Abstract
Being based on the observation that a conjugate pair of representations, or dual logic, is a necessity under the presence of chaos, a new interpretation of quantum theory is proposed as describingproto-chaos. This chaos has to be a result of basic nonlinearity in the dynamic structure, of which, however, the nonchaotic phase seems to lie ourside the reach of experimental technique, thus the term proto-chaos. Nevertheless, assuming no extra degrees of freedom, the interpretation clarifies a number of riddles posed hitherto and throws some light on the overall hierarchical structure of our understanding and description of nature.
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References
D. Ruelle and F. Takens,Commun. Math. Phys. 20, 167 (1971).
G. Takeuti, inModern Logic—A Survey, E. Agazzi, ed. (Reidel, Dordrecht, 1980), pp. 167–171.
N. G. Van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), p. 59.
M. Namiki, “Stochastic quantization and related problems,” inProceedings of the Second International Symposium: Foundations of Quantum Mechanics in the Light of New Technology, M. Namikiet al., eds. (Physical Society of Japan, Tokyo, 1987).
K. Takahashi and N. Saito,Phys. Rev. Lett. 55, 645 (1985).
M. Toda and K. Ikeda,J. Phys. A, to be published.
Mikito Toda, private communication.
Y. S. Lee and K. Tomita, to be published; New York, K. Tomita,Chaos and Statistical Methods (Springer, New York, 1985), p. 1.
H. Sakaguchi and K. Tomita, to be published; K. Tomita,Chaos and Statistical Methods (Springer, New York, 1985), p. 1.
H. Furstenburg, “A conjecture regarding Haussdorff dimension of orbit closure of commuting transformations,” a talk at Symposium “Prospects of Mathematical Science,” Institute of Mathematical Science, Kyoto University, 1986.
O. E. Rössler, in press.
Y. Katayama and H. Yukawa,Prog. Theor. Phys. Suppl. No. 41, 1–21 (1968); Y. Katayama, I. Umemula, and H. Yukawa,Prog. Theor. Phys. Suppl. No. 41, 22–55 (1968).
I. Prigogine, C. George, F. Henin and L. Rosenfeld,Chemica Scripta 4, 5 (1973).
D. J. E. Callaway and A. Rahman,Phys. Rev. Lett. 49, 613 (1982).
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Tomita, K. Conjugate pair of representations in chaos and quantum mechanics. Found Phys 17, 699–711 (1987). https://doi.org/10.1007/BF01889543
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DOI: https://doi.org/10.1007/BF01889543