The Birth of EEQT

 The work on the theory developed by Philippe Blanchard and myself, started in June of 1990. My initial idea was, as I wrote then in my personal diary: “to unify matter fields with information fields, to understand the role of time, the role of the wave function”. 

From Peter Århem, "Popper on the Mind-Brain Relation", 

in "Karl Popper's Science and Philosophy"

I wrote to Philippe Blanchard at the University of Bielefeld, and he accepted my proposal. I went to Bielefeld a year later and that was the beginning of our collaboration. In June of 1991 I wrote in my diary:

Popper advocates the propensity interpretation. Thus propensities exist objectively. They depend on ‘the whole experimental arrangement’. But How and Why the propensity of a certain event to happen at one place and at one time depends on a change of an experimental arrangement at another place and another time. It is time that we can calculate it. But do we understand?

Open Systems

In September 1991 I already understood that the key to the realistic description of Nature is the philosophy of “open systems” and the acceptance of indeterminism and irreversibility at the fundamental level. A year later we sent our first paper “On interaction between classical and quantum systems” for publication in Physics Letters. It appeared in print in March 1993. The Abstract of this first communication was short: “We propose a mathematically consistent model of interaction between classical and quantum systems.” In the text we wrote:

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.

We believe that our approach straightens out some of the conceptual puzzles of quantum theory. (…) As a summary of our project we think that our results reduce the number of puzzles to one i.e. that of ‘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. 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 also addressed there the subject of superselection rules:

In our model the distinct pure states of the classical system (Dirac measures) define superselection rules of the total system.

Thus we label coherent Hilbert spaces of the total system by the pure states of the classical system. Usually superselection quantities (e.g. electric charge) are taken to be constants of motion. It should be stressed that it is not the case with our model. Thus, to avoid misunderstandings, the very term ‘superselection rules’ should be avoided.

In the conclusion of the paper we pointed out the main feature of our proposed solution:

The central idea of these models is based on a modification of quantum mechanics by introducing dissipative elements in the basic dynamical equation and on allowing for a nontrivial dynamics of central quantities.

Thus we took algebra as the fundamental mathematical object, but not “algebra of observables”. Instead, we interpreted it as “algebra of operations”. The elements of algebra operate on “states”. Moreover, we admit our algebra to have “central quantities”, that is elements that behave in a classical way – they commute with all elements of the algebra. In another way we restrict the validity of Heisenberg’s quantum uncertainties, they do not apply to our “central elements”.

P.S.1 This is for my wife. She likes it. I like it too. Which is not a surprise.

Foreigner - I Want To Know What Love Is 

I've gotta take a little time

A little time to think things over
I better read between the lines
In case I need it when I'm older

This mountain, I must climb
Feels like a world upon my shoulders
Through the clouds, I see love shine
Keeps me warm as life grows colder

In my life, there's been heartache and pain
I don't know if I can face it again
Can't stop now, I've traveled so far
To change this lonely life

I wanna know what love is
I want you to show me
I wanna feel what love is
I know you can show me (hey)

Gotta take a little time
Little time to look around me
I've got nowhere left to hide
Looks like love has finally found me

In my life, there's been heartache and pain
I don't know if I can face it again
Can't stop now, I've traveled so far
To change this lonely life

I wanna know what love is
I want you to show me
I wanna feel what love is
I know you can show me

I wanna know what love is (I wanna know)
I want you to show me (I wanna feel)
I wanna feel what love is (I know, I know, and I know)
I know you can show me
Let's talk about love

I wanna know what love is
(Love that you feel inside)
I want you to show me
(I'm feeling so much love)
I wanna feel what love is
(And you know, you just can't hide)
I know you can show me

Oh, I wanna know what love is
(Let's talk about love)
I know you can show me
(I wanna feel)
I wanna feel what love is
(And you know you just can't hide)
I know you can show me
I wanna feel what love is (oh, I wanna know)
I want you to show me

P.S.2 The beginning of "Geometry of the conformally compactified Minkowski space"

With time it will be, little by little,  continuously improved, completed, changed, mutated. Slow evolution. Survival of the fittest, as they say.

I welcome all questions, comments, suggestions concerning these notes. 

Today have completed the proof of the second lemma.

P.S.3. 15-06-23 8:56 Today making changes in the file, without yet adding new stuff, to make it more consistent.

P.S.4. 12:22 Updated the file. Added a commutative diagram on p. 3.