A Classical Analogue to the Standard Model, Chapters 4-11: Particle generations and masses; curved spacetimes and gravitation; heavy weak bosons

The $\mathbb{C}^{\wedge 18}$ analogue model contains counterparts to the particle spectrum and interactions of the Standard Model, and has only three tunable parameters. As the structure of this model is highly constrained, predictive relationships between constants may be obtained. In Chapters 4-6, the masses of the tau, the $W$ and $Z$ bosons, and a Higgs-like scalar boson are calculated as functions of $\alpha$, $m_e$, and $m_\mu$. They are shown to be $1.776867413(43)$ GeV/$c^2$, $80.3587(22)$ GeV/$c^2$, $91.1877(35)$ GeV/$c^2$, and $125.1261(48)$ GeV/$c^2$ respectively, with no free fitting parameters. All are within $0.1\,\sigma$ of the observed values of $1.77686(12)$ GeV/$c^2$, $80.360(16)$ GeV/$c^2$, $91.1876(21)$ GeV/$c^2$, and $125.11(11)$ GeV/$c^2$ respectively. In Chapter 7 the final ungauged freedom of the $\mathbb{C}^{\wedge 18}$ model is used to eliminate the right-handed weak interaction, while simultaneously introducing space-time curvature and a gravitational interaction emulating general relativity. The value of Newton's constant is then calculated from $\alpha$, $m_e$, and $m_\mu$, yielding $G_N=6.67426(230)\times 10^{-11}~\mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$, which is in agreement with the observed value of $G_N=6.67430(15)\times 10^{-11}~\mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$ with tension less than $0.1\,\sigma_\mathrm{exp}$. This persistent consistency with experiment suggests the existence of a unifying relationship between lepton generations, gravitation, and the electroweak mass scale. In the Classical Analogue to the Standard Model this unification arises from an underlying construction from coloured preons, with the low-energy residuals of the preon binding interactions corresponding to the strong nuclear force.Comment: 201 pages, 46 figures. Updated calculation of Higgs boson mass (0.1% correction; Secs. 5:3.3 & 6:4.5). Added some initial discussion of Higgs interactions in CASMIR (Ch. 11

Granular discharge rate for submerged hoppers

The discharge of spherical grains from a hole in the bottom of a right circular cylinder is measured with the entire system underwater. We find that the discharge rate depends on filling height, in contrast to the well-known case of dry non-cohesive grains. It is further surprising that the rate increases up to about twenty five percent, as the hopper empties and the granular pressure head decreases. For deep filling, where the discharge rate is constant, we measure the behavior as a function of both grain and hole diameters. The discharge rate scale is set by the product of hole area and the terminal falling speed of isolated grains. But there is a small-hole cutoff of about two and half grain diameters, which is larger than the analogous cutoff in the Beverloo equation for dry grains

Two controversies in classical electromagnetism

This paper examines two controversies arising within classical electromagnetism which are relevant to the optical trapping and micromanipulation community. First is the Abraham-Minkowski controversy, a debate relating to the form of the electromagnetic energy momentum tensor in dielectric materials, with implications for the momentum of a photon in dielectric media. A wide range of alternatives exist, and experiments are frequently proposed to attempt to discriminate between them. We explain the resolution of this controversy and show that regardless of the electromagnetic energy momentum tensor chosen, when material disturbances are also taken into account the predicted behaviour will always be the same. The second controversy, known as the plane wave angular momentum paradox, relates to the distribution of angular momentum within an electromagnetic wave. The two competing formulations are reviewed, and an experiment is discussed which is capable of distinguishing between the two

Boundary quantum critical phenomena with entanglement renormalization

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.Comment: 8 pages, 12 figures, for a related work see arXiv:0912.289

Simulation of anyons with tensor network algorithms

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons, and demonstrate this process for the 1-D Multi-scale Entanglement Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ansaetze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4 tables, RevTeX 4-1. For a related work, see arXiv:1006.247

Observation of a local gravity potential isosurface by airborne lidar of Lake Balaton, Hungary

Airborne lidar is a remote sensing method commonly used for mapping surface topography in high resolution. A water surface in hydrostatic equilibrium theoretically represents a gravity potential isosurface. Here we compare lidar-based ellipsoidal water surface height measurements all around the shore of a major lake with a local high-resolution quasi-geoid model. The ellipsoidal heights of the 87 km2 we sampled all around the shore of the 597 km2 lake surface vary by 0.8m and strong spatial correlation with the quasi-geoid undulation was calculated (R2 = 0.91). After subtraction of the local geoid undulation from the measured ellipsoidal water surface heights, their variation was considerably reduced. Based on a network of water gauge measurements, dynamic water surface heights were also successfully corrected for. This demonstrates that the water surface heights of the lake were truly determined by the local gravity potential.We conclude that both the level of hydrostatic equilibrium of the lake and the accuracy of airborne lidar were sufficient for identifying the spatial variations of gravity potential

A Theory of Cheap Control in Embodied Systems

We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments show that the sufficient controller complexity predicted by our theory is tight, which means that the theory has direct practical implications. Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machineComment: 27 pages, 10 figure

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure