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The Gestalt problem in quantum theory: Generation of molecular shape by the environment

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Abstract

Quantum systems have a holistic structure, which implies that they cannot be divided into parts. In order tocreate (sub)objects like individual substances, molecules, nuclei, etc., in a universal whole, the Einstein-Podolsky-Rosen correlations between all the subentities, e.g. all the molecules in a substance, must be suppressed by perceptual and mental processes.

Here the particular problems ofGestalt (≡shape)perception are compared with the attempts toattribute a shape to a quantum mechanical system like a molecule. Gestalt perception and quantum mechanics turn out (on an informal level) to show similar features and problems: holistic aspects, creation of objects, dressing procedures, influence of the ‘observer’, classical quantities and structures. The attribute ‘classical’ of a property or structure means thatholistic correlations to any other quantity do not exist or that these correlations are considered as irrelevant and therefore eliminated (either deliberately and by declaration or in a mental process that is not under rational control). An example of animposed classical structure is the nuclear frame of a molecule. Candidates for classical properties that arenot imposed by the observer could be the charge of a particle or the handedness of a molecule. It is argued here that at least part of a molecule's shape can begenerated ‘automatically’ by the environment. A molecular shape of this sort arises in addition to Lamb shift-type energy corrections.

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References

  • Amann, A.: 1988, ‘Chirality as a Classical Observable in Algebraic Quantum Mechanics’, in A. Amann, L. Cederbaum, and W. Gans (eds.),Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics, Kluwer, Dordrecht, pp. 305–25.

    Google Scholar 

  • Amann, A.: 1991a, ‘Chirality: A Superselection Rule Generated by the Molecular Environment?’,J. Math. Chem. 6, 1–15.

    Google Scholar 

  • Amann, A.: 1991b, ‘Ground States of a Spin-Boson Model’,Ann. Phys. 208, 414–48.

    Google Scholar 

  • Amann, A.: 1991c, ‘Molecules Coupled to their Environment’, in Gans, Blumen, and Amann (1991), pp. 3–22.

  • Amann, A.: 1991d, ‘Theories of Molecular Chirality: A Short Review’, in Gans, Blumen, and Amann (1991), pp. 23–32.

  • Amann, A.: 1992a, ‘Applying the Variational Principle to a Spin-Boson Hamiltonian’,J. Chem. Phys. 96, 1317–24.

    Google Scholar 

  • Amann, A.: 1992b, ‘Molecular Superselection Rules Generated by a Bosonic Environment’, preprint.

  • Andreose, M., et al.: 1987,The Arcimboldo Effect: Transformations of the Face from the Sixteen to the Twentieth Century, Bompiani, Milano.

    Google Scholar 

  • Aspect, A., J. Dalibard, and G. Roger: 1982a, ‘Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities’,Phys. Rev. Lett. 49, 91–94.

    Google Scholar 

  • Aspect, A., G. Grainger, and G. Roger: 1982b, ‘Experimental Test of Bell's Inequalities Using Time-varying Analyzers’,Phys. Rev. Lett. 49, 1804–07.

    Google Scholar 

  • Barron, L. D.: 1986, ‘Symmetry and Molecular Chirality’,Chem. Soc. Rev. 15, 189–223.

    Google Scholar 

  • Barron, L. D.: 1991, ‘Fundamental Symmetry Aspects of Molecular Chirality’, in P. G. Mezey (ed.),New Developments in Molecular Chirality, Kluwer, Dordrecht, pp. 1–55.

    Google Scholar 

  • Boeyens, J. C. A.: 1986, ‘Holism and Chemistry’,Suid-Afrikaanse Tydskrif vir Wetenskap 82, 361–63.

    Google Scholar 

  • Bóna, P.: 1988, ‘The Dynamics of a Class of Quantum Mean-Field Theories’,J. Math. Phys. 29, 2223–35.

    Google Scholar 

  • Bóna, P.: 1989, ‘Equilibrium States of a Class of Quantum Mean-Field Theories’,J. Math. Phys. 30, 2994–3007.

    Google Scholar 

  • Born, M.: 1969,Albert Einstein, Hedwig und Max Born, Briefwechsel 1916–1955, Nymphenburger Verlagshandlung, München.

