{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:45:55Z","timestamp":1760233555434,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,26]],"date-time":"2021-01-26T00:00:00Z","timestamp":1611619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Based on quantum origin of the universe, in this article we find that the universal wave function can be far richer than the superposition of many classical worlds studied by Everett. By analyzing the more general universal wave function and its unitary evolutions, we find that on small scale we can obtain Newton\u2019s law of universal gravity, while on the scale of galaxies we naturally derive gravitational effects corresponding to dark matter, without modifying any physical principles or hypothesizing the existence of new elementary particles. We find that an auxiliary function having formal symmetry is very useful to predict the evolution of the classical information in the universal wave function.<\/jats:p>","DOI":"10.3390\/sym13020193","type":"journal-article","created":{"date-parts":[[2021,1,26]],"date-time":"2021-01-26T08:29:16Z","timestamp":1611649756000},"page":"193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Analytical Approach to the Universal Wave Function and Its Gravitational Effect"],"prefix":"10.3390","volume":"13","author":[{"given":"Yunuo","family":"Xiong","sequence":"first","affiliation":[{"name":"College of Science, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9858-2368","authenticated-orcid":false,"given":"Hongwei","family":"Xiong","sequence":"additional","affiliation":[{"name":"College of Science, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1103\/PhysRev.106.162","article-title":"Microscopic Theory of Superconductivity","volume":"106","author":"Cooper","year":"1957","journal-title":"Phys. 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A quantum approach to dark matter. arXiv, arXiv:0406139."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/193\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:15:37Z","timestamp":1760159737000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,26]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020193"],"URL":"https:\/\/doi.org\/10.3390\/sym13020193","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,26]]}}}