{"id":"https://openalex.org/W3097112755","doi":"https://doi.org/10.22331/q-2021-08-27-530","title":"Quantum reference frame transformations as symmetries and the paradox of the third particle","display_name":"Quantum reference frame transformations as symmetries and the paradox of the third particle","publication_year":2021,"publication_date":"2021-08-27","ids":{"openalex":"https://openalex.org/W3097112755","doi":"https://doi.org/10.22331/q-2021-08-27-530","mag":"3097112755"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-08-27-530","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-08-27-530","pdf_url":"https://quantum-journal.org/papers/q-2021-08-27-530/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-08-27-530/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065187735","display_name":"Marius Krumm","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210100980","display_name":"Vienna Center for Quantum Science and Technology","ror":"https://ror.org/014cpn338","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422","https://openalex.org/I138211613","https://openalex.org/I145847075","https://openalex.org/I4210100980"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Marius Krumm","raw_affiliation_strings":["Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria","Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria","institution_ids":["https://openalex.org/I138211613"]},{"raw_affiliation_string":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria","institution_ids":["https://openalex.org/I4210100980","https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109834727","display_name":"Philipp A. H\u00f6hn","orcid":null},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]},{"id":"https://openalex.org/I142637625","display_name":"Okinawa Institute of Science and Technology Graduate University","ror":"https://ror.org/02qg15b79","country_code":"JP","type":"education","lineage":["https://openalex.org/I142637625"]}],"countries":["GB","JP"],"is_corresponding":false,"raw_author_name":"Philipp A. H\u00f6hn","raw_affiliation_strings":["Department of Physics and Astronomy, University College London, London, United Kingdom","Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, University College London, London, United Kingdom","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495, Japan","institution_ids":["https://openalex.org/I142637625"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108631998","display_name":"Markus P. M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]},{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I4210100980","display_name":"Vienna Center for Quantum Science and Technology","ror":"https://ror.org/014cpn338","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422","https://openalex.org/I138211613","https://openalex.org/I145847075","https://openalex.org/I4210100980"]}],"countries":["AT","CA"],"is_corresponding":false,"raw_author_name":"Markus P. M\u00fcller","raw_affiliation_strings":["Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria","Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo ON N2L 2Y5, Canada","Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria","institution_ids":["https://openalex.org/I138211613"]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo ON N2L 2Y5, Canada","institution_ids":["https://openalex.org/I183974707"]},{"raw_affiliation_string":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria","institution_ids":["https://openalex.org/I4210100980","https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065187735"],"corresponding_institution_ids":["https://openalex.org/I129774422","https://openalex.org/I138211613","https://openalex.org/I4210100980"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":4.3396,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.95092089,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"5","issue":null,"first_page":"530","last_page":"530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.6047627925872803},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.569685697555542},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.4661356806755066},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.434100478887558},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4329449236392975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4263218343257904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34326237440109253},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3390958905220032},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3371135890483856},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2952847182750702},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18541625142097473},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14161357283592224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1046563982963562}],"concepts":[{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.6047627925872803},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.569685697555542},