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Journal articles on the topic 'Born rule'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Shrapnel, Sally, Fabio Costa, and Gerard Milburn. "Updating the Born rule." New Journal of Physics 20, no. 5 (2018): 053010. http://dx.doi.org/10.1088/1367-2630/aabe12.

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2

Wilhelm, Isaac. "Centering the Born Rule." Quantum Reports 5, no. 1 (2023): 311–24. http://dx.doi.org/10.3390/quantum5010021.

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The centered Everett interpretation solves a problem that various approaches to quantum theory face. In this paper, I continue developing the theory underlying that solution. In particular, I defend the centered Everett interpretation against a few objections, and I provide additional motivation for some of its key features.

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3

Logiurato, Fabrizio, and Augusto Smerzi. "Born Rule and Noncontextual Probability." Journal of Modern Physics 03, no. 11 (2012): 1802–12. http://dx.doi.org/10.4236/jmp.2012.311225.

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4

Ericksen, J. L. "On the Cauchy—Born Rule." Mathematics and Mechanics of Solids 13, no. 3-4 (2008): 199–220. http://dx.doi.org/10.1177/1081286507086898.

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5

Rae, Alastair I. M. "Everett and the Born rule." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40, no. 3 (2009): 243–50. http://dx.doi.org/10.1016/j.shpsb.2009.06.001.

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6

Monod, Paul, and Ellis Wasson. "Born to Rule: British Political Elites." Albion: A Quarterly Journal Concerned with British Studies 35, no. 1 (2003): 139. http://dx.doi.org/10.2307/4054549.

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7

Rubinstein, W. D. "Born to Rule: British Political Elites." English Historical Review 117, no. 472 (2002): 730. http://dx.doi.org/10.1093/ehr/117.472.730.

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8

De Zela, Francisco. "Gudder’s Theorem and the Born Rule." Entropy 20, no. 3 (2018): 158. http://dx.doi.org/10.3390/e20030158.

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9

Page, Don N. "The Born rule fails in cosmology." Journal of Cosmology and Astroparticle Physics 2009, no. 07 (2009): 008. http://dx.doi.org/10.1088/1475-7516/2009/07/008.

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10

Lawrence, Jay. "The Born rule: Axiom or result?" American Journal of Physics 92, no. 5 (2024): 371–74. http://dx.doi.org/10.1119/5.0151405.

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The Born rule is part of the collapse axioms in the standard version of quantum theory, as presented by most textbooks on the subject. We show here that its signature quadratic dependence on the initial wavefunction's projection onto the measured outcome state follows from a single additional assumption beyond the other axioms. We give two examples of such an assumption, with a separate derivation for each, and we discuss their relationship with existing derivations. Our presentation is suitable for advanced undergraduates or graduate students who have taken a standard course in quantum theory

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11

Prodanov, Dimiter. "The Burgers equations and the Born rule." Chaos, Solitons & Fractals 144 (March 2021): 110637. http://dx.doi.org/10.1016/j.chaos.2020.110637.

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12

Weinberg, S. L. "System/apparatus superposition and the Born rule." Physics Essays 21, no. 1 (2008): 78–83. http://dx.doi.org/10.4006/1.3001691.

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13

Costins, Pauline. "Refining or defining the Born Alive Rule?" Women and Birth 26 (October 2013): S24. http://dx.doi.org/10.1016/j.wombi.2013.08.168.

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14

Cooperman, Joshua H. "Rescuing the Born rule for quantum cosmology." Journal of Cosmology and Astroparticle Physics 2011, no. 02 (2011): 014. http://dx.doi.org/10.1088/1475-7516/2011/02/014.

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15

Arve, Per. "Everett’s Missing Postulate and the Born Rule." Foundations of Physics 50, no. 7 (2020): 665–92. http://dx.doi.org/10.1007/s10701-020-00338-4.

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16

Neumaier, Arnold. "The Born Rule—100 Years Ago and Today." Entropy 27, no. 4 (2025): 415. https://doi.org/10.3390/e27040415.

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The details of the contents and formulations of the Born rule have changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for today’s quantum optics and quantum information theory) to POVMs around 50 years ago, and a modern derivation from an intuitive definition of the notion of a quantum detector. Also discussed is the extent to which the various forms of the Born rule have, like any other statement in physics, a restricted domain of validity, which leads to problems when ap

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17

de Gosson, Maurice. "Short-Time Propagators and the Born–Jordan Quantization Rule." Entropy 20, no. 11 (2018): 869. http://dx.doi.org/10.3390/e20110869.

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We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born–Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

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18

Oeckl, Robert. "Born rule and Schroedinger equation from first principles." Journal of Physics: Conference Series 1275 (September 2019): 012049. http://dx.doi.org/10.1088/1742-6596/1275/1/012049.

