Abstract
To the best of our current understanding, quantum mechanics is part of the most fundamental picture of the universe. It is natural to ask how pure and minimal this fundamental quantum description can be. The simplest quantum ontology is that of the Everett or Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian. Typically one also relies on some classical structure, such as space and local configuration variables within it, which then gets promoted to an algebra of preferred observables. We argue that even such an algebra is unnecessary, and the most basic description of the world is given by the spectrum of the Hamiltonian (a list of energy eigenvalues) and the components of some particular vector in Hilbert space. Everything else—including space and fields propagating on it—is emergent from these minimal elements.
Submitted to the Foundational Questions Institute Essay Competition, “What Is Fundamental?”
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Notes
- 1.
The name is inspired by philosopher Owen Flanagan’s description of his colleague Alex Rosenberg’s philosophy as “Mad-Dog Naturalism.”
- 2.
If time is fundamental rather than emergent, there is a very good reason to believe that the entirety of Hilbert space is infinite-dimensional, even if the factor describing our local region is finite-dimensional; otherwise the dynamics would be subject to recurrences and Boltzmann-brain fluctuations [20].
References
Giddings, S.B.: Hilbert space structure in quantum gravity: an algebraic perspective. JHEP 12, 099 (2015). arXiv:1503.08207 [hep-th]. https://doi.org/10.1007/JHEP12(2015)099
Coleman, S.: Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D 11, 2088–2097 (1975). https://doi.org/10.1103/PhysRevD.11.2088
Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1113–1133 (1999). arXiv:hep-th/9711200. https://doi.org/10.1023/A:1026654312961 [hep-th]
Bao, N., Carroll, S.M., Singh, A.: The Hilbert space of quantum gravity is locally finite-dimensional. Int. J. Mod. Phys. D26(12), 1743013 (2017). arXiv:1704.00066. https://doi.org/10.1142/S0218271817430131
Bekenstein, J.D.: Universal upper bound on the entropy-to-energy ratio for bounded systems. Phys. Rev. D 23, 287–298 (1981)
Carroll, S.M., Chatwin-Davies, A.: Cosmic equilibration: a holographic no-hair theorem from the generalized second law. arXiv:1703.09241 [hep-th]
Fischler, W.: “Taking de Sitter Seriously”. Talk Given at Role of Scaling Laws in Physics and Biology (Celebrating the 60th Birthday of Geoffrey West), Santa Fe, Dec 2000
Banks, T.: QuantuMechanics and CosMology, p. 2000. Stanford University, May, Talk given at the festschrift for L. Susskind (2000)
Cotler, J.S., Penington, G.R., Ranard, D.H.: Locality from the spectrum. arXiv:1702.06142 [quant-ph]
Cao, C., Carroll, S.M., Michalakis, S.: Space from Hilbert space: recovering geometry from bulk entanglement. Phys. Rev. D95(2), 024031 (2017) arXiv:1606.08444 [hep-th]. https://doi.org/10.1103/PhysRevD.95.024031
Cao, C., Carroll, S.M.: Bulk entanglement gravity without a boundary: towards finding Einstein’s equation in Hilbert space. arXiv:1712.02803 [hep-th]
Wallace, D.: How to prove the born rule. arXiv e-prints (2009). arXiv:0906.2718 [quant-ph]
Sebens, C.T., Carroll, S.M.: Self-locating uncertainty and the origin of probability in Everettian quantum mechanics. Brit. J. Phil. Sci. (2014). arXiv:1405.7577
Zurek, W.H.: Pointer basis of quantum apparatus: into what mixture does the wave packet collapse? Phys. Rev. D24, 1516–1525 (1981). https://doi.org/10.1103/PhysRevD.24.1516
Tegmark, M.: Consciousness as a state of matter. Chaos Solitons Fractals 76, 238–270 (2015). arXiv:1401.1219 [quant-ph]. https://doi.org/10.1016/j.chaos.2015.03.014
Carroll, S.M., Singh, A.: Quantum mereology: factorizing Hilbert space into sub-systems with quasi-classical dynamics. In preparation
Jacobson, T.: Entanglement equilibrium and the Einstein equation. Phys. Rev. Lett. 116(20), 201101 (2016). arXiv:1505.04753 [gr-qc]. https://doi.org/10.1103/PhysRevLett.116.201101
Albrecht, A., Iglesias, A.: The clock ambiguity and the emergence of physical laws. Phys. Rev. D77, 063506 (2008). arXiv:0708.2743 [hep-th]. https://doi.org/10.1103/PhysRevD.77.063506
Connes, A., Rovelli, C.: Von Neumann algebra automorphisms and time thermodynamics relation in general covariant quantum theories. Class. Quant. Grav. 11, 2899–2918 (1994). arXiv:gr-qc/9406019 [gr-qc]. https://doi.org/10.1088/0264-9381/11/12/007
Carroll, S.M.: What if time really exists?. arXiv:0811.3772 [gr-qc]
Harlow, D.: The Ryu-Takayanagi formula from quantum error correction. Commun. Math. Phys. 354(3), (2017) 865–912. arXiv:1607.03901 [hep-th]. https://doi.org/10.1007/s00220-017-2904-z
Acknowledgements
We are thankful to ChunJun (Charles) Cao for helpful conversations. This research is funded in part by the Walter Burke Institute for Theoretical Physics at Caltech and by DOE grant DE-SC0011632.
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Carroll, S.M., Singh, A. (2019). Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal. In: Aguirre, A., Foster, B., Merali, Z. (eds) What is Fundamental?. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-11301-8_10
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