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Paul Gauthier

Publications and source records attributed to Paul Gauthier.

3 recordsLinked to original sources

Complementarity Test with Unmeasured, Permanently Inaccessible Path Markers

In prior complementarity tests, path markers were measured and remained causally accessible, leaving the collapse-locality loophole open. We address this loophole using a quantum eraser that isolates the encoding of path information in the joint quantum state from its later measurement and causal accessibility. We launch idler photons -- the sole path markers for entangled signal photons in an interferometer -- on outgoing null trajectories while the joint state remains in a coherent superposition of both interferometer path alternatives. Our flat $Λ$CDM transmission model predicts that 73-82% of launched idlers will propagate forever without absorption, scattering, or environmental path-record formation. For these modeled survivors, each path marker remains perpetually unmeasured, and propagation along its outgoing trajectory precludes later causal contact with its interferometric record. Unconditioned signal detections show no statistically significant launch-induced change in interference, as standard quantum theory predicts. Normalized to the modeled survivors, the 95% confidence upper bound on any launch-induced fringe is 0.16 of full restoration.

quant-ph↗

Spherical arc-length as a global conformal parameter for analytic curves in the Riemann sphere

We prove that for every analytic curve in the complex plane, Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in Euclidean n-space and complex n-space and we discuss the situation of curves in the Riemann sphere.

math.CV↗

Dirichlet approximation and universal Dirichlet series

We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of universal Dirichlet series.

math.CV↗