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We start with recalling John Bell's opinion on quantum measurements. He studied the subject in depth and he concluded emphasizing it repeatedly [Bell]: our difficulties with quantum measurement theory are not accidental - they have a reason. He has pointed out this reason: it is that the very concept of "measurement" can not even be precisely defined within the standard formalism . We agree, and we propose a way out that has not been tried before. Our scheme solves the essential part of the quantum measurement puzzle - it gives a unique algorithm generating time series of pointer readings in a continuous experiment involving quantum systems. We do not pretend that our solution is the only one that solves the puzzle. But we believe that it is a kind of a minimal solution. Even if not yet complete, it may help us to find a way towards a more fundamental theory.

The solution that we propose does not involve hidden variables First, we point out the reason why "measurement" can not be defined within the standard approach. That is because the standard quantum formalism has no place for "events". The only candidate for an event that we could think of - in the standard formalism - is a change of the quantum state vector. But one can not see state vectors directly. Thus, in order to include events, we have to extend the standard formalism. That is what we do, and we are doing it in a minimal way: just enough to accommodate classical events. We add explicitly a classical part to the quantum part, and we couple classical to the quantum. Then we define "experiments", and "measurements", within the so extended formalism. We can show then that the standard postulates concerning measurements - in fact, in an enhanced and refined form - can be derived instead of being postulated.

This "event enhanced quantum theory" or EEQT, as we call it, gives experimental predictions that are stronger than those obtained from the standard theory. The new theory gives answers to more experimental questions than the old one. It provides algorithms for numerical simulations of experimental time series obtained in experiments with single quantum systems. In particular this new theory is falsifiable. We are working out its new consequences for experiments, and we will report the results in due time. But even assuming that we are successful in this respect, even then our program will not be complete. Our theory, in its present form, is based on an explicit selection of an "event carrying" classical subsystem. But how do we select what is classical? Is it our job or is it Nature's job?

When we want to be on a safe side as much as possible, or as long as possible, then we tend to shift the "classical" into the observer's mind. That was von Neumann's way out. But if we decide to blame mind - shall we be save then? For how long? It seems that not too long. This is the age of information. Soon we will need to extend our physical theory to include a theory of mind and a theory of knowledge. That necessity will face us anyhow, perhaps even sooner than we are prepared to admit. But, back to our quantum measurement problem, it is not clear at all that the cut must reside that far from the ordinary, "material" physics. For many practical applications the measuring apparatus itself, or its relevant part, can be considered classical. We need to derive such a splitting into classical and quantum from some clear principles. Perhaps is is a dynamical process, perhaps the classical part is growing with time. Perhaps time is nothing but accumulation of events. We need new laws to describe dynamics of time itself. At present we do not know what these laws are, we can only guess.

At the present stage placement of the split is indeed phenomenological, and the coupling is phenomenological too. Both are simple to handle and easy to describe in our formalism. But where to put the Heisenberg's cut - that is arbitrary to some extent. Perhaps we need not worry too much? Perhaps relativity of the split is a new feature that will remain with us. We do not know. That is why we call our theory "phenomenological". But we would like to stress that the standard, orthodox, pure quantum theory is not better in this respect. In fact, it is much worse. It is not even able to define what measurement is. It is not even a phenomenological theory. In fact, strictly speaking, it is not even a theory. It is partly an art, and that needs an artist. In this case it needs a physicist with his human experience and with his human intuition. Suppose we have a problem that needs quantum theory for its solution. Then our physicist, guided by his intuition, will replace the problem at hand by another problem, that can be handled. After that, guided by his experience, he will compute Green's function or whatsoever to get formulas out of this other problem. Finally, guided by his previous experience and by his intuition, he will interpret the formulas that he got, and he will predict some numbers for the experiment.

That job can not be left to a computing machine in an unmanned space-craft. We, human beings, may feel proud that we are that necessary, that we can not be replaced by machines. But would it not be better if we could spare our creativity for inventing new theories rather than spending it unnecessarily for application of the old ones?


In a recent series of papers (cf.[blaja95a] and references therein) we enhanced the standard framework of quantum mechanics endowing it with event dynamics. In this extension, which will be denoted EEQT (for Event Enhanced Quantum Theory), we go beyond the Schroedinger continuous-time evolution of wave packets - we also propose a class of algorithms generating discrete events. From master equation that describes continuous evolution of ensembles of coupled quantum + classical systems we derive a unique piecewise deterministic random process that provides a stochastic algorithm for generating sample histories of individual systems. In the present contribution we will describe the essence of our approach. But first we make a few comments on similarities and differences between EEQT and several other approaches.

