From white elephant to Nobel Prize: Dennis Gabor’s wavefront reconstruction

Dennis Gabor devised a new concept for optical imaging in 1947 that went by a variety of names over the following decade: holoscopy, wavefront reconstruction, interference microscopy, diffraction microscopy and Gaboroscopy. A well-connected and creative research engineer, Gabor worked actively to publicize and exploit his concept, but the scheme failed to capture the interest of many researchers. Gabor’s theory was repeatedly deemed unintuitive and baffling; the technique was appraised by his contemporaries to be of dubious practicality and, at best, constrained to a narrow branch of science. By the late 1950s, Gabor’s subject had been assessed by its handful of practitioners to be a white elephant. Nevertheless, the concept was later rehabilitated by the research of Emmett Leith and Juris Upatnieks at the University of Michigan, and Yury Denisyuk at the Vavilov Institute in Leningrad. What had been judged a failure was recast as a success: evaluations of Gabor’s work were transformed during the 1960s, when it was represented as the foundation on which to construct the new and distinctly different subject of holography, a re-evaluation that gained the Nobel Prize for Physics for Gabor alone in 1971. This paper focuses on the difficulties experienced in constructing a meaningful subject, a practical application and a viable technical community from Gabor’s ideas during the decade 1947-1957

Spherically Symmetric Black Hole Formation in Painlev\'e-Gullstrand Coordinates

We perform a numerical study of black hole formation from the spherically symmetric collapse of a massless scalar field. The calculations are done in Painlev\'e-Gullstrand (PG) coordinates that extend across apparent horizons and allow the numerical evolution to proceed until the onset of singularity formation. We generate spacetime maps of the collapse and illustrate the evolution of apparent horizons and trapping surfaces for various initial data. We also study the critical behaviour and find the expected Choptuik scaling with universal values for the critical exponent and echoing period consistent with the accepted values of $\gamma=0.374$ and $\Delta = 3.44$, respectively. The subcritical curvature scaling exhibits the expected oscillatory behaviour but the form of the periodic oscillations in the supercritical mass scaling relation, while universal with respect to initial PG data, is non-standard: it is non-sinusoidal with large amplitude cusps.Comment: 12 pages, 7 figure

Spectrum of stochastic evolution operators: Local matrix representation approach

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The result are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.Comment: 7 pages, 2 figures, Third approach to a problem we considered in chao-dyn/9807034 and chao-dyn/981100