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Rothschild lecture: Superoscillations and weak measurement

Presented by: 
M Berry [H H Wills Physics Laboratory, University of Bristol]
Monday 3rd December 2012 - 17:00 to 18:00
INI Seminar Room 1
Session Title: 
Topological gauge theories and particle physics
Session Chair: 
Mark Hindmarsh
Band-limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals. Where such ‘superoscillations’occur, functions are exponentially weak. In typical monochromatic optical fields, substantial fractions of the domain (one-third in two dimensions) are superoscillatory. Superoscillations have implications for signal processing, and raise the possibility of sub-wavelength resolution microscopy without evanescent waves. In quantum mechanics, superoscillations correspond to weak measurements, suggesting ‘weak values’ of observables (e.g photon momenta) far outside the range represented in the quantum state. A weak measurement of neutrino speed could lead to a superluminal result without violating causality, but the effect is too small to explain the speed recently claimed in a recent (and now-discredited) experminent.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons