On the need to adapt de Finetti's probability interpretation to QM
Banach Center Publications (1998)
- Volume: 43, Issue: 1, page 157-166
- ISSN: 0137-6934
Access Full Article
topAbstract
topHow to cite
topEmch, Gérard. "On the need to adapt de Finetti's probability interpretation to QM." Banach Center Publications 43.1 (1998): 157-166. <http://eudml.org/doc/208834>.
@article{Emch1998,
abstract = {von Neumann's reliance on the von Mises frequentist interpretation is discussed and compared with the Dutchbook approach proposed by de Finetti.},
author = {Emch, Gérard},
journal = {Banach Center Publications},
keywords = {von Neumann's reliance; von Mises frequentist interpretation; Dutchbook approach},
language = {eng},
number = {1},
pages = {157-166},
title = {On the need to adapt de Finetti's probability interpretation to QM},
url = {http://eudml.org/doc/208834},
volume = {43},
year = {1998},
}
TY - JOUR
AU - Emch, Gérard
TI - On the need to adapt de Finetti's probability interpretation to QM
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 157
EP - 166
AB - von Neumann's reliance on the von Mises frequentist interpretation is discussed and compared with the Dutchbook approach proposed by de Finetti.
LA - eng
KW - von Neumann's reliance; von Mises frequentist interpretation; Dutchbook approach
UR - http://eudml.org/doc/208834
ER -
References
top- [Ber] F. Bernstein, Ueber eine Anwendung der Mengenlehre auf ein aus der Theorie des säkularen Störungen herrührendes Problem, Math. Annalen, 71 (1912), 417-439. Zbl42.1007.01
- [Blz] L. Boltzmann, Referat Ueber die Abhandlung von J.C. Maxwell ``Ueber Boltzmanns Theorie betreffend mittlere Verteilung der Lebendige Kraft in einem System materieller Punkte'', (1881), WA 2 582-595.
- [Bo1] E. Borel, Sur les principes de la théorie cinétique des gaz, Ann. Ecole Norm. 23 (1906), 9-32. Zbl37.0944.01
- [Bo2] E. Borel, Eléments de la théorie des probabilités, Hermann, Paris, 1909.
- [Bo3] E. Borel, Les probabilités dénombrables et leurs applications arithmétiques, Rend. Cir. mat. Palermo 27 (1909), 247-271. Zbl40.0283.01
- [Brn] M. Born, Quantenmechanik und Statistik, Die Naturwissenschaften 15 (1927) 238-242; Statistical Interpretation of Quantum Mechanics (Nobel Lecture), Sciences 122 (1955), 675-679; reprinted in M. Born Physics in my Generation, Pergamon Press, London, 1969.
- [Can] F. Cantelli, Sulla legge dei grandi numeri, Mem. Acad. Lincei 11 (1916), 330-349; Sulla probabilità come limite della frequenza, Rend. Acad. Lincei 26 (1917), 39-45.
- [Car] R. Carnap, Logical Foundations of Probability, 2nd ed., University of Chicago Press, Chicago, 1962.
- [Chu] A. Church, On the Concept of a Random Sequence, Bull. Amer. Math. Soc. 47 (1940), 130-135. Zbl66.0601.01
- [Cop] A.H. Copeland, Admissible Numbers in the Theory of Geometrical Probability, Amer. J. Math. 53 (1931), 153-162; The theory of Probability from the point of view of Admissible Numbers, Ann. Math. Statist. 3 (1932), 1435-1456.
- [Fel] W. Feller, An Introduction to Probability Theory and its Applications, vols. 1 (3rd ed.) and 2 (2nd ed.), Wiley, New York, 1968, 1966.
- [deF] B. de Finetti, La prévision, ses lois logiques et ses sources subjectives, Annales de l'Institut Henri Poincaré 7 (1937), 1-68; Probability, Induction, and Statistics, Wiley, New York, 1972. Zbl63.1070.02
- [Had] J. Hadamard, Les surfaces à courbures opposées et leurs lignes géodésiques, J. math. pures et appl. 4 (1898), 27-73. Zbl29.0522.01
- [Hau] F. Hausdorff, Grundzüge der Mengenlehre, De Gruyter, Leipzig, 1914.
- [Hi1] D. Hilbert, Sur les problèmes futurs des mathématiques in: Comptes Rendus du Deuxième Congrès International des Mathématiciens, Paris, 1900, Gauthier-Villars, Paris, 1902, 58-114; see also: Mathematical Developments arising from Hilbert problems, F.E. Browder (ed.), Proc. Symp. Pure Math. XXVIII, 1976.
- [Hi2] D. Hilbert, Grundlagen der Geometrie, Teubner, Leipzig, 1899 (1st ed.), 1922 (5th ed.); Foundations of Geometry (L.Unger transl. from the 10th ed.), Open Court, LaSalle IL, 1971.
- [Hod] R.E. Hodel, An Introduction to Mathematical Logic, PWS Publ., Boston, 1995.
