{"id":"https://openalex.org/W2005713271","doi":"https://doi.org/10.3390/e10040441","title":"Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality","display_name":"Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W2005713271","doi":"https://doi.org/10.3390/e10040441","mag":"2005713271"},"language":"en","primary_location":{"id":"doi:10.3390/e10040441","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e10040441","pdf_url":"https://www.mdpi.com/1099-4300/10/4/441/pdf?version=1424784642","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/10/4/441/pdf?version=1424784642","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Y. Jack Ng","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Y. Jack Ng","raw_affiliation_strings":["Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599, USA","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.4638,"has_fulltext":true,"cited_by_count":99,"citation_normalized_percentile":{"value":0.94147299,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"10","issue":"4","first_page":"441","last_page":"461"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11090","display_name":"Dark Matter and Cosmic Phenomena","score":0.23989999294281006,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11090","display_name":"Dark Matter and Cosmic Phenomena","score":0.23989999294281006,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.1777999997138977,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.17260000109672546,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-nonlocality","display_name":"Quantum nonlocality","score":0.8403000235557556},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.73089998960495},{"id":"https://openalex.org/keywords/cosmology","display_name":"Cosmology","score":0.4851999878883362},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.45249998569488525},{"id":"https://openalex.org/keywords/quantum-gravity","display_name":"Quantum gravity","score":0.3837999999523163},{"id":"https://openalex.org/keywords/quantum-field-theory-in-curved-spacetime","display_name":"Quantum field theory in curved spacetime","score":0.3709999918937683},{"id":"https://openalex.org/keywords/dark-energy","display_name":"Dark energy","score":0.34439998865127563},{"id":"https://openalex.org/keywords/holography","display_name":"Holography","score":0.33070001006126404},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.328900009393692}],"concepts":[{"id":"https://openalex.org/C138622882","wikidata":"https://www.wikidata.org/wiki/Q7269079","display_name":"Quantum nonlocality","level":4,"score":0.8403000235557556},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8095999956130981},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.73089998960495},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4350999891757965},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.3837999999523163},{"id":"https://openalex.org/C120484201","wikidata":"https://www.wikidata.org/wiki/Q2246697","display_name":"Quantum field theory in curved spacetime","level":4,"score":0.3709999918937683},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3537999987602234},{"id":"https://openalex.org/C172790937","wikidata":"https://www.wikidata.org/wiki/Q18343","display_name":"Dark energy","level":3,"score":0.34439998865127563},{"id":"https://openalex.org/C187590223","wikidata":"https://www.wikidata.org/wiki/Q527628","display_name":"Holography","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C6947382","wikidata":"https://www.wikidata.org/wiki/Q1143773","display_name":"Vacuum energy","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C2983197053","wikidata":"https://www.wikidata.org/wiki/Q654182","display_name":"Energy spectrum","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C9061790","wikidata":"https://www.wikidata.org/wiki/Q1191211","display_name":"Cosmic censorship hypothesis","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C41254897","wikidata":"https://www.wikidata.org/wiki/Q1139715","display_name":"Causal sets","level":5,"score":0.30649998784065247},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2809000015258789},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2662999927997589},{"id":"https://openalex.org/C61969629","wikidata":"https://www.wikidata.org/wiki/Q911640","display_name":"Hubble volume","level":5,"score":0.263700008392334},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C181868357","wikidata":"https://www.wikidata.org/wiki/Q468999","display_name":"Planck energy","level":5,"score":0.25929999351501465},{"id":"https://openalex.org/C141886431","wikidata":"https://www.wikidata.org/wiki/Q1193821","display_name":"Quantum fluctuation","level":3,"score":0.2583000063896179}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e10040441","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e10040441","pdf_url":"https://www.mdpi.com/1099-4300/10/4/441/pdf?version=1424784642","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0801.2962","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0801.2962","pdf_url":"https://arxiv.org/pdf/0801.2962","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:53111dfd7d5345a5b7a8a1ac7c93ac16","is_oa":true,"landing_page_url":"https://doaj.org/article/53111dfd7d5345a5b7a8a1ac7c93ac16","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 