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Don N. Page

Publications and source records attributed to Don N. Page.

At least 91 records · Page 5Linked to original sources
arXiv2008

Is Our Universe Likely to Decay within 20 Billion Years?

Observations that we are highly unlikely to be vacuum fluctuations suggest that our universe is decaying at a rate faster than the asymptotic volume growth rate, in order that there not be too many observers produced by vacuum fluctuations to make our observations highly atypical. An asymptotic linear e-folding time of roughly 16 Gyr (deduced from current measurements of cosmic acceleration) would then imply that our universe is more likely than not to decay within a time that is less than 19 Gyr in the future.

hep-th↗
arXiv2008

Typicality Derived

Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate normalized probabilities for alternatives obeying what I call the Principle of Observational Discrimination, that each possible complete observation or data set should uniquely distinguish one element from the set of alternatives.

hep-th↗
arXiv2008

No-Bang Quantum State of the Cosmos

A quantum state of the entire cosmos (universe or multiverse) is proposed which is the equal mixture of the Giddings-Marolf states that are asymptotically single de Sitter spacetimes in both past and future and are regular on the throat or neck of minimal three-volume. That is, states are excluded that have a big bang or big crunch or which split into multiple asymptotic de Sitter spacetimes. (For simplicity, transitions between different values of the cosmological constant are assumed not to occur, though different positive values are allowed.) The entropy of this mixed state appears to be of the order of the three-fourths power of the Bekenstein-Hawking A/4 entropy of de Sitter spacetime. Most of the component pure states do not have rapid inflation, but when an inflaton is present and the states are weighted by the volume at the end of inflation, a much smaller number of states may dominate and give a large amount of inflation and hence may agree with observations.

hep-th↗
arXiv2008

Scientific and Philosophical Challenges to Theism

Modern science developed within a culture of Judeo-Christian theism, and science and theism have generally supported each other. However, there are certainly areas in both science and religion that puzzle me. Here I outline some puzzles that have arisen for me concerning everlasting life, human free will, divine free will, the simplicity and probability of God, the problem of evil, and the converse problem of elegance.

physics.gen-ph↗
arXiv2008

Does God So Love the Multiverse?

Monotheistic religions such as Judaism and Christianity affirm that God loves all humans and created them in His image. However, we have learned from Darwin that we were not created separately from other life on earth. Some Christians opposed Darwinian evolution because it undercut certain design arguments for the existence of God. Today there is the growing idea that the fine-tuned constants of physics might be explained by a multiverse with very many different sets of constants of physics. Some Christians oppose the multiverse for similarly undercutting other design arguments for the existence of God. However, undercutting one argument does not disprove its conclusion. Here I argue that multiverse ideas, though not automatically a solution to the problems of physics, deserve serious consideration and are not in conflict with Christian theology as I see it. Although this paper as a whole is {\it addressed} primarily to Christians in cosmology and others interested in the relation between the multiverse and theism, it should be of {\it interest} to a wider audience. Proper subsets of this paper are addressed to other Christians, to other theists, to other cosmologists, to other scientists, and to others interested in the multiverse and theism.

physics.gen-ph↗
arXiv2008

Our Place in a Vast Universe

Scientists have measured that what we can see of space is about a billion billion billion billion billion billion billion billion billion (10^81) times the volume of an average human. Inflationary theory suggests that the entirety of space is vastly larger. Quantum theory suggests that there are very many different copies of space of the same basic kind as ours (same laws of physics). String theory further suggests that there may be many different kinds of space. This whole collection of googolplexes of galaxies within each of googolplexes of different spaces within each of googols of kinds of space makes up an enormously vast universe or multiverse or holocosm. Human beings seem to be an incredibly small part of this universe in terms of physical size. Yet in other ways, we may still be a very significant part of our vast universe.

physics.gen-ph↗
arXiv2007

Observational Selection Effects in Quantum Cosmology

Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary conditions), and the connection with observations or experience or conscious perceptions (laws of psycho-physical parallelism). Principles are proposed for Bayesian meta-theories. One framework that obeys these principles is Sensible Quantum Mechanics (SQM), which is discussed. In principle, it allows one to test between single-history and many-worlds theories, and to discuss threats to certain theories from fake universes and Boltzmann brains. The threat of fake universes may be dismissed if one doubts the substrate-independence of consciousness, which seems very implausible in the SQM framework. Boltzmann brains seem more problematic, though there are many conceivable solutions. SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare that they have occurred nowhere else within the part of the universe that we can observe.

