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This page was updated October 18, 1996. I am working on it. At present the organization of this page is far from being an optimal one. In fact I do not know yet what would be the optimal organization. I am open to suggestions. If You have any - please send me an e-mail...
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Quantum Theory is special. It is the most recent one. It is one that is most difficult to grasp - I mean it needs the most advanced mathematical tools. Understanding it is still another business. As Richard Feynman put it: "nobody understands quantum theory." It is also probably the most successful one. I say "probably," because electrodynamics - which we owe to Ampere, Faraday, Maxwell and Lorentz - is perhaps the best tested. We know its powers and we know its limits. Quantum Theory is unexpectedly successful. It was invented to account for strange regularities of spectral lines - it was supposed to give a useful mathematical description of electrons circling around nuclei on somewhat special orbits. Soon it became apparent that its formal rules apply almost everywhere. Today it is not unusual to find a physicist who would like to "quantize" everything - including space and time and brain and mind. It is true that Quantum Theory was very successful in helping us to get some very precise numbers - that were later confirmed in experiments. But it is also true that it only helped us to compute these numbers. Quantum Theory could not produce these numbers by itself. I mean, there is something very special about QT. The point is that we do not understand it. It is, in a sense, an incomplete theory. I am using here a rather special meaning of incompleteness. Not the one used by Einstein in his combat with Bohr. What I mean here is that in each particular case we - human beings must complete it somehow.

The following long excerpt comes from the introduction to the "Theory of Events." It was written for the experts, so below I am commenting here and there...

The usual formalism of quantum theory fails in this respect ( to provide a solution to the quantum measurement problem). Let us look, for instance, into a recent book on the subject, `The interpretation of quantum theory'.

~This book is devoted mainly to the so called "consistent histories" interpretation of quantum theory. This interpretation contains some new elements, gives some hope to overcome some of the conceptual difficulties. But also it has its own problems. Omnes is well aware of these problems.
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, or will be solved pretty soon within this approach.
~In fact there is no agreement between physicists. There is a school more or less connected to the consistent histories approach and to the so called "decoherence" program. But there is also quite a large school that descends from Bohm's program of non-local hidden variables theories. The problem with the second school is that it does not dare to predict new results which would diverge from that of the orthodox quantum theory. There is also a school related to the "many worlds interpretation." Well, there are several others (e.g. Nelson's stochastic mechanics, stochastic electrodynamics). These schools do not fight at conferences! Rather they tolerate each other. Everybody is well aware of his own week points...
They use a magic spell; and at present the magic spell that is supposed to dissolve the problems is `decoherence.'

~The main idea behind the decoherence program is this: we need to understand why the macroscopic world seems to be, or indeed is "FPP" (for All Practical Purposes) classical, while the microscopic reality (if any "reality" exists on this level at all) obeys strange rules of quantum theory. The decoherence program tries to derive this fact from the ever-present action of "environment." So some "environment" is blamed for destroying quantum interference. But then, what is the environment for the Universe? Well, then we can still blame the mysterious black holes.

