Birth of the Universe as anti-tunnelling from the string perturbative vacuum

The decay of the string perturbative vacuum, if triggered by a suitable, duality-breaking dilaton potential, can efficiently proceed via the parametric amplification of the Wheeler-De Witt wave function in superspace, and can appropriately describe the birth of our Universe as a quantum process of pair production from the vacuum.Comment: 11 pages, Latex, three figures included using epsfig. Essay written for the 2000 Awards for Essays on Gravitation (Gravity Research Foundation, Wellesley Hills, MA), and selected for Honorable Mention. One reference added. To appear in Int. J. Mod. Phys.

Quasiclassical Coarse Graining and Thermodynamic Entropy

Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ``quasiclassical descriptions'' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ``quasiclassical realm'' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th birthday, minor correction

Quantum Physics and Human Language

Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise properties of all the physical situations allowed by fundamental physics. In brief, human languages contain `excess baggage' that must be qualified, discarded, or otherwise reformed to give a clear account in the context of fundamental physics of even the everyday phenomena that the languages evolved to describe. The surest route to clarity is to express the constructions of human languages in the language of fundamental physical theory, not the other way around. These ideas are illustrated by an analysis of the verb `to happen' and the word `reality' in special relativity and the modern quantum mechanics of closed systems.Comment: Contribution to the festschrift for G.C. Ghirardi on his 70th Birthday, minor correction

Dynamical coherent states and physical solutions of quantum cosmological bounces

A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.Comment: 30 pages, 3 figure

Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History

Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one. As we will show, this construction implies that the real history is not completely accessible to experimental or other observational discovery. However, sufficiently and appropriately coarse-grained sets of alternative histories have standard probabilities providing information about the real fine-grained history that can be compared with observation. We recover the probabilities of decoherent histories quantum mechanics for sets of histories that are recorded and therefore decohere. Quantum mechanics can be viewed as a classical stochastic theory of histories with extended probabilities and a well-defined notion of reality common to all decoherent sets of alternative coarse-grained histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment

Exponentially Large Probabilities in Quantum Gravity

The problem of topology change transitions in quantum gravity is investigated from the Wheeler-de Witt wave function point of view. It is argued that for all theories allowing wormhole effects the wave function of the universe is exponentially large. If the wormhole action is positive, one can try to overcome this difficulty by redefinition of the inner product, while for the case of negative wormhole action the more serious problems arise.Comment: 9 pages in LaTeX, 4 figures in PostScript, the brief version of this paper is to appear in Proceedings of the XXIV ITEP Winter School of Physic

Physical Logic

In R.D. Sorkin's framework for logic in physics a clear separation is made between the collection of unasserted propositions about the physical world and the affirmation or denial of these propositions by the physical world. The unasserted propositions form a Boolean algebra because they correspond to subsets of an underlying set of spacetime histories. Physical rules of inference, apply not to the propositions in themselves but to the affirmation and denial of these propositions by the actual world. This physical logic may or may not respect the propositions' underlying Boolean structure. We prove that this logic is Boolean if and only if the following three axioms hold: (i) The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied then its negation, or complement, is affirmed. When a physical system is governed by a dynamical law in the form of a quantum measure with the rule that events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid and need to be modified. One promising scheme for quantum mechanics as quantum measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other minor change

Primordial fluctuations from nonlinear couplings

We study the spectrum of primordial fluctuations in theories where the inflaton field is coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tiltilng it towards the blue. We discuss in some detail whether these fluctuations are quantum or classical in nature.Comment: 12 pages, Revtex, we added an appendix clarifying our assumptions about the initial conditions at the beggining of inflatio

A global picture of quantum de Sitter space

Perturbative gravity about a de Sitter background motivates a global picture of quantum dynamics in `eternal de Sitter space,' the theory of states which are asymptotically de Sitter to both future and past. Eternal de Sitter physics is described by a finite dimensional Hilbert space in which each state is precisely invariant under the full de Sitter group. This resolves a previously-noted tension between de Sitter symmetry and finite entropy. Observables, implications for Boltzmann brains, and Poincare recurrences are briefly discussed.Comment: 17 pages, 1 figure. v2: minor changes, references added. v3: minor changes to correspond to PRD versio

Quantum Creation of Topological Black Hole

The constrained instanton method is used to study quantum creation of a vacuum or charged topological black hole. At the $WKB$ level, the relative creation probability is the exponential of a quarter sum of the horizon areas associated with the seed instanton.Comment: Report-no change onl