Hartle–Hawking proposal
Nowadays, Hartle–Hawking proposal is a topic that has gained significant importance in today's society. Over time, Hartle–Hawking proposal has become a point of interest for many people, as it has a direct impact on our way of life and our environment. It is a topic that has been discussed and analyzed from different perspectives, generating controversy and debate in public opinion. In this article, we will explore various facets of Hartle–Hawking proposal, delving into its origin, development and consequences today. In order to provide a comprehensive view on this topic, we will present different points of view and opinions from experts on the subject. Without a doubt, Hartle–Hawking proposal is a relevant issue that deserves to be addressed seriously and objectively.
The Hartle–Hawking state, also known as the no-boundary wave function, is a cosmological model that applies quantum mechanics to the Big Bang.[2]: 769 It is named after James Hartle and Stephen Hawking, who first proposed it in 1983.[3][4] The concept can also be considered as an initial condition for models of quantum cosmology.[5]: 14
Ingredients
The Hartle-Hawking proposal includes several ingredients. First it uses Richard Feynman's sum over histories approach to quantum mechanics. In this approach every possible path a particle can take through spacetime contributes to the solution with its own an amplitude and phase. Technical challenges with those sums lead to the second ingredient, a transformation to Euclidean space-time: a geometry which combines 3 space dimensions with an imaginary time dimension.[6]: 172 This is related to the Wick rotation, , and it converts the spacetime metric in to a Euclidean metric, . In Hawking approach this rotation is applied to every path, not to the background space of the paths as in Wick's approach and therefore the sum of histories becomes a quantum superposition of spacetimes.[2]: 769 This curved Euclidean spacetime can be analogous to a sphere in being both finite in extent and yet have no boundary.[6]: 174
History
The original 1983 paper by Hartle and Hawking grew out of a summer visit by Hawking to UC Santa Barbara where Hartle worked. Hawking was exploring the idea that the boundary condition for space time was simply no-boundary at all. With Hartle this idea was converted in to a proposal and published.[6]: 175 In 1998 Hawking worked with Neil Turok to expand the Hartle-Hawking concept to include a hyperbolic or open geometry.[7][2][8][1]
See also
References
- ^ a b "Centre for Theoretical Cosmology: The Origins of the Universe: General open inflation". www.ctc.cam.ac.uk. Retrieved 2025-08-23.
- ^ a b c Penrose, Roger (2005). The road to reality: a complete guide to the laws of the universe (1st American ed.). New York: A.A. Knopf. ISBN 978-0-679-45443-4.
- ^ Hartle, J.; Hawking, S. (1983). "Wave function of the Universe". Physical Review D. 28 (12): 2960. Bibcode:1983PhRvD..28.2960H. doi:10.1103/PhysRevD.28.2960. S2CID 121947045.
- ^ Lehners, Jean-Luc (June 2023). "Review of the no-boundary wave function". Physics Reports. 1022: 1–82. arXiv:2303.08802. Bibcode:2023PhR..1022....1L. doi:10.1016/j.physrep.2023.06.002.
- ^ Weinberg, Steven (1989-01-01). "The cosmological constant problem". Reviews of Modern Physics. 61 (1): 1–23. Bibcode:1989RvMP...61....1W. doi:10.1103/RevModPhys.61.1. hdl:2152/61094. ISSN 0034-6861.
- ^ a b c Hawking, Stephen (1996). The illustrated A brief history of time (Updated and expanded ed.). New York: Bantam Books. ISBN 978-0-553-10374-8.
- ^ Hawking, S. W.; Turok, Neil (1998). "Open inflation without false vacua". Physics Letters B. 425 (1): 25–32. arXiv:hep-th/9802030. Bibcode:1998PhLB..425...25H. doi:10.1016/S0370-2693(98)00234-2. ISSN 0370-2693.
- ^ Hawking, S. W.; Turok, Neil (April 16, 1998). "Open inflation without false vacua". Physics Letters B. 425 (1): 25–32. arXiv:hep-th/9802030. Bibcode:1998PhLB..425...25H. doi:10.1016/S0370-2693(98)00234-2. ISSN 0370-2693.