Abstract
We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so-called transformers of information, basic processes are information processes and statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of flows of information in cognitive and social systems, since a p-adic metric gives a quite natural description of the ability to form associations.
Similar content being viewed by others
REFERENCES
N. Bohr, Atomic Theory and the Description of Nature (Cambridge University Press, Cambridge, 1961).
E. Schrödinger, My View of the World (Cambridge University Press, Cambridge, 1964).
E. Schrödinger, Mind and Matter (Cambridge University Press, Cambrigde, 1958).
D. Bohm, Found. Phys. 1, 139–168 (1971).
E. P. Wigner, The Scientist Speculates, Good, I. J., ed. (Basic Books, New York, 1962), pp. 284–302.
B. d'Espagnat, Veiled Reality: An Analysis of Present-Day Quantum Mechanical Concepts (Addison-Wesley, Reading, MA, 1995).
B. d'Espagnat, Reality an Physics (Cambridge University Press, Cambridge, 1989).
G. Ryle, The Concept of Mind (Barnes & Noble, New York, 1949).
L. E. Rhine, Mind over Matter (Macmillan, New York, 1970).
D. O. Hebb, Essay on Mind (Lawrence Erlbaum Associates, Hillsdale, NJ, 1980).
J. R. Searle, Behav. Brain Sci. 3, 417–457 (1980).
H. Schmidt, Found. Phys. 8, 463–480 (1981).
H. Schmidt, Found. Phys. 12, 565–581 (1982)
R. G. Jahn and B. J. Dunne, Found. Phys. 16, 721–772 (1986).
B. J. Dunne, Y. H. Dobyns, R. G. Jahn, and R. D. Nelson, J. Sci. Explor. 8, 197–215 (1994).
D. L. Radin and R. D. Nelson, Found. Phys. 19, 1499–1514 (1989).
H. Smidt, J. Sci. Explor. 1, 1–14 (1987).
A. Yu. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems an Biological Models (Kluwer Academic, Dordrecht, 1997).
A. Yu. Khrennikov, J. Theor. Biol. 193, 179–196 (1998).
S. Albeverio, A. Khrennikov, and P. E. Kloeden, Biosystems 49, 105–115 (1999).
W. Schwikhov, Ultrametric Calculus (Cambridge University Press, Cambridge, 1984).
I. V. Volovich, Class. Quant. Grav. 4, 83–87 (1987).
V. S. Vladimirov and I. V. Volovich, Comun. Math. Phys. 123, 659–676 (1989).
P. G. O. Freud and M. Olson, Phys. Lett. B 199, 186–190 (1987).
P. G. O. Freud and E. Witten, Phys. Lett. B 199, 191–195 (1987).
V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-adic Analysis and Mathematical Physics (World Scientific, Singapore, 1993).
P. H. Frampton and Y. Okada, Phys. Rev. Lett. B 60, 484–486 (1988).
I. Ya. Aref'eva, B. Dragovich, P. H. Frampton, and I. V. Volovich, Int. J. Modern Phys. A 6, 4341–4358 (1991).
A. Yu. Khrennikov, p-Adic Valued Distributions in Mathematical Physics (Kluwer Academic, Dordrecht, 1994).
A. Yu. Khrennikov, Uspekhi Mat. Nauk. 45, 79–110 (1990).
Yu. Manin, New Dimensions in Geometry, Springer Lecture Notes in Math., Vol. 1111 (Springer, New York, 1985), pp. 59–101.
B. Dragovic, in Proceedings 3rd A. Friedmann International Seminar on Gravitation and Cosmology, St. Peterburg, 1995.
A. Yu. Khrennikov, Nuovo Cimento B 112, 555–560 (1996).
S. Albeverio and A. Yu. Khrennikov, J. Modern Phys. 10 (13/14), 1665–1673 (1996).
S. Albeverio and A. Yu. Khrennikov, J. Phys. A 29, 5515–5527 (1996).
R. Cianci and A. Yu. Khrennikov, Phys. Lett. B 328, 109–112 (1994).
A. Yu. Khrennikov, Found. Phys. 26 (8), 1066–1054 (1996).
A. Yu. Khrennikov, J. Math. Phys. 39 (3), 1388–1402 (1997).
A. Yu. Khrennikov, Phys. Lett. A 200, 119–223 (1995).
A. Yu. Khrennikov, Physica A 215, 577–587 (1995).
J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955).
M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966).
J. M. Jauch, Foundations of Quantum Mechanics (Addison-Wesley, Reading, MA, 1968).
L. E. Ballentine, Rev. Mod. Phys. 42, 358–381 (1970).
L. E. Ballentine, Quantum Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1989).
A. Escassut, Analytic Elements in p-Adic Analysis (World Scientific, Singapore, 1995).
S. Freund, New Introduction Lectures on Psychoanalysis (Norton, New York, 1933).
A. N. Kolmogorov, Foundations of the Probability Theory (Chelsea, New York, 1956).
R. von Mises, The Mathematical Theory of Probability and Statistics (Academic, London, 1964).
A. Yu. Khrennikov, Teor. Mat. Fiz. 67 (3), 348–363 (1993).
R. P. Feynman, Quantum Implications: Essays in Honour of David Bohm, B. J. Hiley and F. D. Peat, eds. (Routledge & Kegan Paul, London, 1987), pp. 235–246.
W. Muckenheim, Phys. Rep. 133, 338–401 (1986).
P. A. M. Dirac, Proc. Roy. Soc. London A 180, 1–39 (1942).
A. Yu. Khrennikov, Int. J. Theor. Phys. 34 (12), 2423–2434 (1995).
A. Yu. Khrennikov, J. Math. Phys. 36 (12), 6625–6632 (1995).
E. B. Davies, Quantum Theory of Open Systems (Academic, London, 1976).
A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
G. Ludwig, Foundations of Quantum Mechanics (Springer, Berlin, 1983).
A. Schild, Phys. Rev. 73, 414–425 (1948).
E. J. Hellund and K. Tanaka, Phys. Rev. 94, 192–208 (1954).
Yr. Ahmavaara, J. Math. Phys. 6, 87–93 (1965).
J. C. Eccles, The Understanding of the Brain (McGraw-Hill, New York, 1974).
D. J. Amit, Modeling of Brain Functions (Cambridge University Press, Cambridge, 1989).
J. D. Cohen, W. M. Perlstein, T. S. Braver, L. E. Nystrom, D. C. Noll, J. Jonides, and E. E. Smith, Nature 386, 604–608 (1997).
S. M. Courtney, L. G. Ungerleider, K. Keil, and J. V. Haxby, Nature 386, 608–611 (1997).
F. C. Hoppensteadt, An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domains, 2nd ed. (Cambridge University Press, Cambridge, 1997).
D. Bohm and B; Hiley, The Undivided Universe, An Ontological Interpretation of Quantum Mechanics (Routledge & Kegan Paul, London, 1993).
Rights and permissions
About this article
Cite this article
Khrennivov, A. Classical and Quantum Mechanics on Information Spaces with Applications to Cognitive, Psychological, Social, and Anomalous Phenomena. Foundations of Physics 29, 1065–1098 (1999). https://doi.org/10.1023/A:1018885632116
Issue Date:
DOI: https://doi.org/10.1023/A:1018885632116