{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T04:34:49Z","timestamp":1779251689881,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"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>Herein is a review of the essentials of Modified Newtonian Dynamics (MOND) versus dark matter models based on Superfluids for modeling galactic rotation curves. We review the successes and issues of both approaches. We then mention a recent alternative based on the Superfluid Vacuum Theory (SVT) with a nonlinear logarithmic Schr\u00f6dinger equation (LogSE) which reconciles both approaches, retains the essential success of MOND and the Superfluid nature but does not necessitate the hypothesis of processes including dark matter. We conclude with the implications of this SVT alternative on quantum theory itself.<\/jats:p>","DOI":"10.3390\/e25010012","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T01:33:12Z","timestamp":1671672792000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["From Modified Newtonian Dynamics to Superfluid Vacuum Theory"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0228-1673","authenticated-orcid":false,"given":"Tony","family":"Scott","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Physikalische Chemie, RWTH Aachen University, 52056 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hossenfelder, S. (2019, September 18). Dark Matter\u2014Or What?. Available online: https:\/\/www.slideshare.net\/SabineHossenfelder.","DOI":"10.1088\/1475-7516\/2019\/02\/001"},{"key":"ref_2","unstructured":"Hossenfelder, S. (2020, November 11). Modified Gravity, Demystified. Available online: https:\/\/www.youtube.com\/watch?v=2VNcDoLNJk8."},{"key":"ref_3","unstructured":"Lovell, B. (1981). Emerging Cosmology, Convergence, Columbia University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1847010","DOI":"10.1142\/S0218271818470107","article-title":"The redshift-dependence of radial acceleration: Modified gravity versus particle dark matter","volume":"27","author":"Hossenfelder","year":"2018","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"31410","DOI":"10.4249\/scholarpedia.31410","article-title":"The MOND paradigm of modified dynamics","volume":"9","author":"Milgrom","year":"2014","journal-title":"Scholarpedia"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1086\/161130","article-title":"A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis","volume":"270","author":"Milgrom","year":"1983","journal-title":"Astrophys. J."},{"key":"ref_7","first-page":"215","article-title":"Alternatives to Dark Matter","volume":"13","author":"Milgrom","year":"1989","journal-title":"Comments Astrophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1006\/aphy.1994.1012","article-title":"Dynamics with a Nonstandard Inertia-Acceleration Relation: An Alternative to Dark Matter in Galactic Systems","volume":"229","author":"Milgrom","year":"1994","journal-title":"Ann. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0375-9601(99)00077-8","article-title":"The modified dynamics as a vacuum effect","volume":"253","author":"Milgrom","year":"1999","journal-title":"Phys. Lett. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1086\/162570","article-title":"Does the missing mass problem signal the breakdown of Newtonian gravity?","volume":"286","author":"Bekenstein","year":"1984","journal-title":"Astrophys. J."},{"key":"ref_11","first-page":"661","article-title":"A new method of determining distances to galaxies","volume":"54","author":"Tully","year":"1977","journal-title":"Astron. Astrophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1111\/j.1365-2966.2009.16184.x","article-title":"Quasi-linear formulation of MOND","volume":"403","author":"Milgrom","year":"2010","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_13","first-page":"1129","article-title":"Matter and twin matter in bimetric MOND","volume":"405","author":"Milgrom","year":"2010","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1146\/annurev.astro.40.060401.093923","article-title":"Modified Newtonian Dynamics as an Alternative to Dark Matter","volume":"40","author":"Sanders","year":"2002","journal-title":"Annu. Rev. Astron. Astrophys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10","DOI":"10.12942\/lrr-2012-10","article-title":"Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions","volume":"15","author":"Famaey","year":"2012","journal-title":"Living Rev. Relativ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"083509","DOI":"10.1103\/PhysRevD.70.083509","article-title":"Relativistic gravitation theory for the modified Newtonian dynamics paradigm","volume":"70","author":"Bekenstein","year":"2004","journal-title":"Phys. Rev. D"},{"key":"ref_17","unstructured":"Scott, D., White, M., Cohn, J.D., and Pierpaoli, E. (2001). Cosmological Difficulties with Modified Newtonian Dynamics (or: La Fin du MOND?). arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"044034","DOI":"10.1103\/PhysRevD.78.044034","article-title":"TeVeS gets caught on caustics","volume":"78","author":"Contaldi","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"124018","DOI":"10.1103\/PhysRevD.95.124018","article-title":"Covariant version of Verlinde\u2019s emergent gravity","volume":"95","author":"Hossenfelder","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"001","DOI":"10.1088\/1475-7516\/2019\/02\/001","article-title":"Strong lensing with superfluid dark matter","volume":"2019","author":"Hossenfelder","year":"2019","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"021","DOI":"10.1088\/1475-7516\/2018\/09\/021","article-title":"Phenomenological consequences of superfluid dark matter with baryon-phonon coupling","volume":"2018","author":"Berezhiani","year":"2018","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1119\/1.3254017","article-title":"Drawing an elephant with four complex parameters","volume":"78","author":"Mayer","year":"2010","journal-title":"Am. J. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"124012","DOI":"10.1103\/PhysRevD.76.124012","article-title":"Field-theoretical formulations of MOND-like gravity","volume":"76","author":"Bruneton","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2749","DOI":"10.1142\/S0218271811020561","article-title":"The Real Problem with MOND","volume":"20","author":"Dodelson","year":"2011","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"103510","DOI":"10.1103\/PhysRevD.92.103510","article-title":"Theory of dark matter superfluidity","volume":"92","author":"Berezhiani","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.physletb.2015.12.054","article-title":"Dark matter superfluidity and galactic dynamics","volume":"753","author":"Berezhiani","year":"2016","journal-title":"Phys. Lett. B"},{"key":"ref_27","unstructured":"Hossenfelder, S. (2021, January 01). Superfluid Dark Matter. Available online: https:\/\/www.youtube.com\/watch?v=468cyBZ_cq4&t=248s."