Astronomy&Astrophysicsmanuscriptno.ms (cid:13)c ESO2012 January20,2012 Are OPERA neutrinos faster than light because of non-inertial reference frames? ClaudioGermana` INAF-AstronomicalObservatoryofPadova,Italy e-mail:[email protected] Received/Accepted 2 1 ABSTRACT 0 2 Context.RecentresultsfromtheOPERAexperimentreportedaneutrinobeamtravelingfasterthanlight.Thechallengingexperiment measuredtheneutrinotimeofflight(TOF)overabaselinefromtheCERNtotheGranSassosite,concludingthattheneutrinobeam n arrives∼ 60nsearlierthanalightraywoulddo.Becausetheresult,ifconfirmed,hasanenormousimpactonscience,itmightbe a worthdouble-checking thetimedefinitionswithrespecttothenon-inertialsysteminwhichtheneutrinotraveltimewasmeasured. J Anobserverwithaclockmeasuringthepropertimeτfreeofnon-inertialeffectsistheonelocatedattheSolarSystemBarycenter 9 (SSB). 1 Aims.PotentialproblemsintheOPERAdataanalysisconnectedwiththedefinitionofthereferenceframeandtimesynchronization areemphasized.Weaimtoinvestigatethesynchronizationofnon-inertialclocksonEarthbyrelatingthistimetothepropertimeof ] h aninertialobserveratSSB. p Methods.TheTempo2softwarewasusedtotime-stampeventsobservedonthegeoidwithrespecttotheSSBinertialobservertime. - Results.NeutrinoresultsfromOPERAmightcarrythefingerprintofnon-inertialeffectsbecausetheyaretimedbyterrestrialclocks. n TheCERN-GranSassoclocksynchronizationisaccomplishedbyapplyingcorrectionsthatdependonspecialandgeneralrelativistic e timedilationeffectsattheclocks,dependingonthepositionoftheclocksinthesolarsystemgravitationalwell.Asaconsequence,TOF g distributionsarecenteredonvaluesshorterbytensofnanosecondsthanexpected,integratingoveraperiodfromApriltoDecember, . longerifotherwise.ItisworthremarkingthattheOPERArunshavealwaysbeencarriedoutfromApril/MaytoNovember. s c Conclusions.IftheanalysisbyTempo2holdsfortheOPERAexperiment,theexcellentmeasurementbytheOPERAcollaboration i willturnintoaproofoftheGeneralRelativitytheoryinaweakfieldapproximation.Theanalysispresentedhereisfalsifiablebecause s itpredictsthatperformingtheexperimentfromJanuarytoMarch/April,theneutrinobeamwillbedetectedtoarrive∼50nslaterthan y light. h p Keywords.Instrumentation:detectors–Neutrinos–Methods:numerical–Referencesystems–Time–Gravitation [ 1 v 1. Introduction later reviewed (Besida 2011, Armando V.D.B. Assis 20112). 7 However, several works were based on superluminal neutrino 4 The OPERA experiment (TheOPERAcollaboration 2011) re- anditsimplications,thereforeconsideringtheOPERAneutrino 1 centlyreporteda neutrinobeamtravelingfaster than light.The speedresultfreeofsystematicerrors(e.g.Tamburini&Laveder 4 experiment measures the distributions of neutrino time emis- 2011;Laveder&Tamburini2011). 1. sion/detectionoverabaselinefromtheCERNtotheGranSasso In this letter we focus on the question with respect to 0 (CNGS) site. Data are collected within runs lasting for several what a measure is made. The CNGS baseline has been mea- 2 months1. In these data, the neutrino beam time of flight (TOF) sured through GPS benchmarks to better than 20 cm in the 1 turns out to be ∼ 60 ns shorter than that calculated by taking European Terrestrial Reference Frame (ETRF; Colosimo et al. v: thespeedoflightinvacuum.Ifconfirmed,theresultwouldhave 20113). However, from the point of view of a light ray trav- i fundamental implications for modern physics. Basically, it re- eling over CNGS (or a beam of particles), the TOF might X views the fundamental postulate by Albert Einstein: “Nothing need to be corrected for effects caused by the non-inertial ob- r cantravelfasterthanlight”(Einstein1905). server ETRF, because the Earth rotates, orbits around the Sun a Although the implications are intriguing, one should consider