Abstract
The relativistic quantum mechanics with Lorentz-invariant evolution parameter and indefinite mass is a very elegant theory. But it cannot be derived by quantizing the usual classical relativity in which there is the mass-shell constraint. In this paper the classical theory is modified so that it remains Lorentz invariant, but the constraint disappears; mass is no longer fixed—it is an arbitrary constant of motion. The quantization of this unconstrained theory gives the relativistic quantum mechanics in which wave functions are localized and normalized in spacetime. Though many authors have published good works in support for such a localization in time, the latter has been generally considered as problematic. Here I show that wave packets restricted to a finite region of spacetime are not a nuisance, but just the contrary. They have the physical interpretation in the fact that an observer perceives a world line event by event, as his experience of “now” proceeds in spacetime. Quantum mechanically this means that at a certain value of the evolution parameter τ the event is most probably to occur within the spacetime region around {ie1005-1} occupied by the wave packet; at later value of τ the position {ie1005-2}—and hence the time coordinate t—of the wave packet is changed. This is closely related to the interpretation of quantum mechanics in general.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. C. G. Stueckelberg,Helv. Phys. Acta 14, 316 (1941);15, 23 (1941);15, 51 (1941).
L. P. Horwitz and F. Rohrlich,Phys. Rev. D 24, 1528 (1981);26, 3452 (1982); L. P. Horwitz, “On relativistic quantum theory,” inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York, 1983), p. 169; L. P. Horwitz and Y. Lavie,Phys. Rev. D 24, 2127 (1981).
R. Arshansky, L. P. Horwitz, and Y. Lavie,Found. Phys. 13, 1167 (1983).
M. Henneaux and C. Teitelboim,Ann. Phys. (N.Y.) 143, 127 (1982).
R. E. Collins and J. R. Fanchi,Nuovo Cimento A 48, 314 (1978); A. Herdegen,Acta Phys. Pol. B 13, 863 (1982); J. Samuel,Phys. Rev. D 26, 3475 (1982); A. O. Barut and W. D. Thacker,Phys. Rev. D 31, 1386 (1985); F. Ravndal,Phys. Rev. D 21, 2823 (1980).
M. Pavšič,Nuovo Cimento A 82, 443 (1984).
W. C. Davidon,Phys. Rev. 97, 1131 (1955);97, 1139 (1955).
P. M. Pearle,Phys. Rev. 168, 1429 (1968); R. Arshansky and L. P. Horwitz,J. Math. Phys. 30, 66 (1989);30, 380 (1989).
F. Reuse,Found. Phys. 9, 865 (1979).
L. P. Horwitz and W. C. Schieve,Ann. Phys. (N.Y.) 137, 306 (1981).
J. R. Fanchi,Phys. Rev. A 37, 3956 (1988).
J. R. Fanchi,Phys. Rev. A 34, 1677 (1986).
J. R. Fanchi,Phys. Rev. A 35, 4859 (1987).
J. R. Fanchi,Found. Phys. 20, 189 (1990).
A. B. Evans,Found. Phys. 20, 309 (1990).
L. P. Horwitz and F. C. Rotbart,Phys. Rev. D 24, 2127 (1981).
J. R. Fanchi and W. J. Wilson,Found. Phys. 13, 471 (1983).
L. P. Horwitz, R. I. Arshansky, and A. C. Elitzur,Found. Phys. 18, 1159 (1988).
R. Arshansky and L. P. Horwitz,Found. Phys. 15, 701 (1985).
J. R. Fanchi and R. E. Collins,Found. Phys. 8, 851 (1978).
A. Kypriandis,Phys. Rep. 155, 1 (1987).
M. Pavšič, “Relativistic quantum mechanics and quantum field theory with invariant evolution parameter,” to appear inNuovo Cimento A.
R. Marnelius,Acta Phys. Pol. B 13, 669 (1982); M. Pavšič,Phys. Lett. B 13, 327 (1987); M. Kaku,Introduction to Superstrings (Springer, New York, 1988).
J. R. Fanchi,Phys. Rev. D 20, 3108 (1979); R. Kubo,Nuovo Cimento A 85, 293 (1985).
H. Weyl,Space, Time, Matter (Dover, New York, 1952).
C. F. von Weizsacker, inThe Physicist Conception of Nature, J. Mehra, ed. (D. Reidel, Dordrecht, 1973).
M. Pavšič,Class. Quant. Gravit. 2, 869 (1985).
A. M. Steane,J. Phys. A 23, 2905 (1990).
E. P. Wigner, inSymmetries and Reflections (Indiana University Press, Bloomington, 1967).
M. Tribus and E. C. McIrvine,Sc. Am. 224, 179 (1971).
H. Everett,Rev. Mod. Phys. 29, 454 (1957); J. A. Wheeler,Rev. Mod. Phys. 29, 463 (1957); B. DeWitt, inThe Many Worlds Interpretation of Quantum Mechanics, B. DeWitt and N. Graham, eds. (Princeton University Press, Princeton, 1973).
B. DeWitt,Phys. Rev. 160, 1113 (1967).
M. Pavšič,Nuovo Cimento A 95, 297 (1986).
D. R. Hofstädter,Gödel, Escher, Bach: an Eternal Golden Braid (Penguin, London, 1980); D. C. Dennet and D. R. Hofstädter, eds.,The Mind's Eye (Penguin, London, 1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pavšič, M. On the interpretation of the relativistic quantum mechanics with invariant evolution parameter. Found Phys 21, 1005–1019 (1991). https://doi.org/10.1007/BF00733384
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00733384