Generic violations of Lorentz symmetry can be described by an effective field
theory framework that contains both general relativity and the standard model
of particle physics called the Standard-Model Extension (SME). We obtain new
constraints on the gravitational sector of the SME using recently published
final results from Gravity Probe B. These include for the first time an upper
limit at the 10^(-3) level on the time-time component of the new tensor field
responsible for inducing local Lorentz violation in the theory, and an
independent limit at the 10^(-7) level on a combination of components of this
tensor field.Comment: 8 pages, 1 figur

Bailey, Quentin G.

Everett, Ryan D.

Overduin, James M.

English

arXiv

Generic violations of Lorentz symmetry can be described by an effective field theory framework that contains both general relativity and the Standard Model of particle physics called the Standard-Model extension (SME). We obtain new constraints on the gravitational sector of the SME using recently published final results from Gravity Probe B. These include for the first time an upper limit at the 10_3 level on the time-time component of the new tensor field responsible for inducing local Lorentz violation in the theory, and an independent limit at the 10_7 level on a combination of components of this tensor field

Bailey, Quentin G

Embry-Riddle Aeronautical University

Limits on Violations of Lorentz Symmetry from Gravity Probe B

We use the final results from Gravity Probe B to set new upper limits on the gravitational sector of the Standard-Model Extension, including for the first time the coefficient associated with the time-time component of the new field responsible for inducing local Lorentz violation in the theory