andexhibitsothermotions(precession,nutation,polarmotion). possible systematic errors that are as yet undisclosed. The Nanosecond-precisionmeasurementsofOPERAaredemanded OPERAteampointedoutthattheresearchforpossiblesources tobeinpulsartiming.Tostudytheactualpulsarclockbehavior, ofsystematicerrorsisstillinprogress. thetime taggedbyclocksrunningonEarthhastobe corrected Thescientificcommunityhasproducedaplethoraofworks tothatbyaninertialobserver. tointerpretthepuzzlingneutrinospeedresult.Theseworkswere A reference frame that approximates an inertial one is the based on some systematic errors caused by the Earth’s motion BarycentricCelestialReferenceSystem(BCRS),whichisnon- (Monderen 2011) or errors in synchronization of clocks by ei- rotating and located at the Solar System Barycenter (SSB). To ther a third clock moving into the gravitational field of Earth turn the problem into the inertial frame BCRS, we use the (Contaldi2011)orGPSsatellites(vanElburg2011),whichwere Tempo2 software (Hobbsetal. 2006; Edwardsetal. 2006), a 2 http://vixra.org/pdf/1110.0047v4.pdf 1 http://proj-cngs.web.cern.ch/proj-cngs/ 3 http://operaweb.lngs.infn.it/Opera/publicnotes/note132.pdf 2 Germana`:AreOPERAneutrinosfasterthanlightbecauseofnon-inertialreferenceframes? softwareconceivedtocorrectfornon-inertialeffectsthetimeof arrivalof photonscomingfrompulsars.This uses the mostac- 200 curateplanetaryephemeridestodate(Standish19984),inagree- mentwiththeIAU2000resolutions. Lns 100 H als u d 2. FromETRFtoBCRS:Tempo2 esi 0 r e Tempo2 is the software that best-models light rays traveling elin from a pulsar to the observatory, with an accuracy of ∼ 1 ns. as -100 B Thesoftwarecorrectsthetimeofarrivalofphotons,asmeasured at the observatory, for general relativistic effects on both the -200 photon-pathand clocks runningin a gravitationalfield, against which time is measured. In this framework Tempo2 is used to 55200 55250 55300 55350 55400 55450 55500 55550 studyhowtheinertialobserveratSSBwouldseeasignaltravel- MJD ingoverCNGS. After transforming the ETRF coordinates of the sites into 200 the International Terrestrial Reference System ITRS5, they are insertedinto Tempo2.Thesoftwarecalculatesthe ephemerides otof tthhee svietectoΣrocnomthpeongeenotisdra(tΣ,tetUrrTeCst)r,iaploUinTtiCngtifmroemt the.STShBe HLalsns 100 UTC u software prints the components of the vector r′(Γ,tUTC) from esid 0 the SSB to the geocenter Γ and those of the vector s(Σ,tUTC) ner fsrtroumctethdeingtehoecbeanrtyecretnotrtihcefrasimtee.BTChReSv,ewcthoirlers′((ΣΓ,,tt)UrTeCf)erisstocothne- Baseli -100 GeocentricCelestial Reference System (GCRS), which is non- rotating and located at geocenter. However, s(Σ,t ) would UTC -200 have been equivalent if it had been constructed in the frame BCRS(Edwardsetal.2006).Ins(Σ,t )thesoftwareaccounts 55197 55198 55199 55200 55201 55202 UTC forEarthrotation,precession-nutation,polarmotionandirregu- MJD laritiesinbothpolarmotionandrotation. Fig.1.Top:TimingresidualsaftersubtractingtheexpectedTOF Thevectorr(Σ,t )inBCRSreads UTC fromthatofEq.(4),neglectingtheEinsteindelayterm.Thesim- r(Σ,t )=r (Σ,t )u +r (Σ,t )u +r (Σ,t )u , (1) ulation is performed for the year 2010, expressed in Modified UTC x UTC x y UTC y z UTC z JulianDay(MJD=JD-2400000.5).Thebintimeofthetemporal whereri(Σ,tUTC) = ri′(Γ,tUTC)+si(Σ,tUTC)(i = x,y,z)andux, seriesis10minutes.Bottom:Zoom-inoverfivedays. uy,uzareunitvectorsinthebarycentricframeBCRS. . IfthelightrayisemittedattheCERNatthespace-timecoor- dinater(CN,t )andisdetectedatGranSassoatr(GS,t′ ), thetwoeventsUaTrCelinkedbytheequation UTC The term ∆′E(GS,tU′TC)−∆E(CN,tUTC) is the differenceof the Einsteindelayatthetwoclocksandatt′ ,t .IntheOPERA UTC UTC