Marek Czachor

Quantum aspects of semantic analysis and symbolic artificial intelligence

A zipper tooth has a body portion with an opening at one end for connection to a tape to form a zipper stringer of a slide fastener. At the other end of the body portion is an engaging head. Just behind the engaging head are a pair of grooves, one on each side of the body portion. The grooves are contoured to accommodate portions of the engaging heads of other similar zipper teeth. At each end of each of the grooves are outwardly extending tapered projections. The projections are rolled over to provide endwalls for the grooves so that a cavity is formed for locking accepting portions of engaging heads of other zipper teeth.

Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles

Two aspects of the relativistic version of the Einstein-Podolsky-Rosen-Bohm (EPRB) experiment with massive particles are discussed: (a) a possibility of using the experiment as an implicit test of a relativistic center-of-mass concept, and (b) influence of the relativistic effects on degree of violation of the Bell inequality. The nonrelativistic singlet state average 〈\ensuremath{\psi}|a\ensuremath{\cdot}\ensuremath{\sigma}\ensuremath{\bigotimes}b\ensuremath{\cdot}\ensuremath{\sigma}|\ensuremath{\psi}〉=-a\ensuremath{\cdot}b is relativistically generalized by defining spin via the relativistic center-of-mass operator. The corresponding EPRB average contains relativistic corrections which are stronger in magnitude than standard relativistic phenomena such as the time delay, and can be measured in Einstein-Podolsky-Rosen-Bohm-type experiments with relativistic massive spin- particles. The degree of violation of the Bell inequality is shown to depend on the velocity of the pair of spin- particles with respect to the laboratory. Experimental confirmation of the relativistic formula would indicate that for relativistic nonzero-spin particles centers of mass and charge do not coincide. The result may have implications for quantum cryptography based on massive particles.

Relativistic Bennett-Brassard cryptographic scheme, relativistic errors, and how to correct them

The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least one of them linearly polarized. The problem is that linear polarization formulated in terms of helicities is not a relativistically covariant notion: State which is linearly polarized in one reference frame becomes depolarized in another one. We show that a relativistically moving receiver of information should define linear polarization with respect to projection of Pauli-Lubanskis vector in a principal null direction of the Lorentz transformation which defines the motion, and not with respect to the helicity basis. Such qubits do not depolarize.

Darboux-integrable nonlinear Liouville–von Neumann equation

A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.

Towards a quantum evolutionary scheme: Violating Bell's inequalities in language

We show the presence of genuine quantum structures in human language. The neo-Darwinian evolutionary scheme is founded on a probability structure that satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate quantum-like evolutionary change. In earlier research we revealed quantum structures in processes taking place in conceptual space. We argue that the presence of quantum structures in language and the earlier detected quantum structures in conceptual change make the neo-Darwinian evolutionary scheme strictly too limited for Evolutionary Epistemology. We sketch how we believe that evolution in a more general way should be implemented in epistemology and conceptual change, but also in biology, and how this view would lead to another relation between both biology and epistemology.

Thermostatistics based on Kolmogorov–Nagumo averages: unifying framework for extensive and nonextensive generalizations

Abstract We show that extensive thermostatistics based on Renyi entropy and Kolmogorov–Nagumo averages can be expressed in terms of Tsallis nonextensive thermostatistics. We use this correspondence to generalize thermostatistics to a large class of Kolmogorov–Nagumo means and suitably adapted definitions of entropy. As an application, we reanalyze linguistic data discussed in a paper by Montemurro.

Comment on "Quantum Entropy and Special Relativity"

Two subtleties of this paper are discussed.

On classical models of Spin

We discuss two classical situations that lead to probabilities characteristic for systems with spin-1/2. (a) Pitowsky model: It is demonstrated that the definition of spin functions does not imply which circle (a parallel or a great circle) on the sphere should be taken as a probability space in calculation of conditional probabilities. Pitowskys choice of parallels must be formulated as an assumption about the model. It is shown that the model explicitly avoiding this difficulty is possible and no contradiction with the Bell Theorem is found. The modification is based on a new pathological decomposition of the sphere and belongs to a class of hidden variable theories with undetected signals. (b) Aerts model: We show the importance of the “polarization effect” of the measurements for the sake of obtaining a non-Kolmogorovian probability model. It is also shown that the conditioning by a change of state leads in general to the non-Kolmogorovian probability calculus.

MOBILITY AND NON-SEPARABILITY

A mobility phenomenon is typical for a large class of non-linear evolutions. It is shown that the mobility can be responsible for a “malignant” form of quantum mechanical non separability of two correlated systems. An explicit example based on Weinbergs non linear quantum mechanics is considered. We show that in such a theory a transfer of information without a transfer of energy is possible and discuss physical roots of this phenomenon. In Polchinskis approach this effect is not present.

Correlation experiments in nonlinear quantum mechanics

We show how one can compute multiple-time multi-particle correlation functions in nonlinear quantum mechanics in a way which guarantees locality of the formalism.