arXiv subjects
Publications and source records attributed to Karl Svozil.
Insofar as Sir Karl Raimund Popper's writings deal with political statements, they are evident; yet insofar as they deal with scientific issues, they are misleading. If applied to the concrete implementation of science, such as distribution of research funds and (peer) review, they would seriously impede progress.
Due to the nonvanishing average photon population of the squeezed vacuum state, finite corrections to the scattering matrix are obtained. The lowest order contribution to the electron mass shift for a one mode squeezed vacuum state is given by $δm(Ω, s)/m=α(2/π)(Ω/m)^2\sinh^2(s)$, where $Ω$ and $s$ stand for the mode frequency and the squeeze parameter and $α$ for the fine structure constant, respectively.
In this speculative note some of the conceivable options of supercavitation in the vacuum of quantized field theory are discussed. The resulting modes of propagation could in principle be faster than the velocity of light in unbounded space-time.
Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments in quantum information theory may have appropriate formalizations in the automaton context.
Quantum mechanics is more than the derivation of straightforward theorems about vector spaces, Hilbert spaces and functional analysis. In order to be applicable to experiment and technology, those theorems need interpretation and meaning. Interpretation is to the formalism what a scaffolding in architecture and building construction is to the completed building.
Quantum information is radically different from classical information in that the quantum formalism (Hilbert space) makes necessary the introduction of irreducible ``nits,'' n being an arbitrary natural number (bigger than one), not just bits.
The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the Cartesian and polar decomposition of arbitrary normal operators and the possibility to operationalize the corresponding observables. Thereby we review and emphasize the use of observables which maximally represent the context. (ii) In the second part, we discuss Pitowsky polytopes for automaton logic as well as for generalized urn models and evaluate methods to find the resulting Boole-Bell type (in)equalities. (iii) Finally, so-called ``parameter cheats'' are introduced, whereby parameters are transformed bijectively and nonlinearly in such a way that classical systems mimic quantum correlations and vice versa. It is even possible to introduce parameter cheats which violate the Boole-Bell type inequalities stronger than quantum ones, thereby trespassing the Tsirelson limit. The price to be paid is nonuniformity.
Consequences of the basic and most evident consistency requirement-that measured events cannot happen and not happen at the same time-are shortly reviewed. Particular emphasis is given to event forecast and event control. As a consequence, particular, very general bounds on the forecast and control of events within the known laws of physics are derived. These bounds are of a global, statistical nature and need not affect singular events or groups of events.
We review and extend recent findings of Godsil and Zaks, who published a constructive coloring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the sphere, exactly one ray is red, white and black. They also showed that any consistent coloring of the real sphere requires an additional color. We discuss some of the consequences for the Kochen-Specker theorem.
Classical Pitowsky correlation polytopes are reviewed with particular emphasis on the Minkowski-Weyl representation theorem. The inequalities representing the faces of polytopes are Boole's ``conditions of possible experience.'' Many of these inequalities have been discussed in the context of Bell's inequalities. We introduce CddIF, a Mathematica package created as an interface between Mathematica and the cdd program by Komei Fukuda, which represents a highly efficient method to solve the hull problem for general classical correlation polytopes.
We consider the problem to single out a particular state among $2^n$ orthogonal pure states. As it turns out, in general the optimal strategy is not to measure the particles separately, but to consider joint properties of the $n$-particle system. The required number of propositions is $n$. There exist $2^n!$ equivalent operational procedures to do so. We enumerate some configurations for three particles, in particular the Greenberger-Horne-Zeilinger (GHZ)- and W-states, which are specific cases of a unitary transformation For the GHZ-case, an explicit physical meaning of the projection operators is discussed.
In an experiment featuring nonlinear optics, delayed choice and EPR-type correlations, the possibility of faster-than-light communication appears not totally implausible. Attempts are put forward and discussed to refute this claim.
Rational agents acting as observers use ``knowables'' to construct a vision of the outside world. Thereby, they are bound by the information exchanged with what they consider to be objects. The cartesian cut or, in modern terminology, the interface mediating this exchange, is again a construction. It serves as a ``scaffolding,'' an intermediate construction capable of providing the necessary conceptual means. An attempt is made to formalize the interface, in particular the quantum interface and quantum measurements, by a symbolic information exchange. A principle of conservation of information is reviewed and a measure of information flux through the interface is proposed.
We explore correlation polytopes to derive a set of all Boole-Bell type conditions of possible classical experience which are both maximal and complete. These are compared with the respective quantum expressions for the Greenberger-Horne-Zeilinger (GHZ) case and for two particles with spin state measurements along three directions.
In the information interpretation of quantum mechanics, information is the most fundamental, basic entity. Every quantized system is associated with a definite discrete amount of information (cf. Zeilinger). This information content remains constant at all times and is permutated one-to-one throughout the system evolution. What is interpreted as measurement is a particular type of information transfer over a fictitious interface. The concept of a many-to-one state reduction is not a fundamental one but results from the practical impossibility to reconstruct the original state after the measurement.
Special relativity theory is generalized to two or more ``maximal'' signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more ``light'' cones due to the a ``birefringent'' vaccum, and (iii) as a further extension of conventionality beyond synchrony.
Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables $\{J_1^2,J_2^2,J_3^2\}$ and $\{\bar J_1^2, \bar J_2^2,J_3^2\}$ with $[J_1^2,\bar J_1^2]\neq 0$ are measured. The outcomes of measurements of $J_3^2$ (via $J_1^2,J_2^2$) and $J_3^2$ (via $\bar J_1^2,\bar J_2^2$) are compared. Although formally $J_3^2$ is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether $J_1^2$ or $\bar J_1^2$ is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.