Quantum Mechanics: Principles, New Perspectives, Extensions and Interpretation – Revised Edition


Olavo Leopoldino da Silva Filho
Universidade de Brasília, Instituto de Física, Núcleo de Física Estatística e Física Matemática, Campus Universitário Darcy Ribeiro, Brazil

Series: Physics Research and Technology
BISAC: SPO058000

The book Quantum Mechanics: Principles, New Perspectives, Extensions and Interpretation – Revised Edition deals with the foundations of Quantum Mechanics in a quite novel way. From his own published works throughout these last 20 years in prominent Journals, Prof. L.S.F. Olavo reconstructs Quantum Mechanics (as related to the Schrödinger equation) from the scratch, both in mathematical and interpretive ways.

The picture that emerges is quite different from the one we get from other approaches. While the mainstream approach reinforces some unavoidable weirdness in the Quantum World, Prof. Olavo’s interpretation presents Quantum Mechanics as quite an intuitive theory, using only the pedestrian notions of randomness, fluctuations and the companion notion of statistics. However, it is much more than another stochastic approach. Throughout the first part of the book, Prof. Olavo shows how the various roads to derive the Schrödinger equation can be reduced to his own mathematical construction: Feynman’s path integral and the stochastic approach are but two of them. The book also brings about quite new results, such as the connection between Quantum Mechanics and the Central Limit Theorem and Langevin Equations (by means of which quantum phenomena can be easily simulated and make visualizable). All this is done taking recourse to only three axioms.

This strategy gives the book an impressive power of synthesis in what respects the interpretation of the formalism. In fact, in the last part of the book, Prof. Olavo shows how some of the innumerous proposals for the interpretation of Quantum Mechanics, with some of their constructs, can help us making a rational reconstruction of a Quantum World without any weirdness whatsoever.

In the second part, to remove some of the various obstacles to a Quantum Mechanics without weirdness, the book deals with the most prominent aspects and experiments of the Quantum, such as spin and the Stern-Gerlach experiment, the construction of operators and also Identical Particles.

In the third part, the book presents a fully special and general relativistic extension of the formalism by just making the extension of the three postulates used throughout the first part.

This book is intended to all those interested in the foundations of Quantum Mechanics. (Imprint: Nova)

