{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:24Z","timestamp":1760150904596,"version":"build-2065373602"},"reference-count":83,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,26]],"date-time":"2022-01-26T00:00:00Z","timestamp":1643155200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The classical-quantum dichotomy is analyzed from the perspective of the Process Algebra approach, which views fundamental phenomena through the lens of complex systems theory and Whitehead\u2019s process theory. Broadly, the dichotomy can be framed in terms of differences in ontology (phenomena and their behavior) and differences in epistemology (theoretical languages used in their description). The Process Algebra posits a reality, generated by processes, whose fundamental characteristics include becoming, generativity, transience, locality, and contextuality. From this perspective, the classical-quantum dichotomy appears to be a false dichotomy\u2014it arises because of stereotyped, strawman-like depictions of what it means to be classical or quantum. A more careful examination reveals that reality is unitary, that whether a system behaves in a quantum or classical manner depends upon its particularities, in particular, whether it is complex or not, and how information flows govern its dynamics.<\/jats:p>","DOI":"10.3390\/e24020184","type":"journal-article","created":{"date-parts":[[2022,1,26]],"date-time":"2022-01-26T11:02:53Z","timestamp":1643194973000},"page":"184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Classical-Quantum Dichotomy from the Perspective of the Process Algebra"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0484-381X","authenticated-orcid":false,"given":"William","family":"Sulis","sequence":"first","affiliation":[{"name":"Collective Intelligence Laboratory, McMaster University, Hamilton, ON L8S 2T6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pickering, A. (1995). The Mangle of Practice: Time, Agency and Science, The University of Chicago Press.","DOI":"10.7208\/chicago\/9780226668253.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Smith, B.C. (1996). On the Origin of Objects, MIT Press.","DOI":"10.7551\/mitpress\/5128.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Castellani, E. (1998). Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton University Press.","DOI":"10.1515\/9780691222042"},{"key":"ref_4","unstructured":"Bunge, M. (1995). Causality: The Place of the Causal Principle in Modern Science, Meridian Books."},{"key":"ref_5","unstructured":"Kolmogorov, A.N. (1956). Foundations of the Theory of Probability, Chelsea Publishing."},{"key":"ref_6","first-page":"407","article-title":"Modeling stochastic complexity in complex adaptive systems: Non-Kolmogorov probability and the process algebra approach","volume":"21","author":"Sulis","year":"2017","journal-title":"Nonlinear Dyn. Psychol. Life Sci."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Khrennikov, A. (2010). Ubiquitous Quantum Structure, Springer.","DOI":"10.1007\/978-3-642-05101-2"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Khrennikov, A. (2017). Probability and Randomness: Quantum Versus Classical, Imperial College Press.","DOI":"10.1142\/S0219749916400098"},{"key":"ref_9","unstructured":"Bell, J.S. (1987). Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF00417500","article-title":"Quantum generalizations of Bell\u2032s inequality","volume":"4","year":"1980","journal-title":"Lett. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1038\/nphys2309","article-title":"On the reality of the quantum state","volume":"8","author":"Pusey","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"050403","DOI":"10.1103\/PhysRevLett.101.050403","article-title":"Hidden variable models for quantum theory cannot have any local part","volume":"101","author":"Colbeck","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1038\/ncomms1416","article-title":"No extension of quantum theory can have improved predictive power","volume":"2","author":"Colbeck","year":"2011","journal-title":"Nat. Commun."},{"key":"ref_14","unstructured":"Cohen, J., and Stewart, I. (1994). The Collapse of Chaos, Viking."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mitchell, M. (2009). Complexity: A Guided Tour, Oxford University Press.","DOI":"10.1093\/oso\/9780195124415.001.0001"},{"key":"ref_16","unstructured":"Laughlin, R. (2005). A different Universe: Reinventing Physics from the Bottom Down, Perseus Books."