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 been obtained within this approach. Decoherence does not tell us yet how to program a computer to simulate such events. A physicist, a human being, must intervene to decide what to decohere and how to decohere and on which basis it is to be distinguished.
~The discussion here becomes a little bit technical. In quantum theory we deal with complementary variables. Position alone is good. It is classical. Momentum alone is also good. It is also classical. But position AND momentum - well ... there are certain troubles in quantum theory with assuming that both are well defined at the same time. There is the famous Heisenberg's uncertainty principle. In the decoherence program, it is necessary to end with either position OR momentum, or something else, but only with ONE such classical quantity. It is called the "pointer basis."
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.
~In fact, the "many worlds interpretation" claims that it is able to derive quantum postulates. I tried to understand this - but I failed in disgust. Today my disgust is not as strong as then. This is for the following reason: in "many worlds" approach you assume that every time a measurement is done - the world splits! But WHAT IS MEASUREMENT? WHEN it is done? How often is the world supposed to split? There are no answers to these questions. With the new theory that this paper is part of - these questions CAN get precise answers.
Also the hidden variables theories claim to be able to derive quantum postulates. But when you analyze their assumptions, then you see that you must put in assumptions that must be justified. The proponents are well aware of these difficulties and they are working hard indeed to find these justifications.
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 arbitrary! Must it be so?
~The fact that we are asking here this question is nothing but a straightforward consequence of the other fact: that we think WE CAN do better... :)
Many physicists would oppose this. They disagree with such a criticism. They see that quantum theory is good, is excellent, because it gives excellent results. But there are other voices too. We like to recall John Bell's opinion on this matter. He has studied the subject rather deeply. He emphasized it repeatedly (cf. [bell89], [bell90]): our problems with quantum measurement are based on a very fundamental idea: The reason is that the very concept of ` measurement' can not even be precisely defined within the standard formalism.
~In fact, John Bell was more than disgusted with the way quantum theory is presented and interpreted. He went to the point that he proposed to BAN the very word "measurement," and several other "selfexplanatory" concepts. I am wondering if today he would not ban also the word "environment"... (gh..).
That is also our opinion. But we do not only share his criticism, we also propose a way out that is new.

Our solution does not involve hidden variables (but we like to joke that the standard quantum state vector can be considered as a hidden variable). Our reasoning goes as follows:

First, we point out the reason why `measurement' can not be defined within the standard approach. It is true that the standard formalism of quantum theory has many sophisticated tools: it has Hilbert spaces, wave vectors, operators, spectral measures, POV measures; but it has no place for ` events'. What constitutes an event? The only candidate for an event that we can think of is change of a quantum state vector.

~Most physicists believe in one God - the all quantum God. This all quantum God must be - according to them - all perfect, all quantum coherent. But then, where does the "decoherence" come from? How can anything happen, if all is wave-like and continuous? Well, the only thing that can happen to a wave in a wavy word is that the wave changes its shape. In quantum theory, probability waves, or rather waves of amplitudes of probabilities, are represented by vectors in a "Hilbert space."
But how do we observe state vectors? We can not see them directly.
~That is: we do not see "probability waves." We see facts. They may be good facts or bad facts, right facts, or wrong facts, telling us much or telling us little - but they are facts! Not waves.
We were taught by Bohr and Heisenberg that any observation will disturb a quantum state. Well, unless the state is already known to us, then we can try to be clever and not disturb it.

~At this place we have in mind a rather provocative paper by Y. Aharonov and L. Vaidman. This paper was later criticized by Unruh and others. The question was: is the quantum state an "objective" or "subjective" thing. Can we know it without disturbing it? This question is still open. But a way to answer this question is sketched in [jad94a].

But how can we know the state? We need a theory, that will help us to answer these questions. We are proposing such a theory. We have extended the standard formalism. We do 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.

~That is we follow the line of thought initialized by Niels Bohr. He often stressed that we must talk to our colleagues using the classical language - otherwise communication (and thus science) would not be possible. Also Heisenberg stressed the necessity of placing, at some point, a cut between what is quantum and what is classical. Both Bohr and Heisenberg did not go beyond talking about these matters. The theory that dwells on these pages goes beyond just talk. It is based on the talk, but it proposes mathematics that transform words into quantitative predictions. This mathematics is not easy. But it is not more difficult than that used in statistical predictions of stock market behaviour. In fact, it is the same! There are many phenomena around us that show a somewhat peculiar behaviour: everything goes smoothly ... up to a point. Then there is a crash. This crash takes a certain time, sometimes a fraction of a second (sand pile micro-avalanche), sometimes just few seconds (earthquake), sometimes longer (stock market crash). After the crash all goes again smoothly - for a while... What is important: while the smooth evolution is predictable (although its predictions may be unreliable - like with the weather and other phenomena where prediction is sensitive to errors in the input data), the crash period, the period of catastrophe, has an inbuilt roulette mechanism. Determinism gives up, indeterminism is ruling this short time. And then, everything is quiet again. And we are sure that tomorrow will be much as today. This is good. Because we can plan. This is bad. Because we can influence next to nothing. The theory that dwells on these pages received the name EEQT for Event Enhanced Quantum Theory. Standard Quantum Theory knows not about stock market crashes and catastrophes. It knows only continuous evolution of "probability vectors." We enhance it adding events. They are also known as "quantum jumps." Some physicists say - these events do not exist. Some others say: they exist only in "mind." We do not care. Old physics was based on differential equations. Quantum Theory is based on Schroedinger's Equation. It is time now to look for a new physics. New physics will be based on algorithms rather than differential calculus. EEQT proposes such an algorithm. It is called PDP (piecewise deterministic process). It is borrowed from stock market mathematics. Long periods of determinism (modified, continuous Schroedinger evolution) are interrupted from time to time by discontinuous changes - events. EEQT gives mathematical laws that make it possible to predict as much as can be predicted under these circumstances. It also puts into our hands tools to intervene. It gives us hope to be free - as much as possible in this strange, partially determined, but occasionally not, quanto-classical, spirito-material world.

