According to Classical Mechanics (still nowadays able to launch space laboratories at the other side of the solar system with the highest precision), any particle beam may be converged into a single point-like focus, by the refractive role of a suitable lens system (figure A). Quantum Mechanics asserts, on the contrary, that any particle beam is piloted by a “matter wave”, whose diffractive effect shall generally lead to the formation, due to  the focalizing lens system, of a narrow ( but not pointlike) focal region. And so far… so well. On the basis, however, of the well-known Schrödinger equation, which it isn’t able to exactly solve, the official Quantum Theory attributes to its approximate solutions a merely statistical and probabilistic interpretation. Already in principle, no particle trajectory may exist – not even in God’s  mind! Einstein himself rejected this opinion, maintaining that “God doesn’t play dice with the Universe”  (handwritten letter sent in 1945 to Paul Epstein, a Caltech theoretical physicist). And we have found these “impossible” trajectories solving Schrödinger’s equation: here they are, in figure B!


Orefice, A., Giovanelli, R., Ditto, D. Primary Assumptions and Guidance Laws in Wave Mechanics, Journal of Applied Mathematics and Physics, 6, 2621 (2018). DOI: 10.4236/jamp.2018.612218

Orefice, A., Giovanelli, R., Ditto, D. The Dynamics of Wave-Particle Duality, Journal of Applied Mathematics and Physics, 6, 1840 (2018). DOI: 10.4236/jamp.2018.69157