Valentini has been working on an extension of the causal interpretation of quantum theory. This interpretation had been proposed in conceptual terms in 1927 by Louis de Broglie, was independently re-discovered by David Bohm who brought it to a complete and systematic form in 1952, and was expanded on by Bohm and Hiley. Emphasizing de Broglie's contribution, Valentini has consistently referred to the causal interpretation of quantum mechanics underlying his work as the "de Broglie–Bohm theory".
Quantum equilibrium, locality and uncertainty
In 1991, Valentini provided indications for deriving the quantum equilibrium hypothesis which states that in the frame work of the pilot wave theory. Valentini showed that the relaxation → may be accounted for by a H-theorem constructed in analogy to the Boltzmann H-theorem of statistical mechanics. Valentini showed that his expansion of the De Broglie–Bohm theory would allow "signal nonlocality" for non-equilibrium cases in which ≠. According to Valentini, the universe is fundamentally nonlocal, and quantum theory merely describes a special equilibrium state in which nonlocality is hidden in statistical noise. He furthermore showed that an ensemble of particles with known wave function and known nonequilibrium distribution could be used to perform, on another system, measurements that violate the uncertainty principle. In 1992, Valentini extended pilot wave theory to spin- fields and to gravitation.
Background and implications
Valentini has been described as an "ardent admirer of de Broglie". He noted that "de Broglie emphasized an underlying 'mechanical' picture: particles were assumed to be singularities of physical waves in space". He emphasized that de Broglie, with the assistance of Erwin Schrödinger, had constructed pilot wave theory, but later abandoned it in favor of quantum formalism. Valentini's derivation of the quantum equilibrium hypothesis was criticized by Detlef Dürr and co-workers in 1992, and the derivation of the quantum equilibrium hypothesis has remained a topic of active investigation. "Signal nonlocality", which is forbidden in orthodox quantum theory, would allow nonlocal quantum entanglement to be used as a stand-alone communication channel without the need of a classical light-speed limited retarded signal to unlock the entangled message from the sender to the receiver. This would be a major revolution in physics and would possibly make the cosmic landscapestring theory Popper falsifiable.
Publications
;Book:
Guido Bacciagaluppi, Antony Valentini: Quantum theory at the crossroads: Reconsidering the 1927 Solvay Conference, Cambridge Univ. Press, 2009,
;Articles:
Antony Valentini, Hans Westman: Dynamical origin of quantum probabilities, Proceedings of the Royal Society A 8, vol. 461, no. 2053 , January 2005,
Antony Valentini: Subquantum information and computation, 2002, Pramana Journal of Physics, vol. 59, no. 2, August 2002,
Antony Valentini: Signal-locality in hidden-variables theories, Physics Letters A, vol. 297, no. 5-6, 20 May 2002, p. 273-278
Antony Valentini: Hidden Variables, Statistical Mechanics and the Early Universe, Chance in Physics, Lecture Notes in Physics, Springer 2001, Volume 574/2001, 165-181,
Antony Valentini: On Galilean and Lorentz invariance in pilot-wave dynamics, Physics Letters A, 228, 215–222, 1997
Antony Valentini: Pilot-wave theory of fields, gravitation and cosmology, in: James T. Cushing, Arthur Fine, Sheldon Goldstein : Bohmian mechanics and quantum theory: an appraisal, Kluwer Academic Publishers, 1996,
Antony Valentini: On the Pilot-Wave Theory of Classical, Quantum and Subquantum Physics, Ph.D. Thesis, ISAS, Trieste 1992
Antony Valentini: Signal-locality, uncertainty, and the sub-quantum H-theorem, II, Physics Letters A, vol. 158, no. 1, 1991,
Antony Valentini: Signal-locality, uncertainty, and the sub-quantum H-theorem, I, Physics Letters A, vol. 156, no. 5, 1991