Resolution-scale relativistic formulation of non-differentiable mechanics

This article motivates and presents the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. It stems from the scale relativity proposal to extend the principle of relativity to resolution-scale transformations, which leads to considering non-differentiable dynamical paths. We first define a complex scale-covariant time-differential operator and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator taken as an example reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the rest of the paper, which shows Schrodinger's equation to be a reformulation of Newton's fundamental relation of dynamics as generalized to non-differentiable geometries and leads to an alternative interpretation of the other axioms of standard quantum mechanics in a coherent picture. This exercise validates the scale relativistic approach and, at the same time, it allows to envision macroscopic chaotic systems observed at resolution time-scales exceeding their horizon of predictability as candidates in which to search for quantum-like dynamics and structures.Comment: 30 pages, 4 figure

Stellar intensity interferometry: Optimizing air Cherenkov telescope array layouts

Kilometric-scale optical imagers seem feasible to realize by intensity interferometry, using telescopes primarily erected for measuring Cherenkov light induced by gamma rays. Planned arrays envision 50--100 telescopes, distributed over some 1--4 km$^2$. Although array layouts and telescope sizes will primarily be chosen for gamma-ray observations, also their interferometric performance may be optimized. Observations of stellar objects were numerically simulated for different array geometries, yielding signal-to-noise ratios for different Fourier components of the source images in the interferometric $(u,v)$-plane. Simulations were made for layouts actually proposed for future Cherenkov telescope arrays, and for subsets with only a fraction of the telescopes. All large arrays provide dense sampling of the $(u,v)$-plane due to the sheer number of telescopes, irrespective of their geographic orientation or stellar coordinates. However, for improved coverage of the $(u,v)$-plane and a wider variety of baselines (enabling better image reconstruction), an exact east-west grid should be avoided for the numerous smaller telescopes, and repetitive geometric patterns avoided for the few large ones. Sparse arrays become severely limited by a lack of short baselines, and to cover astrophysically relevant dimensions between 0.1--3 milliarcseconds in visible wavelengths, baselines between pairs of telescopes should cover the whole interval 30--2000 m.Comment: 12 pages, 10 figures; presented at the SPIE conference "Optical and Infrared Interferometry II", San Diego, CA, USA (June 2010

Stellar Intensity Interferometry: Astrophysical targets for sub-milliarcsecond imaging

Intensity interferometry permits very long optical baselines and the observation of sub-milliarcsecond structures. Using planned kilometric arrays of air Cherenkov telescopes at short wavelengths, intensity interferometry may increase the spatial resolution achieved in optical astronomy by an order of magnitude, inviting detailed studies of the shapes of rapidly rotating hot stars with structures in their circumstellar disks and winds, or mapping out patterns of nonradial pulsations across stellar surfaces. Signal-to-noise in intensity interferometry favors high-temperature sources and emission-line structures, and is independent of the optical passband, be it a single spectral line or the broad spectral continuum. Prime candidate sources have been identified among classes of bright and hot stars. Observations are simulated for telescope configurations envisioned for large Cherenkov facilities, synthesizing numerous optical baselines in software, confirming that resolutions of tens of microarcseconds are feasible for numerous astrophysical targets.Comment: 12 pages, 4 figures; presented at the SPIE conference "Optical and Infrared Interferometry II", San Diego, CA, USA (June 2010

Toward a revival of stellar intensity interferometry

Journal ArticleBuilding on technological developments over the last 35 years, intensity interferometry now appears a feasible option by which to achieve diffraction-limited imaging over a square-kilometer synthetic aperture. Upcoming Atmospheric Cherenkov Telescope projects will consist of up to 100 telescopes, each with ~100m2 of light gathering area, and distributed over ~lkm2 . These large facilities will offer thousands of baselines from 50m to more than 1km and an unprecedented (u,v) plane coverage. The revival of interest in Intensity Interferometry has recently led to the formation of a IAU working group. Here we report on various ongoing efforts towards implementing modern Stellar Intensity Interferometry