Constraints on Torsion from Bounds on Lorentz Violation

Abstract

Exceptional sensitivity to spacetime torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10 ÿ31 GeV.DOI: 10.1103/PhysRevLett.100.111102 PACS numbers: 04.50. Kd, 04.20.ÿq, 11.30.Cp In Einstein's general relativity, gravity is the curvature of spacetime and energy-momentum density is its source. Among the numerous alternative theories of gravity, one popular class of models involves introducing an additional warping of spacetime called torsion [1][2][3]. In many models, the torsion has spin density as its source. Some scenarios allow torsion waves to propagate through spacetime, in analogy with the traveling curvature waves that form gravitational radiation in general relativity. In the special class of ''teleparallel'' models, the curvature of spacetime is itself determined in terms of the torsion.Theories extending general relativity via torsion are widely regarded as experimentally challenging to test because the effects of torsion typically are minuscule. Nature contains many sources of energy-momentum density sufficient to curve spacetime, such as stars and planets. However, sources of spin density strong enough to produce torsion effects are difficult to identify or create. Typical limits on torsion in the literature involve dynamical properties, being obtained from searches for spin-spin interactions or for torsion-mass effects [4].In this Letter, we discuss an alternative approach to searching for torsion, based on the little-appreciated fact that background torsion violates effective local Lorentz invariance. The key point is that nonzero torsion over a region of spacetime establishes a preferred orientation for a freely falling observer, which is the defining criterion for local Lorentz violation [5]. Certain tests of Lorentz symmetry can therefore be reinterpreted as torsion searches. Related ideas have been suggested by Lämmerzahl [6] and Shapiro [2]. Here, we use the exquisite sensitivities recently achieved in Lorentz-violation searches to extract tight new constraints on torsion components, including many previously unbounded in the literature.The recent surge of interest in tests of relativity stems from the realization that tiny violations of Lorentz symmetry could emerge from attempts to unify the known forces [7] and from the development of a comprehensive description of Lorentz and CPT violation in the context of realistic effective field theory, called the standard-model extension (SME) [8]. The SME categorizes Lorentz violations by the mass dimension of the corresponding operator in the Lagrange density, which offers a simple measure of their expected size [9]. The physical effects are controlled by coefficients for Lorentz violation, and many experiments have been performed to measure them [10]. This work shows these experiments can be reinterpreted as searches for nonzero torsion. We note in passing that...

Lorentz andCPTtests with hydrogen, antihydrogen, and related systems

“…where the superscripts (A) and (M) indicate the irreducible axial and irreducible mixed-symmetry combinations of the minimal-SME coefficients g w κλν , respectively [81,82]. The frequency shift (49) thereby matches the result reported in Ref.…”

“…(77), while for Paschen-Back transitions it is given in Eq. (81). The 1S-2S transition in free antihydrogen is shown to depend only on nonminimal coefficients for Lorentz and CPT violation, with the corresponding frequency shift specified in Eq.…”

Laboratory tests of Lorentz andCPTsymmetry with muons

“…where the superscripts (A) and (M) denote the irreducible axial and irreducible mixed-symmetry combinations of the coefficients g κλν , respectively [50,51]. This result extends the one derived in the original theoretical treatment [9], which excludes the coefficients g κλν on the grounds of an expected suppression relative to other minimal-SME ð−2.5 AE 2.5Þ × 10 …”

Constraints on Short-Range Spin-Dependent Interactions from Scalar Spin-Spin Coupling in Deuterated Molecular Hydrogen

“…[9]. Another theoretical framework for considering anomalous spin-dependent interactions comes from introducing nonzero torsion into general relativity, which causes gravity to acquire scalar and vector components that manifest as new spin-mass and spin-spin couplings [10][11][12][13]. Spontaneous Lorentz violation may also generate exotic spindependent interactions [14].…”