5,760 research outputs found
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
- …