Quantum theory without Hilbert spaces

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Kopenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems.Comment: 32 pages, Latex, 4 figures. Small changes in the revised version, comments and references added; essentially the version to appear in Found. Phy

Mind-body interaction and modern physics

The idea that mind and body are distinct entities that interact is often claimed to be incompatible with physics. The aim of this paper is to disprove this claim. To this end, we construct a broad mathematical framework that describes theories with mind-body interaction (MBI) as an extension of current physical theories. We employ histories theory, i.e., a formulation of physical theories in which a physical system is described in terms of (i) a set of propositions about possible evolutions of the system and (ii) a probability assignment to such propositions. The notion of dynamics is incorporated into the probability rule. As this formulation emphasises logical and probabilistic concepts, it is ontologically neutral. It can be used to describe mental `degrees of freedom' in addition to physical ones. This results into a mathematical framework for psycho-physical interaction (ΨΦI formalism). Interestingly, a class of ΨΦI theories turns out to be compatible with energy conservation

Cleaning of water-gilded surfaces using hydro- and solvent-gels

This paper describes the implementation of three customized gels on a 19th century panel painting for the removal of its degraded natural resin varnish from a water-gilded surface and a complex solvent-sensitive stratigraphic construction over the gilded substrate. At first, the varnish was unsoiled with a typical hydrogel that was composed of an aqueous phase buffered at pH 5.5 with sodium acetate, poly(ethylene glycol) p-(1,1,3,3-tetramethylbutyl)-phenyl ether surfactant and hydroxy-prorylmethyl cellulose. The removal of the entire aged varnish was facilitated with a microemulsion of an aqueous phase buffered at pH 8.5 with triethanolaminate, a fatty phase of a mineral spirit - benzyl alcohol solution and a polyoxy-ethylene(23)lauryl ether surfactant, altogether incorporated in a viscous gel generated from the dissolution of a polyacrylic acid in poly(oxy-1,2-ethanediyl) cocoalkylamine surfactant. The third gel, which was based on a polyacrylic acid of higher viscosity and incorporating a microemulsion of the same aqueous phase (pH 8.5) as in the second gel, and a fatty phase made of benzyl alcohol and a polyoxyethylene(23)lauryl ether surfactant, enabled the selective removal of the degraded varnish over the elaborate gilded area with a composite stratigraphy over the golden leaf. Fourier transform infrared spectroscopy and UV fluorescence imaging were employed for the analysis of the aged varnish and the monitoring of the cleaning procedure, respectively. The conservation procedure determined the effectiveness of the customized gels employed for this special implementation. The fine preservation of the water-gildings and of the complex solvent-sensitive stratigraphic construction of the painted surface was a satisfactory outcome