A critical look at strings

This is an invited contribution to the Special Issue of "Foundations of Physics" titled "Forty Years Of String Theory: Reflecting On the Foundations". I have been asked to assess string theory as an outsider, and to compare it with the theory, methods, and expectations in my own field.Comment: 7 page

Multiple-event probability in general-relativistic quantum mechanics

We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse" algorithm. We first point out certain difficulties of some natural definitions of multi-event probability, including the conditional probability widely considered in the literature. We then observe that multi-event probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum classical boundary, one can always trade a sequence of non-commuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the "wave function collapse" algorithm can nevertheless be recovered. The discussion bears also on the nature of the quantum collapse

Quantum Theory from Quantum Gravity

We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that 1) the model has a low low energy limit which reproduces the non-relativistic classical dynamics of a system of N particles in flat spacetime, 2) there is a minimum length, and 3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schroedinger equation. The non-local hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low energy limit. In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.Comment: 17 pages, 2 eps figure

A semiclassical tetrahedron

We construct a macroscopic semiclassical state state for a quantum tetrahedron. The expectation values of the geometrical operators representing the volume, areas and dihedral angles are peaked around assigned classical values, with vanishing relative uncertainties.Comment: 10 pages; v2 revised versio

The physical hamiltonian in nonperturbative quantum gravity

A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and diffeomorphism invariant. The problem of constructing this hamiltonian is reduced to a combinatorial and algebraic problem which involves the rearrangements of lines through the vertices of arbitrary graphs. This procedure also provides a construction of the hamiltonian constraint as a finite operator on the space of diffeomorphism invariant states as well as a construction of the operator corresponding to the spatial volume of the universe.Comment: Latex, 11 pages, no figures, CGPG/93/

Modifications in the Spectrum of Primordial Gravitational Waves Induced by Instantonic Fluctuations

Vacuum to vacuum instantonic transitions modify the power spectrum of primordial gravitational waves. We evaluate the new form of the power spectrum for ordinary gravity as well as the parity violation induced in the spectrum by a modification of General Relativity known as Holst term and we outline the possible experimental consequences.Comment: V1: 8 pages. V2: 8 pages, some points clarified, typos corrected, some references added, final result unchanged. V3: 8 pages, title changed, presentation improved, discussion of phenomenological consequences added, comments very welcome. V4: Discussion further improved, comments very very welcom

Hybrid mean field and real space model for vacancy diffusion-mediated annealing of radiation defects

In a fusion or advanced fission reactor, high energy neutrons induce the formation of extended defect clusters in structural component materials, degrading their properties over time. Such damage can be partially recovered via a thermal annealing treatment. Therefore, for the design and operation of fusion and advanced fission nuclear energy systems it is critical to estimate and predict the annealing timescales for arbitrary configurations of defect clusters. In our earlier paper [I. Rovelli, S. L. Dudarev, and A. P. Sutton, J. Mech. Phys. Solids 103, 121 (2017)] we extended the Green function formulation by Gu, Xiang et al. [Y. Gu, Y. Xiang, S. S. Quek, and D. J. Srolovitz, J. Mech. Phys. Solids 83, 319 (2015)] for the climb of curved dislocations, to include the evaporation and growth of cavities and vacancy clusters, and take into account the effect of free surfaces. In this work, we further develop this model to include the effect of radiation defects that are below the experimental detection limit, via a mean field approach coupled with an explicit treatment of the evolution of discrete defect clusters distributed in real space. We show that randomly distributed small defects screen diffusive interactions between larger discrete clusters. The evolution of the coupled system is modelled self-consistently. We also simulate the evolution of defects in an infinite laterally extended thin film, using the Ewald summation of screened Yukawa-type diffusive propagators

The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity

A choice of time-slicing in classical general relativity permits the construction of time-dependent wave functions in the ``frozen time'' Chern-Simons formulation of $(2+1)$-dimensional quantum gravity. Because of operator ordering ambiguities, however, these wave functions are not unique. It is shown that when space has the topology of a torus, suitable operator orderings give rise to wave functions that transform under the modular group as automorphic functions of arbitrary weights, with dynamics determined by the corresponding Maass Laplacians on moduli space.Comment: 8 pages, LaTe

Graphical Evolution of Spin Network States

The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.Comment: 24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections in the final formula in the main body of the paper and in the formula for the Tetrahedral net in the Appendi