    Google Scholar 

  • Bratteli, O., and D. W. Robinson: 1981,Operator Algebras and Quantum Statistical Mechanics, Vol. 2, Springer, New York.

    Google Scholar 

  • Bratteli, O., and D. W. Robinson: 1987,Operator Algebras and Quantum Statistical Mechanics, Vol. 1, 2nd rev. ed., Springer, New York.

    Google Scholar 

  • Clauser, J. F., and A. Shimony: 1978, ‘Bell's Theorem: Experimental Tests and Implications’,Rep. Prog. Phys. 41, 1881–1927.

    Google Scholar 

  • Claverie, P., and S. Diner: 1980, ‘The Concept of Molecular Structure in Quantum Theory: Interpretation Problems’,Israel J. Chem. 19, 54–81.

    Google Scholar 

  • Claverie, P., and G. Jona-Lasinio: 1986, ‘Instability of Tunneling and the Concept of Molecular Structure in Quantum Mechanics: The Case of Pyramidal Molecules and the Enantiomer Problem’,Phys. Rev. A 33, 2245–53.

    Google Scholar 

  • Coulson, C. A.: 1955, ‘The Contributions of Wave Mechanics to Chemistry’,J. Chem. Soc. 2069–84.

  • Davies, E. B., and J. T. Lewis: 1970, ‘An Operational Approach to Quantum Probability’,Commun. Math. Phys. 17, 239–60.

    Google Scholar 

  • Duffner, E., and A. Rieckers: 1988, ‘On the Global Quantum Dynamics of Multi-Lattice Systems with Non-linear Classical Effects’,Z. Naturforschung 43a, 521–32.

    Google Scholar 

  • Einstein, A., et al.: 1935, ‘Can Quantum-Mechanical Description of Physical Reality be Considered Complete?’,Phys. Rev. 47, 777–80.

    Google Scholar 

  • Ellis, R. S.: 1985,Entropy, Large Deviations, and Statistical Mechanics, Springer, New York.

    Google Scholar 

  • Emery, V. J., and A. Luther: 1974, ‘Low-Temperature Properties of the Kondo Hamiltonian’,Phys. Rev. B 9, 215–26.

    Google Scholar 

  • Fannes, M., and B. Nachtergaele: 1988, ‘Translating the Spin-Boson Model into a Classical System’,J. Math. Phys. 29, 2288–93.

    Google Scholar 

  • Fannes, M., et al.: 1987, ‘Quantum Tunneling in the Spin-Boson Model’,Europhys. Lett. 4, 963–65.

    Google Scholar 

  • Fannes, M., et al.: 1988a, ‘The Equilibrium States of the Spin-Boson Model’,Commun. Math. Phys. 114, 537–48.

    Google Scholar 

  • Fannes, M., et al.: 1988b, ‘Tunneling in the Equilibrium State of a Spin-Boson Model’,J. Phys. A 21, 1759–68.

    Google Scholar 

  • Fleig, W.: 1983, ‘On the Symmetry Breaking Mechanism of the Strong-Coupling BCS-Model’,Acta Phys. Austriaca 55, 135–53.

    Google Scholar 

  • French, A. P., and P. J. Kennedy: 1985,Niels Bohr. A Centenary Volume, Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

  • Gans, W., A. Blumen, and A. Amann (eds.): 1991,Large-Scale Molecular Systems: Quantum and Stochastic Aspects, NATO ASI Series B258, Plenum, London.

    Google Scholar 

  • Gombrich, E. H.: 1960,Art and Illusion. A Study in the Psychology of Pictorial Representation, Phaidon Press, London.

    Google Scholar 

  • Gombrich, E. H.: 1979,The Sense of Order, Phaidon Press, Oxford.

    Google Scholar 

  • Harris, R. A., and R. Silbey: 1985, ‘Variational Calculation of the Tunneling System Interacting with a Heat Bath II. Dynamics of an Asymmetric Tunneling System’,J. Chem. Phys. 83, 1069–74.

    Google Scholar 

  • Heisenberg, W.: 1959, ‘Wolfgang Paulis philosophische Auffassungen’,Naturwissenschaften 46, 661–63.

