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In this section we answer a series of questions and objections that
are being raised concerning the formalism and implications of EEQT.
- 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.
- 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
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.
- EEQT is too abstract for immediate applications to any
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
- I doubt if EEQT is sufficiently important that its properties should be of
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.
- 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  - and hidden variables, e.g. Bohm's theory - cf
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.
- 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.
- 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.
- 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
This is true.
- Now Bell criticizes (i) and (ii) because they ascribe a special
fundamental role to measurement, which seems implausible and makes
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.
- 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.
- 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.
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.
- 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.
- 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.
- 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.
- ... 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
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