},{"key":"ref_17","first-page":"209","article-title":"Archetypal dynamics, emergent situations and the reality game","volume":"14","author":"Sulis","year":"2010","journal-title":"Nonlinear Dyn. Psychol. Life Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Rosen, R. (2012). Anticipatory Systems: Philosophical, Mathematical and Methodological Foundations, Springer.","DOI":"10.1007\/978-1-4614-1269-4"},{"key":"ref_19","unstructured":"Hiley, B.J., and Peat, F.D. (1991). Some epistemological issues in physics and biology. Quantum Implications: Essays in Honour of David Bohm, Routledge."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"508","DOI":"10.2495\/DNE-V11-N4-508-521","article-title":"Phenomena of Functional Differentiation (FD) and Fractal Functionality (FF)","volume":"11","author":"Trofimova","year":"2016","journal-title":"Int. J. Des. Nat. Ecodynamics"},{"key":"ref_21","first-page":"441","article-title":"Functional constructivism: In search of formal descriptors","volume":"21","author":"Trofimova","year":"2017","journal-title":"Nonlinear Dyn. Psychol. Life Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"592","DOI":"10.3390\/quantum3040038","article-title":"Contextuality in Neurobehavioural Regulatory Systems and Collective Intelligence","volume":"3","author":"Sulis","year":"2021","journal-title":"Quantum Rep."},{"key":"ref_23","first-page":"30","article-title":"Fundamentals of Collective Intelligence","volume":"1","author":"Sulis","year":"1997","journal-title":"Nonlinear Dyn. Psychol. Life Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Guastello, S., Koopmans, M., and Pincus, D. (2009). Collective intelligence: Observations and models. Chaos and Complexity in Psychology: The Theory of Nonlinear Dynamical Systems, Cambridge University Press.","DOI":"10.1017\/CBO9781139058544"},{"key":"ref_25","unstructured":"Elliott, E., and Kiel, D. (2021). Lessons from Collective Intelligence. Complex Systems in the Social and Behavioral Sciences: Theory, Method and Application, University of Michigan Press."},{"key":"ref_26","unstructured":"Whiting, H. (1984). Human Motor Actions: Bernstein Reassessed, North-Holland."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2008","DOI":"10.1523\/JNEUROSCI.10-06-02008.1990","article-title":"The firing of hippocampal place cells in the dark depends on the rat\u2019s recent experience","volume":"10","author":"Quirk","year":"1990","journal-title":"J. Neurosci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.tics.2019.05.008","article-title":"Consolidating the case for transient hippocampal memory traces","volume":"23","author":"Barry","year":"2019","journal-title":"Trends Cogn. Sci."},{"key":"ref_29","unstructured":"Atmanspacher, H., Filk, T., and Pothos, E. (2016). Contextuality by default: A brief overview of ideas, concepts, and terminology. Lecture Notes in Computer Science 9535, Springer."},{"key":"ref_30","unstructured":"Harris, R. (2017). Rigors Mortis: How Sloppy Science Creates Worthless Cures, Crushes Hope and Wastes Billions, Basic Books."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1086\/269029","article-title":"An Evaluation of a Cognitive Theory of Response-Order Effects in Survey Measurement","volume":"51","author":"Alwin","year":"1987","journal-title":"Public Opin. Q."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1023\/A:1026449716544","article-title":"The violation of Bell inequalities in the macroworld","volume":"30","author":"Aerts","year":"2001","journal-title":"Found. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1037\/dec0000095","article-title":"Snow Queen Is Evil and Beautiful: Experimental Evidence for Probabilistic Contextuality in Human Choices","volume":"5","author":"Cervantes","year":"2018","journal-title":"Decision"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.jmp.2019.04.006","article-title":"True contextuality in a psychophysical experiment","volume":"91","author":"Cervantes","year":"2019","journal-title":"J. Math. Psychol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1038\/44348","article-title":"Wave\u2013particle duality of C60 molecules","volume":"401","author":"Arndt","year":"1999","journal-title":"Nature"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1038\/nature16155","article-title":"Quantum superposition at the half-metre scale","volume":"528","author":"Kovachy","year":"2015","journal-title":"Nature"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"428","DOI":"10.3389\/fpsyg.2015.00428","article-title":"Eliciting mixed emotions: A meta-analysis comparing models, types, and measures","volume":"6","author":"Berrios","year":"2015","journal-title":"Front. Psychol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"223601","DOI":"10.1103\/PhysRevLett.117.223601","article-title":"Ramsey Interference with Single