Session KK02: V: Gravitation - Classical, Quantum, and Numerical

Ergodicity of Moves in 1+1D Causal Dynamical Triangulation

Causal dynamical triangulation (CDT) is an approach to quantum gravity with exciting numerical results. Starting from a triangulation of a manifold, many small random modifications are then applied, and the resulting triangulation is treated as one sample. This is done many times to build up an ensemble of triangulation for study. However, a key assumption in this process, ergodicity, remains unvalidated. Ergodic, here, means that the types of modifications used could potentially access any valid triangulation from any other, in a finite number of steps. In this talk, I will describe a new method which demonstrates this property for the commonly used moves in 1+1D CDT.   

Kinematics in Metric-Affine Geometry

In a given geometry, the kinematics of a congruence of curves is described by a set of three quantities called expansion, rotation, and shear. The equations governing the evolution of these quantities are referred to as kinematic equations. In this paper, the kinematics of congruence of curves in a metric-affine geometry are analysed. Without assuming an underlying theory of gravity, we derive a generalised form of the evolution equations for expansion, namely, Raychaudhuri equation (timelike congruences) and Sachs optical equation (null congruences). The evolution equations for rotation and shear of both timelike and null congruences are also derived. Generalising the deviation equation, we find that torsion and non-metricity contribute to a relative acceleration between neighbouring curves. We briefly discuss the interpretation of the expansion scalars and derive an equation governing angular diameter distances. The effects of torsion and non-metricity on the distances are found to be dependent on which curves are chosen as photon trajectories. We also show that the rotation of a hypersurface orthogonal congruence (timelike or null) is a purely non-Riemannian feature.   

Reveal the lost entanglement for two atoms in higher dimensional spacetime

When atoms are accelerated in the vacuum, entanglement among atoms will degrade compared with the initial situation before the acceleration. We propose a novel and interesting view that the lost entanglement can be recovered completely when the high-dimensional spacetime is exploited, in the case that the acceleration is not too large, since the entanglement loss rate caused by the large acceleration is faster than the recovery process. We also calculate the entanglement change caused by the anti-Unruh effect and found that the lost entanglement could just be recovered part by the anti-Unruh effect, and the anti-Unruh effect could only appear for a finite range of acceleration when the interaction time scale is approximately shorter than the reciprocal of the energy gap in two dimensional spacetime. The limit case of zero acceleration is also investigated, which gives an analytical interpretation for the increase or recovery of entanglement.   

Thermalization and QED corrections for accelerated electrons

For an electron undergoing linear acceleration, low-momentum transverse fluctuations thermalize by interaction with the radiation field. Accelerated-frame arguments suggest thermalization and a fluctuation-dissipation relation but do not determine the magnitude of either the fluctuation or the dissipation. Lab frame analysis reproduces the radiation losses, described by the classical Lorentz-Abraham-Dirac equation, and reveals a classical stochastic force. We derive the fluctuation-dissipation relation between the radiation losses and stochastic force as well as equipartitation 〈p_⊥²〉=2mT from classical electrodynamics alone. The derivation uses only straightforward statistical definitions. Since high accelerations are necessary for these dynamics to become important, we compare classical results to strong-field quantum electrodynamics (QED) results. Experimental realization will require more precise observables.   

Derivation of the Lorentz Transformation Accounting for Two-Way Speeds of Light in the Moving Inertial Reference Frame

Einstein’s “universal constant” speed of light has been the keystone in derivations of the Lorentz transformation up to the present time. This assumed universal constant is discretionary within the empirical/time-averaged unequal two-way speeds of light. Einstein’s (assumed) universal constant may accordingly be replaced by the (empirical) two-way universal constant. (i.e., c becomes c⁺ and c^- in all moving IRFs). Here the Lorentz transformation is operationally derived given (unequal) two-way light-speeds in the moving frame. The two-way transformation exhibits space-time details in the moving frame that are absent in the overarching one-way transformation. Time continuity during the (operational) derivation is one such detail, where any one-way transformation sets-aside (e.g., atomic clock) tracking or following how the moving IRF state is achieved, whereas the procedure is explicit in the two-way light-speeds transformation. Einstein’s same-motion transformation plays a key role in the (novel) derivation. This mathematical development within the IRF system reveals extreme photonic behavior—in particular, the development admits or allows assumed near-infinite incoming light-speed—that helps, together with the Hubble expansion, to explain ongoing challenges—e.g., the dark sector.   

Can measurements change Hilbert space?

The CCR's of quantum fields admit inequivalent representations; a basic step in treating them is the construction of the physically appropriate representation, that is, the Hilbert space.  Once this is done, in textbook treatments, all analysis takes place in that Hilbert space.