Publications 3-2014 Constraints on Violations of Lorentz Symmetry from Gravity Probe B James M. Overduin Towson University Ryan D. Everett Towson University Quentin G. Bailey Embry-Riddle Aeronautical University, baileyq@erau.edu Follow this and additional works at: https://commons.erau.edu/publication  Part of the Cosmology, Relativity, and Gravity Commons Scholarly Commons Citation Overduin, J. M., Everett, R. D., & Bailey, Q. G. (2014). Constraints on Violations of Lorentz Symmetry from Gravity Probe B. , (). https://doi.org/10.1142/9789814566438_0047 This Conference Proceeding is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in Publications by an authorized administrator of Scholarly Commons. For more information, please contact commons@erau.edu. Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry (CPT’13)1CONSTRAINTS ON VIOLATIONS OF LORENTZSYMMETRY FROM GRAVITY PROBE BJAMES M. OVERDUIN∗ and RYAN D. EVERETTDepartment of Physics, Astronomy & Geosciences, Towson UniversityTowson, MD 21252, U.S.A.∗E-mail: joverduin@towson.eduQUENTIN G. BAILEYDepartment of Physics, Embry-Riddle Aeronautical UniversityPrescott, AZ 86301, U.S.A.E-mail: baileyq@erau.eduWe use the final results from Gravity Probe B to set new upper limits on thegravitational sector of the Standard-Model Extension, including for the firsttime the coefficient associated with the time-time component of the new fieldresponsible for inducing local Lorentz violation in the theory.The minimal pure-gravity sector of the Standard-Model Extension (SME)is characterized by nine independent coefficients s¯AB corresponding to thevacuum expectation values of a new tensor field whose couplings to thetraceless part of the Ricci tensor induce spontaneous violations of localLorentz symmetry.1 These coefficients are assumed to be constant in theasymptotically flat (Minkowski) limit. Most are constrained either individ-ually or in various combinations by existing experiments and observations,2but no limits have yet been placed on the s¯TT coefficient.Gravity Probe B (GPB) was a satellite experiment launched in 2004 tomeasure the geodetic and frame-dragging effects predicted by General Rel-ativity (GR). As shown by Bailey and Kostelecky in 2006,3 the orientationof a gyroscope in orbit around a spinning central mass like the earth is sen-sitive to seven of the nine s¯AB coefficients, including s¯TT. Following earlierpreliminary work,4 our goal here is to calculate the resulting constraintsusing the recently released final results from GPB.5Within GR the geodetic and frame-dragging precession rates of a gyro-Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry (CPT’13)2Fig. 1. Experimental results are expressed in GPB coordinates (eˆGS, eˆNS, eˆWE). Theo-retical SME predictions are derived in the (nˆ, σˆ, zˆ) system. Both are ultimately referredto Sun-centered inertial coordinates (xˆ, yˆ, zˆ), where xˆ points toward the vernal equinox.scope with position ~r and velocity ~v in orbit around a central mass M withmoment of inertia I and angular velocity ~ω are:~Ωg,GR =(32GMc2r3)~r × ~v , ~Ωfd,GR =GIc2r3[3~rr2(~ω · ~r)− ~ω]. (1)The combined precession ~ΩGR = ~Ωg,GR + ~Ωfd,GR causes the unit spin vectorSˆ of the gyroscope to undergo a relativistic drift ~R ≡ dSˆ/dt = ~ΩGR × Sˆ.Averaging over a circular, polar orbit of radius r0 around a sphericallysymmetric central mass, one obtains~Rg,GR = −3(GM)2 c2r5/203/2eˆNS , ~Rfd,GR = −GIω cos δGS2 c2r30eˆWE, (2)where eˆGS points toward the guide star (located in the orbit plane at rightascension αGS and declination δGS), eˆWE is an orbit normal pointing alongthe cross-product of eˆGS and the unit vector zˆ (aligned with the earth’srotation axis) and eˆNS is a tangent to the orbit directed along eˆWE × eˆGS(Fig. 1). The choice of polar orbit orthogonalizes the two effects so that~Rg,GR points entirely along eˆNS and ~Rfd,GR points entirely along eˆWE.For GPB with guide star IM Pegasi, r0 = 7018.0 km, δGS = 16.841◦,Rg,GR = 6606.1 mas/yr (including oblateness) and Rfd,GR = 39.2 mas/yrwhere mas=milliarcsecond. The final joint results for all four gyros indicatethat RNS,obs = 6601.8± 18.3 mas/yr and RWE,obs = 37.2± 7.2 mas/yr with1σ uncertainties.5 Thus the NS and WE components of relativistic drift ratemay deviate from the predictions of GR by at most ∆RNS < |Rg,GR−RNS,obs|= 22.6 mas/yr and ∆RWE < |Rfd,GR −RWE,obs| = 9.2 mas/yr.Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry (CPT’13)3Within the SME, Lorentz-violating terms introduce an additional“anomalous” relativistic drift ∆~R whose components along nˆ, σˆ and zˆ aregiven by Eqs. (158-160) of Ref. 3. Here nˆ ≡ σˆ× zˆ and σˆ = −eˆWE is an orbitnormal (Fig. 1). These equations may be expressed in the form∆~R =12ωGS(sYY − sXX) sin 2αGS + ωGSsXY cos 2αGSωTsTT + ωNS(sXX sin2 αGS − sXY sin 2αGS + sYY cos2 αGS)ωWE(sYZ cosαGS − sXZ sinαGS) , (3)where ωGS = ωWE =56(1 − 3I/5Mr20)Rg,GR = 4603 mas/yr, ωT =34(1 − I/3Mr20)Rg,GR = 4503 mas/yr, ωNS =112(1 + 9I/Mr20)Rg,GR =1904 mas/yr and αGS = 343.26◦. To transform to GPB coordinates, wereflect across the orbit plane and rotate about σˆ by δGS. The resulting driftrates along the GS, NS and WE axes are∆~R =ωGS[12(sYY − sXX) sin 2αGS cos δGS + sXY cos 2αGS cos δGS− sXZ sinαGS sin δGS + sYZ cosαGS sin δGS]− ωTsTT − ωNS(sXX sin2 αGS − sXY sin 2αGS + sYY cos2 αGS)ωWE[12(sXX − sYY) sin 2αGS sin δGS − sXY cos 2αGS sin δGS− sXZ sinαGS cos δGS + sYZ cosα cos δGS].(4)Numerically,∆RGS = 1215sXX + 3674sXY + 384sXZ − 1215sYY + 1277sYZ,∆RNS = −4503sTT − 158sXX − 1050sXY − 1746sYY, (5)∆RWE = −368sXX − 1112sXY + 1269sXZ + 368sYY + 4219sYZ,where ∆RNS < 22.6 and ∆RWE < 9.2 from GPB (all units in mas/yr). TheSME can accommodate precessions greater than those predicted by GR,unlike other extensions of the standard model where Einstein’s theory is alimiting case.6 GPB does not constrain the GS component, since the gyrospin axes point along this direction by design. The GS and WE compo-nents are linear combinations of sXY, sXZ, sYZ and (sXX − sYY), so they aresuperseded in any case by existing constraints, which read:2,7|sXY| < (0.6± 1.5)× 10−9 (6)|sXZ| < (2.7± 1.4)× 10−9 (7)|sYZ| < (0.6± 1.4)× 10−9 (8)|sXX − sYY| < (1.2± 1.6)× 10−9 (9)|sXX + sYY − 2sZZ| < (1.8± 38) × 10−9 (10)Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry (CPT’13)4Thus in practice the only new GPB constraint on the SME comes from theNS component of Eqs. (5), associated entirely with geodetic precession instandard GR. It reads:|sTT + 0.035sXX + 0.23sXY + 0.39sYY| < 5.0× 10−3. (11)To get seven conditions on seven unknowns, we supplement Eqs. (6-11)with the requirement that sAB be traceless, |sTT − sXX − sYY − sZZ| = 0.3Inverting, we then find thatsTT < 4.4× 10−3 , sXX, sYY, sZZ < 1.5× 10−3.This constitutes the first experimental upper bound on sTT. (Other testssuch as light deflection are also sensitive to this coefficient at similar levels ofprecision.8) It also lifts a degeneracy between other existing limits, allowingus to extract individual upper bounds on sXX, sYY and sZZ.One should also look at the effect of sAB on the equation of motionfor the gyroscope.3 This has the effect of rescaling Newton’s gravitationalconstant G, increasing our sensitivity to sTT and strengthening our limitsby about 5%.9 If the actual orbit is not perfectly circular, as was the casefor GPB (whose gyros remained in essentially perfect free fall around a non-spherically symmetric Earth), then additional sAB-dependent terms are alsointroduced in the leading-order (GR) expressions for geodetic and frame-dragging precession, Eqs. (1). These do not significantly alter the NS orgeodetic constraint from GPB, but they do strengthen the WE or frame-dragging constraint so that it may potentially become competitive withexisting limits. We will report on these results elsewhere.9References1. V.A. Kostelecky´, Phys. Rev. D69, 105009 (2004); arxiv:hep-th/03123102. V.A. Kostelecky´ and N. Russell, Rev. Mod. Phys. 83, 11 (2011);arxiv:0801.02873. Q.G. Bailey and V.A. Kostelecky´, Phys. Rev. D74, 045001 (2006); arxiv:gr-qc/06030304. J.M. Overduin, in V.A. Kostelecky (ed.) Fourth Meeting on CPT and LorentzSymmetry (Singapore: World Scientific, 2008), 1995. C.W.F. Everitt et al., Phys. Rev. Lett. 106, 221101 (2011)6. J.M. Overduin et al., Gen. Rel. Grav., in press (2013); arxiv:1305.68717. J.B.R. Battat et al., Phys. Rev. Lett. 99, 241103 (2007); arxiv:0710.0702;H. Mu¨ller et al., Phys. Rev. Lett. 100, 031101 (2008); arxiv:0710:3768;K.-Y. Chung et al., Phys. Rev. D80, 016002 (2009); arxiv:0905.19298. R. Tso and Q.G. Bailey, Phys. Rev. D84, 085025 (2011); arxiv:1108.20719. Q.G. Bailey et al., Class. Quant. Grav., submitted (2013)

Limits on violations of Lorentz Symmetry from Gravity Probe B

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