    Google Scholar 

  • Heisenberg, W.: 1986,Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik, Piper, München.

    Google Scholar 

  • Heitler, W.: 1954,The Quantum Theory of Radiation, 3rd rev. ed., Clarendon Press, Oxford.

    Google Scholar 

  • Hepp, K., and E. H. Lieb: 1973, ‘Phase Transitions in Reservoir-Driven Open Systems with Applications to Lasers and Superconductors’,Helv. Phys. Acta 46, 573–603.

    Google Scholar 

  • Jauch, J. M.: 1968,Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  • Julesz, B.: 1971,Foundations of Cyclopean Perception, University of Chicago Press, Chicago.

    Google Scholar 

  • Julesz, B.: 1991, ‘Early Vision and Focal Attention’,Rev. Mod. Phys. 63, 735–72.

    Google Scholar 

  • Kanizsa, G.: 1976, ‘Subjective Contours’,Sci. Am. 234(4), 48–52.

    Google Scholar 

  • Köhler, W.: 1971,Die Aufgabe der Gestaltpsychologie, W. de Gruyter, Berlin.

    Google Scholar 

  • Kukolich, S. G., et al.: 1973, ‘Molecular Beam Maser Measurements of Relaxation Cross Sections in NH3’,Chem. Phys. Lett. 20, 519–24.

    Google Scholar 

  • Lahti, P., and P. Mittelstaedt (eds.): 1991,Symposium on the Foundations of Modern Physics 1990. Quantum Theory of Measurement and Related Philosophical Problems, World Scientific, Singapore.

    Google Scholar 

  • Leggett, A. J., et al.: 1987, ‘Dynamics of the Dissipative Two-State System’,Rev. Mod. Phys. 59, 1–85.

    Google Scholar 

  • Locher, J. L.: 1984,Leben und Werk: M. C. Escher, Rheingauer Verlagsgesellschaft, Eltville am Rhein.

    Google Scholar 

  • Ludwig, G.: 1986, ‘Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories III’,Commun. Math. Phys. 9, 1–12.

    Google Scholar 

  • Maturana, H. R.: 1982,Erkennen: Die Organisation und Verkörperung der Wirklichkeit, Vieweg, Braunschweig.

    Google Scholar 

  • Maturana, H. R., and F. J. Varela: 1987,Der Baum der Erkenntnis, Scherz Verlag, Bern.

    Google Scholar 

  • McKenna, J., and J. M. Blatt: 1962, ‘The Expectation Value of a Many-Body Hamiltonian in the Quasi-chemical Equilibrium Theory’,Progr. Theor. Phys. 27, 511–28.

    Google Scholar 

  • Medawar, P., and J. Shelley (eds.): 1980,Structure in Scientific Art, Excerpta, Median, Amsterdam.

    Google Scholar 

  • Meyer-Abich, K. M.: 1989, ‘Der Holismus im 20. Jahrhundert’, in G. Böhme (ed.),Klassiker der Naturphilosophie, C. H. Beck, München, pp. 313–29.

    Google Scholar 

  • Miller, A. I. (ed.): 1990,Sixty-two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics, Plenum Press, New York.

    Google Scholar 

  • Morchio, G., and F. Strocchi: 1985, ‘Spontaneous Symmetry Breaking and Energy Gap Generated by Variables at Infinity’,Commun. Math. Phys. 99, 153–75.

    Google Scholar 

  • Morchio, G., and F. Strocchi: 1987, ‘Mathematical Structures for Long-range Dynamics and Symmetry Breaking’,J. Math. Phys. 28, 622–35.

    Google Scholar 

  • Müller-Herold, U.: 1980, ‘Disjointness of β-KMS States with Different Chemical Potential’,Lett. Math. Phys. 4, 45–48.

    Google Scholar 

  • Müller-Herold, U.: 1982, ‘Chemisches Potential, Reaktionssysteme und algebraische Quantenchemie’,Fortschr. Physik 30, 1–73.

    Google Scholar 

  • Müller-Herold, U.: 1984, ‘Algebraic Theory of the Chemical Potential and the Condition of Reactive Equilibrium’,Lett. Matt. Phys. 8, 127–33.