Table of Contents

Table of Contents


List of Tables

List of Figures

Part I. Principles

Chapter 1. Historical Background – XIXth Century and Beyond

Chapter 2. The Characteristic Function Derivation

Chapter 3. The Entropy Derivation

Chapter 4. The Stochastic Derivation

Chapter 5. Quantum Mechanics and the Central Limit Theorem

Chapter 6. Langevin Equations for Quantum Mechanics

Part II. New Perspectives

Chapter 7. Classical Representation of the Spin

Chapter 8. Operator Formation and Phase Space Distributions

Chapter 9. On Reality, Locality and Bell’s Inequalities

Chapter 10. Indistinguishability

Part III. Relativistic Extension

Chapter 11. Special and General Relativistic Quantum Mechanics

Part IV. Interpretation

Chapter 12. The Interpretation of Quantum Mechanics




[1] Pullman, B. (1998). The Atom in History of the Human Thought (Oxford University Press, New York).
[2] Descartes, R. (1637). La Geometrie. The Geometry of Rene Descartes, translated to the English by David E. Smith and Marcia L. Latham, (Dover, New York, 1954).
[3] Descartes, R. (1664). Le Monde ou le Traité de la Lumère. El mondo o el Tratado de la Luz, translated to the Spanish by Ana Rioja (Alianza Editorial, Madrid, 1991).
[4] Newton, I. (1730). Optics. Óptica, translated to the Portuguese by André Koch Assis (Edusp, São Paulo, 1996).
[5] Purrington, R. D. (1997). Physics in the Nineteenth Century (Rutgers Univ. Press).
[6] Maxwell, J. C. (1954). A Treatise on Electicity and Magnetism (Dover edition, New York).
[7] Lucretium, (1995). On the Nature of Things: De rerum natura. Anthony M. Esolen, transl. (The Johns Hopkins Univ. Pr., Baltimore).
[8] Mehra, J. (1987). Foundations of Physics 17, 461.
[9] Born, M. (1971). The Born-Einstein Letters (Walker and Company, New York).
[10] Jammer, M. (1974).The Philosophy of Quantum Mechanics (John Wiley & Sons, New York).
[11] Heisenberg, W. (1967). Quantum Theory and its Interpretation in Niels Bohr. His Life and Work as Seen by His Friends and Colleagues, S. Rozental, ed., (North-Holland, Amsterdam), pp. 94-95.
[12] Heisenberg, W. (1960). Erinnerungen an di Zeit der Entwicklung der Quantenmechanik in Theoretical Physics in the Twentieth Century. A Memorial Volume to Wolfgang Pauli, M. Fierz and V. F. Weisskopf, eds. (Interscience, New York), pp. 40-47.
[13] Mehra, J. and Rechenberg, H. (1982-1988). The Historical Development of Quantum Theory (Springer-Verlag, New York), Vols. 1-6.
[14] Pauli, W. (1979). Scientific Correspondence (Springer-Verlag, New York), Vol. I
[15] Heisenberg, W. (1971). Physics and Beyond (Harper and Row, New York).
[16] Jammer, M. (1966). The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York), pp. 285-289.
[17] Heisenberg, W. (1971). Physics and Beyond: Encounters and Conversations (Harper and Row, New York); Mehra, J. and Rechenberg, H. (1977). The Historical Development of Quantum Theory (Springer-Verlag, New York), Vol. 5, Part 2, Chapter IV, section 5.
[18] Heisenberg, W. (1927). Z. Phys. 43, 172.
[19] Chibeni, S. S. (2005). Rev. Bras. Ens. Física 27, 181.
[20] Bohr, N. (1961). The quantum postulate and the recent development of atomic theory, in Atomic Theory and the Description of Nature (Cambridge University Press, Cambridge), (originally published in (1928). Nature 121, 580.)
[21] Heisenberg, W. (1949). The Physical Principles of the Quantum Theory (Dover, New York).
[22] Ballentine, L. E. (1970). Rev. Mod. Phys. 42, 358.
[23] Duane, W. (1923). Proc. Natl. Acad. Sci. USA 9, 158. Compton, A.H. (1923). Proc. Natl. Acad. Sci. USA 9, 359.