The Standard Approach

In the standard approach classical concepts are static. They are introduced via measurement postulates developed by the founders of Quantum Theory. But ``measurement" itself is never precisely defined in the standard approach and therefore measurement postulates cannot be derived from the formalism. One is supposed to believe Born's statistical interpretation simply ``because it works". The standard interpretation alone does not tell us what happens when a quantum system is under a continuous observation (which, in fact, is always the case).

Master Equation Dynamics and Continuous Observation Theory

Continuous observation theory is usually based on successive applications of the projection postulate. Each application of the projection postulate maps pure states into mixed states. Thus repeated application of the postulate leads to a master equation for a density matrix. Replacing Schroedinger's dynamics by a master equation is also popular in quantum optics [...]) and in several attempts to reconcile quantum theory with gravity (for a recent account see [...]). In all these approaches the authors usually believe that no classical system is introduced. All is purely quantum. That is, however, not true. What is true is just the converse: the largest possible classical system is introduced, but because it is so large and so close to the eye, it easily escapes our sight. It is assumed, without any justification, that jumps of quantum state vectors are directly observable (whatever it means). These jumps are supposed to constitute the only classical events. The weak point of this approach is in the fact that going from the master equation, that describes statistical ensembles, to a stochastic algorithm generating sample histories of an individual system is non-unique. There are infinitely many random processes that lead to the same master equation after averaging. One can use diffusion stochastic differential equations or jump processes, one can shift pieces of dynamics between Hamiltonian evolution and collapse events.

The reason for this non-uniqueness is simple: there are infinitely many mixtures that lead to the same density matrix. Diosi [...] invented a clever mathematical procedure for constructing a special orthoprocess. It provides a definite algorithm in special cases of finite degeneracy. It does not however remove non-uniqueness and also there is no reason why Nature should have chosen this special prescription causing quantum state vector always to make the least probable transition: to one of the orthogonal states.

Bohmian Mechanics, Local Beables, Stochastic Mechanics

In these approaches [...] there is an explicit classical system. Quantum state vector knows nothing about this classical system. It evolves according to the unmodified Schroedinger's dynamics. It acts on the classical system affecting the classical dynamics (which is either causal or stochastic) without itself being acted upon. There is a mysterious quantum potential: action without reaction. All such schemes are inconsistent with quantum mechanics. They can be shown to contradict indistinguishability of quantum mixtures that are described by the same density matrix [jad95a]. That it must be so follows from quite general no-go theorems -[...]. The fact that the above schemes allow us to distinguish between mixtures that standard quantum mechanics considers indistinguishable need not be a weakness. In fact, it may be an advantage because it may lead beyond quantum theory, it can provide us with means of faster-than-light communication - provided experiment confirms this feature.

How does our approach compare to those above? First of all, as for today, our approach is explicitly phenomenological. That is not to say that, for instance, the standard approach is not phenomenological. In the standard approach we must decide where do we finish our quantum description and what do we "measure". That does not follow from the theory - it must be imputed from the outside. However, we have been so much indoctrinated by Bohr's philosophy and its apparent victory over Einstein's "realistic" dreams, and we are today so used to this procedure, that we do not feel uneasiness here any more. Somehow we tend to believe that the future "quantum theory of everything" will explain all events that happen. But chances are that this theory of everything will explain nothing. It will be a dead theory. It will not even have a Hamiltonian, because there will be no time. It will be a theory of the world in which nothing happens by itself. It will answer our questions about certain probabilities - when these questions are asked. But it will not explain why anything happens at all.

Our theory of event dynamics starts with an explicit phenomenological split between a quantum system, which is not directly observable, and a classical system, where events happen that can be observed and that are to be described and explained. In other words our starting point is an explicit mathematical formulation of Heisenberg's cut. The quantum system may be as big as one wishes it to be, the classical system may retreat more and more, moved as far as we wish - towards our sense organs, towards our brains, towards our mental processes. But the further we retreat the less facts we explain. At the extreme limit we will be able to explain nothing but changes of our mental states, i.e. only mental events. That state of affairs may be considered satisfactory for those who adhere to idealistic or eastern philosophies, but it need not be the one that enriches our understanding of the true workings of Nature. Probably, for most of practical purposes, it is sufficient to retreat with the quanto-classical cut as far as photon detection processes which can be treated as the primitive events. However, our event mechanics works quite well when the cut between the quantum and the classical is expressed in engineering language: like in the example of quantum SQUID coupled to a classical radio-frequency circuit, or quantum particle coupled to its yes-no position detectors, for instance to a cloud chamber.

