EEQT: FAQ

In this section we answer a series of questions and objections that are being raised concerning the formalism and implications of EEQT.

1. Isn't it so that EEQT is a step backward toward classical mechanics that we all know are inadequate?
   EEQT is based on a simple thesis: not all is "quantum" and there are things in this universe that are NOT described by a quantum wave function. Example, going to an extreme: one such case is the wave function itself. Physicists talk about first and second quantization. Sometimes, with considerable embarassment, a third quantization is considered. But that is usually the end of that. Even the most orthodox quantum physicist controls at some point his "quantize everything" urge - otherwise he would have to "quantize his quantizations" ad infinitum, never beeing able to communicate his results to his colleagues. The part of our reality that is not and must not be "quantized" deserves a separate name. In EEQT we are using the term "classical." This term, as we use it, must be understood in a special, more-general-than-usually-assumed way. "Classical" is not the same as "mechanical." Neither is it the same as "mechanically deterministic." When we say "classical" - it means "outside of the restricted mathematical formalism of Hilbert spaces, linear operators and linear evolutions." It also means: the value of the "Planck constant" does not govern classical parameters. Instead, in a future theory, the value of the Planck constant will be explained in terms of a "non-quantum" paradigm. More on this subject in Section 6.
   
2. The mathematical framework of EEQT seems to be routine.
   EEQT is based on a little known mathematical theory of piecewise deterministic processes. It is impossible to discuss it rigorously without applying this theory. In fact, it is impossible to discuss any variation of a quantum theory that incorporates "events" as an inhomogeneous Poisson process without using PDP's. GRW avoids this requirement only because it assumes a homogeneous Poisson process. And, it is clear that any attempt to incorporate Einstein's relativity or non-uniformly accelerated observers would lead to inhomogeneous processes. In fact, as shown in [5, 6] GRW can be considered as a particular, degenerate, case of EEQT.
   There can be no understanding of what EEQT is about without understanding the rudiments of PDP theory; and there are only two or three books dealing with this theory. The mathematics involved are NOT routine. In fact,it requires a very clever application of PDP. This is due to the fact that, in quantum theory, we have at our disposal not the full algebra of functions on pure states but only small subsets of bilinear functions - given by expectation values of linear operators.
3. EEQT is too abstract for immediate applications to any concrete problems.
   EEQT has been applied to several problems, the most developed being its application to tunneling time.[24, 25] There it gives predictions that can be tested experimentally and compared with those stemming from other approaches. In this respect, orthodox quantum theory gives no predictions at all. Orthodox quantum theory is helpless when it comes to predicting timing of events. The classic paper by Wigner that tried to deal with the subject is inconclusive and has errors. The most evident future application of EEQT that we envisage relate to quantum computations, where EEQT formalism will provide interface between quantum and classical computing units.
   
4. I doubt if EEQT is sufficiently important that its properties should be of wide interest.
   As noted above, EEQT gave predictions concerning tunnling times. These predictions may prove to be right or wrong. If they prove to be wrong - then it will mean that EEQT is wrong. If they prove to be right - then it will mean that EEQT is better than any other competing approach. WE believe that any theory that is based on a healthy and rigorous math, reduces to known theories in a certain domain,AND predicts more in other domains SHOULD be of wide interest. In EEQT, contrary to the standard quantum theory, there is no need to invoke "external observers." ALL is in the equations. EEQT, in contrast to the orthodox QT, provides its own interpretation. We believe that these factors make it of interest to a wide audience.
   
5. EEQT is presented as a solution to the quantum measurement problem. As such it must be compared with the other proposed solutions. The authors mention two alternatives: the spontaneous localization idea of Ghirardi, Rimini, and Weber (GRW) -cf [35] - and hidden variables, e.g. Bohm's theory - cf [36]. Now on the surface these two alternatives seem so vastly superior and so much better developed than EEQT that it is hard to understand why anyone should pay much attention to EEQT.
   GRW has nothing to say about tunnelling time problems. Bohm's theory predictions are different from those of EEQT. Bohm's theory is also more than 40 years old. It takes time to develop a theory. We are not presenting a fully developed theory. We are presenting a theory that is BEING developed, but even at an incomplete stage, EEQT gives new predictions that can be tested experimentally. That is why we believe EEQT requires attention - even if only to disprove it - if possible.
   
6. While the authors give no indication of why EEQT should be regarded as improving in any way on GRW, they do say that their formalism "avoids introducing other hidden variables beyond the wave function itself." But this is not true, except in a sense for which the same thing could be said for any HV theory.
   Hidden variable theories use microscopic hidden variables that are "hidden" indeed from our observations! EEQT deals with classical variables that can be observed. In fact, it states that these are the ONLY variables that can be observed. Classical variables of EEQT are a direct counterpart of physics on the other side of the Heisenberg-von Neumann cut.
   
