Snell’s law for the Schwarzschild black hole

Abstract

The Wheeler equation, for electromagnetic disturbances in a gravitational field, was found by Fiziev to have exact solutions both above and below the event horizon, in the form of waves propagating both inwardly and outwardly. This observation can be interpreted and verified from the optical point of view, entirely on the basis of the Schwarzschild metric for length contraction and time dilation, in order to derive a differential version of Snell's law for the Schwarzschild black hole. It reveals interesting physics, including the correct amount of light deflection by the Sun, internal and external Oppenheimer-Snyder cones of the black hole, properties of its phonon sphere and the conclusion that light-rays are kept below the horizon by length contraction and time dilation rather than deflection.

A shortcut tour of quantum control methods for modern quantum technologies

“…We have used the described STA method in order to maximize entanglement between coupled spins [51] and in a bosonic Josephson junction [57], while we have evaluated its performance for the three-level STIRAP system under the presence of Ornstein-Uhlenbeck noise processes in the energy levels [58]. Other recent works exploit the advantages of this method or its generalizations for quantum state transfer [59][60][61], quantum computation [62][63][64], and sensing [65]. Note that the presented STA method is a specific example of the more general inverse engineering method [12,17,66,67], where the quantum trajectory is prescribed first, eq.…”

CSL reduction rate for rigid bodies

“…Since the CSL model (like all collapse models) makes different predictions from quantum mechanics, it can be tested against it, allowing to bound its parameters. In recent years, experimental interest increased in this direction and a steady improvement on bounding its parameters has been achieved [4][5][6][7][8][9][10][11].…”

“…Since the CSL model (like all collapse models) makes different predictions from quantum mechanics, it can be tested against it, allowing to bound its parameters. In recent years, experimental interest increased in this direction and a steady improvement on bounding its parameters has been achieved [4][5][6][7][8][9][10][11].Previous investigations found that the CSL effects on rigid bodies display an important contribution from the geometry of the object [12][13][14]. However, how exactly the CSL collapse rate depends on the geometry of the body and on the superposition distance has never been analyzed in detail.…”