This paper is dedicated to Klaus Hepp and to Walter Hunziker on the occasion of their sixtieth anniversary

e-mail: blanchard@physik.uni-bielefeld.de

e-mail: ajad@ift.uni.wroc.pl

We use the method chosen by Galileo in his great book "Dialogues Concerning Two New Sciences"[1]. Galileo is often refered to as the founder of modern physics. The most far--reaching of his achievements was his counsel's speech for mathematical rationalism against Aristotle's logico--verbal approach, and his insistence for combining mathematical analysis with experimentation.
In the dialog SG=Sagredo, SV=Salviati, SP=Simplicio

Salviatti refers here to "Event Enhanced Quantum Theory" of reference [6] - paper apparently well know to the participants of the dialog.

Heisenberg proposed the word "event" to replace the word "measurement", the latter word carrying a suggestion of human involvement.

Cf. an illuminating discussion of this point in [15,16].

More generally we would need two Hilbert spaces: 21#21 and 22#22 that can be different, but for the present discussion we need not be pedantic, so we will assume them to be identified.

Known in the literature also under the name of "non-hermitian"

A mathematical theory of a counter that leads to an inhomogeneous Poisson process, starting from formal postulates that are different than ours was given almost fifty years ago by Res Jost [21] .

From this time on the subscript 113#113 may refer to either the initial state, as in 114#114 or to free evolution, as in 115#115, or to initial state evolving under free evolution. In case of confusion the actual meaning should be derived from the context.

The case of Hermitian singular delta--function perturbation was discussed by many authors - see [23,24,25,26,27,28,29] and references therein

We should have 192#192

This is why our time observable does not fall into the family analysed axiomatically by Kijowski [37].

More comments in this direction can be found in [6] and also under WWW address of the Quantum Future Project: http://www.ift.uni.wroc. pl/ 221#221ajad/qf.htm

Arkadiusz Jadczyk
Thu Feb 22 09:58:31 MET 1996