Once the split between the quantum and the classical is fixed, then the coupling between both systems is described in terms of a special master equation. Because of its special form there is a unique random process in the space of pure states of the total system that reproduces this master equation. The process gives an algorithm for generating sample histories. It is of piecewise deterministic character. It consists of periods of continuous evolution interrupted by jumps and events that happen at random times. The continuous evolution of the quantum system is described by a - modified by the coupling - nonunitary Schroedinger's equation. The jump times have a Poissonian character, with their jump rates dependent on the actual state of both the quantum and the classical system. The back action of the classical system on the quantum one shows up in two ways: first of all by modifying the Schroedinger evolution between jumps by a non-unitary damping, second by causing quantum state to jump at event times. Notice that the master equation describing statistical properties is linear, while the evolution of individual system is nonlinear. This agrees with Turing's aphorism stating that prediction must be linear, description must be nonlinear [...].

Our theory, even if it works well and has a practical value, should be considered not as a final scheme of things, but merely as a step that may help us to find a description of Nature that is more satisfactory than the one proposed by the orthodox quantum philosophy. Pure quantum theory proposes a universe that is dead - nothing happens, nothing is real - apart from the questions asked by mysterious "observers". But these observers are metaphysics, are not in the equations. In a sharp contrast to the standard approach, our theory of event mechanics described here makes the universe "running" again, even before there were any observers. It has gotten however the arrow of time that is driven by a fuzzy quantum clock. It also needs a roulette. This is hard to accept for many of us. We would like to believe that Nature is ruled by a perfect order. And to be perfect - this order must be deterministic. Even if we do not share Einstein's dissatisfaction with quantum theory, we tend to understand his disgust at the very thought of God playing dice. But Nature's concept of a perfect order may be not that simple one as we wish. Perhaps using probability theory may be the only way of describing in finite terms the universe that has an infinite complexity. It may be that we will never know the ultimate secret, nevertheless the mechanism proposed by EEQT brings a hope of restoring some order that we are seeking. Namely, the quanto-classical clock that we describe below works "by itself". It is true that it needs a roulette but the roulette is a classical roulette. We need only classical probability and classical random processes. That is good because we understand classical probability by hearts but "quantum probability" we understand only by abstract terms. That is some progress also because nowadays we know more about complexity theory, theory of random sequences, and theory of chaotic phenomena. Each year we find new ways of generating apparently random phenomena out of deterministic algorithms of sufficient complexity. In fact, our event generating algorithm is successfully simulated with a completely deterministic classical computer. The crucial problem here is the necessary computing power. Moreover, the algorithm is nonlocal. We do not know how Nature manages to make its world clock running with no or little effort. We must yet learn it.


We will talk about theory of events. To be honest we should allow for the adjective "phenomenological". We will explain later our reasons for this restraint. This new theory enhances and extends the standard quantum formalism. It provides a solution to the quantum measurement problem. The usual formalism of quantum theory fails in this respect. Let us look, for instance, into a recent book on the subject, The interpretation of quantum theory [Omnes]. There we can see both the difficulties as well as the methods that attempt to overcome them. We disagree with the optimism shared by many, perhaps by a majority of quantum physicists. They seem to believe that the problem is already solved, or almost solved. They use a magic spell, and at present the magic spell that is supposed to dissolve the problems is decoherence. It is true that there are new ideas and new results in the decoherence approach. But these results did not quite solve the problem. Real-world-events, in particular pointer readings of measuring apparata, have never be obtained within this approach. Decoherence does not tell us yet how to programm a computer to simulate such events. A physicist, a human being, must intervene to decide what to decohere and how to decohere. Which basis is to be distinguished. What must be neglected and what must not? Which limit to take? That necessity of a human intervention is not a surprise. The standard quantum formalism simply has no resources that can be called for when we wish to derive the basic postulates about measurements and probabilities. These postulates are repeated in all textbooks. They are never derived. The usual probabilistic interpretation of quantum theory is postulated from outside. It is not deduced from within the formalism. That is rather unsatisfactory. We want to believe that quantum theory is fundamental, but its interpretation is so arbitray! Must it be so?


I. Introduction
Quantum Mechanics occupies a particular place among scientific theories; indeed it is at once one of the most successful and one of the most mysterious ones. Its success lies undoubtedly in the fact that using Quantum Mechanics one can predict properties of atoms, of molecules, of chemical reactions, of conductors and insulators and much more. These predictions were confirmed by precise measurements and by the technological progress that is based on quantum phenomena. The mystery resides in the problem of interpretation of Quantum Theory - which does not follow from the formalism itself but is left to discretion of a physicist. As a result, there is still no general agreement about how Quantum Mechanics is best understood and to what extent it can be considered as exact and complete.
As emphasized already by E. Schroedinger [...] what is definitively and completely missing in Standard Quantum Mechanics is an explanation of experimental facts, as it does not tell us how to generate time series of events recorded during real experiments on single individual systems. H.P. Stapp [...] and R. Haag [...] emphasized the role and importance of events in quantum physics. J. Bell [...] stressed the fundamental necessity of distinguishing definite events from just wavy possibilities .

