We present the theory, the experimental evidence and fundamental physical consequences concerning the existence of families of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞, which are solutions of the homogeneuous wave equation, the Maxwell equations, and Dirac, Weyl, and Klein-Gordon equations.

In a two-channel interference experiment such as that considered in the preceding companion paper, a quantum may be localizable predominantly in one channel by a time-coincident experiment on a correlated quantum. The Copenhagen interpretation of quantum mechanics then requires a coincidence intensity prediction having the same reduced interference between channels as if the probability amplitude in the other channel had been attenuated by a filter. The quantum mechanical treatment of correlated systems originated by von Neumann does predict this reduced interference, (...) but avoids requiring a resulting direct locality violation by predicting that this reduced interference also occurs in a simple singles intensity observation. In contrast, de Broglie's locally causal interpretation of quantum mechanics requires that the experiment on the remote correlated system cannot change the amplitudes or phase relationship of coherent space-time wave propagating through the two channels, so that the full classical optics interference effect should be predicted for both singles and coincidence intensities. (shrink)

We present here solutions of a non-linear Schrödinger equation in presence of an arbitrary linear external potential. The non-linearity expresses a self-focusing interaction. These solutions are the product of the pilot wave with peaked solitons the velocity of which obeys the guidance equation derived by Louis de Broglie in 1926. The degree of validity of our approximations increases when the size of the soliton decreases and becomes negligible compared to the typical size over which the pilot wave varies. We discuss (...) the possibility to reveal their existence by implementing a humpty-dumpty Stern-Gerlach interferometer in the mesoscopic regime. (shrink)