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19

Pozrikidis, C. "On the applicability of the Cauchy-Born rule." Computational Materials Science 46, no. 2 (2009): 438–42. http://dx.doi.org/10.1016/j.commatsci.2009.03.031.

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20

Cour, Brian R. La, and Morgan C. Williamson. "Emergence of the Born rule in quantum optics." Quantum 4 (October 26, 2020): 350. http://dx.doi.org/10.22331/q-2020-10-26-350.

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The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the assumption of a quantum electrodynamic vacuum that is real rather than virtual. The connection to observation is made via classical intensity threshold detectors that are used as a simple, deterministic model of photon detection. By following standard experimental conventions of data analysis on discrete detection events, we show that this model is capable of repr

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21

Saunders, Simon. "Derivation of the Born rule from operational assumptions." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460, no. 2046 (2004): 1771–88. http://dx.doi.org/10.1098/rspa.2003.1230.

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22

Schlosshauer, Maximilian, and Arthur Fine. "On Zurek?s Derivation of the Born Rule." Foundations of Physics 35, no. 2 (2005): 197–213. http://dx.doi.org/10.1007/s10701-004-1941-6.

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23

Choi, Sung W. "The Association of the Publication of a Proposed Public Charge Rule with Preterm Births among Uninsured Foreign-Born Latinx Birthing People in the United States." Healthcare 11, no. 14 (2023): 2054. http://dx.doi.org/10.3390/healthcare11142054.

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Following the inauguration, the Trump administration authorized a series of anti-immigrant policies, including modifications to the public charge regulation. This study analyzed the effect of the publication of a proposed public charge rule in 2018 on the risk of preterm birth between uninsured and privately insured Latinx birthing people in the United States by using natality files from the National Center for Health Statistics. In total, 1,375,580 Latinx birthing people reported private insurance as their primary source of delivery from 2014 to 2019, while 317,056 Latinx birthing people repo

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24

Hsu, Stephen D. H. "Discrete Hilbert space, the Born Rule, and quantum gravity." Modern Physics Letters A 36, no. 03 (2021): 2150013. http://dx.doi.org/10.1142/s0217732321500139.

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Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert

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25

Ojima, Izumi, Kazuya Okamura, and Hayato Saigo. "Derivation of Born Rule from Algebraic and Statistical Axioms." Open Systems & Information Dynamics 21, no. 03 (2014): 1450005. http://dx.doi.org/10.1142/s123016121450005x.

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In this paper we propose a new system of algebraic and statistical axioms as working hypotheses, from which Born rule can be seen to emerge. In this process the concept of sectors defined as quasi-equivalence classes of factor states plays a crucial role.

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26

Towler, M. D., N. J. Russell, and Antony Valentini. "Time scales for dynamical relaxation to the Born rule." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (2011): 990–1013. http://dx.doi.org/10.1098/rspa.2011.0598.

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We illustrate through explicit numerical calculations how the Born rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie–Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie–Bohm ontology, the box contains an objectively existing ‘pilot wave’ which guides the electron trajectory, and this is represented mathematically by a Schrödinger wave funct

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27

Patterson, J. D., and S. L. Lehoczky. "The second Born approximation and the Friedel sum rule." Physics Letters A 137, no. 3 (1989): 137–38. http://dx.doi.org/10.1016/0375-9601(89)90099-6.

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28

Oliva-Leyva, Maurice, and Chumin Wang. "Theory for Strained Graphene Beyond the Cauchy-Born Rule." physica status solidi (RRL) - Rapid Research Letters 12, no. 9 (2018): 1800237. http://dx.doi.org/10.1002/pssr.201800237.

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29

Chandraseker, Karthick, and Subrata Mukherjee. "Coupling of Extension and Twist in Single-Walled Carbon Nanotubes." Journal of Applied Mechanics 73, no. 2 (2005): 315–26. http://dx.doi.org/10.1115/1.2125987.

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This paper presents a study of the deformation behavior of single-walled carbon nanotubes (SWNTs) subjected to extension and twist. The interatomic force description is provided by the Tersoff-Brenner potential for carbon. The rolling of a flat graphene sheet into a SWNT is first simulated by minimizing the energy per atom, the end result being the configuration of an undeformed SWNT. The Cauchy-Born rule is then used to connect the atomistic and continuum descriptions of the deformation of SWNTs, and leads to a multilength scale mechanics framework for simulating deformation of SWNTs under ap

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30

LANDSMAN, N. P. "MACROSCOPIC OBSERVABLES AND THE BORN RULE, I: LONG RUN FREQUENCIES." Reviews in Mathematical Physics 20, no. 10 (2008): 1173–90. http://dx.doi.org/10.1142/s0129055x08003511.

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We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will be the subject of a sequel pa

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31

Riek, Roland. "Revisiting the measurement of a quantum mechanical experiment by an Ehrenfest theorem-based Fourier Transformation." Journal of Physics: Conference Series 3017, no. 1 (2025): 012019. https://doi.org/10.1088/1742-6596/3017/1/012019.

