Ark's
Homepage
Publications
Curriculum
Vitae
Physics
and the Mysterious
Event
Enhanced Quantum Physics (EEQT)
Quantum
Future
My
KaluzaKlein pages
Links
to my other online papers dealing with hyperdimensional physics

Note: These two applets crash
on certain browsers. Internet Explorer seems to be OK and Mozilla
seems to be OK. The applets crash with Opera (for reasons that
are not understood) and with older Netscape. Therefore the best
thing is to download the .jar files from SourceForge,
unpack them, download Java
SDK appropriate to the operating system, install it, and
then run the .jar files with "java jar qf.jar" or
"java jar wave.jar"

EEQT or EventEnhancedQuantumTheory
I. EEQT stands for "Event Enhanced Quantum Theory"
 the term introduced by Ph. Blanchard and A. Jadczyk to describe
the piecewise deterministic algorithm replacing the Schrödinger
equation for continuously monitored quantum systems (and we suspect
all quantum systems fall under this category).
From EEQT
FAQ:
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 embarrassment, a third quantization is considered.
But that is usually the end of that. Even the most orthodox
quantum physicist controls at some point his "quantizeeverything"
urge  otherwise he would have to "quantize his quantizations"
ad infinitum, never being 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, moregeneralthanusuallyassumed
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 "nonquantum"
paradigm.
(...)
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. (...)
II. Most of the essential papers dealing with various aspects
of EEQT are available online.
III. EEQT allows us to simulate "Nature's Real Working".
Of course EEQT is an incomplete theory, yet it tries to
simulate the real world events with an underlying quantum substructure.
The algorithm of EEQT is nonlocal, that suggests that
Nature itself, in its deeper level, is nonlocal too.
IV. Normally students learning quantum mechanics are being taught
that it is impossible to measure position and momentum of a quantum
particle. They learn how to derive Heisenberg's uncertainty relations,
and they are told that these mathematical relations have suchandsuch
interpretation. Some are told that the interpretation itself is
disputable. In EEQT all the probabilistic interpretation
of quantum theory, including Born's interpretation of the wave
function, is derived from the dynamics. EEQT allows us
to simulate and predict behavior of a quantum system when several,
as one normally calls them, incommensurable observables
are being measured. The fact is that in such situation
the dynamics is chaotic, and no joint probability distribution
exists. That explains why ordinary quantum mechanics rightly noticed
the problems with defining such a distribution.
(For visualization purposes physicists, especially those dealing
with quantum
chaos, often use Wigner's distribution (which is not positive
definite) or Husimi's distribution (which does not reproduce marginal
distributions).

Quantum Jumps

According to EEQT quantum jumps are not directly observable. What
we see are the accompanying "events". This part is somewhat
tricky, and I will try to explain the trickiness here, in few paragraphs,
but without any hope that there will be even one person who will
understand what I mean. Well, perhaps mathematicians will do, but
are they going to read this page? I doubt. Physicists certainly
will think that it is too weird. And they have better things to
do than following someone's weird ideas  as every physicist with
guts has weird ideas of his/her own! But I would feel guilty if
I did not give it a try. So here it is.
Physicists do consider quantum jumps. In particular those who deal
with theoretical quantum
optics and/or quantum
computing and information. But these quantum jumps are not being
taken as "real". If not for any other reason, than because
there are infinitely many jump processes that can be associated
with a given Liouville equation, and there is no good reason to
choose one rather than other. Thus discontinuous quantum jumps in
theoretical quantum optics are considered mainly as a convenient
numerical methods for solving the continuous Liouville equation.
It is not so in EEQT. But EEQT splits the world into a quantum and
a classical part, and quantum physicists deny that the classical
part exist. They think all is quantum 
the same way Ptolemeian physicists thought that all is perfectly
round. Can we propose a clever idea that will show that not
all is quantum? Indeed, according to quantum physics the only thing
that exists is the quantum wave function. Now, let us us ask this:
is the wave function itself a classical or a quantum object? That
is, we ask, is location of the wave function in the Hilbert space
governed by classical or by quantum laws? Most quantum physicists
would pretend they do not understand the question. Some will understand,
and will answer: "sure, there is an uncertainty in the state
vector, but that is altogether different story. They will point
me to Braginsky or Vaidman or some other, more recent, paper  but
they will not answer my question: is the quantum wave function a
classical or a quantum object? Is it an object at all? And if it
is an object, then what kind of animal it is, and where it fits?
Philosophers perhaps will point me to Eccles and Popper, but this
is not an answer either.
What is my answer to my own question? I do not know the answer,
but I can speculate. So, here it is: we are talking about models.
Models of "Reality". Perhaps nothing but models "exists",
but that is not our problem now. If all is about models, then we
can think of a model in which wave function is both classical and
quantum. In which Wave Function "observes" itself  as
John Archibald Wheeler has imagined:

"The
universe viewed as a selfexcited circuit. Starting small (thin
U at upper right), it grows (loop of U) to observer participancy
 which in turn imparts 'tangible reality' (cf. the delayedchoice
experiment of Fig. 22.9) to even the earliest days of the universe"
"If the views that we are exploring here are correct,
one principle, observerparticipancy, suffices to build everything.
The picture of the participatory universe will flounder, and have
to be rejected, if it cannot account for the building of the law;
and spacetime as part of the law; and out of law substance. It
has no other than a higgledypiggledy way to build law: out of statistics
of billions upon billions of observer participancy each of which
by itself partakes of utter randomness." (J.A. Wheeler,
"Beyond the Black Hole", in "Some Strangeness in
the Proportion", Ed. Harry Woolf, AddisonWesley, London 1980)

To observe itself "It" must split into two "personalities",
a quantum one and a classical one. So, here comes the model: consider
a pair of wave functions, the function trying to determine its own
shape. One element of the pair is considered to be "quantum"
 as it determines probabilities and quantum jumps, while the second
element of the pair is interpreted as a classical one  its shape
is the classical variable.
They
dance together and they jump together. More details can be found
in "Topics
in Quantum Dynamics". And here we come to the mathematical
description of quantum jumps in EEQT. Of course the simplest situation
is when we separate jumps from the continuous evolution. To analyze
this particular situation let us think of the simplest possible
"toy model". Physicists like toy models, as they usually
provide us with explicit solutions whose properties we can study
in order to try to understand more complex, real world situations,
where the problems get so complicated that there is no hope even
for an approximate solution. Physicists usually replace realworld
problems with other problems, build out of their toy models, which
are still simple enough to be solvable, even if only approximately,
and yet mirror some essential features of the "true problems."
So, what would be the simplest toy model to play with, that teaches
us something about quantum jumps? The quantum system, to be nontrivial,
must live in a Hilbert space of at least two complex dimensions.
The classical system must have at least two states. Such a toy model
was indeed studied in connection to the Quantum
Zeno effect., where it was demonstrated that a flipflop
detector strongly coupled (that is "under intensive observation"
 watched pot never boils... ) to a twostate quantum system effectively
stops the continuous quantum evolution. This model is not interesting
though if we want to study pure quantum jumps. Here we need a more
complicated model and that is how "tetrahedral model"
was developed. It was found that it leads to chaotic dynamics and
to fractals of a new type: fractals drawn by a quantum brush on
the quantum canvas  a complex projective space. And that is how
we come to quantum fractals.

Quantum Fractals

The
details and the bibliography are given in "Quantum
Jumps, EEQT and the Five Platonic Fractals." Here let us
describe the algorithm and the Java applet. (The applet is a part
of an OpenSource project, so additions and enhancements will probably
follow its release. )
The canvas, is a surface of the unit sphere In coordinates its
points are represented by vectors n = (n^{1},n^{2},n^{3})
of unit length, thus (n1)^{2}+(n2)^{2}+(n3)^{2
}= 1. There are five Platonic solids: tetrahedron (N=4), octahedron
(N=6), cube (N=8), icosahedron (N=12), dodecahedron (N=20), where
N is the number of vertices. They have equal faces, bounded by equilateral
polygons. It was Euclid who proved that only five such can exist
in a three dimensional world. In his Mysterium
Cosmographicum (1595) Johannes Kepler attempted to account for
the orbits of the six then known planets by radii of concentric
spheres circumscribing or inscribing the solids.


This site is a member
of WebRing.
To browse visit
Here. 