In 1969 E.B. Davies [...] introduced the space of events in his mathematical theory of quantum stochastic processes which extended the standard formalism of quantum theory. His theory went beyond a standard quantum measurement theory and, in its most general form, was not expressible in terms of quantum master equations alone. Later on Srinivas, in a joint paper with Davies [...], specialized Davies' general and mathematically sophisticated scheme to photodetection processes. Photon counting statistics predicted by this theory were successfully verified in fluorescence experiments which caused R. J. Cook to revisit the question what are quantum jumps[...]. A related question: are there quantum jumps was asked by J. Bell [...] in connection with the idea of spontaneous localization put forward by Ghirardi, Rimini and Weber [...].

In the eighties quantum optics experiments started to call for efficient methods of solving quantum master equations that described effective coupling of atoms to the radiation modes. The works of Carmichael [...], Dalibard, Castin and Moelmer [...], Dum, Zoller and Ritsch [...], Gardiner, Parkins and Zoller [...], developed Quantum Monte Carlo (QMC) algorithm for simulating solutions of master equations. (A less general scheme was proposed by Teich and Mahler [...] who tried to extract a specific jump process directly from the orthogonal decomposition of time evolving density matrix. On the other hand already in 1986 Diosi [...] proposed a pure state, piecewise deterministic process that reproduces a given master equation. His process although canonical in nondegenerate case, is not unique.) The algorithm emerged from the the seminal papers of Davies [...] on quantum stochastic processes, that were followed by numerous works on photon counting and continuous measurements [...]. It was soon realized [...] that the same master equations can be simulated either by Quantum Monte Carlo method based on quantum jumps, or by a continuous quantum state diffusion. Wiseman and Milburn [...] discussed the question of whether experimental detection schemes are better described by continuous diffusions or by discontinuous jump simulations. The two approaches were recently put into comparison also by Garraway and Knight [...], while Gisin et al. [...] argued that the quantum jumps can be clearly seen in the quantum state diffusion plots. Apart from the numerical usefulness of quantum jumps and empirical observability of photon counts, the debate of their reality continued. A brief synthesis of the present state of the debate has been given by Moelmer in the final paragraphs of his 1994 Trieste lectures [...]:

The macroscopic collapse has been explained, the elementary collapse, however remains as an essential and unexplained ingredient of the theory.

A real advantage of the QMC method: We can be sitting there and discussing its philosophical implications and the deep questions of quantum physics while the computer is cranking out numbers which we need for practical purposes and which we could never obtain in any other way. What more can we ask for?

In the present paper we argue that indeed more can be not only asked for, but that it can be also provided. The picture that we propose developed from a series of papers [...] where we treated several applications including SQUID-tank [...] and cloud chamber model (with GRW spontaneous localization) [...]. In the sequel we will refer to it as Event Enhanced Quantum Theory (EEQT). EEQT is a minimal extension of the standard quantum theory that accounts for events. In the next three sections we will describe formal aspects of EEQT, but we will attempt to reduce the mathematical apparatus to the absolute minimum. In the final Sect. 4 we will propose to use EEQT for describing not only quantum measurement experiments, but all the real processes and events in Nature. The new formalism rises new questions, and in Sect. 4 we will point out some of them. One of the problems that can be discussed in a somewhat new light is that of the role of observers and IGUS-es (Information Gathering and Utilizing Systems - using terminology of Gell-Mann and Hartle [...]). We will also make a comment on a possible interpretation of Connes' version of the Standard Model as a stochastic geometry a'la EEQT, with jumps between the two copies of space-time. Finally we will mention relevance of EEQT to the theory and practice of quantum computers.

We have seen that Quantum Theory can be enhanced in a rather simple way. Once enhanced it predicts new facts and straightens old mysteries. The EEQT that we have outlined above has several important advantages. One such advantage is of practical nature: we may use the algorithms it provides and we may ask computers to crank out numbers that are needed in experiments and that can not be obtained in another way . For example in [blaja93c] we have shown how to generate pointer readings in a tank radio-circuit coupled to a SQUID. In [jad94b,c] the algorithm generating detection events of an arbitrary geometrical configuration of particle position detectors was derived. As a particular case, in a continuous homogeneous limit we reproduced GRW spontaneous localization model. Many other examples come from quantum optics, since QMC is a special case of our approach, namely when events are not feed-backed into the system and thus do not really matter.

