Advertisement

Synthese

, Volume 97, Issue 1, pp 125–156 | Cite as

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

  • Anton Amann
Article

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.

Keywords

Quantum Mechanic Mental Process Quantum Theory Quantum System Mechanical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. Amann, A.: 1991a, ‘Chirality: A Superselection Rule Generated by the Molecular Environment?’,J. Math. Chem. 6, 1–15.Google Scholar
  3. Amann, A.: 1991b, ‘Ground States of a Spin-Boson Model’,Ann. Phys. 208, 414–48.Google Scholar
  4. Amann, A.: 1991c, ‘Molecules Coupled to their Environment’, in Gans, Blumen, and Amann (1991), pp. 3–22.Google Scholar
  5. Amann, A.: 1991d, ‘Theories of Molecular Chirality: A Short Review’, in Gans, Blumen, and Amann (1991), pp. 23–32.Google Scholar
  6. Amann, A.: 1992a, ‘Applying the Variational Principle to a Spin-Boson Hamiltonian’,J. Chem. Phys. 96, 1317–24.Google Scholar
  7. Amann, A.: 1992b, ‘Molecular Superselection Rules Generated by a Bosonic Environment’, preprint.Google Scholar
  8. Andreose, M., et al.: 1987,The Arcimboldo Effect: Transformations of the Face from the Sixteen to the Twentieth Century, Bompiani, Milano.Google Scholar
  9. 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
  10. 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
  11. Barron, L. D.: 1986, ‘Symmetry and Molecular Chirality’,Chem. Soc. Rev. 15, 189–223.Google Scholar
  12. 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
  13. Boeyens, J. C. A.: 1986, ‘Holism and Chemistry’,Suid-Afrikaanse Tydskrif vir Wetenskap 82, 361–63.Google Scholar
  14. Bóna, P.: 1988, ‘The Dynamics of a Class of Quantum Mean-Field Theories’,J. Math. Phys. 29, 2223–35.Google Scholar
  15. Bóna, P.: 1989, ‘Equilibrium States of a Class of Quantum Mean-Field Theories’,J. Math. Phys. 30, 2994–3007.Google Scholar
  16. Born, M.: 1969,Albert Einstein, Hedwig und Max Born, Briefwechsel 1916–1955, Nymphenburger Verlagshandlung, München.Google Scholar
  17. Bratteli, O., and D. W. Robinson: 1981,Operator Algebras and Quantum Statistical Mechanics, Vol. 2, Springer, New York.Google Scholar
  18. Bratteli, O., and D. W. Robinson: 1987,Operator Algebras and Quantum Statistical Mechanics, Vol. 1, 2nd rev. ed., Springer, New York.Google Scholar
  19. Clauser, J. F., and A. Shimony: 1978, ‘Bell's Theorem: Experimental Tests and Implications’,Rep. Prog. Phys. 41, 1881–1927.Google Scholar
  20. Claverie, P., and S. Diner: 1980, ‘The Concept of Molecular Structure in Quantum Theory: Interpretation Problems’,Israel J. Chem. 19, 54–81.Google Scholar
  21. 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
  22. Coulson, C. A.: 1955, ‘The Contributions of Wave Mechanics to Chemistry’,J. Chem. Soc. 2069–84.Google Scholar
  23. Davies, E. B., and J. T. Lewis: 1970, ‘An Operational Approach to Quantum Probability’,Commun. Math. Phys. 17, 239–60.Google Scholar
  24. 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
  25. Einstein, A., et al.: 1935, ‘Can Quantum-Mechanical Description of Physical Reality be Considered Complete?’,Phys. Rev. 47, 777–80.Google Scholar
  26. Ellis, R. S.: 1985,Entropy, Large Deviations, and Statistical Mechanics, Springer, New York.Google Scholar
  27. Emery, V. J., and A. Luther: 1974, ‘Low-Temperature Properties of the Kondo Hamiltonian’,Phys. Rev. B 9, 215–26.Google Scholar
  28. Fannes, M., and B. Nachtergaele: 1988, ‘Translating the Spin-Boson Model into a Classical System’,J. Math. Phys. 29, 2288–93.Google Scholar
  29. Fannes, M., et al.: 1987, ‘Quantum Tunneling in the Spin-Boson Model’,Europhys. Lett. 4, 963–65.Google Scholar
  30. Fannes, M., et al.: 1988a, ‘The Equilibrium States of the Spin-Boson Model’,Commun. Math. Phys. 114, 537–48.Google Scholar
  31. Fannes, M., et al.: 1988b, ‘Tunneling in the Equilibrium State of a Spin-Boson Model’,J. Phys. A 21, 1759–68.Google Scholar
  32. Fleig, W.: 1983, ‘On the Symmetry Breaking Mechanism of the Strong-Coupling BCS-Model’,Acta Phys. Austriaca 55, 135–53.Google Scholar
  33. French, A. P., and P. J. Kennedy: 1985,Niels Bohr. A Centenary Volume, Harvard University Press, Cambridge, Massachusetts.Google Scholar
  34. 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