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Abstract In terms of its time trajectory, a physical experiment is comprised of a preparation time, a start time, a time evolution (duration), and an end time (point at which the measurement actually occurs). In non-relativistic quantum mechanics the start of the experiment is described by the wave function at time t = 0 taking into account the starting conditions, the evolution is described by the wave function according to the Schrödinger equation and the measurement is described by the Born rule. While the Schrödinger equation is deterministic, it is the Born rule that renders quantum mecha

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32

LU, S., C. D. CHO, and L. SONG. "ENERGY OF ARMCHAIR NANOTUBE USING THE MODIFIED CAUCHY-BORN RULE." International Journal of Modern Physics B 22, no. 31n32 (2008): 5881–86. http://dx.doi.org/10.1142/s0217979208051315.

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Due to the difference of nanotube diameters, the single-walled carbon nanotubes (SWCNTs) show the different energy and mechanical properties. In order to take the effect of the curvature of nanotubes into account in the modeling of those structures, the present paper proposes an atomistic based continuum model with using a type of modified Cauchy-Born to link the continuum strain energy to the interatomic potential. This modified Cauchy-Born is developed by incorporating the concept of differential mean value theorem into the standard Cauchy-Born rule. The present model not only can bridge the

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33

Hutabarat, Dany Try Hutama, Bunga Cyntia Lutfianur, Duwi Anggun Amsari, et al. "HUBUNGAN NEGARA HUKUM DENGAN HAM DI INDONESIA." JOURNAL OF HUMANITIES, SOCIAL SCIENCES AND BUSINESS (JHSSB) 1, no. 2 (2022): 27–36. http://dx.doi.org/10.55047/jhssb.v1i2.76.

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Laws are regulations made by the government. The rule of law is a state that enforces justice that deviates from the rules of a country. Human rights (HAM) can be interpreted as basic rights in humans. Human rights have been given since we were born, so no one has the right to rob human rights, whoever it is. The rule of law is enforced so that people can obey the rules of a country, one of which is to protect one's human rights. The rule of law with human rights is very attached. Because one indication to be called a state of law, among others, the enforcement of human rights, because a state

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34

Lazarovici, Dustin. "How Everett Solved the Probability Problem in Everettian Quantum Mechanics." Quantum Reports 5, no. 2 (2023): 407–17. http://dx.doi.org/10.3390/quantum5020026.

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A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on the concept of typicality. It argues that Everett’s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett’s typicality argument can successfully ground post-factum explanations of Born statistics, whil

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35

Butcher, Kristin F., Luojia Hu, and Ryan Perry. "The Public Charge Rule and Program Participation Among U.S. Citizens." ANNALS of the American Academy of Political and Social Science 711, no. 1 (2024): 170–98. https://doi.org/10.1177/00027162241293910.

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Use of public assistance by noncitizens is controversial. Before 2018, institutionalization and receipt of cash benefits were considered as evidence of whether immigrants were likely to become a “public charge” and, therefore, ineligible for citizenship. But a new rule—proposed in 2018 and finalized in 2020—also made participation in SNAP/Food Stamps and Medicaid relevant as evidence. We examine whether participation in SNAP/Food Stamps and Medicaid among U.S.-born children—whose own eligibility for program participation should be unaffected by the new rule—has changed, based on the citizenshi

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36

Fauser, Bertfried, Guillaume Raynaud, and Steven Vickers. "The Born rule as structure of spectral bundles (extended abstract)." Electronic Proceedings in Theoretical Computer Science 95 (October 1, 2012): 81–90. http://dx.doi.org/10.4204/eptcs.95.8.

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37

Kollander, Patricia. "Born to Rule: Five Reigning Consorts, Granddaughters of Queen Victoria." History: Reviews of New Books 34, no. 1 (2005): 22. http://dx.doi.org/10.1080/03612759.2005.10526743.

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38

Brezhnev, Yurii V. "The Born rule as a statistics of quantum micro-events." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2244 (2020): 20200282. http://dx.doi.org/10.1098/rspa.2020.0282.

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We deduce the Born rule from a purely statistical take on quantum theory within minimalistic math-setup. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics—a linear, not Hilbert’, vector space—and empirical notion of the Statistical Length of a state. Its statistical nature comes from the lab micro-events (detector-clicks) being formalized into the C -coefficients of quantum superpositions. We also comment that not only has the use not been made of quantum axioms (scalar-product, operators, interpretations , etc.), but that the involving thereof would b

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39

Harris, Jérémie, Frédéric Bouchard, Enrico Santamato, Wojciech H. Zurek, Robert W. Boyd, and Ebrahim Karimi. "Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule." New Journal of Physics 18, no. 5 (2016): 053013. http://dx.doi.org/10.1088/1367-2630/18/5/053013.