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.4661356806755066},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.434100478887558},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4329449236392975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4263218343257904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34326237440109253},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3390958905220032},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3371135890483856},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2952847182750702},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18541625142097473},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14161357283592224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1046563982963562},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2021-08-27-530","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-08-27-530","pdf_url":"https://quantum-journal.org/papers/q-2021-08-27-530/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.01951","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.01951","pdf_url":"https://arxiv.org/pdf/2011.01951","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:06b2dcd3807e4c829553cd3c8a7bf66b","is_oa":true,"landing_page_url":"https://doaj.org/article/06b2dcd3807e4c829553cd3c8a7bf66b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 530 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-08-27-530","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-08-27-530","pdf_url":"https://quantum-journal.org/papers/q-2021-08-27-530/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4000000059604645,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2440218616","display_name":null,"funder_award_id":"CoQuS","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G468046532","display_name":null,"funder_award_id":"FQXi-RFP-1801A","funder_id":"https://openalex.org/F4320311357","funder_display_name":"Foundational Questions Institute"},{"id":"https://openalex.org/G6783783255","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8240083823","display_name":null,"funder_award_id":"FQXi-RFP-1815","funder_id":"https://openalex.org/F4320311357","funder_display_name":"Foundational Questions Institute"}],"funders":[{"id":"https://openalex.org/F4320306192","display_name":"Silicon Valley Community Foundation","ror":"https://ror.org/001ader08"},{"id":"https://openalex.org/F4320306689","display_name":"Fetzer Institute","ror":"https://ror.org/02t1yaf39"},{"id":"https://openalex.org/F4320311357","display_name":"Foundational Questions Institute","ror":"https://ror.org/016en1t86"},{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320322443","display_name":"Okinawa Institute of Science and Technology Graduate University","ror":"https://ror.org/02qg15b79"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3097112755.pdf","grobid_xml":"https://content.openalex.org/works/W3097112755.grobid-xml"},"referenced_works_count":124,"referenced_works":["https://openalex.org/W1500531877","https://openalex.org/W1513995573","https://openalex.org/W1529069840","https://openalex.org/W1546322230","https://openalex.org/W1579193439","https://openalex.org/W1580334901","https://openalex.org/W1586369843","https://openalex.org/W1722023710","https://openalex.org/W1947273351","https://openalex.org/W1964419676","https://openalex.org/W1966107924","https://openalex.org/W1969227315","https://openalex.org/W1987403959","https://openalex.org/W1993269322","https://openalex.org/W1999991959","https://openalex.org/W2004859216","https://openalex.org/W2006620446","https://openalex.org/W2009559386","https://openalex.org/W2018339531","https://openalex.org/W2034864060","https://openalex.org/W2041678328","https://openalex.org/W2045128171","https://openalex.org/W2048691322","https://openalex.org/W2051698581","https://openalex.org/W2059846772","https://openalex.org/W2061620121","https://openalex.org/W2063215998","https://openalex.org/W2075090992","https://openalex.org/W2076068770","https://openalex.org/W2084575582","https://openalex.org/W2098215080","https://openalex.org/W2099487749","https://openalex.org/W2148115906","https://openalex.org/W2150928924","https://openalex.org/W2170208120","https://openalex.org/W2206648280","https://openalex.org/W2285665705","https://openalex.org/W2287712525","https://openalex.org/W2528596804","https://openalex.org/W2588780979","https://openalex.org/W2597376000","https://openalex.org/W2607817427","https://openalex.org/W2608808167","https://openalex.org/W2621447564","https://openalex.org/W2656371124","https://openalex.org/W2775431093","https://openalex.org/W2778864117","https://openalex.org/W2796033630","https://openalex.org/W2806139032","https://openalex.org/W2890914617","https://openalex.org/W2892333274","https://openalex.org/W2896333123","https://openalex.org/W2898894554","https://openalex.org/W2900901910","https://openalex.org/W2904538430","https://openalex.org/W2904555790","https://openalex.org/W2905192198","https://openalex.org/W2918422671","https://openalex.org/W2