The Chronotopic Paradigm: The Cosmological Constant from Quantum Entanglement

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Submitted: August 18, 2025
Published: Oct 10, 2025
DOI: 10.17352/amp.000163

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Rohit Patra
Independent Researcher, India

Abstract

This paper presents a rigorous computational framework—the Chronotopic Paradigm—that demonstrates the emergence of spacetime geometry and a dynamical cosmological constant (Λ) directly from the structure of quantum entanglement. Moving beyond approaches that quantize a classical background, we postulate the primacy of quantum information: geometry is not fundamental but is an emergent, large-scale property of the quantum state. We apply this framework to the ground state of the critical Transverse Field Ising Model (TFIM), which is dual to AdS2 gravity via the Ads/CFT correspondence. By defining geometric quantities (metric and curvature) based on local quantum information (mutual information and Uhlmann holonomy), we successfully derive a hyperbolic, constant-curvature geometry, providing a constructive realization of the holographic principle. The central finding is the derivation of an emergent cosmological constant, Λent, which follows a universal scaling law with respect to the number of entanglement degrees of freedom (N):

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Patra, R. (2025). The Chronotopic Paradigm: The Cosmological Constant from Quantum Entanglement. Annals of Mathematics and Physics, 8(5), 181–201. https://doi.org/10.17352/amp.000163
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Copyright (c) 2025 Patra R. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Ryu S, Takayanagi T. Holographic derivation of entanglement entropy from the anti–de Sitter space/conformal field theory correspondence. Phys Rev Lett. 2006;96(18):181602. Available from: https://doi.org/10.1103/PhysRevLett.96.181602

Van Raamsdonk M. Building up spacetime with quantum entanglement. Gen Relativ Gravit. 2010;42:2323–2329. Available from: https://link.springer.com/article/10.1007/s10714-010-1034-0

Maldacena J. The large-N limit of superconformal field theories and supergravity. Int J Theor Phys. 1999;38(4):1113–1133. Available from: https://link.springer.com/article/10.1023/A:1026654312961

Jacobson T. Thermodynamics of spacetime: The Einstein equation of state. Phys Rev Lett. 1995;75(7):1260. Available from: https://doi.org/10.1103/PhysRevLett.75.1260

Verlinde E. On the origin of gravity and the laws of Newton. J High Energy Phys. 2011;2011(4):29. Available from: https://pure.uva.nl/ws/files/1162156/105001_357036.pdf

Swingle B. Entanglement renormalization and holography. Phys Rev D. 2012;86(6):065007. Available from: https://doi.org/10.1103/PhysRevD.86.065007

Bianchi E, Myers RC. On the architecture of spacetime geometry. Class Quantum Grav. 2014;31(21):214002. Available from: https://doi.org/10.1088/0264-9381/31/21/214002

Uhlmann A. Parallel transport and “quantum holonomy” along density operators. Rep Math Phys. 1986;24(2):229–240. Available from: https://doi.org/10.1016/0034-4877(86)90055-8

Uhlmann A. The metric of Bures and the geometric phase. In: Groups and Related Topics. Dordrecht: Springer. 1991;267–274. Available from: https://link.springer.com/chapter/10.1007/978-94-011-2801-8_23

Nielsen MA, Chuang IL. Quantum computation and quantum information: 10th anniversary edition. Cambridge: Cambridge University Press; 2010. Available from: https://doi.org/10.1017/CBO9780511976667

Witten E. APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory. Rev Mod Phys. 2018;90(4):045003. Available from: https://doi.org/10.1103/RevModPhys.90.045003

Calabrese P, Cardy J. Entanglement entropy and quantum field theory. J Stat Mech Theory Exp. 2004;2004(06):P06002. Available from: https://doi.org/10.1088/1742-5468/2004/06/P06002

Haag R. Local quantum physics: Fields, particles, algebras. Berlin: Springer Science & Business Media; 1996. Available from: https://link.springer.com/book/10.1007/978-3-642-61458-3

Bengtsson I, Życzkowski K. Geometry of quantum states: an introduction to quantum entanglement. Cambridge: Cambridge University Press; 2017. Available from: https://doi.org/10.1017/9781139207010

Petz D. Monotone metrics on matrix spaces. Linear Algebra Appl. 1996;244:81–96. Available from: https://doi.org/10.1016/0024-3795(94)00211-8

Bures D. An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-????-algebras. Trans Am Math Soc. 1969;135:199–212. Available from: https://www.jstor.org/stable/1995012

Di Francesco P, Mathieu P, Sénéchal D. Conformal field theory. New York: Springer Science & Business Media; 1997. Available from: https://doi.org/10.1007/978-1-4612-2256-9

Sachdev S. Quantum phase transitions. Cambridge: Cambridge University Press; 2011. Available from: https://doi.org/10.1017/CBO9780511973765

Henkel M. Conformal invariance and critical phenomena. Berlin: Springer Science & Business Media; 1999. Available from: https://doi.org/10.1007/978-3-662-03937-3

Wald RM. General relativity. Chicago: University of Chicago Press; 1984. Available from: https://fma.if.usp.br/~mlima/teaching/PGF5292_2021/Wald_GR.pdf

Petersen P. Riemannian geometry. Vol. 171. New York: Springer Science & Business Media; 2006. Available from: https://link.springer.com/book/10.1007/978-0-387-29403-2

Nakahara M. Geometry, topology, and physics. Boca Raton: CRC Press; 2003. Available from: https://doi.org/10.1201/9781315275826

Pfeuty P. The one-dimensional Ising model with a transverse field. Ann Phys. 1970;57(1):79–90. Available from: https://www.math.ucdavis.edu/~bxn/pfeuty1970.pdf

Calabrese P, Campostrini M, Essler F, Nienhuis B. Parity effects in the scaling of block entanglement in gapless spin chains. Phys Rev Lett. 2010;104(9):095701. Available from: https://doi.org/10.1103/PhysRevLett.104.095701

Latorre JI, Rico E, Vidal G. Ground state entanglement in quantum spin chains. Quantum Inf Comput. 2004;4(1):48–92. Available from: https://dl.acm.org/doi/abs/10.5555/2011572.2011576

Takesaki M. Theory of operator algebras II. Vol. 125. Berlin: Springer Science & Business Media; 2003. Available from: https://link.springer.com/series/5515?srsltid=AfmBOoo0Y4y-YTsUwwHm8rk8KJ4-R_XDOjysTqpRU5xOqdLeAF4fzA_G

Borchers HJ. On revolutionizing quantum field theory with Tomita’s modular theory. J Math Phys. 2000;41(6):3604–3673. Available from: https://doi.org/10.1063/1.533323

Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes: The art of scientific computing. 3rd ed. Cambridge: Cambridge University Press; 2007. Available from: https://books.google.co.in/books/about/Numerical_Recipes_3rd_Edition.html?id=1aAOdzK3FegC&redir_esc=y

Taylor JR. An introduction to error analysis: The study of uncertainties in physical measurements. Sausalito (CA): University Science Books; 1997. Available from: https://www.scirp.org/reference/referencespapers?referenceid=2927559