  35. Gombrich, E. H.: 1960,Art and Illusion. A Study in the Psychology of Pictorial Representation, Phaidon Press, London.Google Scholar
  36. Gombrich, E. H.: 1979,The Sense of Order, Phaidon Press, Oxford.Google Scholar
  37. 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
  38. Heisenberg, W.: 1959, ‘Wolfgang Paulis philosophische Auffassungen’,Naturwissenschaften 46, 661–63.Google Scholar
  39. Heisenberg, W.: 1986,Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik, Piper, München.Google Scholar
  40. Heitler, W.: 1954,The Quantum Theory of Radiation, 3rd rev. ed., Clarendon Press, Oxford.Google Scholar
  41. 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
  42. Jauch, J. M.: 1968,Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.Google Scholar
  43. Julesz, B.: 1971,Foundations of Cyclopean Perception, University of Chicago Press, Chicago.Google Scholar
  44. Julesz, B.: 1991, ‘Early Vision and Focal Attention’,Rev. Mod. Phys. 63, 735–72.Google Scholar
  45. Kanizsa, G.: 1976, ‘Subjective Contours’,Sci. Am. 234(4), 48–52.Google Scholar
  46. Köhler, W.: 1971,Die Aufgabe der Gestaltpsychologie, W. de Gruyter, Berlin.Google Scholar
  47. Kukolich, S. G., et al.: 1973, ‘Molecular Beam Maser Measurements of Relaxation Cross Sections in NH3’,Chem. Phys. Lett. 20, 519–24.Google Scholar
  48. 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
  49. Leggett, A. J., et al.: 1987, ‘Dynamics of the Dissipative Two-State System’,Rev. Mod. Phys. 59, 1–85.Google Scholar
  50. Locher, J. L.: 1984,Leben und Werk: M. C. Escher, Rheingauer Verlagsgesellschaft, Eltville am Rhein.Google Scholar
  51. Ludwig, G.: 1986, ‘Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories III’,Commun. Math. Phys. 9, 1–12.Google Scholar
  52. Maturana, H. R.: 1982,Erkennen: Die Organisation und Verkörperung der Wirklichkeit, Vieweg, Braunschweig.Google Scholar
  53. Maturana, H. R., and F. J. Varela: 1987,Der Baum der Erkenntnis, Scherz Verlag, Bern.Google Scholar
  54. 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
  55. Medawar, P., and J. Shelley (eds.): 1980,Structure in Scientific Art, Excerpta, Median, Amsterdam.Google Scholar
  56. 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
  57. 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
  58. 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
  59. Morchio, G., and F. Strocchi: 1987, ‘Mathematical Structures for Long-range Dynamics and Symmetry Breaking’,J. Math. Phys. 28, 622–35.Google Scholar
  60. Müller-Herold, U.: 1980, ‘Disjointness of β-KMS States with Different Chemical Potential’,Lett. Math. Phys. 4, 45–48.Google Scholar
  61. Müller-Herold, U.: 1982, ‘Chemisches Potential, Reaktionssysteme und algebraische Quantenchemie’,Fortschr. Physik 30, 1–73.Google Scholar
  62. Müller-Herold, U.: 1984, ‘Algebraic Theory of the Chemical Potential and the Condition of Reactive Equilibrium’,Lett. Matt. Phys. 8, 127–33.Google Scholar
  63. Müller-Herold, U.: 1985, ‘A Simple Derivation of Chemically Important Classical Observables and Superselection Rules’,J. Chem. Ed. 62, 379–82.Google Scholar
  64. Nachtergaele, B.: 1987,Exakte Resultaten voor het Spin-Boson Model, Thesis, Katholieke Universiteit Leuven, Leuven.Google Scholar
  65. 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
  66. Piron, C.: 1976,Foundations of Quantum Physics, Benjamin, New York.Google Scholar
  67. Popper, K.: 1980, Commentary, in Medawar and Shelley (1980), pp. 75.Google Scholar
  68. Primas, H.: 1983,Chemistry, Quantum Mechanics, and Reductionism. Perspectives in Theoretical Chemistry, Springer, Berlin.Google Scholar
  69. Primas, H.: 1990a, ‘Induced Nonlinear Time Evolution of Open Quantum Objects’, in Miller (1990), pp. 259–80.Google Scholar
  70. Primas, H.: 1990b, ‘Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems’, in Miller (1990), pp. 233–57.Google Scholar
  71. 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
  72. Primas, H.: 1990d, ‘Realistic Interpretation of the Quantum Theory for Individual Objects’,La Nuova Critica. Nuova Serie 13–14, 41–72.Google Scholar
  73. Primas, H.: 1991, ‘Necessary and Sufficient Conditions for an Individual Description of the Measurement Process’, in Lahti and Mittelstaedt (1991), pp. 332–46.Google Scholar