Another advantage of EEQT is of a conceptual nature: in EEQT we need only one postulate: that events can be observed. All the rest can and should be derived from this postulate. All probabilistic interpretation, everything that we have learned about eigenvalues, eigenvectors, transition probabilities etc. can be derived from the formalism of EEQT. Thus in [blaja93a] we have shown that the probability distribution of the eigenvalues of Hermitian observables can be derived from the simplest coupling, while in [blaja94c,blaja95c], we have shown that Born's interpretation can be derived from the simplest possible model of a position detector. Moreover, in [jad94a] it was shown that EEQT can also give definite predictions for non-standard measurements, like those involving noncommuting operators (notice that in our scheme contributions gab from different, possibly non-commuting, devices add).

It is also possible that using the ideas of EEQT may throw a new light into some applications of non-commutative geometry. Namely, when C consists of two points, then our V can be interpreted as Quillen's superconnection [...] and references there). (Cf. also [...] for relation between superconnections and classical Markov processes.)

Another potential field of application of EEQT is in the theory and practice of quantum computation. Computing with arrays of coupled quantum rather than classical systems seems to offer advantages for special classes of problems [...] and references therein). Quantum computers will have however to use classical interfaces, will have to communicate with, and be controlled by classical computers. Moreover, we will have to understand what happens during individual runs. Only EEQT is able to provide an effective framework to handle these problems. It keeps perfect balance of probabilities without introducing negative probabilities and it needs only standard random number generators for its simulations. For a recent work where similar ideas are considered cf. [...]

EEQT is a precise and predictive theory. Although it appears to be correct, it is also yet incomplete. The enhanced formalism and the enhanced framework not only give enhanced answers, they also invite asking new questions. Indeed, we are tempted to consider the possibility that PDP can be applied not only to what we call experiments, but also, as a world process to the entire universe (including all kinds of observers ). Thus we may assume that all the events that happened were generated by a particular PDP process, with some unknown Q,C,H and V. Then, assuming that past events are known, the future is partly determined and partly open. Knowing Q,C,H,V and knowing the actual state (even if this knowledge is fuzzy and uncertain), we are in position to use the PDP algorithm to generate the probable future series of events. With such a promotion of the PDP to the role of a universal world process questions arise that could not be asked before: what is C and what is V?, and perhaps also: what is t? and what are we. Of course we are not in a position to provide answers. But we can discuss possibilities and we can provide hints.

What is time?

Let us start with the question: what is time? Answering that time is determined by the thermodynamic state of the system [...] is not enough, as we would like to know how did it happen that a particular thermodynamic state has evolved, and to understand this we must assume evolution, and thus we are back with the question: what is time if not just counting steps of this evolution. We are tempted to answer: time is just a measure of the number of events that happened in a given place. If so, then time is discrete, and there is another time, that counts the deterministic steps between events. In that case die tossing to decide whether the next step is to be an event or not is probably uneconomic and unnecessary; it is quite possible that the Poissonian character of events is a result of some ergodic theorem, when we use not the truediscrete time, but some continuous averaged time (averaged over a neighborhood of a given place). Thus a possible algorithm for a finite universe would be discrete, with die tossing every N steps, N being a fixed integer, and continuous, averaged time would appear only in a thermodynamic limit. In fact, in a finite universe, dice tossing should be replaced by a deterministic algorithm of sufficient complexity. A spectrum of different approaches to the problem of time, some of them similar to the one presented above, can be found in Ref. [...]. In a recent paper J. Schneider [...] proposes that a passing instant is the production of a meaningful symbol, and must be therefore formalized in a rigorous way as a transition. He also states that the linear time of physics is the counting of the passing instants, that time is linked with the production of meaning and is irreversible per se. We agree only in part, as we strongly believe that physical events, and the information that is gained due to these events, are objective and primary with respect to secondary mental or semantic events.

What is classical?

We consider now the question: what is classical? In each practical case, when we want to explain a given phenomenon, it is clear what constitutes events for us that we want to account for. These events are classical, and usually we can safely extend the classical system C towards Q gaining a lot and loosing a little. But here we are asking not a practical question, we are asking a fundamental question: what is true C? There are several possibilities here, each one having advantages and disadvantages, depending on circumstances in which the question is being asked. If we believe in quantum field theory and if we are ready to take its lesson, then we must admit that one Hilbert space is not enough, that there are inequivalent representations of the canonical commutation relations, that there are superselection sectors associated to different phases. In particular there are inequivalent infrared representations associated to massless particles [...]. Then classical events would be, for instance, soft photon creation and annihilation events. That idea has been suggested by Stapp [...] some ten years ago, and is currently being developed in a rigorous, algebraic framework by D. Buchholz [...].

Another possibility is that not only photons, but also long range gravitational forces may take part in the transition from the potential to the actual. That hypothesis has been expressed by several authors (see e.g. contributions of F. Karolyhazy et al., and R. Penrose in [...]; also L. Diosi [...]).

