{"id":"https://openalex.org/W7099782894","doi":null,"title":"Discreteness without symmetry breaking: a theorem, pre-print","display_name":"Discreteness without symmetry breaking: a theorem, pre-print","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W7099782894"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.340.1099","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.340.1099","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/gr-qc/0605006v1.pdf","raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Luca Bombelli","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Bombelli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058887261","display_name":"Joe Henson C","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joe Henson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5107909258","display_name":"Rafael D. Sorkin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rafael D. Sorkin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.9976000189781189,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.9976000189781189,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.0010999999940395355,"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"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/water-sprinkling","display_name":"sprinkling","score":0.7369999885559082},{"id":"https://openalex.org/keywords/poisson-process","display_name":"Poisson process","score":0.7239999771118164},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.8270000219345093},{"id":"https://openalex.org/keywords/causal-set-theory","display_name":"causal sets","score":0.8799999952316284},{"id":"https://openalex.org/keywords/lorentz-invariance","display_name":"Lorentz invariance","score":0.8220000267028809},{"id":"https://openalex.org/keywords/symmetry-breaking","display_name":"symmetry breaking","score":0.6800000071525574},{"id":"https://openalex.org/keywords/preferred-reference-frame","display_name":"preferred frame","score":0.5960000157356262},{"id":"https://openalex.org/keywords/modified-dispersion-relations","display_name":"modified dispersion relations","score":0.8859999775886536},{"id":"https://openalex.org/keywords/discrete-spacetime","display_name":"discrete spacetime","score":0.6349999904632568}],"concepts":[{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.8166000247001648},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7005000114440918},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5719000101089478},{"id":"https://openalex.org/C41254897","wikidata":"https://www.wikidata.org/wiki/Q1139715","display_name":"Causal sets","level":5,"score":0.5401999950408936},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C71993908","wikidata":"https://www.wikidata.org/wiki/Q1093427","display_name":"Lorentz covariance","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3271999955177307},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.30390000343322754},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C153782549","wikidata":"https://www.wikidata.org/wiki/Q175116","display_name":"Discrete space","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.2623000144958496}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.340.1099","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.340.1099","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/gr-qc/0605006v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3101084584","https://openalex.org/W2972690780","https://openalex.org/W3098694105","https://openalex.org/W3017903733","https://openalex.org/W7099460627","https://openalex.org/W1980481221","https://openalex.org/W1982474071","https://openalex.org/W7089215202","https://openalex.org/W2800566633","https://openalex.org/W6947863207"],"abstract_inverted_index":{"This":[0,52],"paper":[1],"concerns":[2],"sprinklings":[3,19],"into":[4],"Minkowski":[5],"space":[6],"(Poisson":[7],"processes).":[8],"It":[9],"proves":[10],"that":[11,54,78],"there":[12,79],"exists":[13],"no":[14,81],"equivariant":[15],"measurable":[16],"map":[17],"from":[18],"to":[20,32,66,83,88],"spacetime":[21],"directions":[22],"(even":[23],"locally).":[24],"Therefore,":[25],"if":[26],"a":[27,33,46,58,85,89],"discrete":[28],"structure":[29,41],"is":[30,77,80],"associated":[31],"sprinkling":[34,90],"in":[35],"an":[36],"intrinsic":[37],"manner,":[38],"then":[39],"the":[40,55],"will":[42,62],"not":[43,63],"pick":[44],"out":[45],"preferred":[47],"frame,":[48],"locally":[49],"or":[50],"globally.":[51],"implies":[53],"discreteness":[56],"of":[57],"sprinkled":[59],"causal":[60],"set":[61],"give":[64],"rise":[65],"\u201cLorentz":[67],"breaking":[68],"\u201d":[69],"effects":[70],"like":[71],"modified":[72],"dispersion":[73],"relations.":[74],"Another":[75],"consequence":[76],"way":[82],"associate":[84],"finite-valency":[86],"graph":[87],"consistently":[91],"with":[92],"Lorentz":[93],"invariance.":[94],"1":[95]},"counts_by_year":[],"updated_date":"2026-10-17T09:40:24.721904","created_date":"2025-10-27T00:00:00"}
