Quantum Physics

Karim Thebault Canonical quantization techniques are generally considered to provide one of the most rigorous methodologies for passing from a classical to a quantum description of reality. For classical Hamiltonian systems with constraints a number of such techniques are available (i.e. gauge fixing, Dirac constraint quantization, BRST quantization and geometric quantization) but all are arguably equivalent to the quantization of an underlying reduced phase space that parameterizes the "true degrees of freedom" and displays a symplectic geometric structure. The philosophical coherence of making any ontological investment in such a space for the case of canonical general relativity will be questioned here. Further to this, the particular example of Dirac quantization will be critically examined. Under the Dirac scheme the classical constraint functions are interpreted as quantum constraint operators restricting the allowed state vectors. For canonical general relativity this leads to the Wheeler-de Witt equation and the infamous problem of time but, prima facie, seems to rely on our interpretation of the classical Poisson bracket algebra of constraints as the phase space realization of the theory's local symmetries (i.e. the group of space-time diffeomorphisms). As with the construction of an interpretively viable symplectic reduced phase space, this straight forward connection between constraints and local symmetry will be questioned for the case of GR. These issues cast doubt on the basis behind the derivation of the so-called wave function of the universe and give us some grounds for re-examining the entire canonical quantum gravity program as currently constituted.

Shan Gao We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributed in space, proportional to the square of the absolute value of its wave function. If the wave function is a description of a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations.

Maki Takahashi We present a formalism describing the transport of the quantum spin state of massive fermions in curved space-time for the purpose of studying relativistic quantum information phenomena such as entanglement and teleportation. We are concerned with answering the elementary question of how the state of a qubit transforms as it moves through a curved space-time manifold. This transport equation takes the form of the Fermi-Walker transport of a two component spinor, which will be shown to be unitary in the spinor's rest frame. The talk will summarise key results and highlight foundational issues such as the absence of global parallelism and conceptual issues/difficulties regarding entanglement and teleportation.

Quantum error correcting codes and topological quantum order (TQO) are inter-connected fields that study non-local correlations in highly entangled many-body quantum states. In this talk I will argue that each of these fields offers valuable techniques for solving problems posed in the other one. First, we will discuss the zero-temperature stability of TQO and derive simple conditions that guarantee stability of the spectral gap and the ground state degeneracy under generic local perturbations. These conditions thus can be regarded as a rigorous definition of TQO. Our results apply to any quantum spin Hamiltonian that can be written as a sum of geometrically local commuting projectors on a D-dimensional lattice. This large class of Hamiltonians includes Levin-Wen string-net models and Kitaev's quantum double models. Secondly, we derive upper bounds on the parameters of quantum codes with local check operators and discuss the implications for feasibility of a quantum self-correcting memory.

Tony Downes The geometry of space-time can only be determined by making measurements on physical systems. The ultimate accuracy achievable is then determined by quantum mechanics which fundamentally governs these systems. In this talk I will describe uncertainty principles constraining how well we can estimate the components of a metric tensor describing a gravitational field. I shall outline a number of examples which can be easily constructed with a minimum of mathematical complexity. I will also attempt to derive a general bound on the uncertainty in any attempt to determine the metric tensor which is expected to hold in an arbitrary globally hyperbolic space-time. I shall use tools developed within the algebraic approach to quantum field theory on a classical space-time background. I shall not consider limits on estimating space-time metrics that might arise from a quantisation of gravity itself.

I will present a recent result showing that general relativity admits a dual description in terms of a 3D scale invariant theory. The dual theory was discovered by starting with the basic observation that, fundamentally, all observations can be broken down into local comparisons of spatial configurations. Thus, absolute local spatial size is unobservable. Inspired by this principle of "relativity of size", I will motivate a procedure that allows the refoliation invariance of general relativity to be traded for 3D local scale invariance. This trade does away with "many fingered time" and offers a new possibility for dealing with the many technical and conceptual difficulties associated with the Wheeler-DeWitt equation.

Basic epistemological considerations suggest that the laws of nature should be scale invariant and no fundamental length scale should exist in nature. Indeed, the standard model action contains only two terms that break scale invariance: the Einstein-Hilbert term and the Higgs mass term. We give a simple introduction to Weyl's 1918 scale invariant gravity based on basic epistemology and discuss the three main objections put forth by Einstein: 1) the hydrogen spectrum depends on their previous history of the atom (something which is empirically ruled out to a high precision), 2) there is no account for proper time in Weyl's theory, and 3) fieldequations are 4th order leading to Ostrogradsky-type instabilities. We show that the first two objections can readily be answered. In particular the second objection is answered by developing a physical model of an ideal clock from which proper time is identified as the reading of the clock. We then outline an attempt to tackle the third objection by breaking foliation invariance and so introduce a preferred simultaneity. We show that Lorentz invariance can still be maintained if only the gravitational sector is sensitive to the preferred foliation. We impose the restrictions I) the new theory should contain general relativity in the limit of zero scale curvature, II) no fundamental length scales should appear, III) the field equations should be of second order.

Tamara Davis The last decade of astrophysics has shown more than ever before that cosmology can teach us about the nuts-and-bolts of basic physics. This has been driven by the discovery of the accelerating universe (dark energy) --- the theories being proposed to explain dark energy often invoke new physics such as brane-worlds arising from fledgling models of quantum-gravity. It has become evident that the large timescales and spatial-scales probed by cosmology allow us to learn about fundamental physics in a way inaccessible to any earth-bound experiment. This talk will review my work as part of the ESSENCE and SDSS supernova surveys, and the WiggleZ Baryon Acoustic Oscillation survey, to test new fundamental physics. I'll present the latest data and discuss how the cosmological constraints will be improved in the future with more data, different types of data, and improved analysis techniques.

I will review some recent advances on the line of deriving quantum field theory from pure quantum information processing. The general idea is that there is only Quantum Theory (without quantization rules), and the whole Physics---including space-time and relativity---is emergent from the processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. Here's the TOC of the talk: a) Very short review of the informational axiomatization of Quantum Theory; b) How space-time and relativistic covariance emerge from the quantum computation; c) Special relativity without space: other ideas; d) Dirac equation derived as information flow (without the need of Lorentz covariance); e) Information-theoretical meaning of inertial mass and Planck constant; f) Observable consequences (at the Planck scale?); h) What about Gravity? Three alternatives as a start for a brainstorming.

I'll describe a connection between uncertainty relations, information locking and low-distortion embeddings of L2 into L1. Exploiting this connection leads to the first explicit construction of entropic uncertainty relations for a number of measurements that is polylogarithmic in the dimension d while achieving an average measurement entropy of (1-e) log d for arbitrarily small e. From there, it is straightforward to obtain the first strong information locking scheme that is efficiently computable using a quantum computer. This locking scheme can be interpreted as a method for encrypting classical messages using a key of size much smaller than the message length. Other applications include efficient encodings for amortized quantum identification over classical channels and new string commitment protocols.

The second law of thermodynamics tells that physics imposes a fundamental constraint on the efficiency of all thermal machines. Here I will address the question of whether size imposes further constraints upon thermal machines, namely whether there is a minimum size below which no machine can run, and whether when they are small if they can still be efficient? I will present a simple model which shows that there is no size limitation and no limit on the efficiency of thermal machine and that this leads to a unified view of small refrigerators, pumps and engines.