Talks

As discussed in last week’s colloquium, the use of the p-adic metric in state space provides a route to resolving the Bell Theorem in favour of realism and local causality, without fine tuning. Here the p-adic integers provide a natural way to describe the fractal geometry of Invariant Set Theory’s state space. In this talk I first explore the role of complex numbers in Invariant Set Theory (arXiv:1605.01051), and describe a novel realistic perspective on quantum interferometry. Then I will describe a programme of work to synthesise quantum and gravitational physics realistically and causally within the framework of Invariant Set Theory. I will describe a p-adic generalisation of the field equations of General Relativity, and discuss the consequent novel perspectives for understanding the dark (energy and matter) universe. 

We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric N=4 Yang-Mills theory, three-dimensional conformal field theories and QCD.

An unbroken U(1)' is a minimal possibility for a dark matter self interaction, and may even be associated with dark matter stability. However, such an interaction faces incredibly strong constraints due to collective plasma effects, which dominate over 2-to-2 scattering by an order-of-magnitude of orders-of-magnitude. I will discuss the physics of these collective effects, and show preliminary results of simulation. The constraint of such a self interaction is estimated to be nearly as weak as gravity. 

Gravitational lensing by matter clumps can magnify various transient bursts in the sky, making them more detectable from the high redshift Universe. For one example, chirping gravitational waves from stellar-mass black hole binary mergers, as first detected by LIGO recently, can appear louder due to intervening galaxies. In the absence of electromagnetic counterpart, as I will discuss, lensing magnification can bias the determination of binary mass and redshift, which needs to be corrected for when testing source evolution and formation models through event statistics. As another example, compact dark matter of masses 10-100 solar masses can gravitationally lens fast radio bursts, creating double-peaked time-domain signature with a resolvable time delay on the order of milliseconds. I discuss that forthcoming fast radio burst surveys can directly probing this interesting mass range for compact dark matter by detecting 10^4 bursts per year.

In the last few years, we have made remarkable progress in understanding the properties of our observable Universe which appears to have evolved from a hot Big Bang 13.7 billion years ago. The fine-tuning of initial conditions required to reproduce our present day Universe suggests that our Universe may merely be a region within an eternally inflating super-region. Many other regions could exist beyond our observable Universe with each such region governed by a different set of physical parameters than the ones we have measured for our Universe. Collision between these regions, if they occur, should leave signatures of anisotropy in the cosmic microwave background. I will present our analysis of the Planck data which had led to the detection of spectral anisotropies at the location of some high-latitude cold spots associated with the CMB. I will argue that the excess emission may be due to enhanced Hydrogen Paschen-series emission from the epoch of recombination. The strength of the emission would favor a collision with an alternate Universe with a much higher baryon to photon ratio than our own and suggest an anthropic explanation for the value of the cosmological constant. Future, observational tests of this hypothesis will also be discussed.

We numerically investigate the expansion of clouds of hard-core bosons in a 2D square lattice using a matrix-product state based method. This non-equilibrium setup is induced by quenching a trapping potential to zero and is specifically motivated by an experiment with ultracold atoms [1]. As the anisotropy for hopping amplitudes in different spatial directions is varied from 1D to 2D, we observe a crossover from a fast ballistic expansion in the 1D limit to much slower dynamics in the isotropic 2D lattice [2].

Introducing a site-dependent disorder potential allows to study many body localization (MBL). In a very recent experiment, the melting of a domain wall gave evidence for an MBL transition in 2D [3]. We study 1D and quasi-1D models, for which the phase diagram in the presence of disorder is known, such as the Anderson insulator, Aubry-Andre model and interacting fermions in 1D and on a two-leg ladder [4]. By considering several observables, we demonstrate that the domain wall melting can indeed yield quantitative information on the transition from an ergodic to the MBL phase as a function of disorder.

[1] J. P. Ronzheimer et al., PRL 110, 205301 (2013) [2] J. Hauschild et al., PRA 92, 053629 (2015) [3] J. Choi et al., arXiv:1604.04178 (2016) [4] J. Hauschild et al., in preparation

Entanglement is both a central feature of quantum mechanics and a powerful tool for studying quantum systems. Even empty spacetime is a highly entangled state, and this entanglement has the potential to explain puzzling thermodynamic properties of black holes. In order to apply the methods of quantum information theory to problems in gravity we have to confront a more fundamental question: what is a local subsystem, and what are its physical degrees of freedom? I will show that local subsystems in gravity come with new physical degrees of freedom living on the boundary, as well as new physical symmetries. These structures offer us new insight into how spacetime is entangled, and a new perspective on the problem of quantizing gravity.

How well can we predict our future climate? If the flap of a butterfly’s wings can change the course of weather a week or so from now, what hope trying to predict anything about our climate a hundred years hence? In this talk I will discuss the science of climate change from a perspective which emphasises the chaotic (and hence uncertain) nature of our climate system. In so doing I will outline the fundamentals of climate modelling, and discuss the emerging concept of inexact supercomputing, needed - paradoxically perhaps - if we are to increase the accuracy of predictions from these models. Indeed, revising the notion of a supercomputer from its traditional role as a fast but precise deterministic calculating machine, may be important not only for climate prediction, but also for other areas of science such as astrophysics, cosmology and neuroscience.

In this talk I will: 1) review the results of my work on a geometric approach to foundations for a postquantum information theory; 2) discuss how it is related to other foundational approaches, including some resource theories of knowledge and quantum histories; 3) present some of my research on a category theoretic framework for a multi-agent information relativity. More details on part 1: this approach does not rely on probability theory, spectral theory, or Hilbert spaces. Normalisation of states, convexity, and tensor products are allowed but not assumed foundationally. Nonlinear generalisation of quantum kinematics and dynamics is constructed using geometric structures (quantum relative entropies and Banach Lie--Poisson structure) over the sets of quantum states on W*-algebras. In particular, unitary evolution is generalised to nonlinear hamiltonian flows, while Lueders' rules are generalised to constrained relative entropy maximisations. Combined together, they provide a framework for causal inference that is a generalisation and replacement for completely positive maps, with information dynamics determined directly by epistemic constraints, and no requirement for lack of correlation. Orthodox probability theory and quantum mechanics are special cases of this framework. I will also give the progress report on the reconstruction conjecture: given the category of sets of abstract "states" equipped with the suitably defined entropic distances and BLP structure, how one reconstructs the W*-algebraic case? The discussion of the consistent operational semantics for this approach will lead us to the parts 2 and 3.