# Foundations of Probabilities and Physics

International Conference at Växjö University, November 27 - December 1, 2000. Arranged by the ICMM (International Center for Mathematical Modeling in physics, technique and cognitive sciences, Vaxjo University, Sweden)

The main aim of this Conference is to reconsider foundations of probability theory in connection with foundations of physics (quantum as well as statistical).

The following problems will be discussed during the Conference:

**A.**Creation of the conventional probability theory (Kolmogorov's axiomatics, 1933).

1). Measure-theoretical approach (Borel, Kolmogorov, Frechet).

2). Frequency approach (von Mises, Ville, Tornier, Wald).

3). Others (Bayesian , comparative, negative, complex, nonstandard and p-adic probabilities). Is probability a measure or a frequency? A role of ergodicity. Why did Kolmogorov's model become dominating in mathematics and physics?**B.**Creation of probabilistic foundations of quantum mechanics.

Is quantum probability a measure, frequency, potentiality or degree of my belief?

The great diversity of opinions. Why do everybody use finally Kolmogorov's

measure-theoretical approach?**C.**Probability in statistical physics.

The role of ergodicity. Individual and statistical ergodicity.**D.**Einstein-Podolsky-Rosen paradox, Bell's inequality, locality, reality, probability.

1) Conventional probabilities and Bell's inequality (via Bell, Clauser, Horne, Shimony, Holt, Aspect, Home, Selleri, d'Espagnat, Fine, Rastal, Greenberger, Zeilinger,…).

2) Thermodynamical approach (via de Broglie, Lochak, de Muynck).

3) Quantum fluctuations, stochastic dynamics.

4). Von Mises frequency approach and Bell's inequality.

5). Fluctuating probabilities, modified Bell's inequality.

6). Quantum probabilities.

7). Negative probabilities .

8). p-adic probabilities; p-adic model of fluctuating reality.**E.**Quantum computers and information and probability (foundations).**F.**Paradoxes of probability theory (in particular, violations of the law of large numbers or ergodicity). Randomness, complexity and foundations of probability theory and physics.

### Proceedings

At the moment Prof. T. Hida discuss the possibility to publish Proceedings of the conference as a volume of journal *Inf. Dim. Analysis and Quantum Probablity.* If somebody can advice us some other variants it might be very useful.

### Local organizer

Prof. Andrei Khrennikov, Institute of Mathematics and System Engineering (ICMM), Växjö University, Sweden.

### Programme

#### Monday, 27 November

8.30 - 9.30: Registration

9.30 - 10.20 *T. Hida, Nagoya, Japan*: **Innovation approach to stochastic process and quantum dynamics**

10.30- 11.20 *L. Ballentine, Simon Fraser University, Burnaby, Canada*: **Interpretations of Probability and Quantum Theory**

11.20-11.40 Coffee-Break

11.40-12.30 *A. Khrennikov, Vaxjo University:* **R.von Mises approach to probability, Bell's inequalities and mystery of quantum probablistic rule**

12.30-14.00 Lunch

14.00-14.30 *P. Rocchi, IBM, Roma, Italy*: **Is the random event modeling a core question?**

14.40-15.25 *V. M. Maximow, University in Biallystok, Inst. of Computer Sci. Poland*: **On Abstract Mathematical Models of Probability**

15.30 -16.00 *V. I. Serdobolskii, Moscow*: **Constructive foundations of****randomness**

16.00-16.20 Coffee-Break

16.20-16.45 *E. R. Loubenets, Moscow State Institute of Electronics and Mathematics, Technical University, Quantum Stochastics*: **The New Approach to ****the Description of Generalized Quantum Measurements**

#### Tuesday, 28 November

9.30 - 10.20 *W. M. De Muynck, Eindhoven University of Technology, Eindhoven, Netherlands*: **Interpretations of quantum mechanics and interpretations of violation of Bell´s inequality**

10.30-11.20 *L. Accardi, University of Rome-2*

11.20-11.40 Coffee-Break

11.40-12.30 *H. Narnhofer, Intitut für Theoretische Physik Universität, Wien, Austria:* **Quantum K-Systems**

12.30- 12.55 *W. Ehm, Frieburg, Germany*: **Innovation approach to stochastic ****process and quantum dynamics**

13.00 -14.00 Lunch

14.00-14.30: *I. Aref´eva, Steklov Math. Institute, Moscow*: **p-adic string theory**

14.40-15.10 *A. Boutet de Monvel*: **Random matrices: Some universality****results in the mesoscopic regime**

15.15- 16.00 *I. Volovich, Steklov Math. Institute, Moscow*: **Quantum computers…**

16.00-16.20 Coffee-Break.

16.20-16.50 *B. Nilsson, Vaxjo University,*

#### Wednesday, 29 November (short day: excursion + conference dinner)

9.00-9.50 *T. Kolsrud, KTH, Stockholm:* **Symmetries and conserved quantities for heat equations.**

9.55- 10.45 *S. Albeverio, Bonn University:* **Stochastic quantization.**

10.50- 11.40 *S. Gudder, Departement of Mathematics, University of Denver, Denver Coloroado, U.S.A*: **An approach to quantum probability**

Lunch until 13.00

13.00-17.00 **Exursion:** "The Kingdom of Crystal", glasblowing

18.00-… Conference Dinner, Stadshotel.

#### Thursday, 30 November.

10.00- 10.40 *H. Atmanspacher, Freiburg, Germany and R. C. Bishop, Garching Germany:* **Intrinsic and Extrinsic Irreversibility in Probabilistic Dynamical Laws.**

10.45- 11.25 *E. G. Beltrametti and S. Bugajski, Department of Physics,University of Genova, Italy:* **Operational probability theory**

11.25-11.40 Coffee Break

11.40 - 12.20* P. Lahti, Turku, Finland:*** State teleportation without the projection postulate**

12.25-13.05 *J. Summhammer, Atominstitut, Vienna, Austria*: **Information from probabilistic data and quantum structure**

13 .05-14.30 Lunch

14.30-15.00 *D. H. E Gross, Hahn-Meitner-Institut, Berlin, Germany:* **Microcanonical statistical mechanics an phase transitions for "Small" systems**

15.00-15.25 *L. Polley, Oldenburg University, Germany*: **Position eigenstates, the superposition principle, and the Statistical Axiom of quantum mechanics**

15.30-15.55 *A. F. Kracklauer, University, Weimar, Germany*: **Complimentarity or Schizophrenia?**

15.55-16.15 Coffee Break

16.15-… **Round table: Probablity and Quantum Theory**.

#### Friday, 1 December

9.30-10.10 *J-Å. Larsson, Matematiska Inst. Linköpings Universitet, Sweden*: **A probabilistic inequality for the Kochen-Specker paradox**

10.10 - 10.40 *O. V. Viskov,Steklov Matematical Institute, Moscow:* **The random walks generate the infinitely divisible distributions**

10.45- 11.10 *B. Coecke, Department of Mathematics, Free University of Brussels*: **Classification of classical representations for quantum-like system via a minimal axiomatics for context dependence**

11.10-11.20 Coffee break

11.20-11.45 *H. Ishio, Dept. of Physics and Measurement Technology, Linköping University, Sweden*: **Statistics and Ergodicity of Wave Functions in Chaotic Open Systems**