940570551","https://openalex.org/W2949551244","https://openalex.org/W2962980132","https://openalex.org/W2980172449","https://openalex.org/W2984224373","https://openalex.org/W2987113943","https://openalex.org/W2990961515","https://openalex.org/W2991406412","https://openalex.org/W2994736278","https://openalex.org/W2995539390","https://openalex.org/W2996252020","https://openalex.org/W3006138111","https://openalex.org/W3014933332","https://openalex.org/W3021720044","https://openalex.org/W3024600218","https://openalex.org/W3027137586","https://openalex.org/W3032367681","https://openalex.org/W3034194423","https://openalex.org/W3035396551","https://openalex.org/W3035720389","https://openalex.org/W3035872230","https://openalex.org/W3036477908","https://openalex.org/W3037145107","https://openalex.org/W3037572308","https://openalex.org/W3037620826","https://openalex.org/W3038174850","https://openalex.org/W3042241855","https://openalex.org/W3042790869","https://openalex.org/W3087904440","https://openalex.org/W3094230383","https://openalex.org/W3096711531","https://openalex.org/W3096904542","https://openalex.org/W3098156971","https://openalex.org/W3098312404","https://openalex.org/W3099369503","https://openalex.org/W3099690987","https://openalex.org/W3100288004","https://openalex.org/W3100396634","https://openalex.org/W3100559328","https://openalex.org/W3101095343","https://openalex.org/W3101645287","https://openalex.org/W3101785787","https://openalex.org/W3102743794","https://openalex.org/W3103190760","https://openalex.org/W3103769813","https://openalex.org/W3103842771","https://openalex.org/W3104067352","https://openalex.org/W3104366717","https://openalex.org/W3104895145","https://openalex.org/W3104896384","https://openalex.org/W3105647635","https://openalex.org/W3106434624","https://openalex.org/W3106593475","https://openalex.org/W3111893162","https://openalex.org/W3113107637","https://openalex.org/W3124741447","https://openalex.org/W3126558472","https://openalex.org/W3129771632","https://openalex.org/W3154815856","https://openalex.org/W3169032360","https://openalex.org/W3177292295","https://openalex.org/W4233500204","https://openalex.org/W4243337140","https://openalex.org/W4287758409","https://openalex.org/W4298222025","https://openalex.org/W4309037153"],"related_works":["https://openalex.org/W1994680671","https://openalex.org/W2000283393","https://openalex.org/W2002320543","https://openalex.org/W2061947244","https://openalex.org/W2150232912","https://openalex.org/W2054940838","https://openalex.org/W3106170641","https://openalex.org/W4321855183","https://openalex.org/W2952513607","https://openalex.org/W3102440103"],"abstract_inverted_index":{"In":[0,26],"a":[1,23,94,125,138,160],"quantum":[2,8,24,32,87,162],"world,":[3],"reference":[4,33],"frames":[5],"are":[6,80,170],"ultimately":[7],"systems":[9],"too":[10],"\u2013":[11],"but":[12],"what":[13],"does":[14],"it":[15,107,152],"mean":[16],"to":[17,48,62,93,111,116,137,180],"\"jump":[18],"into":[19,120],"the":[20,77,98,101,112,141,149,189],"perspective":[21],"of":[22,41,76,100,114,131,140,156,193],"particle\"?":[25],"this":[27,132,173],"work,":[28],"we":[29,176],"show":[30],"that":[31,79,106,199],"frame":[34],"(QRF)":[35],"transformations":[36,54],"appear":[37],"naturally":[38],"as":[39,97,166],"symmetries":[40],"simple":[42,161],"physical":[43,127,191],"systems.":[44],"This":[45,134],"allows":[46],"us":[47,136,197],"rederive":[49],"and":[50,61,69,89,123,128,151,186],"generalize":[51],"known":[52,96],"QRF":[53],"within":[55,159],"an":[56,73],"alternative,":[57],"operationally":[58],"transparent":[59],"framework,":[60],"shed":[63],"new":[64],"light":[65],"on":[66],"their":[67],"structure":[68],"interpretation.":[70],"We":[71,104],"give":[72,124],"explicit":[74],"description":[75],"observables":[78,168],"measurable":[81],"by":[82,85],"agents":[83],"constrained":[84],"such":[86,165],"symmetries,":[88],"apply":[90],"our":[91,178,194],"results":[92,195],"puzzle":[95],"`paradox":[99],"third":[102],"particle'.":[103],"argue":[105],"can":[108],"be":[109],"reduced":[110],"question":[113],"how":[115],"relationally":[117],"embed":[118],"fewer":[119],"more":[121,204],"particles,":[122],"thorough":[126],"algebraic":[129],"analysis":[130],"question.":[133],"leads":[135],"generalization":[139],"partial":[142],"trace":[143],"(`relational":[144],"trace')":[145],"which":[146,169],"arguably":[147],"resolves":[148],"paradox,":[150],"uncovers":[153],"important":[154],"structures":[155],"constraint":[157],"quantization":[158],"information":[163],"setting,":[164],"relational":[167],"key":[171],"in":[172,203],"resolution.":[174],"While":[175],"restrict":[177],"attention":[179],"finite":[181],"Abelian":[182],"groups":[183],"for":[184],"transparency":[185],"mathematical":[187],"rigor,":[188],"intuitive":[190],"appeal":[192],"makes":[196],"expect":[198],"they":[200],"remain":[201],"valid":[202],"general":[205],"situations.":[206]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":5}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}