The two possibilities quoted above are not satisfactory when we think of a finite universe, evolving step by step, with a finite number of events. In that case we do not yet know what is gravity and what is light, as they, together with space, are to emerge only in the macroscopic limit of an infinite number of events. In such a case it is natural to look for C in Q. We could just define event as a nonunitary change of state of Q. In other words, we would take for the space S of classical pure states the only available set - the unit ball of the Hilbert space. This possibility has been already discussed in [jad94]. This choice of S is also necessary when we want to discuss the problem of objectivity of a quantum state. If quantum states are objective (even if they can be determined only approximately), then the question: what is the actual state of the system is a classical question - as an attempt to quantize also the position of psi would lead to a nonsense. We should perhaps remark here that our picture of a fixed Q and fixed C that we have discussed in this paper is oversimplified. When attempting to use the PDP algorithm to create a finite universe in the spirit of space-time code of D. Finkelstein [...] and references therein), or bit-string universe of P. Noyes (cf. Noyes' contribution to [...]) we would have to allow for Q and C to grow with the number of events. Our formalism is flexible enough to adjust to such a change.

Dynamics and Binamics

Having provided tentative answers to some of the new questions, let us pause to discuss possible conceptual implications of the EEQT. We notice that EEQT is a dualistic (and even syncretistic) theory. In fact, we propose to call the part of time evolution associated to V by the name of binamics - in contrast to the part associated to H, which is called dynamics. While dynamics deals with the laws of exchange of forces, binamics deals with the laws of exchange of bits (of information). We believe that these two sets of laws refer to different projections of one reality and neither one of these projections can be completely reduced to another one. Moreover, concerning the reality status, we believe that bits, are as real as forces. That this is indeed the case should be clear if we apply the famous A. Landes criterion of reality: real is what can kick. We know that information, when applied in an appropriate way, may cause changes and may kick - not less than a force.

What are we?

We have used the term we too many times to leave it without a comment. Certainly we are partly Q and partly C (and partly of something else). But not only we are subjects and spectators - sometimes we are also actors. In particular we can ain and utilize information [...]. How can this happen? How can we control anything? Usually it is assumed that we can prepare states by manipulating Hamiltonians. But that can not be exactly true. It is beyond our power to change coupling constants or Hamiltonians that are governing fundamental forces of Nature. And when we say that we can manipulate Hamiltonians, we really mean that we can manipulate states in such a way that the standard fundamental Hamiltonians act on these special states as if they were phenomenological Hamiltonians with classical control parameters and external fields that we need in order to explain our laboratory procedures. So, how can we manipulate states without being able to manipulate Hamiltonians? We can only guess what could be the answer of other interpretations of Quantum Theory. Our answer is: we have some freedom in manipulating C and V. We can not manipulate dynamics, but binamics is open. It is through V and C that we can feedback the processed information and knowledge - thus our approach seems to leave comfortable space for IGUS-es. In other words, although we can exercise little if any influence on the continuous, deterministic evolution [...], we may have partial freedom of intervening, through C and V, at bifurcation points, when die tossing takes place. It may be also remarked that the fact that more information can be used than is contained in master equation of standard quantum theory, may have not only engineering but also biological significance. In particular, we provide parameters (C and V) that specify event processes that may be used in biological organization and communication. Thus in EEQT, we believe, we overcome criticism expressed by B.D. Josephson concerning universality of quantum mechanics [...] . The interface between Quantum Physics and Biology is certainly also concerned with the fact that a lot of biological processes (like the emergence of naturally catalytic molecules or the the evolution of the genetic code) can be in principle described and understood in terms of physical quantum events of the kind that we have discussed above.

We believe that are our proposal as outlined in this paper and elaborated on several examples in the quoted references is indeed the minimal extension of quantum theory that accounts for events. We believe that, apart of its practical applications, it can also serve as a reminder of existence of new ways of looking at old but important problems.


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.
We proposed mathematical and physical rules to describe
  • the two kinds of evolution of quantum systems namely continuous and stochastic
  • the flow of information from quantum systems to the classical event-space
  • the control of quantum states and processes by classical parameters.
It follows that as long as the usual locality assumptions [...] are satisfied, the event statistics seen on the right does not depend on what is measured on the left, and whether anything is measured there at all. We stress that this observation alone should not be used to conclude that superluminal signalling using EPR is impossible - this for the very reason that we were considering above a particular and simplified model. What we proved above is only that superluminal communicators must necessarily use more refined methods than the one considered above.
We are not saying however that we are satisfied with our understanding of Quantum Mechanics and we agree with Feynman's belief that no one really understands Quantum Mechanics. In this context it is perhaps appropriate to quote a statement by Nagel "The main event of this century will be the first human contact with the invisible quantum world". "Real black magic calculus" is how Einstein described Quantum Mechanics in a letter in 1925. Our models of coupling quantum systems to classical event-spaces can be rightly criticized as being too phenomenological. But we offer some new ways of seeing things and new mathematics providing an additional perspective on Quantum Theory and links between the old and the new, the possible and the actual, statistical ensembles and individual systems, waves and particles and the deterministic and the random. Despite exciting results, however, an outstanding challenge remains.


