with a prior probability that a history has a total lifetime number which is very large, without assuming that we are in such a history, this more basic probability is not reduced by the observation of how early in history we exist.

gr-qc↗
arXiv2012

Spectral Methods in General Relativity and Large Randall-Sundrum II Black Holes

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS_5-CFT_4 solution to the Einstein equation with a negative cosmological constant Lambda that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS_5-CFT_4 solution, showing that our solution agrees closely with theirs. We have also deduced the new results that to first order in 1/(-ΛM^2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

hep-th↗
arXiv2012

Large Randall-Sundrum II Black Holes

Using a novel numerical spectral method, we have constructed an AdS_5-CFT_4 solution to the Einstein equation with a negative cosmological constant Lambda that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall-Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in 1/(-Lambda M^2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Lambda).

hep-th↗
arXiv2012

Massless Scalar Field Vacuum in de Sitter Spacetime

As a spacetime with compact spatial sections, de Sitter spacetime does not have a de Sitter-invariant ground state for a minimally-coupled massless scalar field that gives definite expectation values for any observables not invariant under constant shifts of the field. However, if one restricts to observables that are shift invariant, as the action is, then there is a unique vacuum state. Here we calculate the shift-invariant four-point function that is the vacuum expectation value of the product of the difference of the field values at one pair of points and of the difference of the field values at a second pair of points. We show that this vacuum expectation value obeys a cluster-decomposition property of vanishing in the limit that the one pair of points is moved arbitrarily far from the other pair. We also calculate the shift-invariant correlation of the gradient of the scalar field at two different points and show that it also obeys a cluster-decomposition property. Possible relevance to a putative de Sitter-invariant quantum state for gravity is discussed.

hep-th↗
arXiv2012

Generalized Jarzynski Equality

The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to the initial equilibrium partition functions of the system at that fixed temperature. It thus relates two thermal equilibrium quantum states. Here a generalization is given that relates any two quantum states of a system.

hep-th↗
arXiv2011

Quantum Uncertainties in the Schmidt Basis Given by Decoherence

A common misconception is that decoherence gives the eigenstates that we observe to be fairly definite about a subsystem (e.g., approximate eigenstates of position) as the elements of the Schmidt basis in which the density matrix of the subsystem is diagonal. Here I show that in simple examples of linear systems with gaussian states, the Schmidt basis states have as much mean uncertainty about position as the full density matrix with its combination of different possibilities.

hep-th↗
arXiv2011

Ab Initio Estimates of the Size of the Observable Universe

When one combines multiverse predictions by Bousso, Hall, and Nomura for the observed age and size of the universe in terms of the proton and electron charge and masses with anthropic predictions of Carter, Carr, and Rees for these masses in terms of the charge, one gets that the age of the universe should be roughly the inverse 64th power, and the cosmological constant should be around the 128th power, of the proton charge. Combining these with a further renormalization group argument gives a single approximate equation for the proton charge, with no continuous adjustable or observed parameters, and with a solution that is within 8% of the observed value. Using this solution gives large logarithms for the age and size of the universe and for the cosmological constant that agree with the observed values within 17%.

hep-th↗
arXiv2011

Finite Canonical Measure for Nonsingular Cosmologies

The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-Lemaitre-Robertson-Walker classical universes with a minimally coupled massive scalar field and a positive cosmological constant. For a cosmological constant very small in units of the square of the scalar field mass, most of the measure is for nearly de Sitter solutions with no inflation at a much more rapid rate. However, if one restricts to solutions in which the scalar field energy density is ever more than twice the equivalent energy density of the cosmological constant, then the number of e-folds of rapid inflation must be large, and the fraction of the measure is low in which the spatial curvature is comparable to the cosmological constant at the time when it is comparable to the energy density of the scalar field. The measure for such classical FRW-Lambda-phi models with both a big bang and a big crunch is also finite. Only the solutions with a big bang that expand forever, or the time-reversed ones that contract from infinity to a big crunch, have infinite measure.

hep-th↗
arXiv2011

Consciousness and the Quantum

Sensible Quantum Mechanics or Mindless Sensationalism is a framework for relating consciousness to a quantum universe. It states that each conscious perception has a measure that is given by the expectation value of a corresponding quantum "awareness operator" in a fixed quantum state of the universe. The measures can be interpreted as frequency-type probabilities for a large set of perceptions that all actually exist with varying degrees of reality, so detailed theories within this framework are testable. The measures are not propensities for potentialities to be actualized, so there is nothing indeterministic in this framework, and no free will in the incompatibilistic sense. As conscious perceptions are determined by the awareness operators and the quantum state, they are epiphenomena. No fundamental relation 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 or MS, a variant of Everett's "many-worlds" framework, is a "many-perceptions" framework but not a "many-minds" framework.

quant-ph↗
arXiv2011

Agnesi Weighting for the Measure Problem of Cosmology

The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann brain problem (that observations arising from thermal or quantum fluctuations may dominate over ordinary observations if the universe expands sufficiently and/or lasts long enough) may be ameliorated by volume averaging, but that still leaves problems if the universe lasts too long. Here a solution is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to make the time integral convergent. The resulting Agnesi measure appears to avoid problems other measures may have with vacua of zero or negative cosmological constant.

hep-th↗
arXiv2011

Preliminary Inconclusive Hint of Evidence Against Optimal Fine Tuning of the Cosmological Constant for Maximizing the Fraction of Baryons Becoming Life

The effective coupling `constants' of physics, especially the cosmological constant, are observed to have highly biophilic values. If this is not a hugely improbable accident, or a consequence of some mysterious logical necessity or of some simple principle of physics, it might be explained as a consequence either of an observership selection principle within a multiverse of many sets of effective coupling constants, or else of some biophilic principle that fine tunes the constants of physics to optimize life. Here a very preliminary inconclusive hint of evidence is presented against the hypothesis of optimal fine tuning of the cosmological constant by a biophilic principle that would maximize the fraction of baryons that form living organisms or observers.

hep-th↗
arXiv2011

Statistical Evidence Against Simple Forms of Wavefunction Collapse

If the initial quantum state of the universe is a multiverse superposition over many different sets of values of the effective coupling "constants" of physics, and if this quantum state collapses to an eigenstate of the set of coupling "constants" with a probability purely proportional to the absolute square of the amplitude (with no additional factor for something like life or consciousness), then one should not expect that the coupling `constants' would be so biophilic as they are observed to be. Therefore, the observed biophilic values (apparent fine tuning) of the coupling "constants" is statistical evidence against such simple forms of wavefunction collapse.

hep-th↗