c(cid:0)τ′(cid:0)GS,tU′TC(cid:1)−τ(CN,tUTC)(cid:1)=(cid:12)(cid:12)(cid:12)r(cid:0)GS,tU′TC(cid:1)−r(CN,tUTC)(cid:12)(cid:12)(cid:12),(2)experimentclockswerenotcorrectedfor∆E,thereforetheytick atUTCtime,whichisnotapropertime. where c is the speed of light, τ(Σ,t ) is the Barycentric UTC Coordinate Time (TCB) as a function of the site Σ and UTC time.TheTCBisthepropertimeexperiencedbytheinertialob- 3. Results server at the SSB (Standish 1998). The TCB time is linked to The geocentric coordinates of both the CERN and the Gran UTCtimebytherelation SassositesreportedinColosimoetal.(2011)wereinsertedinto τ(Σ,t )=t +ls+∆ (Σ,t ), (3) Tempo2. These coordinates refer to the origin of the OPERA UTC UTC E UTC detector reference frame at Gran Sasso and to the target focal wherelsareleapsecondstotietheUTCtimetoTerrestrialTime pointat the CERN, 730534.61m away. An additionalbaseline (TT) (∼ 66 s; Seidelmann&Fukushima 1992), ∆E(Σ,tUTC) is isthatbetweenthebeamcurrenttransformer(BCT)andthefo- the Einstein delay, which accounts for relativistic effects on cal point at the CERN (743.391 m; TheOPERAcollaboration clocksrunninginagravitationalfield. 2011).BecausethegeocentriccoordinatesoftheBCTwerenot Expressingequation(2)inUTCweobtain found in the literature, we assume the CNGS baseline to be 730534.61m. An additional baseline of 743.391m is equal to c(cid:0)tU′TC −tUTC(cid:1) = (cid:12)(cid:12)(cid:12)r(cid:0)GS,tU′TC(cid:1)−r(CN,tUTC)(cid:12)(cid:12)(cid:12)+ ∼20arcsecontheEarth’ssurfaceandwouldinduceanegligible − c(cid:0)∆′ (cid:0)GS,t′ (cid:1)−∆ (CN,t )(cid:1), (4) timingcorrectionintherelativistictermv·s/c2(seeSec.3.1). E UTC E UTC fromwhichtheTOF(t′ −t )ofthesignalinUTCproper UTC UTC timecanbededuced. 3.1.Tyingnon-inertialclocksonEarthtotheclockatBCRS 4 ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/de405.iom.pdf We now study the TOF from equation (4) neglecting the term 5 ForfullaccuracyitissuggestedtousecoordinatesinITRS.ETRF ∆′E(GS,tU′TC)−∆E(CN,tUTC),likeinOPERA.Fig.1(top)shows coordinatesweretransformedintoITRSthroughtheonlineconverterat the TOF of the signal after subtracting the value one expects, http://www.epncb.oma.be/ dataproducts/coord trans/index.php. 730534.61 m/c=0.002436801 s. There is an excess of up to Germana`:AreOPERAneutrinosfasterthanlightbecauseofnon-inertialreferenceframes? 3 1.5 200 HLΜs 1.0 B C 100 ->UTCT 00..05 HLctionsns 0 e ctions -0.5 Corr -100 e orr -1.0 C -200 -1.5 55197 55198 55199 55200 55201 55202 55200 55250 55300 55350 55400 55450 55500 55550 MJD MJD Fig.2.Einsteindelay correctionto tie the clockatCERN from 3 UTCtoTCBtimeafterremovingthefitfirst-orderpolynomial. 2 ∼ 240 ns modulated by both an annual component and the (cid:144)Lms 1 Earth’s rotation(Fig. 1 bottom).Fig. 1 shows that the neutrino k H TOF is never constant and depends on the epoch at which the city 0 measurementisperformed. Velo -1 Tounderstandwhathappens,weneedtoanalyzetheEinstein delay difference ∆′E(GS,tU′TC) − ∆E(CN,tUTC). We print the -2 Einstein delay for the clock at the CERN to tie UTC to TCB time (eq. [3]). The amount of the correction at MJD=55197.0 -3 (January 1, 2010) is up to ∼ 16 s and grows with a slope of ∼1.5×10−8s/ssinceMJD=43144.0003725.Thelineardriftof 55200 55250 55300 55350 55400 55450 55500 55550 ∼1.5×10−8s/stakesintoaccountthelineartermoftheEinstein MJD time-dilationintegral,andanothertermaccountingforthegrav- Fig.3. Top: Corrections that the non-inertial observer ETRF itational redshift due to Earth’s potential (Irwin&Fukushima shouldapplytokeeptheclockatGranSassosynchronizedwith 1999).TheEinsteinintegralaccountsforthespecialrelativistic thatattheCERN.Bottom:Thedifferencebehavioroftheveloc- time-dilation (v2/c2, v velocity of the geocenter) and