SVIBOR - Project code: 1-03-176

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Project code: 1-03-176


ALGEBRAICO-PROBABILISTIC STRUCTURES OF QUANTUM MECHANICS


Main researcher: PAVIČIĆ, MLADEN (77362)


Assistants
Type of research: basic
Duration from: 01/01/91. to 05/31/95.
Papers on project (total): 25
Papers on project quoted in Current Contents: 9
Institution name: Građevinski fakultet, Zagreb (82)
Department/Institute: Department of Mathematics
Address: Kačićeva 26, Pošt. pret. 217
City: HR-41001 - Zagreb, Hrvatska
Communication
Fax: 385 (1) 416621
Phone: 385 (1) 4551189
E-mail: pavicic@master.grad.hr
Summary: At present there is a gap between quantum logic as a propositional system and the full predicative system of the second order underlying quantum formalism in the Hilbert space. The usual way out is to impose states on quantum logic proper, i.e., on a propositional system whose Lindenbaum algebra is a genuine orthomodular lattice and to obtain the Hilbert space as a model for such a structure. In doing so we lose a possible physical understanding of individual quantum measurements, i.e., of elementary propositons of quantum logic. The way out of the present project is to find a proper propositional part of the algebraico-probabilistic structure underlying the Hilbert space. Such a system is considered to be a particular variety of an orthomodular system however directly encompassing probabilistic structure which is in the standard approach imposed on it through states defined on it. The project establishes a deductive axiomatic system underlying quantum Hilbert space frame as a particular variety of quantum logic with a unique operation which defines orthomodularity in a way in which classical implication defines distributivity. The found variety enabled solving many previously unsovled problems (See Sec. AIMS AND RESULTS, below). On the other hand, the system turns out to be more general than the standard quantum mechanics in the Hilbert frame and the appropriate observables which turn out to be more general than the standard ones might stem directly from many particle states. The project's research along this line brought us to a discovery of two following new physical effects in the domain of the fourth-order interference (See Sec. AIMS AND RESULTS, below). The first effect reads that the fourth-order interference entangles formerly unpolarized photons into a spin singlet state and that it depolarizes formerly polarized photons. The second effects reads that the fourth-order interference between two photons from two spin singlets entangles the other two photons (which nowhere interacted and whose paths nowhere crossed) into a spin singlet. In other words, subsystems of a pure state need not have a common origin.

Keywords: quantum logic, orthomodular lattices, quantum measurement theory, foundations of quantum mechanics, quantum optics, intensity interference, interference of the fourth order

Research goals: The objectives of the project are: 1. Providing a statistical basis for the algebra underlying quantum measurements. 2. Founding quantum logic on a unique operation corresponding to the ordering relation of its model, orthomodular lattice. 3. Giving a probabilistic representation for quantum logic. 4. Atacking finite model property problem of quantum logic. 5. Conceiving and carring out experiments which can test possible quantum observables extending standard ones. From 1991-1993 I achieved the following: 1. In 1991 I proved theorems which link the frequency (via central limit theorem) with the elements of quantum logic. 2. In 1992 I found the long wanted operation: The unique bi-implication being equal to one whenever the corresponding ortholattice elements are equal - amounts to orthomodularity. 3. In 1992-1993 I proved soundness and completeness for a new YES-NO representation of quantum logic and orthomodular lattices based on a new intransitive and symmetric relation. 4. In 1993 I proved that quantum logic possesses the finite model property if it contains finitely many elementary propositions. 5. In 1993 I investigated the interference of the 4th order of photons correlated in polarizations coming from two independent sources and found significant new results which also enable feasible experiments. Two most significant results are that two unpolarized photons from independent sources get correlated in polarization by interfering in the fourth order and that one can preselect with certainty pairs of photons correlated in polarization and being in the singlet state from the set of independent, unpolarized, and uncorrelated photons. (See the papers in Phys. Rev. Lett., Phys. Rev. A, and J. Opt. Soc. Am. B)

COOPERATION - PROJECTS


  1. Name of project: P8781-PHY "Interferenz mit Electronen und Ionen"
    Name of institution: Fonds zur F”rderung der wissenschaftlichen Forschung, ™sterreich
    City: A-1020 - Wien, Austrija

COOPERATION - INSTITUTIONS


  1. Name of institution: Laboratoire de M‚chanique Quantique, Facult‚ des Sciences, Universit‚ de Reims, B.P. 347, F-51062 Reims Cedex, France.
    Type of institution: Economical/Production
    City: F-51062 - Reims, Francuska

  2. Name of institution: Atominstitut der ™stereichischen Universit„ten, Schttelstr. 115, A-1020 Wien, ™sterreich.
    Type of institution: University/Faculty
    City: A-1020 - Wien, Austrija

  3. Name of institution: Technische Universit„t Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, ™sterreich.
    Type of institution: Economical/Production
    City: A-1040 - Wien, Austrija

  4. Name of institution: Max-Planck-Ges. Institut fr Nichtklassische Strahlung, Humboldt-Universit„t zu Berlin, Rudower Chaussee 5, Geb„ude 10.16, D-12484 Berlin, Deutschland.
    Type of institution: University/Faculty
    City: D-12484 - Berlin, Njemačka

  5. Name of institution: Institut fr Theoretische Physik, Technische Universit„t Berlin, Hardenbergerstr. 36, D-10623 Berlin, Deutschland.
    Type of institution: Economical/Production
    City: D-1000 - Berlin, Njemačka

OTHER ACHIEVEMENTS


  1. Name: Izbor u Organizing Committee i u Scientific Council International Quantum Structures Asociation, Inc. na period 1992-1994 i izborni prijedlog članstvu (250 članova iz 27 zemalja svijeta) za izglasavanje produljenja mog mandata do 1996.
    Type of achievement: Other
Other information about the project.
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