I show that there are physically plausible circumstances in which infinitely many commuting measurements may be made, which would alter the representation, and that it seems inescapable this behavior must occur in open cosmological models.  In the most conservative scenarios, causality restricts the consequences of this to only gradually become apparent on any one worldline, the evidence for it accumulating at later and later events.  But I will also describe a situation in which it would seem that the effects could become known at finite events. 

It is, however, possible that this behavior is far more pervasive.  While conventional quantum theory specifies what happens in a measurement, it is silent about which measurements are likely to occur in which circumstances.  We should ask what measurements are likely to have occurred over the 14 Gy evolution of the Universe, and what their consequences on physics have been.  It is possible that the Hilbert space of the Universe has been remade many times.   

Spin-Precession in Eccentric Spinning Binary Black Hole Mergers

We use the Einstein Toolkit, an open-source numerical relativity software, to gain new insights into the complex dynamics of eccentric, spin-precessing binary black hole mergers. Our focus is on systems with mass ratios q = (2, 4, 6). We present a new set of numerical relativity waveforms, and quantify the impact of spin-precession and eccentricity on the time evolution of gravitational waves. This research is timely and relevant to enhance our understanding of black hole binaries and the astrophysical environments where they are assembled and evolve. Our work also sheds new light on the importance of including higher order wave modes to detect and characterize these complex signals with available gravitational wave observatories.   

Refining Refinement in Binary Black Hole Simulations

To produce high-accuracy simulations of binary black hole inspirals at high mass ratios, we use the code Dendro-GR. This solves Einstein's equations on an adaptive grid, using wavelets to determine where increased refinement is needed. Simulations of black hole binaries with large mass ratios require balancing waveform accuracy with computational efficiency. Non-physical features of the solutions—such as junk radiation and an outward-propagating gauge wave—complicate the task of choosing optimal refinement strategies. In this talk, I describe how we alter refinement regions to address these challenges, vastly reducing cpu hours needed for binary simulations with large mass ratios.   

a gravifrequency field equations system

abstract

In this work:

- a gravitational (gravifrequency) field equations system is theoretically obtained;

- the Pointing’s vector analogue is built for gravifrequency interactions;

- Poynting's theorem for gravidynamics is formulated;

- definition of the term "electric charge" is given;

- the Reynolds number analogue for electrodynamics was built;

- the equations generality of electrodynamics and gravidynamics is shown;

- an attempt was made to reveal the physical meaning of the quantities included to the gravitational (gravifrequency) field equations system;

- the action type is proposed for mass in the gravifrequency field;

- applying the obtained equations, an explanation is offered of Kozyrev N.A.'s experiments;

- it is shown that force lines of an angular velocity vector are closed, similar to the magnetic force lines;

- the some facts analyzing possibility of microworld (spin-spin and spin-orbit interactions, Pauli's prohibition principle) in terms of the frequency interactions is offered.

Key words: gravitational waves, gravifrequency field equations system, gravitomagnetic interaction, Poynting’s vector for gravidynamics, the Reynolds number analogue for

                   electrodynamics.   

Generalized Gauss's Law of Gravity with off-Spherical Symmetry Transition of Gravitational Field Flux Distribution

 A gravitational field flux conservation and redistribution picture is proposed by generalizing the Integral Gauss's law of gravity at non-relativistic limit. 1/r dependence along with a disk thickness dependence of gravitational field and the flat rotation curves are obtained by a Gaussian surface with cylindrical symmetry, where most of the gravitational fluxes are assumed to be distributed eventually along the disk plane. For disk galaxies, a spherical to cylindrical transition, across a critical field strength, of the Gaussian surface symmetry is shown to give directly the algebraic M ∝ v⁴ baryonic Tully-Fisher relation. The Faber-Jackson relation of the elliptical galaxies can also be shown by a similar off-spherical symmetry transition for the flux distribution. The transition suggests that the 10^-10 m/s² acceleration scale can be alternatively interpreted as a critical field strength where gravitational flux redistribution occurs. The generalized Gauss's law of gravity is compared with the theoretical MOND Lagrangian modeling. One benefit of this non-dark matter field flux re-distribution picture with asymmetrically focused field lines is apparently the feasibility of extension to even larger scales where the current MOND modeling appears to be still short of mass. This gravitational flux redistribution picture may create the need for a non-Newtonian non-relativistic limit for the General Relativity. The possible applications of the temporal evolution of the "cylindrical to spherical transition" from the gravitational field flux re-distribution mechanism is also discussed.