- [Hud] R.L. Hudson, Analogs of de Finetti's Theorem and the Interpretative Problems of Quantum Mechanics, Found. Phys. 11 (1981), 805-808; see also: R.L. Hudson and G.R. Moody, Locally Normal Symmetric States and an Analogue of de Finetti's Theorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete 33 (1976), 343-351.
- [Jay] E.T. Jaynes, Papers on Probability, Statistics, and Statistical Physics, 2nd ed., Kluwer, 1989. Zbl0687.60085
- [Khi] A. Khintchine, Ueber einem Satz der Wahrscheinlichkeitsrechnung, Fundam. Math. 6 (1924), 9-20.
- [Knu] D. E. Knuth, The Art of Computer Programming, vol. 2, 2nd ed., Addison-Wesley, Reading, Mass., 1981.
- [Ko1] A.N. Kolmogorov, Das Gesetz des iterierten Logarithmus, Math. Annalen 101 (1929), 126-135.
- [Ko2] A.N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, Berlin, 1933; Foundations of the Theory of Probability (N. Morrison, transl.), Chelsea, 1956.
- [Ko3] A. Kolmogorov, On Tables of Random Numbers, Sankhya, The Indian Journal of Statistics, Ser. A 25 (1963), 369-376; Logical Basis for Information Theory and Probability Theory, IEEE Trans. Inform. Theory 14 (1968), 662-664.
- [LiV] M. Li and P. Vitanyi An Introduction to Kolmogorov Complexity and its Applications, 2nd ed., Springer, New York, 1997.
- [ML1] P. Martin-Löf, The Definition of Random Sequences, Information and Control, 9 (1966), 602-619. Zbl0244.62008
- [ML2] P. Martin-Löf, The Literature on von Mises' Kollektivs Revisited, Theoria, 35 (1969), 12-37. Zbl0198.23103
- [ML3] P. Martin-Löf, Complexity Oscillations in Infinite Binary Sequences, Z. Wahrsch. verw. Geb. 19 (1971), 225-230. Zbl0212.23103
- [vM1] R. von Mises, Grundlagen der Wahrscheinlichkeitsrechnung, Math. Z. 5 (1919) 52-99. Zbl47.0483.01
- [vM2] R. von Mises, Wahrscheinlichkeit, Statistik und ihre Wahrheit, Springer, Wien, 1928; Probability, Statistics and Truth, MacMillan, New York, 1939.
- [vM3] R. von Mises, Kleines Lehrbuch der Positivismus, Einführung in die empiristische Wissenschaftsauffassung, W. P. van Stockum, Den Haag, and University of Chicago Press, Chicago, Ill., 1939; transl. by J. Bernstein and R.G. Newton, as: Positivism, Harvard University Press, Cambridge, Mass., 1951.
- [vN1] J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932; Mathematical Foundations of Quantum Mechanics (R.T. Beyer, transl.) Princeton University Press, Princeton NJ, 1955.
- [vN2] J. von Neumann, Various Techniques used in Connection with Random Digits, J. Res. Nat. Bur. Stand. Appl. Math Series 3 (1951), 36-38; Collected Works, vol. V, MacMillan, New York, 1963, 768-770.
- [HP2] H. Poincaré, La science et l'hypothèse, Flammarion, Paris, 1902. Zbl34.0080.12
- [Pop] K.R. Popper, Logik der Forschung, Vienna, 1935; The Logic of Scientific Discovery, Basic Books, New York, 1959; Harper & Row, New York, 1968.
- [Ste] H. Steinhaus, Les probabilités dénombrables et leur rapport à la théorie de la mesure, Fundam. Math. 4 (1923), 286-310. Zbl49.0361.01
- [Vil] J. Ville, Sur la notion de collectif, C.R. Acad. Sci. Paris, 203 (1936), 26-27; Etude critique de la notion de collectif, Gauthier-Vilars, Paris, 1939.
- [Wal] A. Wald, Sur la notion de collectif dans le calcul des probabilités, C.R. Acad. Sci. Paris, 202 (1936), 180-183; Die Wiederspruchfreiheit des Kollektivbegriffes der Wahrscheinlichkeitsrechnung, Ergerbnisse eines Kolloquium (Vienna) 8 (1937), 38-72; Die Wiederspruchfreiheit des Kollektivbegriffes, Actualités Sci. Indust. 735 (1938), 79-99. Zbl0013.12304
- [Wig] E.P. Wigner, Review of the Quantum-Mechanical Measurement Problem, in: Science, Information Onslaught, D.M. Kerr et al., eds., Academic Press, New York, 1984, 63-82. Collected Works, vol 6, Springer, Heidelberg, 1994, 225-244.
- [Wey] H. Weyl, Ueber die Gleichverteilung von Zahlen mod Eins, Math. Annalen, 77 (1916) 313-352. Zbl46.0278.06
- [Zeh] H.D. Zeh, On the Interpretation of Measurement in Quantum Theory, Found. of Phys. 1 (1970), 69-76.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.