Abstract
It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumptions that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to quantum mechanics. In particular, an argument is made for why there are probability amplitudes that are complex numbers. This argument generalizes the Feynman path integral formulation of quantum mechanics to include all possible terms in the action that are allowed by the symmetries, but only the lowest order terms are observable at the presently accessible energy scales, which is consistent with observation. The notion of relational reality is introduced in order to give physical meaning to probabilities. This appears to give rise to a new interpretation of quantum mechanics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Anandan,Found. Phys. 29 (11) 1647–1672 (1999); quantph/9808045.
R. P. Feynman,The Strange Theory of Light and Matter (Princeton University Press, Princeton, 1985), Chap. 1.
A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).
R. P. Feynman,Rev. Mod. Phys. 20, 367–87 (1948). R. P.Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
D. Bohm,Phys. Rev. 85, 166–193 (1952).
H. Everett,Rev. Mod. Phys. 29, 454–462 (1957).
A. Einstein and M. Born,The Born-Einstein Letters,29 April 1924.
Steven Weinberg,The Quantum Theory of Fields I (Cambridge University Press, Cambridge, 1995), pp. 144, 145, and 198.
Y. Aharonov and D. Bohm,Phys. Rev. 115, 485 (1959).
B. Kayser and L. Stodolsky,Phys. Lett. B 359, 343–350 (1995).
J. Anandan and H. R. Brown,Found. Phys. 25, 349 (1995).
Y. Aharonov, J. Anandan, and L. Vaidman,Phys. Rev. A 47 (6) 4616 (1993). Y. Aharonov and L. Vaidman,Phys. Lett. A 178, 38 (1993). J. Anandan,Found. Phys. 6 (6) 503 (1993).
A. Horwitz,Nachr. Gesell. Wiss. Göttingen, Math.-Phys. Kl. 309 (1898).
A. A. Albert,Ann. Math. 48, 495 (1947).
Y. Aharonov and M. Vardi,Phys. Rev. D 21, 2235 (1980). J. Anandan and Y. Aharonov,Phys. Rev. D 38 (6) 1863-1870 (1988).
S. L. Adler,Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, Oxford, 1995), pp. 6–7, 109–111.
R. P. Feynman and F. L. Vernon,Ann. Phys. 24, 118 (1963). A. Stern, Y. Aharonov, and Y. Imry,Phys. Rev. A 41, 3436 (1990). J. Anandan and Y. Aharonov,Phys. Rev. Lett. 65, 1697-1700 (1990).
David Gross, inRecent Developments in Quantum Field Theory, J. Ambjorn, B. J. Durnhuus, and J. L. Peterson, eds. (Elsevier, Amsterdam, 1985), p. 151. Howard Georgi,Ann. Rev. Nucl. Part. Sci. 43, 209 (1993). S. Weinberg,Phys. Rev. D 56, 2303 (1997).
Y. Aharonov, D. Albert and L. Vaidman,Phys. Rev. Lett. 60, 1351 (1988).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Anandan, J. Causality, symmetries and quantum mechanics. Found Phys Lett 15, 415–438 (2002). https://doi.org/10.1023/A:1023918429687
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1023918429687