[24] Landé, A. (1965). Foundations of Quantum Theory (Cambridge University Press, Cambridge). A. Landé, (1965). New Foundations of Quantum Theory (Cambridge University Press, Cambridge).
[25] Reif, F. (1965). Fundamentals of Statistical and Thermal Physics (McGraw-Hill, Singapore).
[26] Wallstrom, T. C. (1994). Phys. Rev. A 49, 1613.
[27] Gruber, G.R. (1971). Found. of Phys. 1, 227.
[28] Gruber, G.R. (1972). Prog. Theo. Phys. 6, 31.
[29] Pauli, W. (1950). Die Allgemeinen Prinzipien der Wellenmechanik (J.W. Edwards Publishing Co., Ann Arbor, Michigan).
[30] Mehra, J. (1974). The Quantum Principle: its interpretation and epistemology (D. Heidel Publishing Co., Holland).
[31] Lanczos, C. (1970). The Variational Principles of Mechanics (Dover, New York), 4th ed.
[32] Gradshteyn, I. S. and Ryzhik, I. M. (1980). Table of Integrals, Series and Products (Academic Press, London).
[33] Brillouin, L. (1949). Les Tenseurs en Mechanique et en Elasticite (Masson et Cie., Paris)
[34] Goldstein, H. (1950). Classical Mechanics (Addison-Wesley, Cambridge).
[35] Weinberg, S. (1972). Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity (Willey, New York).
[36] Kim, Y.S. and Noz, M. E. (1991). Phase Space Picture of Quantum Mechanics:group theoretical approach (World Scientific, Singapore) , chapter four.
[37] Feynman, R. P. and Hibbs, A.R. (1965). Quantum Mechanics and Path Integrals (McGraw-Hill, New York).
[38] Pauling, L. and Wilson, E.B. (1963). Introduction to Quantum Mechanics, with applications to chemistry (Dover, New York).
[39] Liboff, R. (1990). Kinetic Theory (Prentice-Hall, New Jersey).
[40] Born, M. (1949). Natural Philosophy of Cause and Chance (Oxford University Press, Oxford).
[41] Moyal, J. E. (1949). Proc. Cambridge Phil. Soc. 45, 99.
[42] Takabayasi, T. (1954). Prog. Theoret. Phys. 11, 341.
[43] Callen, H. B. (1985). Thermodynamics: an introduction to thermostatistics (John Wiley & Sons, New York), 2nd Ed.
[44] Wigner, E. (1932). Phys. Rev. 40, 749.
[45] Bohm, D. (1952). Phys. Rev. 85, 166,180.
[46] Hillery, M., O’Connell, R. F., Scully, M. O., Wigner, E. P. (1984). Phys. Rep. 106, 121.
[47] Parr, R. G. and Yang, W. (1989). Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York).
[48] Gosh, S. K., Berkowitz, M. and Parr, R. G. (1984). Proc. Natl. Acad. Sci USA 81, 8028-8031.
[49] Gosh, S. K. and Parr, R. G. (1986). Phys. Rev.A 34, 785-791.
[50] Berkowitz, M. (1986). Chem. Phys. Lett 129, 486-488.
[51] Bartolotti, L. J. and Parr, R. G. (1980). J. Chem. Phys. 72, 1593-1596.
[52] Gosh, S. K. (1987). J. Chem. Phys. 87, 3513-1517.
[53] Robles, J. (1986). J. Chem. Phys. 85, 7245-7250.
[54] Gosh, S. K. and Berkowitz, M. (1985). J. Chem. Phys. 83, 2976-2983.
[55] Braffort, P. and Tzara, C. R. (1954). Hebd. Seances Acad. Sci. 239, 157.
[56] Keynes, I. (1952). Z. Phys. 132, 81.
[57] Weizel, W. (1953). Z. Phys. 134, 264. Weizel, W. (1953). Z. Phys. 135, 270. Weizel, W. (1954). Z. Phys. 136, 582.
[58] Kershaw, D. (1964). Phys. Rev. 138, B1850.
[59] Comisar, G. G. (1965). Phys. Rev. 138, B1332.
[60] Braffort, P., Surdin, M. and Taroni, A. (1965). Hebd. Seahces Acad. Sci. 261,4339.
[61] Marshall, T. (1965). Proc. Cambridge Philos. Soc. 61, 537.
[62] Bourret, R. C. (1965). Can. J. Phys. 43, 619.
[63] Nelson, E. (1966). Phys. Rev. 150, 1079.
[64] de la Peña-Auerbach, L. (1982). Found. Phys. 12, 1017.
[65] de la Peña-Auerbach, L. (1969). J. Math. Phys. 10, 1620.
[66] Pawula, R. F. (1967). Phys. Rev. 162, 186.
