Born rule (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Born rule" in English language version.

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ams.org

mathscinet.ams.org

Gleason, Andrew M. (1957). "Measures on the closed subspaces of a Hilbert space". Indiana University Mathematics Journal. 6 (4): 885–893. doi:10.1512/iumj.1957.6.56050. MR 0096113.

ams.org

Chernoff, Paul R. (November 2009). "Andy Gleason and Quantum Mechanics" (PDF). Notices of the AMS. 56 (10): 1253–1259.

aps.org

journals.aps.org

Zurek, Wojciech H. (25 May 2005). "Probabilities from entanglement, Born's rule from envariance". Physical Review A. 71: 052105. arXiv:quant-ph/0405161. doi:10.1103/PhysRevA.71.052105. Retrieved 6 December 2022.

arxiv.org

Peres, Asher; Terno, Daniel R. (2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. S2CID 7481797.
Mermin, N. David (1993-07-01). "Hidden variables and the two theorems of John Bell". Reviews of Modern Physics. 65 (3): 803–815. arXiv:1802.10119. Bibcode:1993RvMP...65..803M. doi:10.1103/RevModPhys.65.803. S2CID 119546199.
Deutsch, David (8 August 1999). "Quantum Theory of Probability and Decisions". Proceedings of the Royal Society A. 455 (1988): 3129–3137. arXiv:quant-ph/9906015. Bibcode:1999RSPSA.455.3129D. doi:10.1098/rspa.1999.0443. S2CID 5217034. Retrieved December 5, 2022.
Wallace, David (2010). "How to Prove the Born Rule". In Kent, Adrian; Wallace, David; Barrett, Jonathan; Saunders, Simon (eds.). Many Worlds? Everett, Quantum Theory, & Reality. Oxford University Press. pp. 227–263. arXiv:0906.2718. ISBN 978-0-191-61411-8.
Zurek, Wojciech H. (25 May 2005). "Probabilities from entanglement, Born's rule from envariance". Physical Review A. 71: 052105. arXiv:quant-ph/0405161. doi:10.1103/PhysRevA.71.052105. Retrieved 6 December 2022.
Sebens, Charles T.; Carroll, Sean M. (March 2018). "Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics". The British Journal for the Philosophy of Science. 69 (1): 25–74. arXiv:1405.7577. doi:10.1093/bjps/axw004.
Saunders, Simon (24 November 2021). "Branch-counting in the Everett interpretation of quantum mechanics". Proceedings of the Royal Society A. 477 (2255): 1–22. arXiv:2201.06087. Bibcode:2021RSPSA.47710600S. doi:10.1098/rspa.2021.0600. S2CID 244491576.
Masanes, Lluís; Galley, Thomas; Müller, Markus (2019). "The measurement postulates of quantum mechanics are operationally redundant". Nature Communications. 10 (1): 1361. arXiv:1811.11060. Bibcode:2019NatCo..10.1361M. doi:10.1038/s41467-019-09348-x. PMC 6434053. PMID 30911009.
DeBrota, John B.; Fuchs, Christopher A.; Pienaar, Jacques L.; Stacey, Blake C. (2021). "Born's rule as a quantum extension of Bayesian coherence". Phys. Rev. A. 104 (2). 022207. arXiv:2012.14397. Bibcode:2021PhRvA.104b2207D. doi:10.1103/PhysRevA.104.022207.

