The Hatsopoulos-Gyftopoulos resolution of the Schroedinger-Park paradox about the concept of "state" in quantum statistical mechanics

A seldom recognized fundamental difficulty undermines the concept of individual ``state'' in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by E. Schroedinger in 1936 and perused by J.L. Park, Am. J. Phys., Vol. 36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resolution proposed in 1976 by G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol. 6, 15, 127, 439, 561 (1976).Comment: RevTeX4, 7 pages, corrected a paragraph and added an example at page 3, to appear in Mod. Phys. Lett.

Bell's Theorem and Chemical Potential

Chemical potential is a property which involves the effect of interaction between the components of a system, and it results from the whole system. In this paper, we argue that for two particles which have interacted via their spins and are now spatially separated, the so-called Bell's locality condition implies that the chemical potential of each particle is an individual property. Here is a point where quantum statistical mechanics and the local hidden variable theories are in conflict. Based on two distinct concepts of chemical potential, the two theories predict two different patterns for the energy levels of a system of two entangled particles. In this manner, we show how one can distinguish the non-separable features of a two-particle system.Comment: 11 pages,1 figure, To appear in J. Phy. A: Math. Gen., Special Issue: Foundations of Quantum Theor

Joint reality and Bell inequalities for consecutive measurements

Some new Bell inequalities for consecutive measurements are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive hypothesis advantageously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be expected to be more severe than in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations, in which the new inequalities could be tested, are roughly considered.Comment: 7 pages, no figure

Relation between the Dynamics of the Reduced Purity and Correlations

A general property of the relation between the dynamics of the reduced purity and correlations is investigated in quantum mechanical systems. We show that a non-zero time-derivative of the reduced purity of a system implies the existence of non-zero correlations with its environment under any unbounded Hamiltonians with finite variance. This shows the role of local dynamical information on the correlations, as well as the role of correlations in the mechanism of purity change.Comment: 7 page

This elusive objective existence

Zurek's existential interpretation of quantum mechanics suffers from three classical prejudices, including the belief that space and time are intrinsically and infinitely differentiated. They compel him to relativize the concept of objective existence in two ways. The elimination of these prejudices makes it possible to recognize the quantum formalism's ontological implications - the relative and contingent reality of spatiotemporal distinctions and the extrinsic and finite spatiotemporal differentiation of the physical world - which in turn makes it possible to arrive at an unqualified objective existence. Contrary to a widespread misconception, viewing the quantum formalism as being fundamentally a probability algorithm does not imply that quantum mechanics is concerned with states of knowledge rather than states of Nature. On the contrary, it makes possible a complete and strongly objective description of the physical world that requires no reference to observers. What objectively exists, in a sense that requires no qualification, is the trajectories of macroscopic objects, whose fuzziness is empirically irrelevant, the properties and values of whose possession these trajectories provide indelible records, and the fuzzy and temporally undifferentiated states of affairs that obtain between measurements and are described by counterfactual probability assignments.Comment: To appear in IJQI; 21 pages, LaTe

Undecidability as solution to the problem of measurement: fundamental criterion for the production of events

In recent papers we put forth a new interpretation of quantum mechanics, colloquially known as ``the Montevideo interpretation''. This interpretation is based on taking into account fundamental limits that gravity imposes on the measurement process. As a consequence one has that situations develop where a reduction process is undecidable from an evolution operator. When such a situation is achieved, an event has taken place. In this paper we sharpen the definition of when and how events occur, more precisely we give sufficient conditions for the occurrence of events. We probe the new definition in an example. In particular we show that the concept of undecidability used is not ``FAPP'' (for all practical purposes), but fundamental.Comment: 10 pages, contributed to the Castagnino Festschrif

Purification of Mixed State with Closed Timelike Curve is not Possible

In ordinary quantum theory any mixed state can be purified in an enlarged Hilbert space by bringing an ancillary system. The purified state does not depend on the state of any extraneous system with which the mixed state is going to interact and on the physical interaction. Here, we prove that it is not possible to purify a mixed state that traverses a closed time like curve (CTC) and allowed to interact in a consistent way with a causality-respecting (CR) quantum system in the same manner. Thus, in general for arbitrary interactions between CR and CTC systems there is no universal 'Church of the larger Hilbert space' for mixed states with CTC. This shows that in quantum theory with CTCs there can exist 'proper' and 'improper' mixtures.Comment: Latex2e, No Figs, 4 + pages, An error corrected, Results unchange

Tests of Basic Quantum Mechanics in Oscillation Experiments

According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the density operator itself. The presence of such modifications of quantum theory can be tested in long baseline oscillation experiments.Comment: 8 pages, LaTeX; no macros neede