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40

Bacci, Marco, and Paolo Maria Mariano. "Protein dynamics: An approach based on the Cauchy–Born rule." Physica E: Low-dimensional Systems and Nanostructures 61 (July 2014): 69–82. http://dx.doi.org/10.1016/j.physe.2014.03.009.

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41

Donoghue, Victoria A., and David H. Nachman. "Foreign-born scientists and the two-year home residency rule." JOM 62, no. 4 (2010): 80. http://dx.doi.org/10.1007/s11837-010-0065-z.

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42

Hansson, Johan. "The Magical “Born Rule” and Quantum “Measurement”: Implications for Physics." Foundations 3, no. 4 (2023): 634–42. http://dx.doi.org/10.3390/foundations3040038.

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I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real physical world—is the classical four-dimensional physical spacetime. III. The “Born rule” is the random process “magically” transforming I into II. Wavefunctions are superposed and entangled only in the abstract space I, never in spacetime II. Attempted formulations of quantum theory directly in real physical spacetime actually constitute examples o

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43

Bonness, Dania Jovanna. "The Northern Subject Rule in the Irish diaspora." English World-Wide 38, no. 2 (2017): 125–52. http://dx.doi.org/10.1075/eww.38.2.01bon.

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Abstract This article examines the Northern Subject Rule in the Irish diaspora, studying letters from two generations of an Ulster emigrant family in 19th-century New Zealand. The study shows that the concord pattern frequently used by the parent generation almost completely disappeared in the language of their New Zealand-born children. The results suggest that the children skipped the stage of “extreme variability” that is claimed to be characteristic of the language of the first colony-born immigrants in the new-dialect formation framework (Trudgill 2004). This study aims to contribute to w

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44

Hanson, Robin D. "Drift–diffusion in mangled worlds quantum mechanics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2069 (2006): 1619–27. http://dx.doi.org/10.1098/rspa.2005.1640.

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In Everett's many-worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world measure. I solve a growth–drift–diffusion–absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus, inexact decoherence may allow the Born rule to be derived in a many-worlds approach via world counting, using a finite number of worlds and no new fundamental physics.

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45

ENDO, RIKA, RIE KURIKI, AKIO SUGAMOTO, and SHIN'ICHI NOJIRI. "A RULE OF THUMB DERIVATION OF BORN–INFELD ACTION FOR D-BRANES." Modern Physics Letters A 13, no. 16 (1998): 1309–17. http://dx.doi.org/10.1142/s0217732398001364.

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A rule of thumb derivation of the Dirac–Born–Infeld action for D-branes is studied à la Fradkin and Tseytlin, by simply integrating out of the superstring coordinates in a narrow strip attached to the D-branes. In case of superstrings, the coupling of Ramond–Ramond fields as well as the Dirac–Born–Infeld type coupling of the Neveu Schwarz–Neveu Schwarz fields come out in this way.

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46

Živković, Velimir. "ISDS and Nazis or History Without Context: A Reply to Gary Born." Journal of International Arbitration 39, Issue 4 (2022): 575–92. http://dx.doi.org/10.54648/joia2022025.

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Gary Born’s article ‘The 1933 Directives on Arbitration of the German Reich: Echoes of the Past?’ fascinates for good and not so good reasons in almost equal measure. The author skillfully illuminated a rarely-discussed episode of arbitral legal history and aimed to apply its lessons to current debates surrounding investor-state dispute settlement (ISDS) reform. The overarching argument is that criticism and/or reform of investor-state arbitration is reckless and reminiscent of National Socialist efforts to curb private-public arbitration – risking undermining the rule of law and even allowing

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47

Lill, Sascha, and Roderich Tumulka. "Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces." Annales Henri Poincaré 23, no. 4 (2021): 1489–524. http://dx.doi.org/10.1007/s00023-021-01130-4.

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AbstractIn 2017, Lienert and Tumulka proved Born’s rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born’s rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born’s rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $$\Sigma $$ Σ , t

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48

Luo, Tao, Yang Xiang, Jerry Zhijian Yang, and Cheng Yuan. "Cauchy–Born rule and stability of crystalline solids at finite temperature." Communications in Mathematical Sciences 19, no. 6 (2021): 1461–90. http://dx.doi.org/10.4310/cms.2021.v19.n6.a1.

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49

Schumann, Thomas G. "Three arguments for the quantum dream analogy plus Born Rule derivation." Physics Essays 24, no. 4 (2011): 564–69. http://dx.doi.org/10.4006/1.3655848.

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50

Powell, James M. "Calixtus II (1119-1124): A Pope Born to Rule. Mary Stroll." Speculum 81, no. 3 (2006): 925–27. http://dx.doi.org/10.1017/s0038713400016511.

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