Then we define `experiments' and `measurements' within the so extended formalism. We can show that the standard postulates concerning measurements - in fact, in an enhanced and refined form - can be derived instead of being postulated.


~ In this respect our theory differs from Bohm's theory. As we noted above, Bohm's theory refrains from making new predictions. Our theory, EEQT, is testable. It is falsifiable. It gives new predictions. For a while however, we do not treat this theory as the last word. We want to check first to see if it survives a difficult test: if it can be made relativistic.

This `event enhanced quantum theory', 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 given by experiments with single quantum systems. In particular this new theory is falsifiable. But our program is not yet complete. Our theory is based on an explicit selection of a classical subsystem. How to select what is classical? If we want to be on the safe side as much as possible, or as long as possible, then we will shift `classical' into the observer's mind. But will we be safe then? For how long? Soon we will need to extend our theory and to include a theory of mind and a theory of knowledge. That necessity will confront us anyway, perhaps even soon.


~These sentences show clearly that the spirit of Popper's metaphysics is behind these ideas. On my other pages I am quite open about metaphysical ideas that were responsible for this, and not some other, approach.

But it is not clear that the cut must reside that far from ordinary 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. At present we do not know what these principles are, we can only guess.
~Let me be frank: I have two guesses at present: my first guess is that "classical has something to do with light. I remember the title of H.P. Stapp's paper "Light at the foundation of being" - or something similar. Another possibility is : classical is logic, or word, or mind. These two options are not exclusive...
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.
~Here comes criticism of the standard quantum theory. I do not expect that this criticism will be understood. Quantum theory is so difficult, and there is so much brainwashing, that the student, after learning some of its abstract mathematics, after being discouraged so many times to ask questions that are said to make no sense - every student, no exception starts to believe that he now knows the secret of secrets. Teaching of QM is, in this respect, very much similar to teaching of TM. (If you want to know the results of the last - see Trancenet site )
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 may feel proud that we are so necessary, that we can not be replaced by machines.

~In July 1995, in Bielefeld, Germany, there was a conference "Quantum Theory Without Observers." It was mostly dominated by the proponents of Bohmian mechanics, but not totally. All the main currents of QM were represented there. One of the ideas that was heard again and again was this: a theory, a physical theory, should have all in the equations. Not in the "background." The present day QM is not of this kind. EEQT aspires to be such.
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?
~What I mean here is this: any theory, quantum theory should not be an exception here, should give us algorithms that are able to predict the future events given past events. This prediction should include not only "what will happen," but also "when it will happen." Clear: predictions will have a probabilistic character. Standard QM is not able to give such predictions - it does not even know the concept of an event. In fact, it denies that events exist (well... perhaps approximately...). EEQT aspires to be such a theory.

Our theory is better in this respect. Once we have chosen a model - then reality, with all its events as they happen in time, can be simulated by a sufficiently powerful digital computer.