the grav- ity componentsparallelto the positionvectors at the two sites itational redshift at geocenter (U/c2, U gravitational potential fortheyear2010. where the geocentermoves).Because v ∼ 30 km/s, the special . time-dilationisv2/c2 ∼10−8s/s. Fig.2showsthebehavioroftheEinsteindelaycorrectionafter fittingafirst-orderpolynomialoverfivedaysandsubtractingit.6 Theoveralllinearbehaviorhidesadiurnalmodulationofsome microsecondsowing to Earth’s rotation. The modulation origi- Fig.1,asonewouldexpect. natesfromthespecialrelativistictime-dilationonthegeoidwith BecausetheUTCtimeinOPERAisnotcorrectedfor∆′ −∆ , respect to the geocenter. The correction reads v · s/c2, with v E E the two clocks at the CERN and Gran Sasso are not properly thevelocityvectorofthegeocenterandsthesitepositionvector synchronized.To keep them synchronized,the non-inertialob- pointing from the geocenter to the site. Because |v| ∼ 30 km/s serveratETRFhastoapplythecorrectionsinFig.3(top)tothe and |s| ∼ 6300km (radiusof Earth),the correctionsamountto UTCtimeatGranSasso. upto∼2µsmodulatedbyEarth’srotation. Thenon-zeroslopeinFig.2afterremovingthelineardriftsig- LikeFig.1(bottom),thecorrectionstokeepclockssynchro- nifies that the correctionshide other terms. The Einstein delay nizedoscillatewithadiurnalbehavior.Consequently,eventsthat integral,referringtothemotionofthegeocenter,hasseveralpe- aresimultaneousinTCBtimearesimultaneousinUTCtimeas riodicterms(Seidelmann&Fukushima1992). wellonlywhenthecorrectionin Fig. 3(top)iszero.Thishap- TheinertialobservertiestheUTCtimeoftheclockatGran pens whenever the special relativistic correction on the geoid Sasso to the TCB as well. The corrections to the clock at the withrespecttothegeocenter,v·s/c2,isequalatbothsites. CERN aresubtractedfromthe GranSasso clock correctionsto To verify that the behavior in Fig. 3 (top) is indeed caused by givetheEinsteindelaydifference∆′(GS,t′ )−∆ (CN,t ). differencesinthetermv·s/c2betweenthesites,Fig.3(bottom) Fig.3(top)showstheresult.ThebEehaviorUiTsCequalEtothatUsTeCen showsthedifferenceofthedotproductv·jbetweentheCERN inFig.1.Hence,thecausefortheresidualoneachsingleTOF andGranSasso(junitvectoralongs).Thedifferenceoftheve- measurement shown in Fig. 1 is that the UTC time is not cor- locitycomponentparalleltosisupto3km/s,modulatedbyboth rected for relativistic effects through the Einstein delay differ- diurnalandannualcomponents.Itsshapereflectsthatoftherel- ence∆′ −∆ ,asequation(4)wouldinsteadrequire.Correcting ativistic corrections in Fig. 3 (top). A difference in velocity of the UTEC timEe for the Einstein delay implies null residuals in up to 3 km/s corresponds to a difference in timing corrections (δ|v|×|s|)/c2 ∼ 210ns.Theannualcomponentcomesfromthe 6 The coefficient of the polynomial obtained from the fit is modulationoverthe seasons of the angle between v and s (see ∼1.5×10−8s/s,asexpected. alsoMonderen2011). 4 Germana`:AreOPERAneutrinosfasterthanlightbecauseofnon-inertialreferenceframes? 3.2.Distributionoftimingcorrections 1400 To checkwhether the overalleffect of the correctionsin Fig. 3 1200 completelyvanishes,wecanstudytheirdistribution. 1000 We divide the y-axis of Fig. 3 (top) into 10 ns long channels. For each channel we count the number of events, integrating nel n 800 over a typical OPERA run. Fig. 4 (top) shows the distribution ha c oMvJeDr=an55O3P1E4R.0AtoruMnJfrDo=m5A55p2r2il.02)9.tIot Npeoavkesmabtebro2t2h,t2h0e1-02(4f0ronms (cid:144)ents 600 v and+160nschannel,thereforeitmightinduceanoverallerror e 400 ontheclocksynchronizationof∼-80ns7. 200 Toinvestigatefartherout,westudythedistributionformeasures takenoveranentireyear,fromJanuary1toDecember31,2010. 