It was also John Bell's point of view that "something is rotten" in the state of Denmark and that no formulation of orthodox quantum mechanics was free of fatal flows. This conviction motivated his last publication [...]. As he says "Surely after 62 years we should have an exact formulation of some serious part of quantum mechanics. By "exact" I do not mean of course "exactly true". I only mean that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist ...".
Two options are possible for completing Quantum Mechanics. According to John Bell [...] "Either the wave functions is not everything or it is not right ...".
The class of models we consider aims at providing an answer to the question of how and why quantum phenomena become real as a result of interaction between quantum and classical domains. Our results show that a simple dissipative time evolution can allow a dynamical exchange of information between classical and quantum levels of Nature. Indeterminism is an implicit part of classical physics and an explicit ingredient of quantum physics. Irreversible laws are fundamental and reversibility is an approximation.
We extend the model of Quantum Theory in such a way that the successful features of the exisiting theory are retained but the transitions between equilibria in the sense of recording effects are permitted.
To the Liouville equation describing the time evolution of statistical states of total system we will be in position to associate a piecewise deterministic process taking values in the set of pure states of this sytem. Knowing this process one can answer all kinds of questions about time correlations of the events as well as simulate numerically the possible histories of individual quantum-classical systems. Let us emphasize that nothing more can be expected from a theory without introducing some explicit dynamics of hidden variables. What we achieved is the maximum of what can be achieved, which is more than orthodox interpretation gives. There are also no paradoxes; we cannot predict individual events (as they are random), but we can simulate the observations of individual systems.
It is tempting to use the Zeno effect for slowing down the time evolution in such a way, that the state of a quantum system Q can be determined by carrying out measurements of sufficiently many observables. This idea, however, would not work, similarly like would not work the proposal of "protective measurements" of Y. Aharonov et al [...]. To apply Zeno-type measurements just as to apply a "protective measurement" one would have to know the state beforhand. Our results suggest that obtaining a reliable knowledge of the quantum state may necessarily lead to a significant, irreversible disturbance of the state. This negative statement does not mean that we have shown that the quantum state cannot be objectively determined. We believe however that dynamical, statistical and information-theoretical aspects of the important problem of obtaining a maximal reliable knowledge of the unknown quantum state with a least possible disturbance are not yet sufficiently understood.


From a philosophical point of view, it is worth noting that in the present paper, in a sharp contrast to the standpoint taken by H.P. Stapp in his recent paper [...], we deliberately avoid the concepts of an "observer". Our model aims at being as objective as the concept of probability allows for it. A philosophical summary of our results can be formulated as follows: Quantum Theory, once invented by human minds and ones asked questions that are of interest for human beings, needs not "minds" or "observers" any more. What it needs is lot of computing power and effective random number generators, rather than "observers". The fundamental question, to which we do not know the answer yet, can be thus formulated as follows: can random number generators be avoided and replaced by deterministic algorithms of a simple and clear meaning?
The crucial concept of our approach to quantum measurements is that of an "event".
Our aim is to explain the "nice linear tracks" that quantum particles leave on photographs and in cloud chambers.These tracks are indeed hard to explain if one assumes that there are no particles and no events - only Schroedinger's waves.
We have seen that a simple coupling between quantum particle and classical continuous medium of two-state detectorsleads to a piecewise deterministic random process that accounts fortrack formation in cloud chambers and photographic plates.
As mentioned in the Introduction, to simulate track formations only random number generators and computing power is necessary. Our model does not involve observers and minds. This does not mean that we do not appreciate the importance of the mind-body problem. In our opinion understanding the problems of minds needs also quantum theory, and perhaps even more - that is still beyond the horizon of the present-day physics.
But our model indicates that quantum theory does not need human minds. Quantum theory should be formulated in a way that involves neither observers nor minds - at least not more than any other branch of physics.


