Measurement of Quantum Fluctuations in Geometry

A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the limits of measurement possible with Planck wavelength radiation. The indeterminacy predicts fluctuations from a classically defined geometry in the form of ``holographic noise'' whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature, and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions, and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometer GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as LIGO, where beam power is much less in the beamsplitter than in the arms.Comment: 7 pages, 2 figures, LaTeX. Extensive rewrite of original version, including more detailed analysis. Main result is the same but the estimate of noise in strain units for GEO600, showing 1/f behavior at low f and flat at high f, is improved. To appear in Phys. Rev.

Indeterminacy of Holographic Quantum Geometry

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of quasi-monochromatic radiation. It is shown that the product of standard deviations of two position wavefunctions in the plane of a holographic light sheet is equal to the product of their normal separation and the Planck length. For macroscopically separated positions the transverse uncertainty is much larger than the Planck length, and is predicted to be observable as a "holographic noise" in relative position with a distinctive shear spatial character, and an absolutely normalized frequency spectrum with no parameters once the fundamental wavelength is fixed from the theory of gravitational thermodynamics. The spectrum of holographic noise is estimated for the GEO600 interferometric gravitational-wave detector, and is shown to approximately account for currently unexplained noise between about 300 and 1400Hz. In a holographic world, this result directly and precisely measures the fundamental minimum interval of time.Comment: 4 pages, LaTeX. Considerably shortened from earlier version. Conclusions are unchanged. Submitted to PR

Holographic Geometry and Noise in Matrix Theory

Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic noise, with phenomenology similar to that previously derived on the basis of a quasi-monochromatic wave theory. Traces of matrix operators on a light sheet with a compact dimension of size $R$ are interpreted as transverse position operators for macroscopic bodies. An effective quantum wave equation for spacetime is derived from the Matrix Hamiltonian. Its solutions display eigenmodes that connect longitudinal separation and transverse position operators on macroscopic scales. Measurements of transverse relative positions of macroscopically separated bodies, such as signals in Michelson interferometers, are shown to display holographic nonlocality, indeterminacy and noise, whose properties can be predicted with no parameters except $R$. Similar results are derived using a detailed scattering calculation of the matrix wavefunction. Current experimental technology will allow a definitive and precise test or validation of this interpretation of holographic fundamental theories. In the latter case, they will yield a direct measurement of $R$ independent of the gravitational definition of the Planck length, and a direct measurement of the total number of degrees of freedom.Comment: 19 pages, 2 figures; v2: factors of Planck mass written explicitly, typos correcte

Interferometers as Probes of Planckian Quantum Geometry

A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, $t_P$. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wavefunctions in two dimensions displays a new kind of directionally-coherent quantum noise of transverse position. The amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wavefunctions on a 2D spacelike surface with the entropy density of a black hole event horizon of the same area. In a region of size $L$, the effect resembles spatially and directionally coherent random transverse shear deformations on timescale $\approx L/c$ with typical amplitude $\approx \sqrt{ct_PL}$. This quantum-geometrical "holographic noise" in position is not describable as fluctuations of a quantized metric, or as any kind of fluctuation, dispersion or propagation effect in quantum fields. In a Michelson interferometer the effect appears as noise that resembles a random Planckian walk of the beamsplitter for durations up to the light crossing time. Signal spectra and correlation functions in interferometers are derived, and predicted to be comparable with the sensitivities of current and planned experiments. It is proposed that nearly co-located Michelson interferometers of laboratory scale, cross-correlated at high frequency, can test the Planckian noise prediction with current technology.Comment: 23 pages, 6 figures, Latex. To appear in Physical Review

Upper-Ocean Response to Hurricane Ivan in a 1/25 Degrees Nested Gulf of Mexico HYCOM

