This paper describes how the entire universe might be considered an eigenstate determined by classical limiting conditions within it. This description is in the context of an approach in which the path of each relativistic particle in spacetime represents a fine-grained history for that particle, and a path integral represents a coarse-grained history as a superposition of paths meeting some criteria. Since spacetime paths are parametrized by an invariant parameter, not time, histories based on such paths do not evolve in time but are rather histories of all spacetime. Measurements can then be represented by orthogonal states that correlate with specific points in such coarse-grained histories, causing them to decohere, allowing a consistent probability interpretation. This conception is applied here to the analysis of the two slit experiment, scattering and, ultimately, the universe as a whole. The decoherence of cosmological states of the universe then provides the eigenstates from which our “real” universe can be selected by the measurements carried out within it.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Stueckelberg E.C.G. (1941). Helv. Phys. Acta 14: 588
E. C. G. Stueckelberg, Helv. Phys. Acta 15, 23 (1942).
Feynman R.P. (1950). Phys. Rev. 80: 440
Feynman R.P.(1951). Phys. Rev 84: 108
Fanchi J.R. (1993). Parametrized Relativistic Quantum Theory. Kluwer Academic, Dordrecht
Griffiths R.B. (1984). J. Stat. Phys 36: 219
Omnès R.(1988). J. Stat. Phys. 53: 893
M. Gell-Mann and J. Hartle, in Complexity, Entropy and the Physics of Information, W. Zurek, ed. (Addison-Wesley, Reading, 1990), Vol. VIII of Sante Fe Institute Studies in the Science of Complexity.
J. B. Hartle, in Gravitation and Quantizations: Proceedings of the 1992 Les Houches Summer School, B. Julia and J. Zinn-Justin, eds. (North Holland, Amsterdam, 1995), gr-qc/9304006.
Everett H. (1957). Rev. Mod. Phys. 29: 454
J. J. Halliwell (2003), quant-ph/0301117.
Halliwell J.J.(2004). Contemp. Phys 46: 93
Teitelboim C. (1982). Phys. Rev. D 25: 3159
Halliwell J.J., Thorwart J. (2002). Phys. Rev. D 65: 104009
E. Seidewitz, J. Math. Phys. 47, 112302 (2006), quant-ph/0507115.
Halliwell J.J., Thorwart J. (2001). Phys. Rev. D 64: 124018
Feynman R.P. (1948). Rev. Mod. Phys. 20: 367
Feynman R.P., Hibbs A.R. (1965). Quantum Mechanics and Path Integrals. McGraw Hill, New York
Horwitz L.P., Piron C. (1973). Helv. Phys. Acta 46: 316
Fanchi J.R., Collins R.E. (1978). Found. Phys. 8: 851
Land M.C., Horwitz L.P.(1991). Found. Phys 21: 299
Frastai J., Horwitz L.P. (1995). Found. Phys. 25: 1485
Enatsu H.(1963). Prog. Theor. Phys 30: 236
Enatsu H. (1986). Nuovo Cimento A 95: 269
Feynman R.P.(1949). Phys. Rev 76: 749
Hartle J.B., Marolf D. (1997). Phys. Rev. D. 56: 6247
N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space (Pitman, London, 1981), translated by E. R. Dawson from Teoriya Lineĭnykh Operatorov V Gilbertovom Prostranstve, 1978.
Muynck W.M.D.(2002). Foundations of Quantum Mechanics, an Empericist Approach. Kluwer Academic, Dordrecht
Griffiths R.B. (2002). Consistent Quantum Mechanics. Cambridge University Press, Cambridge
J. B. Hartle, in Quantum Cosmology and Baby Universes: Proceedings of the 1989 Jerusalem Winter School for Theoretical Physics, S. Coleman, J. Hartle, T. Piran, and S. Weinberg, eds. (World Scientific, Singapore, 1991).
Weinberg S.(1995). The Quantum Theory of Fields, Vol 1 Foundations. Cambridge University Press, Cambridge
Horwitz L.P., Rohrlich F. (1981). Phys. Rev. D 24: 1528
N. Graham, in The Many Worlds Interpretation of Quantum Mechanics, B. S. DeWitt and N. Graham, eds. (Princeton University Press, Princeton, 1973).
Hartle J.B. (1968). Am. J. Phys. 36: 704
A. Kent, Int. J. Mod. Phys. A 1745 (1990).
E. J. Squires, Phys. Lett. A 67 (1990).
Zurek W.H.(2003). Rev. Mod. Phys. 75: 715
Zurek W.H. (2005). Phys. Rev. A 71: 052105
Hartle J.B., Hawking S.W. (1983). Phys. Rev. D 28: 2960
Zurek W.H.(1998). Philos. Trans. R. Soc. Lond. A 356: 1793
DeWitt B.S., Graham N. (eds) (1973). The Many Worlds Interpretation of Quantum Mechanics. Princeton University Press, Princeton
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Seidewitz, E. The Universe as an Eigenstate: Spacetime Paths and Decoherence. Found Phys 37, 572–596 (2007). https://doi.org/10.1007/s10701-007-9123-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-007-9123-y
Keywords
- path integrals
- relativistic quantum mechanics
- quantum cosmology
- relativistic dynamics
- decoherence
- consistent history interpretation