    Google Scholar 

  • Müller-Herold, U.: 1985, ‘A Simple Derivation of Chemically Important Classical Observables and Superselection Rules’,J. Chem. Ed. 62, 379–82.

    Google Scholar 

  • Nachtergaele, B.: 1987,Exakte Resultaten voor het Spin-Boson Model, Thesis, Katholieke Universiteit Leuven, Leuven.

    Google Scholar 

  • Pfeifer, P.: 1980,Chiral Molecules — A Superselection Rule Induced by the Radiation Field, Thesis ETH-Zürich No. 6551, ok Gotthard S + D AG, Zürich.

    Google Scholar 

  • Piron, C.: 1976,Foundations of Quantum Physics, Benjamin, New York.

    Google Scholar 

  • Popper, K.: 1980, Commentary, in Medawar and Shelley (1980), pp. 75.

  • Primas, H.: 1983,Chemistry, Quantum Mechanics, and Reductionism. Perspectives in Theoretical Chemistry, Springer, Berlin.

    Google Scholar 

  • Primas, H.: 1990a, ‘Induced Nonlinear Time Evolution of Open Quantum Objects’, in Miller (1990), pp. 259–80.

  • Primas, H.: 1990b, ‘Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems’, in Miller (1990), pp. 233–57.

  • Primas, H.: 1990c, ‘The Measurement Process in the Individual Interpretation of Quantum Mechanics’, in M. Cini and J.-M. Lévy-Leblond (eds.),Quantum Theory without Reduction, IOP Publishing, Bristol, pp. 49–68.

    Google Scholar 

  • Primas, H.: 1990d, ‘Realistic Interpretation of the Quantum Theory for Individual Objects’,La Nuova Critica. Nuova Serie 13–14, 41–72.

    Google Scholar 

  • Primas, H.: 1991, ‘Necessary and Sufficient Conditions for an Individual Description of the Measurement Process’, in Lahti and Mittelstaedt (1991), pp. 332–46.

  • Primas, H.: 1993, ‘Realism and Quantum Mechanics’, in D. Prawitz, B. Skyrms, and D. Westerståhl (eds.),Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science, Uppsala 1991, North-Holland, Amsterdam, forthcoming.

    Google Scholar 

  • Primas, H., and U. Müller-Herold: 1984,Elementare Quantenchemie, Teubner, Stuttgart.

    Google Scholar 

  • Quack, M.: 1986, ‘On the Measurement of the Parity Violating Energy Difference Between Enantiomers’,Chem. Phys. Lett. 132, 147–53.

    Google Scholar 

  • Quack, M.: 1989, ‘Structure and Dynamics of Chiral Molecules’,Angew. Chem. Int. Ed. Engl. 28, 571–86.

    Google Scholar 

  • Raggio, G.: 1981,States and Composite Systems in W*-Algebraic Quantum Mechanics, Thesis ETH-Zürich No. 6824, ADAG AG, Zürich.

    Google Scholar 

  • Resnikoff, H. L.: 1989,The Illusion of Reality, Springer, New York.

    Google Scholar 

  • Rock, I.: 1984,Perception, Scientific American Books, New York.

    Google Scholar 

  • Schrödinger, E.: 1935a, ‘Die gegenwärtige Situation in der Quantenmechanik’,Naturwissenschaften 23, 807–12, 823–28, 844–49.

    Google Scholar 

  • Schrödinger, E.: 1935b, ‘Discussion of Probability Relations Between Separated Systems’,Proc. Cambr. Phil. Soc. 31, 555–63.

    Google Scholar 

  • Schrödinger, E.: 1936, ‘Probability Relations Between Separated Systems’,Proc. Cambr. Phil. Soc. 32, 466–52.

    Google Scholar 

  • Sewell, G. L.: 1986,Quantum Theory of Collective Phenomena, Clarendon Press, Oxford.

    Google Scholar 

  • Silbey, R.: 1991, ‘Tunneling and Relaxation in Low Temperature Systems’, in Gans, Blumen, and Amann (1991), pp. 147–52.

  • Silbey, R., and R. A. Harris: 1984, ‘Variational Calculation of the Dynamics of a Two-Level System Interacting with a Bath’,J. Chem. Phys. 80, 2615–17.