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1139\/cjp-2014-0203","article-title":"A tale of two paradigms: The mutual incommensurability of \u039bCDM and MOND","volume":"93","author":"McGaugh","year":"2015","journal-title":"Can. J. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104045","DOI":"10.1103\/PhysRevD.84.104045","article-title":"Nonperturbative loop quantization of scalar-tensor theories of gravity","volume":"84","author":"Zhang","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"084017","DOI":"10.1103\/PhysRevD.93.084017","article-title":"Canonical reduction for dilatonic gravity in 3+1 dimensions","volume":"93","author":"Scott","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"064040","DOI":"10.1103\/PhysRevD.84.064040","article-title":"Loop quantum f(R) theories","volume":"84","author":"Zhang","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1103\/PhysRev.183.1186","article-title":"Dilatation Covariance and Exact Solutions in Local Relativistic Field Theories","volume":"183","author":"Rosen","year":"1969","journal-title":"Phys. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1007\/s10714-008-0661-1","article-title":"Republication of: The dynamics of general relativity","volume":"40","author":"Arnowitt","year":"2008","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"075014","DOI":"10.1088\/2399-6528\/aad302","article-title":"Solution of the logarithmic Schr\u00f6dinger equation with a Coulomb potential","volume":"2","author":"Scott","year":"2018","journal-title":"J. Phys. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"325","DOI":"10.2478\/s11534-012-0159-z","article-title":"Singularity-free model of electric charge in physical vacuum: Non-zero spatial extent and mass generation","volume":"11","author":"Dzhunushaliev","year":"2013","journal-title":"Open Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1140\/epjc\/s10052-013-2333-x","article-title":"A higgs-like dilaton","volume":"73","author":"Bellazzini","year":"2013","journal-title":"Eur. Phys. J. C"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1063\/10.0000200","article-title":"Resolving the puzzle of sound propagation in liquid helium at low temperatures","volume":"45","author":"Scott","year":"2019","journal-title":"Low Temp. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2250121","DOI":"10.1142\/S0217979222501211","article-title":"Resolving the puzzle of sound propagation in a dilute Bose-Einstein condensate","volume":"36","author":"Zloshchastiev","year":"2022","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zloshchastiev, K.G. (2020). An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory. Universe, 6.","DOI":"10.3390\/universe6100180"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1134\/S1063772921100437","article-title":"On Asymptotic Behavior of Galactic Rotation Curves in Superfluid Vacuum Theory","volume":"65","author":"Zloshchastiev","year":"2021","journal-title":"Astron. Rep."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1088\/0031-8949\/20\/3-4\/033","article-title":"Gaussons: Solitons of the Logarithmic Schr\u00f6dinger Equation","volume":"20","author":"Mycielski","year":"1979","journal-title":"Phys. Scr."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"065004","DOI":"10.1088\/2399-6528\/ab941d","article-title":"Solution of the 3D logarithmic Schr\u00f6dinger equation with a central potential","volume":"4","author":"Shertzer","year":"2020","journal-title":"J. Phys. Commun."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1046\/j.1365-8711.2000.03075.x","article-title":"The extended rotation curve and the dark matter halo of M33","volume":"311","author":"Corbelli","year":"2000","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"A89","DOI":"10.1051\/0004-6361\/200913297","article-title":"A wide-field H I mosaic of Messier 31\u2014II. The disk warp, rotation, and the dark matter halo","volume":"511","author":"Corbelli","year":"2010","journal-title":"Astron. Astrophys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s12043-022-02480-2","article-title":"Galaxy rotation curves in superfluid vacuum theory","volume":"97","author":"Zloshchastiev","year":"2022","journal-title":"Pramana"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0375-9601(98)00289-8","article-title":"Consistency and linearity in quantum theory","volume":"244","author":"Caticha","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1515\/zna-2018-0096","article-title":"On the Dynamical Nature of Nonlinear Coupling of Logarithmic Quantum Wave Equation, Everett-Hirschman Entropy and Temperature","volume":"73","author":"Zloshchastiev","year":"2018","journal-title":"Z. Fuer Naturforschung A"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/0003-4916(76)90057-9","article-title":"Nonlinear wave mechanics","volume":"100","author":"Mycielski","year":"1976","journal-title":"Ann. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"8283","DOI":"10.1088\/1361-6544\/ac3144","article-title":"Logarithmic Schr\u00f6dinger equation with quadratic potential","volume":"34","author":"Carles","year":"2021","journal-title":"Nonlinearity"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0168-9002(97)00059-4","article-title":"Numerical computation of molecular integrals via optimized (vectorized) FORTRAN code","volume":"389","author":"Scott","year":"1997","journal-title":"Nucl. Instrum. Methods Phys. Res. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/S0010-4655(98)00114-3","article-title":"Maple programs for generating efficient FORTRAN code for serial and vectorised machines","volume":"115","author":"Gomez","year":"1998","journal-title":"Comput. Phys. Commun."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.cpc.2015.02.009","article-title":"Efficient hybrid-symbolic methods for quantum mechanical calculations","volume":"191","author":"Scott","year":"2015","journal-title":"Comput. Phys. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:46:56Z","timestamp":1760147216000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":52,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010012"],"URL":"https:\/\/doi.org\/10.3390\/e25010012","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,21]]}}}