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local lorentz invariance is at the foundation of both the standard model of particle physics and general relativity , but is generally poorly tested for the latter theory .
violation of lorentz symmetry would break the isotropy of spacetime , permitting the vacuum to fill with ` background ' fields that have a preferred direction .
interaction of the test masses in a terrestrial gravity experiment with these fields could result in a sidereal modulation of the force between the masses , thus providing a test of lorentz invariance in gravity .
a quantitative description of lorentz violation consistent with local field theory is given by the standard - model extension ( sme ) , which has recently been expanded to include gravitational effects.@xcite the expression for the potential between two test masses @xmath2 and @xmath3 in the ` pure gravity ' sector of the sme is given by : @xmath4 where @xmath5 is the vector separating @xmath2 and @xmath3 , @xmath6 is the projection of the unit vector along @xmath5 in the @xmath7th direction , and @xmath8 is a set of 9 dimensionless coefficients for lorentz violation in the standard laboratory frame.@xcite motivated by ref .
, this report presents a test of eq .   in a laboratory gravity experiment
the indiana experiment is optimized for sensitivity to possible new forces in nature at short range , which in turn could arise from new elementary particles or even extra spacetime dimensions.@xcite it is described in detail elsewhere;@xcite here we concentrate on the essential features . to attain sensitivity at short range , the test masses must in general
be scaled to that range , so as not to be overwhelmed by newtonian forces at larger scales .
the experiment is illustrated in fig .
[ fig : expt ] .
the test masses consist of 250  @xmath9 m thick planar tungsten oscillators , separated by a gap of 100  @xmath9 m , with a stiff conducting shield in between them to suppress electrostatic and acoustic backgrounds .
the planar geometry concentrates as much mass as possible at the scale of interest , and is nominally null with respect to @xmath0 forces .
this is effective in suppressing the newtonian background relative to new short - range effects , but has detrimental consequences for testing the pure gravity sector of the sme .
the force  sensitive ` detector ' mass is driven by the force  generating ` source ' mass at a resonance near 1  khz , placing a heavy burden on vibration isolation .
the 1 khz operation is chosen since at this frequency it is possible to construct a simple , passive vibration isolation system .
the entire apparatus is enclosed in a vacuum chamber and operated at @xmath10 torr to further reduce the acoustic coupling .
detector oscillations are read out with a capacitive transducer and jfet amplifier .
this design has proven effective for suppressing all background forces to the extent that the only effect observed is thermal noise due to dissipation in the detector mass . after a run over the course of several days in 2002
, this experiment set the strongest limits on new forces of nature between 10 and 100  @xmath9m.@xcite the experiment has since been optimized to explore gaps below 50  @xmath9 m ; operation at the thermal noise limit has recently been demonstrated but with limited statistics .
analysis of the 2002 data for evidence of lorentz violation requires a theoretical expression for the lorentz violating force for the particular test mass geometry .
the @xmath11th component of the differential force corresponding to the modified potential in eq .   is given by : @xmath12 where @xmath13 and @xmath14 can be understood as components of the unit vector pointing from a differential mass element @xmath15 in the source mass to a corresponding element @xmath16 in the detector .
the sme coefficients in the lab frame @xmath8 are related to the coefficients in the sun - centered celestial equatorial frame @xmath17 by @xmath18 , where the matrix @xmath19 is given by eq .
( c1 ) of ref .  .
the detector is a constrained mechanical oscillator with distributed mass , so the experiment is sensitive to the force density averaged over the free modal displacement : @xmath20 here , the modal displacement @xmath21 is derived from a finite - element model of the detector mass with overall normalization factor @xmath22 , and the components of the force density @xmath23 are given by eq .
equation is evaluated by monte carlo integration with the sme coefficients expressed in the sun - centered frame and the geometrical parameters listed in table 2 of ref .  . as the experiment is done on resonance ,
the monte carlo algorithm computes the fourier amplitude of eq .
averaged over a complete cycle of the source mass oscillation , taking into account the measured source mass curvature and mode shape .
the result can be expressed as a fourier series of the time dependence , @xmath24 where @xmath25 is the earth s sidereal rotation frequency , and the time @xmath26 is measured in the sun - centered frame .
the @xmath27 are functions of the sme coefficients and test mass geometry ( and the laboratory colatitude angle ) and are given explicitly in table  [ tab : sig ] .
the statistical errors from the monte carlo on the numerical coefficient of each @xmath17 term in table  [ tab : sig ] are at most a few percent and ignored for the purpose of computing preliminary limits on the sme coefficients .
[ tab : sig ]
a preliminary analysis of the 2002 data set ( incorporating statistical errors only ) for signals of lorentz violation has been completed , following ref .  .
in this analysis , the time stamps in the data are extracted and offset relative to the effective @xmath28 in the sun - centered frame ( solar noon on the 2002 vernal equinox ) .
the results are shown in fig .  2 of ref .  .
the discrete fourier transforms of the data at each frequency component of the signal ( @xmath29 ) are computed , with errors .
gaussian probability distributions for the experiment at each signal frequency component are constructed , using the difference between the fourier transforms and the predicted signals ( table  [ tab : sig ] ) as the means . as in ref .  ,
the overlap of the fourier components characteristic of the finite data set ( fig .  2 of ref .  ) is quantified by scaling each term of the predicted signal with the element of a covariance matrix formed from the time stamps of the data .
finally , an overall probability distribution for the experiment is constructed from the product of the component distributions .
means and errors of particular @xmath17 ( for example , @xmath30 ) are then computed by integration of the distribution over all @xmath17 except @xmath30 .
results for each @xmath17 ( except one ) are shown in table  [ tab : results ] .
[ tab : results ]    this procedure is sufficient to determine the sme coefficients and account for their correlations , as long as the number of signal components equals or exceeds the number of coefficients in table  [ tab : sig ] , which is not the case ; for this analysis , @xmath31 , to which the experiment is apparently least sensitive , has been set to zero .
the limits are on the order of @xmath32-@xmath33 .
this is as expected , since , as pointed out in ref .
, lorentz violation leads to a misalignment of the force associated with eq .
relative to the vector @xmath5 , however the @xmath0 behavior of the force is preserved .
the planar test mass geometry renders the indiana experiment insensitive to @xmath0 forces ( about @xmath32 times gravitational strength at 10  @xmath9 m ) which is directly reflected in the limits on the sme coefficients .
the authors would like to thank h. muller for useful discussions of ref .  .
an experimental test of the newtonian inverse square law at short range has been used to set limits on lorentz violation in the pure gravity sector of the standard - model extension . on account of the planar test mass geometry , nominally null with respect to @xmath0 forces , the limits derived for the sme coefficients of lorentz violation are on the order @xmath1 .