  74. 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
  75. Primas, H., and U. Müller-Herold: 1984,Elementare Quantenchemie, Teubner, Stuttgart.Google Scholar
  76. Quack, M.: 1986, ‘On the Measurement of the Parity Violating Energy Difference Between Enantiomers’,Chem. Phys. Lett. 132, 147–53.Google Scholar
  77. Quack, M.: 1989, ‘Structure and Dynamics of Chiral Molecules’,Angew. Chem. Int. Ed. Engl. 28, 571–86.Google Scholar
  78. Raggio, G.: 1981,States and Composite Systems in W*-Algebraic Quantum Mechanics, Thesis ETH-Zürich No. 6824, ADAG AG, Zürich.Google Scholar
  79. Resnikoff, H. L.: 1989,The Illusion of Reality, Springer, New York.Google Scholar
  80. Rock, I.: 1984,Perception, Scientific American Books, New York.Google Scholar
  81. Schrödinger, E.: 1935a, ‘Die gegenwärtige Situation in der Quantenmechanik’,Naturwissenschaften 23, 807–12, 823–28, 844–49.Google Scholar
  82. Schrödinger, E.: 1935b, ‘Discussion of Probability Relations Between Separated Systems’,Proc. Cambr. Phil. Soc. 31, 555–63.Google Scholar
  83. Schrödinger, E.: 1936, ‘Probability Relations Between Separated Systems’,Proc. Cambr. Phil. Soc. 32, 466–52.Google Scholar
  84. Sewell, G. L.: 1986,Quantum Theory of Collective Phenomena, Clarendon Press, Oxford.Google Scholar
  85. Silbey, R.: 1991, ‘Tunneling and Relaxation in Low Temperature Systems’, in Gans, Blumen, and Amann (1991), pp. 147–52.Google Scholar
  86. 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
  87. 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
  88. Smuts, J. C.: 1987,Holism and Evolution, N&S Press, Cape Town (rep. of 1st ed.: 1926).Google Scholar
  89. Spohn, H.: 1989, ‘Ground State(s) of the Spin-Boson Hamiltonian’,Commun. Math. Phys. 123, 277–304.Google Scholar
  90. Spohn, H., et al.: 1990, ‘Localisation for the SpinJ-boson Hamiltonian’,Ann. Inst. Henri Poincaré 53, 225–44.Google Scholar
  91. Strocchi, F.: 1985,Elements of Quantum Mechanics of Infinite Systems, World Scientific Publishing, Singapore.Google Scholar
  92. 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
  93. Sutcliffe, B. T.: 1992, ‘The Chemical Bond and Molecular Structure’,J. Mol. Struct. (Theochem)259, 28–58.Google Scholar
  94. Takesaki, M.: 1970, ‘Disjointness of the KMS States of Different Temperatures’,Commun. Math. Phys. 17, 33–41.Google Scholar
  95. Thomas, I. L.: 1969, ‘Protonic Structure of Molecules. I. Ammonia Molecules’,Phys. Rev. 185, 90–94.Google Scholar
  96. Unnerstall, T.: 1990, ‘Schrödinger Dynamics and Physical Folia of Infinite Mean-Field Quantum Systems’,Commun. Math. Phys. 130, 237–55.Google Scholar
  97. Watanabe, S.: 1969,Knowing and Guessing. A Quantitative Study of Inference and Information, John Wiley, New York.Google Scholar
  98. Watzlawick, P., et al.: 1967,Pragmatics of Human Communication. A Study of Interactional Patterns, Pathologies, and Paradoxes, W. W. Norton, New York.Google Scholar
  99. Weininger, S. J.: 1984, ‘The Molecular Structure Conundrum: Can Classical Chemistry be Reduced to Quantum Chemistry?’,J. Chem. Ed. 61, 939–44.Google Scholar
  100. Wheeler, J. A.: 1980, ‘Law without Law’, in Medawar and Shelley (1980), pp. 132–54.Google Scholar
  101. Wilson, E. B.: 1979, ‘On the Definition of Molecular Structure in Quantum Mechanics’,Int. J. Quantum Chem. S13, 5–14.Google Scholar
  102. Woolley, R. G.: 1978, ‘Must a Molecule have a Shape?’,J. Amer. Chem. Soc. 100, 1073–78.Google Scholar
  103. Woolley, R. G.: 1986, ‘Molecular Shapes and Molecular Structures’,Chem. Phys. Letts. 125, 200–05.Google Scholar
  104. Woolley, R. G.: 1988, ‘Must a Molecule Have a Shape?’,New Scientist 120 (22 October 1988), 53–57.Google Scholar
  105. Woolley, R. G.: 1991, ‘Quantum Chemistry Beyond the Born-Oppenheimer Approximation’,J. Mol. Struct. (Theochem)230, 17–46.Google Scholar
  106. 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.Google Scholar
  107. Zwerger, W.: 1983, ‘Dynamics of a Dissipative Two Level System’,Z. Phys. B 53, 53–62.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Anton Amann
    • 1
  1. 1.Laboratory of Physical ChemistryETH-ZentrumZürichSwitzerland

Personalised recommendations