Foundations of Quantum Gravity : The Role of Principles Grounded in Empirical Reality

When attempting to assess the strengths and weaknesses of various principles in their potential role of guiding the formulation of a theory of quantum gravity, it is crucial to distinguish between principles which are strongly supported by empirical data - either directly or indirectly - and principles which instead (merely) rely heavily on theoretical arguments for their justification. These remarks are illustrated in terms of the current standard models of cosmology and particle physics, as well as their respective underlying theories, viz. general relativity and quantum (field) theory. It is argued that if history is to be of any guidance, the best chance to obtain the key structural features of a putative quantum gravity theory is by deducing them, in some form, from the appropriate empirical principles (analogous to the manner in which, say, the idea that gravitation is a curved spacetime phenomenon is arguably implied by the equivalence principle). It is subsequently argued that the appropriate empirical principles for quantum gravity should at least include (i) quantum nonlocality, (ii) irreducible indeterminacy, (iii) the thermodynamic arrow of time, (iv) homogeneity and isotropy of the observable universe on the largest scales. In each case, it is explained - when appropriate - how the principle in question could be implemented mathematically in a theory of quantum gravity, why it is considered to be of fundamental significance and also why contemporary accounts of it are insufficient.Comment: 21 pages. Some (mostly minor) corrections. Final published versio

The Origin of Chaos in the Outer Solar System

Classical analytic theories of the solar system indicate that it is stable, but numerical integrations suggest that it is chaotic. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the Jovian planets results from the overlap of the components of a mean motion resonance among Jupiter, Saturn, and Uranus, and provides rough estimates of the Lyapunov time (10 million years) and the dynamical lifetime of Uranus (10^{18} years). The Jovian planets must have entered the resonance after all the gas and most of the planetesimals in the protoplanetary disk were removed.Comment: 19 pages, 3 figures, to appear in Scienc

A possible contribution to CMB anisotropies at high l from primordial voids

We present preliminary results of an analysis into the effects of primordial voids on the cosmic microwave background (CMB). We show that an inflationary bubble model of void formation predicts excess power in the CMB angular power spectrum that peaks between 2000 < l < 3000. Therefore, voids that exist on or close to the last scattering surface at the epoch of decoupling can contribute significantly to the apparent rise in power on these scales recently detected by the Cosmic Background Imager (CBI).Comment: 5 pages, 3 figures. MNRAS accepted versio

First order resonance overlap and the stability of close two planet systems

Motivated by the population of multi-planet systems with orbital period ratios 1<P2/P1<2, we study the long-term stability of packed two planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a first order mean motion resonance can be reduced to a one degree of freedom problem (Sessin & Ferraz Mello (1984), Wisdom (1986), Henrard et al. (1986)). Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of large scale chaotic motion in close two planet systems. The reduced Hamiltonian has only a weak dependence on the planetary mass ratio, and hence the overlap criterion is independent of the planetary mass ratio at lowest order. Numerical integrations confirm that the planetary mass ratio has little effect on the structure of the chaotic phase space for close orbits in the low eccentricity (e <~0.1) regime. We show numerically that orbits in the chaotic web produced primarily by first order resonance overlap eventually experience large scale erratic variation in semimajor axes and are Lagrange unstable. This is also true of the orbits in this overlap region which are Hill stable. As a result, we can use the first order resonance overlap criterion as an effective stability criterion for pairs of observed planets. We show that for low mass (<~10 M_Earth) planetary systems with initially circular orbits the period ratio at which complete overlap occurs and widespread chaos results lies in a region of parameter space which is Hill stable. Our work indicates that a resonance overlap criterion which would apply for initially eccentric orbits needs to take into account second order resonances. Finally, we address the connection found in previous work between the Hill stability criterion and numerically determined Lagrange instability boundaries in the context of resonance overlap.Comment: Accepted for publication in Ap

Patents from government-financed research and development

Data on numbers, sources, and kinds of patented inventions from government financed research and developmen