"All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dickand Harry thinks he knows it, but he is mistaken." (Albert Einstein, 1951) We report on the simultaneous determination of complementary wave and particle
We respond to criticism of our paper "Paradox in Wave-Particle Duality for NonPerturbative Measurements". We disagree with Steuernagel's derivation of the visibility of the Afshar experiment. To calculate the fringe visibility, Steuernagel utilizes two different experimental situations, i.e. the wire grid in the pattern minima and in the pattern maxima. In our assessment, this procedure cannot lead to the correct result for the complementarity properties of a wave-particle in one particular experimental set-up.
The Afshar experiment is a relatively simple two-slit experiment with results that appear to show a discrepancy with the predictions of Bohr's Principle of Complementarity. We report on the results of a calculation using a simpler but equivalent set-up called the KEY WORDS: principle of complementarity; wave-particle duality; non-perturbative measurements; double-slit experiment; Afshar experiment.
In an analysis of the Afshar experiment R.E. Kastner points out that the selection system used in this experiment randomly separates the photons that go to the detectors, and therefore no which-way information is obtained. In this paper we present a modified but equivalent version of the Afshar experiment that does not contain a selection device.The double-slit is replaced by two separate coherent laser beams that overlap under a small angle. At the intersection of the beams an interference pattern can be inferred in a non-perturbative manner, which confirms the existence of a superposition state. In the far field the beams separate without the use of a lens system. Momentum conservation warranties that which-way information is preserved. We also propose an alternative sequence of Stern-Gerlach devices that represents a close analogue to the Afshar experimental set up.
The classical tautochrone problem involves motion along curves caused by the special potential V(y)ϭmgy. We use fractional derivatives to find tautochrone curves under arbitrary potentials V(y). We generalize these further to potentials that are functions of two variables V(x,y). An Appendix gives intuitive motivation for the fractional calculus employed.
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