Our approach to the quantum mechanical measurement problem was
originally shaped to a large extent by the important paper by
Klaus Hepp .
He wrote there, in the concluding section: The solution of the
problem of measurement is closely connected with the yet unknown
correct description of irreversibility in quantum mechanics...
Our approach does not pretend to give an ultimate solution. But
it attempts to show that this "correct description" is, perhaps,
not too far away.
In the present paper we have only been able to scratch the surface of some of the new mathematical techniques and physical ideas that are enhancing quantum theory in the framework of EEQT, that free the quantum theory from the limitations of the standard formulation. For a long time it was considered that quantum theory is only about averages. Its numerical predictions were supposed to come only from expectation values of linear operators. On the other hand in his 1973 paper  Wigner wrote: It seems unlikely, therefore, that the superposition principle applies in full force to beings with consciousness. If it does not, or if the linearity of the equations of motion should be invalid for systems in which life plays a significant role, the determinants of such systems may play the role which proponents of the hidden variable theories attribute to such variables. All proofs of the unreasonable nature of hidden variable theories are based on the linearity of the equations ... . Weinberg  attempted to revive and to implement Wigner's idea of non-linear quantum mechanics. He proposed a nonlinear framework and also methods of testing for linearity. Warnings against potential dangers of nonlinearity are well known, they were summarized in a recent paper by Gisin and Rigo . The scheme of EEQT avoids these pitfalls and presents a consistent and coherent theory. It introduces necessary nonlinearity in the algorithm for generating sample histories of individual systems, but preserves linearity on the ensemble level. It is not only about averages but also about individual events (cf. the event generating PDP algorithm of ref. ). Thus it explains more, it predicts more and it opens a new gateway leading beyond today's framework and towards new applications of Quantum Theory. These new applications may involve the problems of consciousness. But in our opinion (supported in the all quoted papers on EEQT, and also in the present one) quantum theory does not need neither consciousness nor human observers - at least not more than any other probabilistic theory. On the other hand, to understand mind and consciousness we may need Event Enhanced Quantum Theory. And more.
In the abstract to the present paper we stated that we "enhance elementary quantum mechanics with three simple postulates". In fact the PDP algorithm replaces the standard measurement postulates and enables us to derive them in a refined form. This is because EEQT defines\ precisely what measurement and experiment is - without any involvement of consciousness or of human observers. It is only for the purpose of the present paper - to introduce time observable into elementary quantum mechanics as simply as possible - that we have chosen to present our three postulates as postulates rather than theorems. The time observable that we introduced and investigated in the present paper is just one (but important) trace of this nonlinearity. Time of arrival, time of detector response, is an "observable", is a random variable whose probability distribution function can be computed according to the prescription that we gave in the previous section. But its probability distribution is not a bilinear functional of the state and as a result "time of arrival" can not be represented by a linear operator, be it Hermitian or not. Nevertheless our "time" of arrival is a "safe" nonlinear observable. Its safety follows from the fact that what we called "postulates" in the present paper are in fact "theorems" of the general scheme EEQT. And EEQT is the minimal extension of quantum mechanics that accounts for events: no extra unnecessary hidden variables, and linear Liouville equation for ensembles.
Our definition of time of arrival bears some similarity to the one proposed long ago by Allcock . Although we disagree in several important points with the premises and conclusions of this paper, nevertheless the detailed analysis of some aspects of the problem given by Allcock was prompting us to formulate and to solve it using the new perspective and the new tools that EEQT endowed us with. Our approach to the problem of time of arrival goes in a similar direction as the one discussed in an (already quoted) interesting recent paper by Muga and co--workers . We share many of his views. The difference being that what the authors of  call "operational model" we promote to the role of a fundamental new postulate of quantum theory. We justify it and point out that it is a theorem of a more fundamental theory - EEQT. Moreover we take the non--unitary evolution before the detection event seriously and point out that the new theory is experimentally falsifiable.
Once the time of arrival observable has been defined, it is rather straightforward to apply it. In particular our time observable solves Mielnik's "waiting screen problem" . But not only that; with our precise definition at hand, one can approach again the old puzzle of time--energy uncertainty relation in the spirit of Wigner's analysis  (cf. also [41,42]. One can also approach afresh the other old problem: that of decay times (see  and references therein) and of tunneling times ([44,45,46] and references therein). This last problem needs however more than just one detector. We need to analyse the joint distribution probability for two separated detector. We must also know how to describe the unavoidable disturbance of the wave function when the first detector is being triggered. For this the simple postulates of this paper do not suffice. But the answer is in fact quite easy if using the event generating algorithm of EEQT.
More investigations needs also our "shadowing effect" of section 2.3. Every "real" detector acts not only as an information exchange channel, but also as an energy--momentum exchange channel. Every real detector has not only its "information temperature" described by our coupling constant (cf. Sec. 2.1), but also ordinary temperature. Experiments to test the effect must take care in separating these different contributions to the overall phenomenon. This is not easy. But the theory is falsifiable in the laboratory and critical experiments might be feasible within the next couple of years.
In the introductory chapter the problem of extension of the present framework to the relativistic case has been shortly mentioned. Work in this direction is well advanced and we hope to be able to report its result soon. But this will not be end of the story. At the very least we have much to learn about the nature and the mechanism of the coupling between Q and C.
One of us (A.J) acknowledges with thanks support of A. von Humboldt Foundation. He also thanks Larry Horwitz for encouragement, Rick Leavens for his interest and pointing out the relevance of Muga's group papers and to Gonzalo Muga for critical comments. We are indebted to Walter Schneider for his interest, critical reading of the manuscript and for supplying us with relevant informations. We thank Rudolph Haag for sending us the first draft of .