0 Fig. 4 (middle) shows that the distribution is symmetric with -300 -200 -100 0 100 200 300 respecttochannelzero,inducinganulleffectontheclocksyn- ∆tHnsL chronization. The differencebetweenthetwo distributionsinFig. 4(top- middle)mightbeexplainedintermsofthevariationoftheangle 1500 betweenvandsoverthe seasons(see also Fig.3 bottom).The OPERA runs have always been carried out from April/May to el November,i.e., they missed the period from January to March n an 1000 that would be needed to complete one angle cycle. Therefore, h c if the measures are taken only in a window of the entire Earth (cid:144)nts orbit, it might be possible that the clock synchronizationis af- e v fectedby thissystematic errorandthe non-inertialobserveron e 500 Earth would measure a TOF shorter by ∼80ns. Because he is unawareofnon-inertialeffects,thenon-inertialobservershould take careto carefullysynchronizethe clocks.Alternatively,the 0 measurementscouldbeintegratedoveroneanglecycle:Inthis -300 -200 -100 0 100 200 300 way,fromtheperiheliontotheaphelionandback,theeffectvan- ∆tHnsL ishes. 800 If we add the ∼ +80 ns correction to the discrepancy claimed intheOPERAexperiment(-60ns),theresultmightchange:We obtainaneutrinobeamarrivinglaterthanlight. 600 el n n 4. Conclusions ha c 400 (cid:144) TheanalysisbyTempo2suggeststhatclocksonEarthshouldbe nts e v tiedto theTCBtime toensuretheirsynchronization.TheTCB e time is the proper time experienced by an inertial observer lo- 200 catedatthesolarsystembarycenter.TheUTCtimeensuressyn- chronizationonlywhentherelativisticcorrectionv·s/c2(dubbed differentialspecialtime-dilation;Edwardsetal.2006)isequalat 0 bothclocks.Differencesinthiscorrectionofupto∼ 240nsare -300 -200 -100 0 100 200 300 seenandaremodulatedbyboththeEarth’srotationandrevolu- ∆tHnsL tion. Fig.4.Distributionoftimingcorrections.Top:Distributioncal- The overall effect of a non-synchronization of clocks may culated over a typical OPERA run (April to November 2010). vanish over one Earth orbit. Integrating the non-synchronized It would imply an overall miss-synchronization of ∼ -80 ns. clockovermonthsmightinduceanoveralleffectontheorderof Middle: Distribution over an entire year. Bottom: Distribution severaltensofnanoseconds. from January 1 to March 31. It would imply an overall If the analysis described in this letter holds for the miss-synchronizationof∼+50ns. OPERA experiment, the excellent measurement by . TheOPERAcollaboration (2011) would turn into a proof of relativistic theories (Einstein 1905, 1916). The analysis might cast doubts on interpretationsdealing with superluminal neutrino that are, or are not, accounting for relativistic effects (e.g.Tamburini&Laveder2011;Laveder&Tamburini2011). To check whether or not the present study holds, it might be interesting to see results from OPERA runs performed in a different period of the year than usual. Fig. 4 (bottom) shows the distribution of the corrections for non-inertial effects from January-March.Again,itisnotsymmetricwithrespecttochan- 7 The∼-80nsoveralleffectholdsforthelastOPERAresultsrelease nelzero,butshowsanoppositeresulttothatofthedistribution aswell(TheOPERAcollaboration2011),becausetherunlastedfrom onthetop.Fromthisresulttheneutrinobeamshouldarrive∼50 October21toNovember7,2011. nslaterthanlight. Germana`:AreOPERAneutrinosfasterthanlightbecauseofnon-inertialreferenceframes? 5 Acknowledgments I would like to thank Andrej Cˇadezˇ (Faculty of Mathematics and Physics, University of Ljubljana) and Massimo Calvani (INAF- AstronomicalObservatoryofPadova)forstimulatingdiscussions.Ialso thank Rodolfo Angeloni (Departamento de Astronom´ıa y Astrof´ısica, PontificiaUniversidadCato´licadeChile)forhiskindsupport. 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