7. In EEQT, quantum mechanics is supplemented by a "classical system" (an apparatus?) given by an Abelian algebra of observables that also commute with all quantum observables. The spectrum of this algebra corresponds precisely to the possible values of the classical variables. Now in fact, any (hidden) variables in addition to the wave function could also be similarly regarded as corresponding to the spectrum of the center of an algebra of observables containing the quantum algebra.
   This is not true. Hidden variable theories of Bohm and of Bell are incompatible with linearity. They can not be formulated in algebraic terms at all. The statement that their hidden variables could be considered as corresponding to the spectrum of the center of an algebra of observables containing the quantum algebra is incorrect. It is based on misconception. EEQT is compatible with linearity. There is a reflection of this fact in the following: In hidden variable theories there is NO back action of classical variables on the wave function. In EEQT there is such an action. Linearity imposes the need for such a reciprocical action.
   
8. In his celebrated analysis of the quantum measurement problem, "Against Measurement," John Bell indicates that to make sense of the usual mumbo jumbo one must assume either that (i) in addition to the wave function psi of a system one must also have variables X describing the classical configuration of the apparatus or (ii) one must abrogate the Schrödinger evolution during measurement, replacing it by some sort of collapse dynamics. EEQT is a theory combining (i) and (ii): there are additional classical variables and because of the interaction between these variables and the quantum degrees of freedom, the evolution is not exactly the Schrödinger evolution and leads to collapses in measurement situations.
   This is true.
9. Now Bell criticizes (i) and (ii) because they ascribe a special fundamental role to measurement, which seems implausible and makes vagueness unavoidable.
   In EEQT we distinguish between a measurement and an experiment. Our universe can be considered as being "an experiment." This is in total agreement with Bell.
   
10. He then goes on to suggest two ways to overcome this difficulty: by not limiting X to macroscopic variables one arrives at Bohm's theory and by introducing a suitable microscopic collapse mechanism at GRW (as the simplest possibility).
    This is what Bell knew at the time of writing his papers. EEQT did not exist at this time. There are certainly more options available. EEQT shows that there are such options. But, as stated, EEQT is not yet a complete theory. It is semi-phenomenological. Its aim is to find the ultimate classical parameters without stating a-priori restrictions on their nature. They may prove to be related to gravity a'la GRW and Penrose; they can be related to consciousness a'la Stapp and Penrose-Hameroff; they can be related to new kind of fields that are yet to be discovered. John Bell was open minded. EEQT is open-minded as well.
    
11. We've made a great deal of progress in the past few decades, progress that is not reflected in EEQT.
    None of this progress helps us to better understand such a simple phenomenon as predicting tunelling time for an individual particle. Much of the so called "progress" leads to no new predictions. EEQT does.
    
12. The name "Event Enhanced Quantum Theory" is misleading.
    As we have stated: "EEQT is the minimal extension of orthodox quantum theory that allows for events." It DOES enhance quantum theory by adding the new terms to the Liouville equation. When the coupling constant is small, events are rare and EEQT reduces to orthodox quantum theory. Thus it IS an enhancement.
    
13. The possibility is thus opened for experimental discrimination between the two theories. Unfortunately, EEQT is formulated in too abstract and schematic a manner to permit any such discrimination.
    We agree that what is lacking is a textbook presentation of EEQT, with a thorough presentation of its experimental consequences and its relation to the orthodox QT. Writing such a textbook is presently being considered.
    
14. It seems almost as if the coupling of classical to quantum degrees of freedom, given by the matrix of linear operators and defining EEQT for the case at hand, is to be just so chosen as to reproduce the quantum predictions for the measurements under discussion.
    It is such that it reproduces those quantum predictions that have already been tested, but it also gives new predictions, about which quantum theory is silent, concerned with timing of the events and with the back action of the classical variables on the wave function. Any new, useful theory must be built in such a way that it is in agreement with the succesful aspects of the old one. EEQT is no exception in this respect. The point is that it differs from OQT in predicting more, and in predicting corrections to OQT predictions.
    
15. If the authors could provide a more general formulation of their theory, first by being clear about how the line is to be drawn between classical degrees of freedom and quantum ones; how the autonomy of the classical degrees of freedom fits with the fact, presumably accepted by the authors, that classical degrees of freedom are built out of quantum degrees of freedom...
    No, the authors do NOT presume this! Such a presumption is not justified by experiments. Experiments show that we are living in the world of FACTS, not the world of POSSIBILITIES. The authors do presume, that THERE IS a classical part of the universe that is not reducible to quantum degrees of freedom. Assuming that all must be quantum is similar to believing that the Sun revolves around the Earth. Without adequate knowledge, this seems to be observably so. EEQT is in agreement with all observable facts in at least the same degree as pure quantum theory is. But EEQT accomodates a knowledge base which accounts for events while quantum theory can't.
    
16. ... and then by providing some general specification of the interaction between classical and quantum degrees of freedom, analogous to specifying that electrons are governed by the Coulomb interaction or by QED, we would thereby have an alternative to quantum theory making perhaps dramatically different predictions from that theory. This might well be worth our consideration.
    When such a theory is finished and ready - it will certainly deserve a Nobel Prize! EEQT is not yet at this stage. Nor are any of the competing theories. However, we are working toward this end.