We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a (...) new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof. (shrink)

Cet article établit que John Toland, né à la fin du xvne siècle, partageait la culture des Irlandais de langue maternelle gaélique. Il met en évidence l'intérêt de J. Toland, tout au long de sa vie, pour la culture et les langues celtes et repère l'influence de celles-ci sur le contenu et la présentation de ses idées peu orthodoxes.

On 18 September 1697, Christainity not Mysterious was burned in Dublin by order of Parliament. This edition of the text is now available 300 years later and also includes John Toland's defences of the work and eight critical essays.