{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T18:17:33Z","timestamp":1771265853545,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"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>Some recent studies exposed preliminary but rather intriguing statistical evidence of in vacuo dispersion-like spectral lags for gamma-ray bursts (GRBs), a linear correlation between time of observation and energy of GRB particles, which is expected in some models of quantum geometry. Those results focused on testing in vacuo dispersion for the most energetic GRB particles, and in particular only included photons with energy at emission greater than 40 GeV. We here extend the window of the statistical analysis down to 5 GeV and find results that are consistent with what had been previously noticed at higher energies.<\/jats:p>","DOI":"10.3390\/sym13040541","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T21:09:45Z","timestamp":1616706585000},"page":"541","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["In Vacuo Dispersion-Like Spectral Lags in Gamma-Ray Bursts"],"prefix":"10.3390","volume":"13","author":[{"given":"Giovanni","family":"Amelino-Camelia","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica Ettore Pancini, Universit\u00e0 di Napoli \u201cFederico II\u201d, and INFN, Sezione di Napoli, Complesso University Monte S. Angelo, I-80126 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giacomo","family":"D\u2019Amico","sequence":"additional","affiliation":[{"name":"Department of Physics and Technology, University of Bergen, 5020 Bergen, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabrizio","family":"Fiore","sequence":"additional","affiliation":[{"name":"INAF-Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34143 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simonetta","family":"Puccetti","sequence":"additional","affiliation":[{"name":"Agenzia Spaziale Italiana, Unit\u00e0 di Ricerca Scientifica, Via del Politecnico, 00133 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michele","family":"Ronco","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Roma \u201cLa Sapienza\", P.le A. 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D"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1038\/31647","article-title":"Tests of quantum gravity from observations","volume":"393","author":"Ellis","year":"1998","journal-title":"Nature"},{"key":"ref_5","first-page":"124021","article-title":"Nonstandard Optics from Quantum Space-Time","volume":"D59","author":"Gambini","year":"1999","journal-title":"Phys. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2318","DOI":"10.1103\/PhysRevLett.84.2318","article-title":"Quantum Gravity Corrections to Neutrino Propagation","volume":"84","author":"Alfaro","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4301","DOI":"10.1142\/S0217751X00002779","article-title":"Waves on noncommutative space-time and gamma-ray bursts","volume":"15","author":"Majid","year":"2000","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"211601","DOI":"10.1103\/PhysRevLett.90.211601","article-title":"Ultraviolet modifications of dispersion relations in effective field theory","volume":"90","author":"Myers","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1088\/0004-637X\/806\/2\/269","article-title":"Icecube Neutrinos and Lorentz Invariance Violation","volume":"806","author":"Guetta","year":"2015","journal-title":"Astrophys. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"045009","DOI":"10.1103\/PhysRevD.91.045009","article-title":"Searching for traces of Planck-scale physics with high energy neutrinos","volume":"91","author":"Stecker","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"116002","DOI":"10.1103\/PhysRevD.58.116002","article-title":"Lorentz-violating extension of the standard model","volume":"58","author":"Colladay","year":"1998","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kostelecky, V.A., and Russell, N. (2008). Data Tables for Lorentz and CPT Violation. arXiv.","DOI":"10.1142\/9789812779519_0052"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"043008","DOI":"10.1103\/PhysRevD.102.043008","article-title":"Improved constraints on anisotropic birefringent Lorentz invariance and CPT violation from broadband optical polarimetry of high redshift galaxies","volume":"102","author":"Friedman","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"023507","DOI":"10.1103\/PhysRevD.100.023507","article-title":"Future CMB constraints on cosmic birefringence and implications for fundamental physics","volume":"100","author":"Pogosian","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"035045","DOI":"10.1103\/PhysRevD.99.035045","article-title":"Constraints on Lorentz invariance and CPT violation using optical photometry and polarimetry of active galaxies BL Lacertae and S5","volume":"99","author":"Friedman","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kislat, F. (2018). Constraints on Lorentz Invariance Violation from Optical Polarimetry of Astrophysical Objects. Symmetry, 10.","DOI":"10.20944\/preprints201809.0147.v1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"083013","DOI":"10.1103\/PhysRevD.95.083013","article-title":"Planck-scale constraints on anisotropic Lorentz and CPT invariance violations from optical polarization measurements","volume":"95","author":"Kislat","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/j.physletb.2016.07.075","article-title":"IceCube and GRB neutrinos propagating in quantum spacetime","volume":"761","author":"Barcaroli","year":"2016","journal-title":"Phys. Lett. B"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Amelino-Camelia, G., Barcaroli, L., D\u2019Amico, G., Loret, N., and Rosati, G. (2016). Quantum-gravity-induced dual lensing and IceCube neutrinos. arXiv.","DOI":"10.1142\/S0218271817500766"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"0139","DOI":"10.1038\/s41550-017-0139","article-title":"In-vacuo-dispersion features for GRB neutrinos and photons","volume":"1","author":"Rosati","year":"2017","journal-title":"Nat. Astron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.astropartphys.2014.04.008","article-title":"Lorentz violation from gamma-ray bursts","volume":"61","author":"Zhang","year":"2014","journal-title":"Astropart. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.astropartphys.2016.05.008","article-title":"Light speed variation from gamma-ray bursts","volume":"82","author":"Xu","year":"2016","journal-title":"Astropart. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/j.physletb.2016.07.044","article-title":"Light speed variation from gamma ray burst GRB 160509A","volume":"760","author":"Xu","year":"2016","journal-title":"Phys. Lett. B"},{"key":"ref_24","first-page":"597384","article-title":"Quantum-spacetime scenarios and soft spectral lags of the remarkable GRB130427A","volume":"2014","author":"Fiore","year":"2014","journal-title":"Adv. High Energy Phys."},{"key":"ref_25","unstructured":"Planck Collaboration: Ade, P.A.R., Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J., Baccigalupi, C., Banday, A.J., Bartlett, J.G., Bartolo, N., and Battaner, E. (2016). Planck 2015 results. XIII. Cosmological parameters. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"L7","DOI":"10.1051\/0004-6361\/200913980","article-title":"The onset of the GeV afterglow of GRB 090510","volume":"510","author":"Ghirlanda","year":"2010","journal-title":"Astron. Astrophys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"122001","DOI":"10.1103\/PhysRevD.87.122001","article-title":"Constraints on Lorentz invariance violation from Fermi-Large Area Telescope observations of gamma-ray bursts","volume":"87","author":"Vasileiou","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1038\/nature08574","article-title":"A limit on the variation of the speed of light arising from quantum gravity effects. [Fermi LAT\/GBM Collaborations]","volume":"462","author":"Abdo","year":"2009","journal-title":"Nature"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/4\/541\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:41:11Z","timestamp":1760161271000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/4\/541"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,25]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["sym13040541"],"URL":"https:\/\/doi.org\/10.3390\/sym13040541","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,25]]}}}