Observer in Quantum Cosmology
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Abstract
A mechanism for the decoherence of the quantum state of the universe is proposed. It reduces to local observation in a certain region, which we call the “observer.” The observer differs from the rest of the universe by an additional condition—the Noether identity for the energy-momentum tensor of matter. This additional condition is introduced into gravity theory using undetermined Lagrange multipliers, which act as new independent variables in the region of observation. This modification does not violate the covariance of the theory and also implies a covariant quantization method. The quantum principle of least action, based on the generalized canonical De Donder-Weyl representation, is proposed as such. The real part of the eigenvalue of the De Donder-Weyl action operator is proposed to be considered as an action functional for the quantum universe with an observer.
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Everett H. ‘Relative State’ formulation of quantum mechanics. Rev Mod Phys. 1957;29:454‑62. Available from: https://doi.org/10.1103/RevModPhys.29.454 DOI: https://doi.org/10.1103/RevModPhys.29.454
Castagino M, Fortin S, Laura R, Lombardy O. A general theoretical framework for decoherence in open and closed systems. Class Quantum Grav. 2008;25:154002. Available from: https://dx.doi.org/10.1088/0264-9381/25/15/154002 DOI: https://doi.org/10.1088/0264-9381/25/15/154002
Hackermuller L, Hornberger K, Brezger B. Decoherence of matter waves by thermal emission of radiation. Nature. 2004;427:711‑4. Available from: https://doi.org/10.1038/nature02276 DOI: https://doi.org/10.1038/nature02276
Mensky MB. Uspehy Phys Nauk. 1998;168:1017‑35. DOI: https://doi.org/10.3367/UFNr.0168.199809e.1017
Zhou H, Zhao C, Cain M, Bluvstein D, Maskara N, Duckering C, et al. arXiv [Preprint]. 2025. Available from: arXiv:2406.17653v2
Penrose R, Gardner M. The emperor’s new mind: concerning computers, minds and laws of physics. 1st ed. Oxford: Oxford University Press; 2002.
Davis M. Is mathematical insight algorithmic? Behav Brain Sci. 2002;13:659‑60. Available from: https://dx.doi.org/10.1017/S0140525X00080730 DOI: https://doi.org/10.1017/S0140525X00080730
Noether E. Invariante Variations probleme. Nachr Ges Wiss Göttingen. 1918:235‑57.
Konopleva NP, Popov VN. Kalibrovochnye Polya. Moscow: Atomizdat; 1972.
Misner CW, Thorne KS, Wheeler JA. Gravitation. San Francisco: W.H. Freeman and Company; 1973.
Vilenkin A. Quantum cosmology and the initial state of the universe. Phys Rev D. 1988;37:888. Available from: https://doi.org/10.1103/PhysRevD.37.888 DOI: https://doi.org/10.1103/PhysRevD.37.888
Hartle JB, Hawking SW. Wave function of the universe. Phys Rev D. 1983;28:2960. Available from: https://doi.org/10.1103/PhysRevD.28.2960 DOI: https://doi.org/10.1103/PhysRevD.28.2960
Gorobey N, Lukyanenko A, Goltsev AV. No boundary wave functional and own mass of the universe. Universe. 2024;10:101. Available from: https://dx.doi.org/10.3390/universe10020101 DOI: https://doi.org/10.3390/universe10020101
Gorobey N, Lukyanenko A, Goltsev AV. Initial state in quantum cosmology and the proper mass of the universe. Universe. 2024;10:366. Available from: https://doi.org/10.3390/universe10090366 DOI: https://doi.org/10.3390/universe10090366
Feynman RP, Hibbs AR. Quantum mechanics and path integrals. New York: McGraw‑Hill Book Company; 1965.
Arnowitt R, Deser S, Misner C. Republication of: The dynamics of general relativity. Gen Relativ Gravit. 2008;40:1997‑2027. DOI: https://doi.org/10.1007/s10714-008-0661-1
Christodoulakis T, Zanelli J. Operator ordering in quantum mechanics and quantum gravity. Nuovo Cimento B. 1986;93:1‑21. Available from: https://doi.org/10.1007/BF02728299 DOI: https://doi.org/10.1007/BF02728299
Christodoulakis T, Zanelli J. Consistent algebra for the constraints of quantum gravity. Nuovo Cimento B. 1986;93:22‑35. Available from: https://dx.doi.org/10.1007/BF02728300 DOI: https://doi.org/10.1007/BF02728300
De Donder T. Théorie invariantive du calcul des variations. Paris: Gauthier‑Villars; 1930.
Weyl H. Geodesic fields in the calculus of variation for multiple integrals. Ann Math. 1935;36:607-629. Available from: https://doi.org/10.2307/1968645 DOI: https://doi.org/10.2307/1968645
Landau LD, Lifshitz EM. The classical theory of fields. Vol. 2. 4th ed. Oxford: Butterworth‑Heinemann; 1980.
Kijowski J. General relativity theory and its canonical structure. In: Geometric methods in physics. XXXV Workshop 2016 Trends in Mathematics. Cham: Springer International Publishing; 2018. p. 255‑60. DOI: https://doi.org/10.1007/978-3-319-63594-1_26
Kanatchikov IV. Towards precanonical quantum teleparallel gravity. arXiv [Preprint]. 2023. Available from: arXiv:2302.10695.
Witten E. A note on complex spacetime metrics. In: Wilczek F, editor. 50 years of theoretical physics. Singapore: World Scientific Publishing Co. Inc.; 2022. p. 245‑80. Available from: https://dx.doi.org/10.48550/arXiv.2111.06514 DOI: https://doi.org/10.1142/9789811251948_0020
Hawking SW. In: Hawking SW, Israel W, editors. General relativity: an Einstein centenary survey. Cambridge: Cambridge University Press; 1979.
De Donder TH. La gravifique einsteinienne: six conférences données à l’Institut Henri Poincaré. Ann Inst Henri Poincaré. 1930;77‑116.
Dirac PAM. Recollections of an exciting era. In: History of twentieth century physics: proceedings of the International School of Physics ‘Enrico Fermi’. New York; London: Academic Press; 1977. p. 109‑46. Available from: https://doi.org/10.3390/mmphys1010000.