Photons","volume":"117","author":"Clemmen","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Hagar, A. (2014). Discrete or Continuous? The Quest for Fundamental Length in Physics, Cambridge University Press.","DOI":"10.1017\/CBO9781107477346"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2891","DOI":"10.1088\/1751-8113\/40\/12\/S01","article-title":"Some reflections inspired by my research activity in quantum mechanics","volume":"40","author":"Ghirardi","year":"2007","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Joos, E., Zeh, H., Kiefer, C., Giulini, D., Kupsch, J., and Stamatescu, I. (2003). Decoherence and the Appearance of a Classical World in Quantum Theory, Springer.","DOI":"10.1007\/978-3-662-05328-7"},{"key":"ref_42","unstructured":"Griffiths, R. (2003). Consistent Quantum Theory, Cambridge University Press."},{"key":"ref_43","first-page":"79","article-title":"The wave mechanics of \u03b1-ray tracks","volume":"126","author":"Mott","year":"1929","journal-title":"Proc. R. Soc. A"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Nation, J., Trofimova, I., Rand, J., and Sulis, W. (2002). Archetypal dynamics and emergence. Formal Descriptions of Developing Systems, Kluwer Press.","DOI":"10.1007\/978-94-010-0064-2"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Sulis, W. (2019). Transients as the basis for information flow in complex adaptive systems. Entropy, 21.","DOI":"10.3390\/e21010094"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Sulis, W. (2020). An information ontology for the process algebra model of non-relativistic quantum mechanics. Entropy, 22.","DOI":"10.3390\/e22020136"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF02478347","article-title":"A quantum-theoretic approach to genetic problems","volume":"22","author":"Rosen","year":"1960","journal-title":"Bull. Math. Biophys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/BF02476608","article-title":"Analogous systems","volume":"30","author":"Rosen","year":"1968","journal-title":"Bull. Math. Biophys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1063\/1.3141952","article-title":"What\u2019s bad about this habit?","volume":"62","author":"Mermin","year":"2009","journal-title":"Phys. Today"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1007\/s10701-013-9725-5","article-title":"Non-Kolmogorovian approach to the context-dependent systems breaking the classical probability law","volume":"43","author":"Asano","year":"2013","journal-title":"Found. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Haven, E., and Khrennikov, A. (2014). Quantum Social Science, Cambridge University Press.","DOI":"10.1017\/CBO9781139003261"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Berlekamp, E.R., Conway, J.H., and Guy, R.K. (2004). Winning Ways for Your Mathematical Plays, A K Peters\/CRC Press. [2nd ed.].","DOI":"10.1201\/9780429487309"},{"key":"ref_53","unstructured":"Born, M. (1989). Atomic Physics, Dover Publications."},{"key":"ref_54","first-page":"113","article-title":"Causal Tapestries for Psychology and Physics","volume":"16","author":"Sulis","year":"2012","journal-title":"Nonlinear Dyn. Psychol. Life Sci."},{"key":"ref_55","unstructured":"Whitehead, A.N. (1978). Process and Reality, The Free Press."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Shimony, A. (1993). Search for a Naturalistic World View, Volume II: Natural Science and Metaphysics, Cambridge University Press.","DOI":"10.1017\/CBO9781139172196"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"360","DOI":"10.3389\/fphy.2020.00360","article-title":"Locality is dead. Long live locality!","volume":"8","author":"Sulis","year":"2020","journal-title":"Front. Phys."},{"key":"ref_58","unstructured":"Reichenbach, H. (1991). The Direction of Time, University of California Press."},{"key":"ref_59","first-page":"031021","article-title":"Quantum common causes and quantum causal models","volume":"7","author":"Allen","year":"2017","journal-title":"Phys. Rev. X"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Khrennikov, A., and Alodjants, A. (2019). Classical (local and contextual) probability model for Bohm-Bell type experiments: No signaling as independence of random variables. Entropy, 21.","DOI":"10.3390\/e21020157"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Dzhafarov, E., and Kujala, J. (2018). Contextuality analysis of the double slit experiment (with a glimpse into three slits). Entropy, 20.","DOI":"10.3390\/e20040278"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"022117","DOI":"10.1103\/PhysRevA.101.022117","article-title":"Nonlocality claims are inconsistent with Hilbert space quantum