[67] Heisenberg, W. (1955). The Development of the Interpretation of the Quantum Theory, in Niels Bohr and the Development of Physics, W. Pauli ed. (McGraw-Hill, New York), pp. 12-29.
[68] Meyer, P. L. (1969). Probabilidade, aplicações à estatstica. Translated by R.C. Lourenço Filho from Introductory Probability and Statistical Applications (Addison-Wesley, Massachusetts).
[69] Hagar, A. (2005). Phil. Sci. 72, 468.
[70] Schiff, L. I. (1968). Quantum Mechanics (McGraw-Hill, Singapore).
[71] Jackson, J. D. (1975). Classical Electrodynamics, (John Wiley & Sons, New York), 2nd Ed.
[72] Deaver, B.S. and Fairbank, W. (1961). Phys. Rev. Lett. 7, 43. See also Döll, R. and Nabauer, M. (1961). Phys. Rev. Lett. 7, 51.
[73] Boyer, T. H. (1975). Phys. Rev. D 11, 790 and references therein.
[74] Boyer, T. H. (1978). Phys. Rev. A 18, 1238.
[75] de la Peña, L. (1970). Phys. Lett. 31A, 403.
[76] Vigier, J. P. (1979). Lett. Nuovo cimento Soc. Ital. Fis. 24, 265.
[77] de la Peña, L. (1971). J. Math. Phys. 12, 453.
[78] Berrondo, M. (1973). Nuovo Cimento Soc. Ital. Fis. B18, 95.
[79] Weaver, D. L. (1978). Phys. Rev. Lett. 40, 1473.
[80] Kuhn, T. (1962). The Structure of Scientific Revolutions (University of Chigago Press, Chicago).
[81] Goldberg, A. Schey, H. M., and Schwartz, J. L. (1967). Am. J. Phys. 35, 177.
[82] Campi, M. and Harrison, M. (1967). Am. J. Phys. 35, 133.
[83] Khinchin, A. I. (1949). Mathematical Foundations of Statistical Mechanics (Dover, New York).
[84] Levy, P. (1976). Théorie des erreurs. La loi de Gauss et les lois exceptionelles. In Oeuvres de Paul Levy (Ecole Polytechnique, France).
[85] Alonso, D., Muga, J. G., and SalaMayato, R. (2001). Phys. Rev. A 64, 016101.
[86] Feynman, R. P. (1998). Statistical Mechanics, a set of lectures (Addison-Wesley, Massachussets).
[87] Brody, T. (1993). The Philosophy behind Physics (Springer, Berlin).
[88] Landé, A. (1960). From Dualism to Unit in Quantum Mechanics (Cambridge University Press, Cambridge).
[89] Morse, P.M. (1929). Phys. Rev. 34, 57.
[90] Hanson, N.R. (1959). Am. J. Phys. 27, 1. Shimony, A. (1963). Am. J. Phys. 31, 755. Witmer, E.E. (1963). Am. J. Phys. 35, 40. Wigner, E.P. (1963). Am. J. Phys. 31, 6. Pearle, P. (1967). Am. J. Phys. 35, 742. Wesley, J.P. (1984). Found. of Phys. 14, 155 and many, many others.
[91] Dechoum, K., França, H.M. and Malta, C.P., Phys. Lett. A 248, 93 (1998).
[92] Stern, O. (1921). Z. Phys. 7, 249. There is an English translation of this papper in Z. Phys. D10, 114 (1988).
[93] Gerlach, W. and Stern, O. (1921). Z. Phys. 8, 110, Gerlach, W. and Stern, O. (1922). Z. Phys. 9, 349. See also Taylor, J.B. (1926). Phys. Rev. 28, 581.
[94] A. P. French and Taylor, E. F. (1978). An Introduction to Quantum Physics (Norton, New York), chap. 10.
[95] Lee, H-W (1995). Phys. Rep. 259, 147.
[96] Cohen, L. (1966). J. Math. Phys. 7, 781.
[97] Cohen, L. and Zaparovanny, Y.I. (1980). J. Math. Phys. 21, 794.
[98] Shewell, J. R. (1959). Amer. J. Phys. 27, 5.
[99] Shewell, J.R. (1958). I On the formation of quantum mechanical operators. II The Wigner distribution function. Doctoral Thesis presented to the Rice Institute. Shewell’s doctoral thesis can be downloaded at http://scholarship.rice.edu/bitstream/handle/
[100] Wigner, E.P. (1971). In Perspectives in Quantum Theory, edited by W. Yourgrau and A. van der Merwe (MIT, Cambridge).
[101] O’Connel, R.F. and Wigner, E.P. (1981). Phys. Lett. A 83, 145.
[102] Parr, R. G., and Yang, W. (1986). Density-functional theory of atoms and molecules (Oxford, New York).
[103] Bell, J. (1964). Physics 1, 195.