Replacing Schroedinger's evolution, which governs the dynamics of pure states, by an equation of the Liouville type, that describes time evolution of mixed states, is a necessary step - but it does not suffice for modeling of real world events. One must take, to this end, two further steps. First of all we should admit that in our reasoning, our communication, our description of facts - we are using classical logic. Thus somewhere in the final step of transmission of information from quantum systems to macroscopic recording devices and further, to our senses and minds, a translation between quantum and classical should take place. That such a translation is necessary is evident also when we consider the opposite direction: to test a physical theory we perform controlled experiments. But some of the controls are always of classical nature - they are external parameters with concrete numerical values. So, we need to consider systems with both quantum and classical degrees of freedom, and we need evolution equations that enable communication in both directions, i.e. :
  • flow of information from quantum to classical
  • control of quantum states and processes by classical parameters
Our point is that "measurement" is an undefined concept in standard quantum theory, and that the probabilistic interpretation must be, because of that, brought from outside. What we propose is to define measurement as a CP semigroup coupling between a classical and a quantum system and to derive the probabilistic interpretation of the quantum theory from that of the classical one
Recently Aharonov and Vaidman [...] discussed this problem in some details. I do not think that they found the answer, as their arguments are circular, and they seem to be well aware of this circularity. The difficulty here is in the fact that we have to discriminate between non-orthogonal projections (because different states are not necessarily orthogonal), and this implies necessity of simultaneous measuring of non-commuting observables. There have been many papers discussing such measurements, different authors taking often different positions. However they all seem to agree on the fact that predictions from such measurements are necessarily fuzzy. This fuzziness being directly related to the Heisenberg uncertainty relation for non-commuting observables. Using methods and ideas presented in the previous sections of this chapter it is possible to build models corresponding to the intuitive idea of a simultaneous measurement of several non-commuting observables, like, for instance, different spin components,


Our results show that a simple dissipative time evolution can result in a dynamical exchange of information between classical and quantum levels of Nature.
In our model the quantum system is coupled to a classical recording device which will respond to its actual state. We thus give a minimal mathematical semantics to describe the measurement process in Quantum Mechanics. For this reason the toy model that we proposed can be seen as the elementary building block used by Nature in the communications that take place between the quantum an classical levels. The model has not only nice mathematical properties but it is also of great practical accesibility and, therefore, it is natural to formulate any practical problem by starting from the general structure of the "Ansatz" we have proposed.
The exceptionally brilliant calculational successes of Quantum Mechanics cannot cause to forget the degree of conceptual confusion still present. The essential problem follows from the fact that Quantum Mechanics is the most fundamental theory we know. But if it is really fundamental, it should be universally applicable. In particular quantum physics should be able to explain also the properties of macroscopic objects and occurence of macroscopic events. But measurement situations show clearly that it is impossible to apply standard Quantum Mechanics in a consistent way to all relevant situations. If there is such a universal theory, it is therefore not Quantum Theory.
Indeterminism is an implicit part of classical physics. Irreversible laws are fundamental and reversibility is an approximation. We cannot refrain quoting from R. Haag's paper "Irreversibility introduced on a fundamental level" ... once one accepts indeterminism, there is no reason against including irreversibility as part of the fundamental laws of Nature.
Lot of work must still be done, lot of prejudices overcomed. What we propose does not aspire to be a magic medicine that will rejuvenate Quantum Theory and make it Universal-And-True-For-Ever. But, perhaps, it will help to stop the bleeding from some open scars


According to Niels Bohr [...] there is an indispensable fundamental duality between the classical and the quantum levels of Nature. Our approach provides a mathematical form to such a view, and thus transfers its contents from the realm of philosophy into that of physics. The model that we present below shows that a mathematically consistent description of interaction between classical and quantum systems is feasible. Following Niels Bohr, we believe that the very fact that we can communicate our discoveries to our fellow men constitutes an experimental proof that interactions of the type that our model describes do exist in Nature.
As a summary of our project we think that our results reduce the number of puzzles to one i.e. that of the arrow of time whereas initially we believed that two important ones had to be solved i.e. the puzzle of irreversibility and that of quantum measurement. (as exemplified, for instance, by the paradoxes of von Neuman's infinite chain, Schroedinger's cat and of Wigner's friend ). We also believe that this remaining puzzle can be solved only after we have acquired a radically new understanding of the nature of time.
We propose to discuss the hypothesis that the yes-no-flip mechanism that we exploit in our model may constitute an elementary building block used by Nature in the communication between Her quantum and classical levels.
The philosophical motivation for this investigation came from the works of Niels Bohr and Karl Popper.
We formulated a model that provides an answer to one of the important conceptual problems of quantum theory, the problem of how and when a quantum phenomenon becomes real as a result of a suitable dissipative time evolution.
Thus if the universality hypothesis expressed in the Introduction is to be taken seriously, it will naturally lead to consequences that are at variance with some of the elements of the prevailing paradigm. Space (and thus also time) is to be build out of the discrete elements.


Last modified on: June 27, 2005.