mechanics","volume":"101","author":"Griffiths","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/S0031-8914(46)80096-X","article-title":"On the energy levels of a mode of the compressed hydrogen atom","volume":"12","year":"1946","journal-title":"Physica"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1016\/S0031-8914(37)80196-2","article-title":"Remarks concerning molecular interaction and their influence on the polarizability","volume":"4","author":"Michels","year":"1937","journal-title":"Physica"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Bancal, J.D., Pironio, S., Acin, A., Liang, Y.C., Scarani, V., and Gisin, N. (2013). Quantum Nonlocality Based on Finite-Speed Causal Influences Leads to Superluminal Signalling, Springer.","DOI":"10.1007\/978-3-319-01183-7_10"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1140\/epjp\/i2019-12987-0","article-title":"Quantum entanglement in physical and cognitive systems: A conceptual analysis and a general representation","volume":"134","author":"Aerts","year":"2019","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Unger, R.M., and Smolin, L. (2015). The Singular Universe and the Reality of Time, Cambridge University Press.","DOI":"10.1017\/CBO9781139696487"},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Elitzur, A., Dolev, S., and Kolenda, N. (2005). Quantum phenomena within a new theory of time. Quo Vadis Quantum Mechanics?, Springer.","DOI":"10.1007\/b137897"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Gisin, N. (2016). Time really passes, science can\u2019t deny that. Time in Physics, Birkh\u00e4user.","DOI":"10.1007\/978-3-319-68655-4_1"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Petkov, V. (2007). Relativity does not imply that the future already exists: A counterexample. Relativity and the Dimensionality of the World, Springer.","DOI":"10.1007\/978-1-4020-6318-3"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.4236\/jmp.2014.516176","article-title":"A process model of quantum mechanics","volume":"5","author":"Sulis","year":"2014","journal-title":"J. Mod. Phys."},{"key":"ref_72","unstructured":"Sienicki, K. (2017). Completing quantum mechanics. Quantum Mechanics Interpretations, Open Academic Press."},{"key":"ref_73","unstructured":"Martinez, R. (2017). A process algebra approach to quantum electrodynamics: Physics from the top up. Complex Systems: Theory and Applications, Nova Publishing."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"3869","DOI":"10.1007\/s10773-017-3366-y","article-title":"A process algebra approach to quantum electrodynamics","volume":"56","author":"Sulis","year":"2017","journal-title":"Int. J. Theoret. Phys."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Nation, J., Trofimova, I., Rand, J., and Sulis, W. (2002). Sociability, diversity and compatibility in developing systems: EVS approach. Formal Descriptions of Developing Systems, Kluwer.","DOI":"10.1007\/978-94-010-0064-2"},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Conway, J.H. (2001). On Numbers and Games, A.K. Peters.","DOI":"10.1201\/9781439864159"},{"key":"ref_77","unstructured":"Hodges, W. (2006). Building Models by Games, Dover Publications."},{"key":"ref_78","unstructured":"Hirsch, R., and Hodkinson, I. (2002). Relation Algebras by Games, Elsevier."},{"key":"ref_79","unstructured":"Zayed, A.I. (1993). Advances in Shannon\u2019s Sampling Theory, CRC Press."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF02395039","article-title":"Necessary density conditions for sampling and interpolation of certain entire functions","volume":"117","author":"Landau","year":"1967","journal-title":"Acta Math."},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Borchers, H.J., and Sen, R.N. (2006). Mathematical Implications of Einstein-Weyl Causality, Springer.","DOI":"10.1007\/3-540-37681-X"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"115001","DOI":"10.1088\/1367-2630\/12\/11\/115001","article-title":"Spacetime could be simultaneously continuous and discrete in the same way that information can","volume":"12","author":"Kempf","year":"2010","journal-title":"New J. Phys."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1103\/PhysRevLett.59.521","article-title":"Space-time as a causal set","volume":"59","author":"Bombelli","year":"1987","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/184\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:08:23Z","timestamp":1760134103000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,26]]},"references-count":83,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["e24020184"],"URL":"https:\/\/doi.org\/10.3390\/e24020184","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,1,26]]}}}