doi.org

Hall, Brian C. (2013). "Quantum Theory for Mathematicians". Graduate Texts in Mathematics. New York, NY: Springer New York. pp. 14–15, 58. doi:10.1007/978-1-4614-7116-5. ISBN 978-1-4614-7115-8. ISSN 0072-5285.
Peres, Asher; Terno, Daniel R. (2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. S2CID 7481797.
Born, Max (1926). "Zur Quantenmechanik der Stoßvorgänge" [On the quantum mechanics of collisions]. Zeitschrift für Physik. 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477. S2CID 119896026. Reprinted as Born, Max (1983). "On the quantum mechanics of collisions". In Wheeler, J. A.; Zurek, W. H. (eds.). Quantum Theory and Measurement. Princeton University Press. pp. 52–55. ISBN 978-0-691-08316-2.
Gleason, Andrew M. (1957). "Measures on the closed subspaces of a Hilbert space". Indiana University Mathematics Journal. 6 (4): 885–893. doi:10.1512/iumj.1957.6.56050. MR 0096113.
Mackey, George W. (1957). "Quantum Mechanics and Hilbert Space". The American Mathematical Monthly. 64 (8P2): 45–57. doi:10.1080/00029890.1957.11989120. JSTOR 2308516.
Mermin, N. David (1993-07-01). "Hidden variables and the two theorems of John Bell". Reviews of Modern Physics. 65 (3): 803–815. arXiv:1802.10119. Bibcode:1993RvMP...65..803M. doi:10.1103/RevModPhys.65.803. S2CID 119546199.
Deutsch, David (8 August 1999). "Quantum Theory of Probability and Decisions". Proceedings of the Royal Society A. 455 (1988): 3129–3137. arXiv:quant-ph/9906015. Bibcode:1999RSPSA.455.3129D. doi:10.1098/rspa.1999.0443. S2CID 5217034. Retrieved December 5, 2022.
Greaves, Hilary (21 December 2006). "Probability in the Everett Interpretation" (PDF). Philosophy Compass. 2 (1): 109–128. doi:10.1111/j.1747-9991.2006.00054.x. Retrieved 6 December 2022.
Zurek, Wojciech H. (25 May 2005). "Probabilities from entanglement, Born's rule from envariance". Physical Review A. 71: 052105. arXiv:quant-ph/0405161. doi:10.1103/PhysRevA.71.052105. Retrieved 6 December 2022.
Sebens, Charles T.; Carroll, Sean M. (March 2018). "Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics". The British Journal for the Philosophy of Science. 69 (1): 25–74. arXiv:1405.7577. doi:10.1093/bjps/axw004.
Vaidman, Lev (2020). "Derivations of the Born Rule" (PDF). Quantum, Probability, Logic. Jerusalem Studies in Philosophy and History of Science. Springer. pp. 567–584. doi:10.1007/978-3-030-34316-3_26. ISBN 978-3-030-34315-6. S2CID 156046920.
Saunders, Simon (24 November 2021). "Branch-counting in the Everett interpretation of quantum mechanics". Proceedings of the Royal Society A. 477 (2255): 1–22. arXiv:2201.06087. Bibcode:2021RSPSA.47710600S. doi:10.1098/rspa.2021.0600. S2CID 244491576.
Masanes, Lluís; Galley, Thomas; Müller, Markus (2019). "The measurement postulates of quantum mechanics are operationally redundant". Nature Communications. 10 (1): 1361. arXiv:1811.11060. Bibcode:2019NatCo..10.1361M. doi:10.1038/s41467-019-09348-x. PMC 6434053. PMID 30911009.
DeBrota, John B.; Fuchs, Christopher A.; Pienaar, Jacques L.; Stacey, Blake C. (2021). "Born's rule as a quantum extension of Bayesian coherence". Phys. Rev. A. 104 (2). 022207. arXiv:2012.14397. Bibcode:2021PhRvA.104b2207D. doi:10.1103/PhysRevA.104.022207.

harvard.edu

ui.adsabs.harvard.edu

Peres, Asher; Terno, Daniel R. (2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. S2CID 7481797.
Born, Max (1926). "Zur Quantenmechanik der Stoßvorgänge" [On the quantum mechanics of collisions]. Zeitschrift für Physik. 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477. S2CID 119896026. Reprinted as Born, Max (1983). "On the quantum mechanics of collisions". In Wheeler, J. A.; Zurek, W. H. (eds.). Quantum Theory and Measurement. Princeton University Press. pp. 52–55. ISBN 978-0-691-08316-2.
Mermin, N. David (1993-07-01). "Hidden variables and the two theorems of John Bell". Reviews of Modern Physics. 65 (3): 803–815. arXiv:1802.10119. Bibcode:1993RvMP...65..803M. doi:10.1103/RevModPhys.65.803. S2CID 119546199.
Deutsch, David (8 August 1999). "Quantum Theory of Probability and Decisions". Proceedings of the Royal Society A. 455 (1988): 3129–3137. arXiv:quant-ph/9906015. Bibcode:1999RSPSA.455.3129D. doi:10.1098/rspa.1999.0443. S2CID 5217034. Retrieved December 5, 2022.
Saunders, Simon (24 November 2021). "Branch-counting in the Everett interpretation of quantum mechanics". Proceedings of the Royal Society A. 477 (2255): 1–22. arXiv:2201.06087. Bibcode:2021RSPSA.47710600S. doi:10.1098/rspa.2021.0600. S2CID 244491576.
Masanes, Lluís; Galley, Thomas; Müller, Markus (2019). "The measurement postulates of quantum mechanics are operationally redundant". Nature Communications. 10 (1): 1361. arXiv:1811.11060. Bibcode:2019NatCo..10.1361M. doi:10.1038/s41467-019-09348-x. PMC 6434053. PMID 30911009.
DeBrota, John B.; Fuchs, Christopher A.; Pienaar, Jacques L.; Stacey, Blake C. (2021). "Born's rule as a quantum extension of Bayesian coherence". Phys. Rev. A. 104 (2). 022207. arXiv:2012.14397. Bibcode:2021PhRvA.104b2207D. doi:10.1103/PhysRevA.104.022207.

indiana.edu

iumj.indiana.edu

Gleason, Andrew M. (1957). "Measures on the closed subspaces of a Hilbert space". Indiana University Mathematics Journal. 6 (4): 885–893. doi:10.1512/iumj.1957.6.56050. MR 0096113.

jstor.org

Mackey, George W. (1957). "Quantum Mechanics and Hilbert Space". The American Mathematical Monthly. 64 (8P2): 45–57. doi:10.1080/00029890.1957.11989120. JSTOR 2308516.