    Google Scholar 

  • Silbey, R., and R. A. Harris: 1989, ‘Tunneling of Molecules in Low-Temperature Media: An Elementary Description’,J. Phys. Chem. 93, 7062–71.

    Google Scholar 

  • Smuts, J. C.: 1987,Holism and Evolution, N&S Press, Cape Town (rep. of 1st ed.: 1926).

    Google Scholar 

  • Spohn, H.: 1989, ‘Ground State(s) of the Spin-Boson Hamiltonian’,Commun. Math. Phys. 123, 277–304.

    Google Scholar 

  • Spohn, H., et al.: 1990, ‘Localisation for the SpinJ-boson Hamiltonian’,Ann. Inst. Henri Poincaré 53, 225–44.

    Google Scholar 

  • Strocchi, F.: 1985,Elements of Quantum Mechanics of Infinite Systems, World Scientific Publishing, Singapore.

    Google Scholar 

  • Sutcliffe, B. T.: 1990, ‘The Concept of Molecular Structure’, in Z. B. Maksiç (ed.),Theoretical Models of Chemical Bonding, Part 1: Atomic Hypothesis and the Concept of Molecular Structure, Springer, Berlin, pp. 1–28.

    Google Scholar 

  • Sutcliffe, B. T.: 1992, ‘The Chemical Bond and Molecular Structure’,J. Mol. Struct. (Theochem)259, 28–58.

    Google Scholar 

  • Takesaki, M.: 1970, ‘Disjointness of the KMS States of Different Temperatures’,Commun. Math. Phys. 17, 33–41.

    Google Scholar 

  • Thomas, I. L.: 1969, ‘Protonic Structure of Molecules. I. Ammonia Molecules’,Phys. Rev. 185, 90–94.

    Google Scholar 

  • Unnerstall, T.: 1990, ‘Schrödinger Dynamics and Physical Folia of Infinite Mean-Field Quantum Systems’,Commun. Math. Phys. 130, 237–55.

    Google Scholar 

  • Watanabe, S.: 1969,Knowing and Guessing. A Quantitative Study of Inference and Information, John Wiley, New York.

    Google Scholar 

  • Watzlawick, P., et al.: 1967,Pragmatics of Human Communication. A Study of Interactional Patterns, Pathologies, and Paradoxes, W. W. Norton, New York.

    Google Scholar 

  • Weininger, S. J.: 1984, ‘The Molecular Structure Conundrum: Can Classical Chemistry be Reduced to Quantum Chemistry?’,J. Chem. Ed. 61, 939–44.

    Google Scholar 

  • Wheeler, J. A.: 1980, ‘Law without Law’, in Medawar and Shelley (1980), pp. 132–54.

  • Wilson, E. B.: 1979, ‘On the Definition of Molecular Structure in Quantum Mechanics’,Int. J. Quantum Chem. S13, 5–14.

    Google Scholar 

  • Woolley, R. G.: 1978, ‘Must a Molecule have a Shape?’,J. Amer. Chem. Soc. 100, 1073–78.

    Google Scholar 

  • Woolley, R. G.: 1986, ‘Molecular Shapes and Molecular Structures’,Chem. Phys. Letts. 125, 200–05.

    Google Scholar 

  • Woolley, R. G.: 1988, ‘Must a Molecule Have a Shape?’,New Scientist 120 (22 October 1988), 53–57.

    Google Scholar 

  • Woolley, R. G.: 1991, ‘Quantum Chemistry Beyond the Born-Oppenheimer Approximation’,J. Mol. Struct. (Theochem)230, 17–46.

    Google Scholar 

  • Zaoral, W.: 1991, ‘Towards a Derivation of a Non-linear Stochastic Schrödinger Equation for the Measurement Process from Algebraic Quantum Mechanics’, in Lahti and Mittelstaedt (1991), pp. 479–86.

  • Zwerger, W.: 1983, ‘Dynamics of a Dissipative Two Level System’,Z. Phys. B 53, 53–62.

    Google Scholar 

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Amann, A. The Gestalt problem in quantum theory: Generation of molecular shape by the environment. Synthese 97, 125–156 (1993). https://doi.org/10.1007/BF01255834

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