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

A substructure coupling procedure applicable to general linear time-invariant dynamic systems

A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method

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

Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform guide field

Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov–Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium

Probing photoinduced spin states in spin-crossover molecules with neutron scattering

We report a neutron scattering investigation of the spin crossover compound \rm [Fe(ptz)6](BF4)2 which undergoes an abrupt thermal spin-transition from high-spin (HS) S=2 to low-spin (LS) S=0 around 135 K. The HS magnetic state can be restored at low temperature under blue/green light irradiation. We have developed a specially designed optical setup for neutron scattering to address the magnetic properties of the light-induced HS state. By using neutron diffraction, we demonstrate that significant HS/LS ratios (of up to 60 \%) can be obtained with this experimental setup on a sample volume considered large (400 mg), while a complete recovery of the LS state is achieved using near infrared light. With inelastic neutron scattering (INS) we have observed, for the first time in a photo-induced phase, magnetic transitions arising from the metastable HS S=2 state split by crystal field and spin-orbit coupling. We interpret the INS data assuming a spin-only model with a zero-field splitting (ZFS) of the S=2 ground state. The obtained parameters are D \approx -1.28 \pm 0.03 meV and |E| \approx 0.08 \pm 0.03 meV. The present results show that in situ magnetic inelastic neutron scattering investigations on a broad range of photomagnetic materials are now possible

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

Graphical explanation in an expert system for Space Station Freedom rack integration

The rationale and methodology used to incorporate graphics into explanations provided by an expert system for Space Station Freedom rack integration is examined. The rack integration task is typical of a class of constraint satisfaction problems for large programs where expertise from several areas is required. Graphically oriented approaches are used to explain the conclusions made by the system, the knowledge base content, and even at more abstract levels the control strategies employed by the system. The implemented architecture combines hypermedia and inference engine capabilities. The advantages of this architecture include: closer integration of user interface, explanation system, and knowledge base; the ability to embed links to deeper knowledge underlying the compiled knowledge used in the knowledge base; and allowing for more direct control of explanation depth and duration by the user. The graphical techniques employed range from simple statis presentation of schematics to dynamic creation of a series of pictures presented motion picture style. User models control the type, amount, and order of information presented

Age and size at maturity: sex, environmental variability and developmental thresholds

In most organisms, transitions between different life-history stages occur later and at smaller sizes as growth conditions deteriorate. Day and Rowe recently proposed that this pattern could be explained by the existence of developmental thresholds (minimum sizes or levels of condition below which transitions are unable to proceed). The developmental-threshold model predicts that the reaction norm of age and size at maturity will rotate in an anticlockwise manner from positive to a shallow negative slope if: (i) initial body size or condition is reduced; and/or (ii) some individuals encounter poor growth conditions at increasingly early developmental stages. We tested these predictions by rearing replicated populations of soil mites Sancassania berlesei (Michael) under different growth conditions. High-food environments produced a vertical relationship between age and size at maturity. The slope became increasingly shallow as food was reduced. By contrast, high food in the maternal environment reduced the slope of the reaction norm of age and size at maturity, whereas low food increased it. Overall, the reaction norm of age and size at maturity in S. berlesei was significantly nonlinear and differed for males and females. We describe how growth conditions, mother's environment and sex determine age and size at maturity in S. berlesei