Replies are given to arguments advanced in this journal that claim to show that it is to nonlinear classical mechanics rather than quantum mechanics that one must look for the physical underpinnings of consciousness. ∗This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy und...

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanic...

The Casimir energy for a compact dielectric sphere is considered in a novel way, using the quantum statistical method introduced by Høye-Stell and others. Dilute media are assumed. It turns out that this method is a very powerful one: we are actually able to derive an expression for the Casimir energy that contains also the negative part resulting from the attractive van der Waals forces betwee...

We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter introduced in [1] is shown to provide the conditions under which quantum statistical distributions can be derived from the quantum dynamics of a classical ergodic Hamiltoni...

In this investigation, we have suggested a special two-slit experiment which can distinguish between standard and Bohmian quantum mechanics, even at the statistical level. At the first step, we have shown that observable individual predictions at suitable time intervals, obtained from these theories, are inconsistent. But, at the statistical level, they are consistent as was expected. Then, usi...

Abstract: An experimental test of the “special state” theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern–Gerlach setup. The “special state” theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this arti...

In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum mechanics itself—that is, the formation of operators. We then investigate all the subtleties involved in forming operators from their classical counterparts. We s...

A statistical multi-parameter estimation theory for quantum pure state models is presented, based on right logarithmic derivatives. It gives a new information theoretical insight into the coherent states in quantum mechanics.

Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems are matters of intensive investigation and debate. This essay review has been prepared at the occasion of awarding the 'Mexico Prize for Science and Technol...