Classical Mechanics is about bodies. Bodies can be small or big. Can be rigid or can be fluid. In the simplest possible case we have just one body and this body is just a point. This point is a point in space. Nobody knows exactly what space is, but we all know that it is a very useful concept. What can a point in space do? It can move. It can change its position with time. Again, nobody knows what time is - but we believe: somebody will know one day, and so we continue. There are two more important concepts without which we can not discuss what classical mechanics is. The first concept is that of force. Again, force is not something that you can define. But we can talk about force in a descriptive way. For instance, we can say: when there no forces acting on a body, then it moves along a straight line with a constant velocity. Or, we can say: when there are no other bodies around, then no force acts on our body - because forces may come only from other bodies. Of course, this sentence assumes that we know what we mean by "straight line," what is "constant velocity", and what we mean by "around." And, precisely speaking, we do not know. But science is always this way. It is impossible to base it only on logic. It exists because of experience.
When we know forces, we say that we know dynamics. And when we know dynamics - then we can use Newton's equation to calculate future positions of the bodies, provided we know their positions and velocities now. It is because of this that we call the pair (position,velocity) by the name state. (By the way: this is not always the case, because for bodies with spin, or with variable mass, things are not that simple.) So state in physics and in engineering is a something with the property that, if we know it now, then we can compute it for later times - provided we know forces and other external factors (and provided we know what is later, which is not that evident in Einstein's Relativity.) We do not need necessarily to consider dynamics to speak about classical states. For instance, when we consider a switch - then it can be in one of the two states: on or off. And a digital voltmeter that can, at most, show the number 999, (poor quality indeed) can be in one of its 1000 states. And its state can change with time. It will either change by jumping or continuously as our material point.

Now, let us compare this with Quantum Mechanics. Here we do not know what state is at all. But nevertheless it is the most important concept. There are two ways that Quantum Theory is introduced in textbooks. The first way is through waves. To hypnotize the minds of young students one starts talking about waves that they already know about. Waves on a water, acoustic waves, electromagnetic waves... Then waves in general. One introduces complex numbers - because "they are so convenient." Then one shows beautiful diffraction pictures, and then one tells about de Broglie hypothesis and about Schroedinger's equation. Then it becomes very difficult, so difficult that everybody easily accepts when he is being told: that these are not real waves, but probability waves, that they are not even probability waves but rather complex amplitude waves, and that they do not propagate in our space but rather in a multidimensional configuration space... feynman.gif And that they are in fact not so much waves, but vectors in Hilbert space, and not so much vectors, but rather rays, and that usually they are not in Hilbert space because their norm is infinite so that they reside in a rigged Hilbert space - whatever that means....
At that moment everybody stops thinking and moves to calculate - because they are sure there are many things about these waves that can be calculated! Nobody dares to ask: what is that nonsense about these complex probability waves. OK, some people do dare. Like R.P. Feynman. But isn't he joking?

There is also another way of teaching Quantum Theory. This second method is similar to how engineers are being taught about system theory. I do prefer this second method, as it does not pretend at all that something is to be understood. We have a black box, and we want simple mathematical models that are useful for calculating some characteristics of the black box - from the knowledge of some other characteristics. So, we are building phenomenological models, and do not pretend that these models reside in the box. Model is model, and box is box. These models reside on a paper and in a computer that is doing simulations. While the box resides in Nature. This second way of teaching quantum mechanics has advantages. It is, so to say, more moral. But it has disadvantages as well. Why? Because, as Feynman has noticed, "nobody understands quantum mechanics." Because of this, to get from it numbers, we have to resort to all kinds of analogies and to cheating. This necessity of cheating, of replacing one problem that we can't solve - even in principle, by another one - that we can, became so much a normal affair that we do not even notice it. In this way Quantum Theory, the best physical theory that we ever had, contributes to an exponential decrease of morale of physicists. Hopefully EEQT, or something even better, will stop this fatal descent...

To be continued ...

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Last modified on: June 27, 2005.