hep-th↗
arXiv2007

The Height of a Giraffe

A minor modification of the arguments of Press and Lightman leads to an estimate of the height of the tallest running, breathing organism on a habitable planet as the Bohr radius multiplied by the three-tenths power of the ratio of the electrical to gravitational forces between two protons (rather than the one-quarter power that Press got for the largest animal that would not break in falling over, after making an assumption of unreasonable brittleness). My new estimate gives a height of about 3.6 meters rather than Press's original estimate of about 2.6 cm. It also implies that the number of atoms in the tallest runner is very roughly of the order of the nine-tenths power of the ratio of the electrical to gravitational forces between two protons, which is about 3 x 10^32.

hep-th↗
arXiv2007

Typicality Defended

Hartle and Srednicki have argued that there is no observational evidence favoring our typicality. Here it is shown that such evidence does arise from including the `normalization principle' requirement that the sum of the likelihoods for all possible observations is normalized to unity in each theory.

hep-th↗
arXiv2007

Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes

In [arXiv:hep-th/0611083] we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [arXiv:hep-th/0612029] is also briefly discussed.

hep-th↗
arXiv2007

Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields

Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0 sech^2 (t/T). The integration of the quadratic part of WKB instanton actions over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method, including the prefactor, of Phys. Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown that the WKB instanton action plus the next-to-leading order contribution in spinor QED equals the WKB instanton action in scalar QED, thus justifying why the WKB instanton in scalar QED can work for the pair production of fermions. Finally we obtain the pair-production rate in a spatially localized electric field together with a constant magnetic field in the same direction.

hep-th↗
arXiv2006

Boundary Conditions and Predictions of Quantum Cosmology

A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (1) is often called a `theory of everything,' and item (2) is the quantum state of the cosmos. Hartle and Hawking have made the `no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that have the 3-dimensional argument of the wavefunction on their one and only boundary. This proposal has had several partial successes, mainly when one takes the zero-loop approximation of summing over a small number of complex extrema of the action. However, it has also been severely challenged by an argument by Susskind.

hep-th↗
arXiv2006

Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions

Given the observed cosmic acceleration, Leonard Susskind has presented the following argument against the Hartle-Hawking no-boundary proposal for the quantum state of the universe: It should most likely lead to a nearly empty large de Sitter universe, rather than to early rapid inflation. Even if one adds the condition of observers, they are most likely to form by quantum fluctuations in de Sitter and therefore not see the structure that we observe. Here I present my own amplified version of this argument and consider possible resolutions, one of which seems to imply that inflation expands the universe to be larger than 10^{10^{10^{122}}} Mpc.

hep-th↗
arXiv2006

Is Our Universe Decaying at an Astronomical Rate?

Unless our universe is decaying at an astronomical rate (i.e., on the present cosmological timescale of Gigayears, rather than on the quantum recurrence timescale of googolplexes), it would apparently produce an infinite number of observers per comoving volume by thermal or vacuum fluctuations (Boltzmann brains). If the number of ordinary observers per comoving volume is finite, this scenario seems to imply zero likelihood for us to be ordinary observers and minuscule likelihoods for our actual observations. Hence, our observations suggest that this scenario is incorrect and that perhaps our universe is decaying at an astronomical rate.

hep-th↗
arXiv2006

Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).

hep-th↗
arXiv2006

Return of the Boltzmann Brains

Linde in hep-th/0611043 shows that some (though not all) versions of the global (volume-weighted) description avoid the "Boltzmann brain" problem raised in hep-th/0610079 if the universe does not have a decay time less than 20 Gyr. Here I give an apparently natural version of the volume-weighted description in which the problem persists, highlighting the ambiguity of taking the ratios of infinite volumes that appear to arise from eternal inflation.

hep-th↗
arXiv2006

Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes

We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.

hep-th↗