On the quadratic invariant of binary sextics
We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
math.DG↗
arXiv subjects
Roger Penrose
Publications and source records attributed to Roger Penrose.
A Test of General Relativity Using the LARES and LAGEOS Satellites and a GRACE Earth's Gravity Model
We present a test of General Relativity, the measurement of the Earth's dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS and LAGEOS 2 laser-ranged satellites together with the Earth's gravity field model GGM05S produced by the space geodesy mission GRACE. We measure $μ= (0.994 \pm 0.002) \pm 0.05$, where $μ$ is the Earth's dragging of inertial frames normalized to its General Relativity value, 0.002 is the 1-sigma formal error and 0.05 is the estimated systematic error mainly due to the uncertainties in the Earth's gravity model GGM05S. Our result is in agreement with the prediction of General Relativity.
gr-qc↗
Fundamental Physics and General Relativity with the LARES and LAGEOS satellites
Current observations of the universe have strengthened the interest to further test General Relativity and other theories of fundamental physics. After an introduction to the phenomenon of frame-dragging predicted by Einstein's theory of General Relativity, with fundamental astrophysical applications to rotating black holes, we describe the past measurements of frame-dragging obtained by the LAGEOS satellites and by the dedicated Gravity Probe B space mission. We also discuss a test of String Theories of Chern-Simons type that has been carried out using the results of the LAGEOS satellites. We then describe the LARES space experiment. LARES was successfully launched in February 2012 to improve the accuracy of the tests of frame-dragging, it can also improve the test of String Theories. We present the results of the first few months of observations of LARES, its orbital analyses show that it has the best agreement of any other satellite with the test-particle motion predicted by General Relativity. We finally briefly report the accurate studies and the extensive simulations of the LARES space experiment, confirming an accuracy of a few percent in the forthcoming measurement of frame-dragging.
gr-qc↗
Testing General Relativity and gravitational physics using the LARES satellite
The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of `dark energy' constituting most of the Universe, has further revived the interest in testing Einstein's theory of General Relativity. At the very foundation of Einstein's theory is the geodesic motion of a small, structureless test-particle. Depending on the physical context, a star, planet or satellite can behave very nearly like a test-particle, so geodesic motion is used to calculate the advance of the perihelion of a planet's orbit, the dynamics of a binary pulsar system and of an Earth orbiting satellite. Verifying geodesic motion is then a test of paramount importance to General Relativity and other theories of fundamental physics. On the basis of the first few months of observations of the recently launched satellite LARES, its orbit shows the best agreement of any satellite with the test-particle motion predicted by General Relativity. That is, after modelling its known non-gravitational perturbations, the LARES orbit shows the smallest deviations from geodesic motion of any artificial satellite. LARES-type satellites can thus be used for accurate measurements and for tests of gravitational and fundamental physics. Already with only a few months of observation, LARES provides smaller scatter in the determination of several low-degree geopotential coefficients (Earth gravitational deviations from sphericity) than available from observations of any other satellite or combination of satellites.
gr-qc↗
Foreword: A Computable Universe, Understanding Computation and Exploring Nature As Computation
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws, known or yet unknown, governing the universe in which we live. Fundamentally deep questions are indeed being grappled with here, and the fact that we find so many different viewpoints is something to be expected, since, in truth, we know little about the foundational nature and origins of these basic laws, despite the immense precision that we so often find revealed in them. Accordingly, it is not surprising that within the viewpoints expressed here is some unabashed speculation, occasionally bordering on just partially justified guesswork, while elsewhere we find a good deal of precise reasoning, some in the form of rigorous mathematical theorems. Both of these are as should be, for without some inspired guesswork we cannot have new ideas as to where look in order to make genuinely new progress, and without precise mathematical reasoning, no less than in precise observation, we cannot know when we are right -- or, more usually, when we are wrong.
cs.GL↗
Towards quantum superpositions of a mirror
We propose a scheme for creating quantum superposition states involving of order $10^{14}$ atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. All experimental requirements appear to be within reach of current technology.
quant-ph↗
Drawing with Complex Numbers
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using simple geometry and setting them in a broader context.
math.MG↗