[ 1] A 20-layer, 1/25 degrees nested Gulf of Mexico (GoM) Hybrid Coordinate Ocean Model (HYCOM) has been employed to examine the evolving three-dimensional ocean response to Hurricane Ivan during 14 - 16 September 2004. Results from several combinations of numerical experiments with and without assimilation of satellite-altimetry sea-surface height (SSH) are being analyzed and compared for the September 2004 hurricane period. A comparison of simulated zonal and meridional velocities using data assimilation shows improved agreement with profiler observations. The amplitude of the cold wake ( similar to 6 degrees C) produced by these simulations compared reasonably well with the observed changes in SST before and after the storm; however, the region of extreme cooling varied depending on the simulated location of the warm core eddy (WCE) that had detached from the Loop Current ( LC). While the simulated location of the WCE and LC in the assimilation runs agree better with satellite altimetry, the storm-induced SST cooling was 40% - 50% greater than the observed cooling. Overall, similar to 64% of the cooling was due to vertical mixing caused by turbulence generated from strong shear-stress across the base of the mixed layer. Vertical advection (upwelling) caused a significant portion of cooling (23.4%) in those runs that included data assimilation; a three fold increase from the nonassimilative runs (7%). This enhanced upper- ocean cooling was caused primarily by the prestorm thermal stratification; a shallower thermocline ( similar to 40 m) and a stronger upper- thermocline temperature gradient compared with the nonassimilative runs. In all the experiments the air-sea exchange was a small component of the mixed-layer heat budget which overall accounted for similar to 4

Peeling properties of lightlike signals in General Relativity

The peeling properties of a lightlike signal propagating through a general Bondi-Sachs vacuum spacetime and leaving behind another Bondi-Sachs vacuum space-time are studied. We demonstrate that in general the peeling behavior is the conventional one which is associated with a radiating isolated system and that it becomes unconventional if the asymptotically flat space-times on either side of the history of the light-like signal tend to flatness at future null infinity faster than the general Bondi-Sachs space-time. This latter situation occurs if, for example, the space-times in question are static Bondi-Sachs space- times.Comment: 14 pages, LaTeX2

Multichannel Si Photonic Crystal filters with Fine-Tuning Capability of Individual Channels for WDM optical interconnects

This is the author accepted manuscriptWe demonstrate a simple, low-cost solution for a single multi-channel WDM (Wavelength Division Multiplexing) filter with fine-tuning capability at the level of the individual channels. The filter is based on silicon photonic crystal and microfluidic technologies and can be integrated with CMOS processes.Engineering and Physical Sciences Research Council (EPSRC

Sensitivity of the Brewer-Dobson circulation and polar vortex variability to parameterized nonorographic gravity wave drag in a high-resolution atmospheric model

The role of parametrized nonorographic gravity wave drag (NOGWD) and its seasonal interaction with the resolved wave drag in the stratosphere has been extensively studied in low-resolution (coarser than 1.9 x 2.5 degrees) climate models but is comparatively unexplored in higher-resolution models. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecast System at 0.7 x 0.7 degrees resolution, the wave drivers of the Brewer-Dobson circulation are diagnosed and the circulation sensitivity to the NOGW launch flux is explored. NOGWs are found to account for nearly 20% of the lower stratospheric Southern Hemisphere (SH) polar cap downwelling and for less than 10% of the lower-stratospheric tropical upwelling and Northern Hemisphere (NH) polar cap downwelling. Despite these relatively small numbers, there are complex interactions between NOGWD and resolved wave drag, in both polar regions. Seasonal cycle analysis reveals a temporal offset in the resolved and parametrized wave interaction: The NOGWD response to altered source fluxes is largest in mid-winter, while the resolved wave response is largest in the late winter and spring. This temporal offset is especially prominent in the SH. The impact of NOGWD on sudden stratospheric warming (SSW) life-cycles and the final warming date in the SH is also investigated. An increase in NOGWD leads to an increase in SSW frequency, reduction in amplitude and persistence, and an earlier recovery of the stratopause following a SSW event. The SH final warming date is also brought forward when NOGWD is increased. Thus, NOGWD is still found to be a very important parameterization for stratospheric dynamics even in a high-resolution atmospheric model

Report on Stratosphere Task Force

Recognising the importance of the stratosphere for skilful seasonal and sub-seasonal prediction, the Stratosphere Task Force was set up in 2016 to improve the representation of the stratosphere in ECMWF forecast and analysis systems. This report synthesizes the most notable findings of the Task Force and provides recommendations for the way forward. The main focus is on: 1) Global-mean temperature biases; 2) Horizontal resolution sensitivity of the mid- to lower stratospheric temperatures; 3) Stratospheric meridional circulation and polar vortex variability; 4) Extratropical lower stratospheric cold temperature bias; 5) New sponge design; and, 6) Representation of tropical winds