**[blaja95d]:**
**Events
and Piecewise Deterministic Dynamics in Event Enhanced Quantum Theory** |

We enhance the standard formalism of quantum
theory to enable events. The concepts of experiment and of measurement
are defined. Dynamics is given by Liouville's equation that couples
quantum system to a classical one. It implies a **unique** Markov
process involving quantum jumps, classical events and describing sample
histories of individual systems. |

**[blaja95c]:** |

Event generating algorithm corresponding
to a linear master equation of Lindblad's 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 |

**[blaja95b]:** |

We review what we call **event-enhanced
formalism** of quantum theory. In this approach we explicitly assume
classical nature of events. Given a quantum system, that is coupled
to a classical one by a suitable coupling, classical events are being
triggered. The trigerring process is partly random and partly deterministic.
Within this new approach one can modelize real experimental events,
including pointer readings of measuring devices. Our theory gives,
for the first time, a unique algorithm that can be used for computer
generation of experimental runs with individual quantum objects. |

**[blaja95a]:** |

The standard formalism of quantum theory
is enhanced and definite meaning is given to the concepts of experiment,
measurement and event. Within this approach one obtains a uniquely
defined piecewise deterministic algorithm generating quantum jumps,
classical events and histories of single quantum objects. The wave-function
Monte Carlo method of Quantum Optics is generalized and promoted to
the level of a fundamental process generating all the real events
in Nature. The already worked out applications include SQUID-tank
model and generalized cloud chamber model with GRW spontaneous localization
as a particular case. Differences between the present approach and
quantum measurement theories based on environment induced master equations
are stressed. Questions: what is classical, what is time, and what
are observers are addressed. Possible applications of the new approach
are suggested, among them connection between the stochastic commutative
geometry and Connes' noncommutative formulation of the Standard Model,
as well as potential applications to the theory and practice of quantum
computers. |

**[blaja94c]:** |

The standard formalism of quantum theory
is enhanced to allow for a definite meaning to the concepts of measurement
and events. Within this approach one obtains not only Liouville equation
that describes statistical ensembles but also a piecewise deterministic
Markov process that can be used for a computer simulation of real
time series of experiments on single quantum objects. Events follow
laws of probabilities but probabilities obey a causal law. A generalized
cloud chamber model is discussed. The classical events account for
particle tracks while the quantum jumps are shown to be identical
to the spontaneous localization model of Ghirardi, Rimini and Weber.
Moreover we show that the Born's postulate is automatically satisfied.
Bohm's version of the EPR experiment is also discussed within the
enhanced |

**[blaja94b]:** |

Model interactions between classical and
quantum systems are briefly reviewed. These include: general measurement
- like couplings, Stern-Gerlach experiment, model of a counter, quantum
Zeno effect, piecewise deterministic Markov processes and meaning
of the wave function. |

**[jad94c]:** |

We propose a precise meaning to the concepts
of **experiment**, **measurement**, and **event**, in the
event-enhanced formalism of quantum theory. A minimal piecewise deterministic
process is given that can be used for a computer simulation of real
time series of experiments on single quantum objects. As an example
a generalized cloud chamber is described, including multiparticle
case. Relation to the GRW spontaneous localization model is discussed. |

**[jad94b]:** |

The law of track formation in cloud chambers
is derived from the Liouville equation with a simple Lindblad's type
generator that describes coupling between a quantum particle and a
classical, continuous, medium of two--state detectors. Piecewise deterministic
random process (PDP) corresponding to the Liouville equation is derived.
The process consists of pairs (*classical event, quantum jump*),
interspersed with random periods of continuous (in general, non--linear)
Schroedinger's--type evolution. The classical events are flips of
the detectors -- they account for tracks. Quantum jumps are shown,
in the simplest, homogeneous case, to be identical to those in the
early spontaneous localization model of Ghirardi, Rimini and Weber
(GRW). The methods and results of the present paper allow for an elementary
derivation and numerical simulation of particle track formation and
provide an additional perspective on GRW's proposal. |

**[jad94a]:** |

The paper consists of two parts. In the first
part Schroedinger's equation for a charged quantum particle in a Galilei-Newton
curved space-time is derived in a fully geometrical way. Gravitational
and electromagnetic fields are coded into space metric and space-time
connection. The fundamental geometrical object is a quantum connection
in a Hermitian line bundle over the 7-dimensional jet space of 3-velocities.
The secondary object is the bundle of Hilbert spaces over absolute
time. Time appears as a superselection quantity while Shroedinger
equation is interpreted as parallel transport in this bundle. In the
second part the problem of measurement in quantum theory is discussed
as a part of a more general problem of coupling between quantum and
classical systems. The standard framework of quantum theory is extended
so as to allow for dynamical central observables within dissipative
dynamics. It is shown that within this approach one obtains not only
Liouville equation that describes statistical ensembles, but also
a piecewise-deterministic random process describing sequences of **events**
that can be monitored by a continuous observation of the single, coupled
classical system. It also describes **quantum jumps** or **wave
packet reductions** that accompany these events. Two example are
worked out in some details. The last one deals with the problem of
**how to determine the wave function ?**. |

**[blaja93d]:** |

Model interactions between classical and
quantum systems are briefly discussed. These include: general measurement-like
couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno
effect, SQUID--tank model |

**[blaja93b]:** |

A model interaction between a two-state quantum
system and a classical switching device is analysed and shown to lead
to the quantum Zeno effect for large values of the coupling costant
kappa. A minimal piecewise deterministic random process compatible
with the Liouville equation is described, and it is shown that 1/kappa
can be interpreted as the jump frequency of the classical device. |

**[blaja93a]:**
**On interaction between classical and quantum systems** |

We propose a mathematically consistent model
of interaction between classical and quantum systems |

**[jad90]:**
**Bioelectronics as seen by a theoretical physicist** |

A subjective view of the author on the present
status of theoretical physics and bioelectronics is presented. A believe
is expressed that nearly all essential **life processes** can be
explained by a joint effort of mathematics, physics, chemistry and
biology in the framework of the actual paradigm. It is also pointed
out that, in the author's opinion, in order to explain the phenomenon
of **life itself** as well as that of **consciousness**, we
need a new theory of complex and selforganized systems, and also a
new theory uniting quantum matter with information fields. While the
first theory is developing rapidly in recent years, the second one
needs a radical change in the foundations of quantum theory. One may
need to this end to implement Wigner's ideas of nonlinear quantum
evolution equations, and to take into account the essential role of
light in mediating between classical and quantum universes and in
quantum-theoretical description of "events" and "measurements". |