nih.gov

ncbi.nlm.nih.gov

Masanes, Lluís; Galley, Thomas; Müller, Markus (2019). "The measurement postulates of quantum mechanics are operationally redundant". Nature Communications. 10 (1): 1361. arXiv:1811.11060. Bibcode:2019NatCo..10.1361M. doi:10.1038/s41467-019-09348-x. PMC 6434053. PMID 30911009.

pubmed.ncbi.nlm.nih.gov

Masanes, Lluís; Galley, Thomas; Müller, Markus (2019). "The measurement postulates of quantum mechanics are operationally redundant". Nature Communications. 10 (1): 1361. arXiv:1811.11060. Bibcode:2019NatCo..10.1361M. doi:10.1038/s41467-019-09348-x. PMC 6434053. PMID 30911009.

nobelprize.org

Born, Max (11 December 1954). "The statistical interpretation of quantum mechanics" (PDF). www.nobelprize.org. nobelprize.org. Retrieved 7 November 2018. Again an idea of Einstein's gave me the lead. He had tried to make the duality of particles - light quanta or photons - and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. This concept could at once be carried over to the psi-function: |psi|² ought to represent the probability density for electrons (or other particles).

pitt.edu

philsci-archive.pitt.edu

Greaves, Hilary (21 December 2006). "Probability in the Everett Interpretation" (PDF). Philosophy Compass. 2 (1): 109–128. doi:10.1111/j.1747-9991.2006.00054.x. Retrieved 6 December 2022.
Vaidman, Lev (2020). "Derivations of the Born Rule" (PDF). Quantum, Probability, Logic. Jerusalem Studies in Philosophy and History of Science. Springer. pp. 567–584. doi:10.1007/978-3-030-34316-3_26. ISBN 978-3-030-34315-6. S2CID 156046920.

quantamagazine.org

Ball, Philip (February 13, 2019). "Mysterious Quantum Rule Reconstructed From Scratch". Quanta Magazine. Archived from the original on 2019-02-13.

royalsocietypublishing.org

Deutsch, David (8 August 1999). "Quantum Theory of Probability and Decisions". Proceedings of the Royal Society A. 455 (1988): 3129–3137. arXiv:quant-ph/9906015. Bibcode:1999RSPSA.455.3129D. doi:10.1098/rspa.1999.0443. S2CID 5217034. Retrieved December 5, 2022.

ru.nl

math.ru.nl

Landsman, N. P. (2008). "The Born rule and its interpretation" (PDF). In Weinert, F.; Hentschel, K.; Greenberger, D.; Falkenburg, B. (eds.). Compendium of Quantum Physics. Springer. ISBN 978-3-540-70622-9. The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle

semanticscholar.org

api.semanticscholar.org

Peres, Asher; Terno, Daniel R. (2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. S2CID 7481797.
Born, Max (1926). "Zur Quantenmechanik der Stoßvorgänge" [On the quantum mechanics of collisions]. Zeitschrift für Physik. 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477. S2CID 119896026. Reprinted as Born, Max (1983). "On the quantum mechanics of collisions". In Wheeler, J. A.; Zurek, W. H. (eds.). Quantum Theory and Measurement. Princeton University Press. pp. 52–55. ISBN 978-0-691-08316-2.
Mermin, N. David (1993-07-01). "Hidden variables and the two theorems of John Bell". Reviews of Modern Physics. 65 (3): 803–815. arXiv:1802.10119. Bibcode:1993RvMP...65..803M. doi:10.1103/RevModPhys.65.803. S2CID 119546199.
Deutsch, David (8 August 1999). "Quantum Theory of Probability and Decisions". Proceedings of the Royal Society A. 455 (1988): 3129–3137. arXiv:quant-ph/9906015. Bibcode:1999RSPSA.455.3129D. doi:10.1098/rspa.1999.0443. S2CID 5217034. Retrieved December 5, 2022.
Vaidman, Lev (2020). "Derivations of the Born Rule" (PDF). Quantum, Probability, Logic. Jerusalem Studies in Philosophy and History of Science. Springer. pp. 567–584. doi:10.1007/978-3-030-34316-3_26. ISBN 978-3-030-34315-6. S2CID 156046920.
Saunders, Simon (24 November 2021). "Branch-counting in the Everett interpretation of quantum mechanics". Proceedings of the Royal Society A. 477 (2255): 1–22. arXiv:2201.06087. Bibcode:2021RSPSA.47710600S. doi:10.1098/rspa.2021.0600. S2CID 244491576.

stanford.edu

plato.stanford.edu

Goldstein, Sheldon (2017). "Bohmian Mechanics". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.

web.archive.org

Ball, Philip (February 13, 2019). "Mysterious Quantum Rule Reconstructed From Scratch". Quanta Magazine. Archived from the original on 2019-02-13.

worldcat.org

search.worldcat.org

Hall, Brian C. (2013). "Quantum Theory for Mathematicians". Graduate Texts in Mathematics. New York, NY: Springer New York. pp. 14–15, 58. doi:10.1007/978-1-4614-7116-5. ISBN 978-1-4614-7115-8. ISSN 0072-5285.
Nielsen, Michael A.; Chuang, Isaac L. (2000). Quantum Computation and Quantum Information (1st ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-63503-5. OCLC 634735192.