Arkadiusz Jadczyk

Quantum mechanics of a spin particle in a curved spacetime with absolute time

We present a new covariant approach to the quantum mechanics of a charged 1/2-spin particle in given electromagnetic and gravitational fields. The background space is assumed to be a curved Galileian spacetime, that is a curved spacetime with absolute time. This setting is intended both as a suitable approximation for the case of low speeds and feeble gravitational fields, and as a guide for eventual extension to fully Einstenian space-time. Moreover, in the flat spacetime case one completely recovers standard nonrelativistic quantum mechanics. This work is a generalization of [JM93], where the quantum mechanics of scalar particles was formulated with a similar approach.

HOW AND WHEN QUANTUM PHENOMENA BECOME REAL

We discuss recent developments in the foundations of quantum theory with a particular emphasis on description of measurement—like couplings between classical and quantum systems. The SQUID-tank coupling is described in some details, both in terms of the Liouville equation describing statistical ensambles and piecewise deterministic random process describing random behaviour of individual systems.

Fundamental Geometric Structures for the Dirac Equation in General Relativity

We present an axiomatic approach to Diracs equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory.

EVENT-ENHANCED FORMALISM OF QUANTUM THEORY OR COLUMBUS SOLUTION TO THE QUANTUM MEASUREMENT PROBLEM

Quantum Mechanics has proved to be tremendously powerful, practical, and successful in the description of the micro-world of elementary particles, atoms and molecules. There seems to be no limit to the versality of the Schrodinger equation and to the power of Quantum Theory as an incredibly accurate computational tool for the physicist, chemist, and biologist. The progress made in the last 70 years has really been a matter of sharpening the quantum mechanical mathematical formalism rather than of our understanding of it. As Quantum Mechanics amassed success after success only a few physicists remained fascinated by the fundamental problems that remained unsolved. The proposed solutions to the quantum measurement problem by e.g. von Neumann and Wigner — are no solution at all. They merely shift the focus from one unsolved problem to another. On the other hand the predictions for the outcomes of measurements performed on statistical ensembles of physical systems are excellent. What is however completely missing in the standard interpretation is an explanation of experimental facts i.e. a description of the actual individual time series of events of the experiment. That an enhancement of Quantum Theory allowing the description of single systems is necessary is nowadays clear. Indeed advances in technology make fundamental experiments on quantum systems possible. These experiments give us series of events for which there are definitely no place in the original, standard version of quantum mechanics, since each event is classical, discrete and irreversible. In recent papers [1–8] we provided a definite meaning to the concepts of experiment and event in the framework of mathematically consistent models describing the information transfer between classical event-space and quantum systems. We emphasize that for us the adjective ‘classical’ has to be understood in the following sense: to each particular experimental situation corresponds a class of classical events revealing us the Heisenberg transition from the possible to the actual and these events obey the rules of classical logic of Aristotle and Boole. The World of the Potential is governed by quantum logic and has to account for the World of Actual, whose logic is classical. We accept both and we try to see what we gain this way. It appears that working with so enhanced formalism of quantum theory we gain a lot. 1 We proposed mathematical and physical rules to describe n n nthe two kinds of evolution of quantum systems namely continuous and stochastic n n nthe flow of information from quantum systems to the classical event-space n n nthe control of quantum states and processes by classical parameters.

Graded Lie-Cartan pairs I

Abstract The Lie-Cartan pairs proposed in [1] as an algebraic frame for the classical operators of differential geometry are generalized to the Z /2-graded case (graded Lie-Cartan pairs of a graded Lie algebra and a graded commutative algebra). The generalized case is reduced to the Abelian case by tensoring with arbitrary graded commutative algebras.

Quantum mechanics with event dynamics

Abstract Event generating algorithm corresponding to a linear master equation of Lindblads type is described and illustrated on two examples: that of a particle detector and of a fuzzy clock. Relation to other approaches to the foundations of quantum theory and to the description of quantum measurements is briefly discussed.

On Quantum Iterated Function Systems

A Quantum Iterated Function System on a complex projective space is defined through a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.

Time and Events

Time plays a special role in Standard QuantumTheory. The concept of time observable causes manycontroversies there. In Event-Enhanced Quantum Theory(EEQT) Schrodingers differential equation is replaced by a piecewise deterministic algorithm thatdescribes also the timing of events. This allows us torevisit the problem of time of arrival in quantumtheory.

Born’s Reciprocity in the Conformal Domain

Max Born’s reciprocity principle is revisited and complex four dimensional Kahler manifold D4 ≈ SU (2, 2)/S (U (2) × U(2)) is proposed as a replacement for spacetime on the micro scale. It is suggested that the geodesic distance in D 4 plays a role of a quark binding super-Hamiltonian.

A Comment on “On the Rotation Matrix in Minkowski Space-Time” by Özdemir and Erdoğdu

We comment on the article by M. Ozdemir and M. Erdogdu. We indicate that the exponential map onto the Lorentz group can be obtained in two elementary ways. The first way utilizes a commutative algebra involving a conjugate of a semi-skew-symmetric matrix, and the second way is based on the classical epimorphism from SL(2,C) onto SO_0(3,1)