[104] Bell, J., Found. of Phys. 12, 989 (1982). Reprinted in Speakable and unspeakable in quantum mechanics: collected papers on quantum philosophy. CUP, 2004, p. 161.
[105] Einstein, A., Podolsky, B., Rosen, N. (1935). Phys. Rev. 47, 777.
[106] von Neumann, J. (1996). Mathematical Foundations of Quantum Mechanics (Princeton University Press).
[107] Aspect, A., Grangier, P., Roger, G. (1982). Phys. Rev. Lett. 49, 91. J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt (1969). Phys. Rev. Lett. 23, 880. J.F. Clauser, M.A. Horne (1974). Phys. Rev. D 10, 526. Weihs, G., Jennewein, T., Simon C., Weinfurter, H., Zeilinger, A. (1998). Phys. Rev. Lett. 81, 5039.
[108] Gibbs, J. W. (1902). Elementary Principles in Statistical Mechanics (New Haven: Yale University Press).
[109] Ehrenfest, P. (1959). Welche Züge der Lichquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentliche Rolle? (1911). Annalen der Physik, 36, 91-118. Reprinted in Bush, (ed.), P. Ehrenfest, Collected Scientific Papers (North-Holland, Amsterdam).
[110] Bach, A. (1997). Indistinguishable Classical Particles (Springer, Berlin).
[111] Jaynes, E.T. (, 1992). The Gibbs Paradox, In Maximum Entropy and Bayesian Methods, C. R. Smith, G. J. Erickson, & P. O. Neudorfer, Editors (Dordrecht: Kluwer Academic Publishers).
[112] Dewdney, C., Holland, P.R., Kyprianidis, A., Maric, Z. and Vigier, J.P. (1986). Phys. Lett. 113A, 359.
[113] Kyprianidis, A. (1985), Phys.Lett. 111A, 111.
[114] Baym, G. (1973), Lectures on Quantum Mechanics (Addison-Wesley, California).
[115] Bohm, D. & Hilley, B. J. (1993). The undivided universe (Routledge, London).
[116] Weinberg, S. (1972). Gravitation and Cosmology, principles and applications of the general theory of relativity (John Wiley & Sons, New York).
[117] Oppenheimer, J. R. & Snyder, H. (1939). Phys. Rev., 56, 455.
[118] Feshbach, H. & Villars, M. (1958).Rev. Mod. Phys. 30, 24.
[119] Martin, P. C. & Glauber, R. J. (1958). Phys. Rev., 109, 1307.
[120] Greiner, W. (1994). Relativistic Quantum Mechanics Wave Equations (Springer-Verlag, Berlim).
[121] Kraus, L. M. (1998). Astroph. J., 494, 95.
[122] Nieto, M. M. & Goldman, T. (1991). Phys. Rep., 205 (5), 221.
[123] Wigner, E. P. (1957). Rev. Mod. Phys., 29, 255.
[124] Wigner, E. P. (1979). Bull. Am. Phys. Soc., 24, 633 (Abstract GA 5).
[125] Salecker, H. & Wigner, E. P. (1958). Phys. Rev., 109, 571.
[126] Greenberger, D. (1968). Ann. Phys., 47, 116.
[127] Davies, P. C. W. & Fang, J. (1982). Proc. Roy. Soc. London A, 381, 469.
[128] Hartle, J. B. Time and Prediction in Quantum Cosmology, in Proc. 5th Marcel Grossman Meeting on General Relativity, eds. D.G.Balir and M.J.Buckingham (World Scientific, Singapore, 1989), 107-204.
[129] Hartle, J. B. Progress in Quantum Cosmology, in: General Relativity and Gravitation (1989), eds. N.Ashby, D.F.Bartlett and W.Wyss (Cambridge Univ. Press, Cambridge, 1990), 391-417.
[130] Alfven, H. (1966). Worlds-Antiworlds, antimatter in cosmology (Freeman, San Francisco).
[131] Goldhaber, M. (1956). Science, 124, 218.
[132] Morrison, P. (1958). Am. J. Phys., 26, 358.
[133] Schiff, L. (1958). Phys. Rev. Lett., 1, 254.
[134] Good, M. L. (1961). Phys. Rev., 121, 311.
[135] Everett III, H. (1957). Rev. Mod. Phys. 29, 454.
[136] Omnès, R. (1999).Understanding Quantum Mechanics (Princeton University Press.), pp. 179, 257.
[137] Griffiths, R. B. (2003). Consistent Quantum Theory (Cambridge University Press).
[138] Omnès, R. (1999). Quantum Philosophy (Princeton University Press).


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