10, Iss 4, Pp 441-461 (2008)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/10/4/441/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e10040441","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 10; Issue 4; Pages: 441-461","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e10040441","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e10040441","pdf_url":"https://www.mdpi.com/1099-4300/10/4/441/pdf?version=1424784642","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2005713271.pdf","grobid_xml":"https://content.openalex.org/works/W2005713271.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W1497486557","https://openalex.org/W1505803128","https://openalex.org/W1653690130","https://openalex.org/W1853767801","https://openalex.org/W1864482988","https://openalex.org/W1886147477","https://openalex.org/W1906317546","https://openalex.org/W1964033965","https://openalex.org/W1969401651","https://openalex.org/W1981808539","https://openalex.org/W1992476023","https://openalex.org/W1993466133","https://openalex.org/W1999664967","https://openalex.org/W1999739013","https://openalex.org/W1999804456","https://openalex.org/W2008103122","https://openalex.org/W2019217825","https://openalex.org/W2024164590","https://openalex.org/W2024852085","https://openalex.org/W2025046661","https://openalex.org/W2026056410","https://openalex.org/W2026229290","https://openalex.org/W2026504934","https://openalex.org/W2030422689","https://openalex.org/W2032214963","https://openalex.org/W2036414566","https://openalex.org/W2042064026","https://openalex.org/W2043764757","https://openalex.org/W2046525569","https://openalex.org/W2048390511","https://openalex.org/W2050062115","https://openalex.org/W2053099033","https://openalex.org/W2062750063","https://openalex.org/W2073832139","https://openalex.org/W2074135006","https://openalex.org/W2075628611","https://openalex.org/W2075884494","https://openalex.org/W2088802347","https://openalex.org/W2089760028","https://openalex.org/W2090386790","https://openalex.org/W2091628548","https://openalex.org/W2092816691","https://openalex.org/W2092883612","https://openalex.org/W2108016273","https://openalex.org/W2113094295","https://openalex.org/W2132218952","https://openalex.org/W2141586044","https://openalex.org/W2142397325","https://openalex.org/W2142595523","https://openalex.org/W2146478425","https://openalex.org/W2147633035","https://openalex.org/W2150317287","https://openalex.org/W2156788484","https://openalex.org/W2170399496","https://openalex.org/W2171807753","https://openalex.org/W2200363524","https://openalex.org/W2248979493","https://openalex.org/W2594322094","https://openalex.org/W4233642328","https://openalex.org/W6641632142","https://openalex.org/W6789049938"],"related_works":[],"abstract_inverted_index":{"Due":[0],"to":[1,16,70,126,136,170,184],"quantum":[2,46],"fluctuations,":[3],"spacetime":[4,67,138],"is":[5,14,81],"foamy":[6],"on":[7,34,53],"small":[8,183],"scales.":[9],"The":[10],"degree":[11],"of":[12,27,38,45,64,75,83,87,90,106,147,173],"foaminess":[13],"found":[15],"be":[17,124,185],"consistent":[18],"with":[19,49],"holography,":[20],"a":[21],"principle":[22],"prefigured":[23],"in":[24,102,118,130,144,160],"the":[25,35,43,58,62,65,73,107,115,127,145,157,161],"physics":[26,44],"black":[28],"hole":[29],"entropy.":[30],"It":[31],"has":[32],"bearing":[33],"ultimate":[36],"accuracies":[37],"clocks":[39],"and":[40,42,113,150,167],"measurements":[41],"computation.":[47],"Consistent":[48],"existing":[50],"archived":[51],"data":[52],"active":[54],"galactic":[55],"nuclei":[56],"from":[57,178],"Hubble":[59],"Space":[60],"Telescope,":[61],"application":[63],"holographic":[66,131],"foam":[68,139],"model":[69],"cosmology":[71],"requires":[72],"existence":[74],"dark":[76],"energy":[77,163,175],"which,":[78],"we":[79],"argue,":[80],"composed":[82],"an":[84],"enormous":[85],"number":[86],"inert":[88],"\u201cparticles\u201d":[89,98],"extremely":[91],"long":[92],"wavelength.":[93],"We":[94,133],"suggest":[95],"that":[96,114,152],"these":[97],"obey":[99],"infinite":[100,121],"statistics":[101,122],"which":[103],"all":[104],"representations":[105],"particle":[108],"permutation":[109],"group":[110],"can":[111],"occur,":[112],"nonlocality":[116,128],"present":[117,129],"systems":[119],"obeying":[120],"may":[123],"related":[125],"theories.":[132],"also":[134],"propose":[135],"detect":[137],"by":[140],"looking":[141],"for":[142],"halos":[143],"images":[146],"distant":[148,179],"quasars,":[149],"argue":[151],"it":[153],"does":[154],"not":[155],"modify":[156],"GZK":[158],"cutoff":[159],"ultra-high":[162],"cosmic":[164],"ray":[165],"spectrum":[166],"its":[168],"contributions":[169],"time-offlight":[171],"differences":[172],"high":[174],"gamma":[176],"rays":[177],"GRB":[180],"are":[181],"too":[182],"detectable.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2016-06-24T00:00:00"}