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Test of the Equivalence Principle Using a Rotating Torsion Balance

Test of the Equivalence Principle Using a Rotating Torsion Balance
Test of the Equivalence Principle Using a Rotating Torsion Balance

a r X i v :0712.0607v 1 [g r -q c ] 4 D e c 2007

Test of the Equivalence Principle Using a Rotating Torsion Balance

S.Schlamminger,K.-Y.Choi,T.A.Wagner,J.H.Gundlach,and E.G.Adelberger

Center for Experimental Nuclear Physics and Astrophysics,University of Washington,Seattle,WA,98195

(Dated:February 2,2008)

We used a continuously rotating torsion balance instrument to measure the acceleration di?er-ence of beryllium and titanium test bodies towards sources at a variety of distances.Our result ?a N,Be ?T i =(0.6±3.1)×10?15m /s 2improves limits on equivalence-principle violations with ranges from 1m to ∞by an order of magnitude.The E¨o tv¨o s parameter is ηEarth,Be ?T i =(0.3±1.8)×10?13.By analyzing our data for accelerations towards the center of the Milky Way we ?nd equal attrac-tions of Be and Ti towards galactic dark matter,yielding ηDM,Be ?T i =(?4±7)×10?5.Space-?xed di?erential accelerations in any direction are limited to less than 8.8×10?15m /s 2with 95%con?-dence.

PACS numbers:https://www.sodocs.net/doc/4913718312.html,

The equivalence of gravitational mass and inertial mass is assumed as one of the most fundamental principles in nature.Practically every theoretical attempt to con-nect general relativity to the standard model allows for a violation of the equivalence principle[1].Equivalence principle tests are therefore important tests of uni?cation scale physics far beyond the reach of traditional particle physics experiments.The puzzling discoveries of dark matter and dark energy provide strong motivation to ex-tend tests of the equivalence principle to the highest pre-cision possible.

Over the past two decades we have conducted labora-tory tests of the equivalence principle[2,3,4,5].This letter reports our latest and most precise measurement using a new,continuously-rotating torsion balance.The torsion balance compares the horizontal accelerations of test bodies made from two di?erent materials.Acceler-ation di?erences that depend only on the test-body ma-terial violate the equivalence principle.We parameter-ize such equivalence-principle violating interactions by a Yukawa potential,which for two point objects is

V (r )=αG (

q

μ)2m 1m 2

2

FIG.1:Cross section of the apparatus(upper part).The entire torsion balance is suspended below a continuously ro-tating turntable.Gravity gradient compensator masses were placed around the pendulum to reduce coupling to ambient gravitational gradients.The pendulum(lower part)carries four Ti and four Be masses in a composition dipole. heads.The loop is realized by a digital signal processor controlling an eddy-current drive.The constancy of the rotation rate was limited by the angle encoder’s linear-ity.Angle encoder imperfections were mapped by oper-ating the torsion balance at rotation periods T t?T0 and the corrections were included in the feedback algo-rithm.The turntable rotation frequency was normally set toωt/(2π)=2/3T?1

=0.835mHz,where the signal-to-noise ratio was found to be optimal.The pendulum’s angular position and the signals of31sensors for temper-ature,tilt,etc.were recorded every2.76s. Gravitational forces between our pendulum and local gravitational gradients can occur at the signal frequency. To minimize coupling to ambient gravitational?eld gra-dients,Q l1,the pendulum was highly symmetrical,with the nominal mass moments,q l1,vanishing for l<7. In addition,the pendulum’s q20,q30and q40moments were designed to be zero to avoid gravitational coupling due to a small misalignments of the pendulum[3].The ambient Q21and Q31?elds at the pendulum’s position were compensated with888kg of lead and8.8kg of alu-minum,respectively.Lead bricks placed about1m from the pendulum were used to null the remnant Q21-?eld. The gradient?elds were measured with a special gra-diometer pendulum that was con?gured to have either a large q21or q31moment.We found that the Q21-?eld varied by as much as±1%during a year,which we at-tribute to changes of the water table.Once the equiva-lence principle pendulum was installed,its residual q21-and q31-moments were measured by rotating the Q21-and Q31-compensators by180?,doubling the uncompensated ?elds.The pendulum’s unwanted mass moments were then minimized by adjusting four screws on the pendu-lum body until only a small gravitational coupling re-mained(see Table I),which was later subtracted from the data.

The turntable must rotate about local vertical since a tilt of the attachment point of the torsion?ber causes a small apparent rotation of the pendulum.The tilt of the turntable was continuously measured with level sensors on the rotating platform.The once-per-revolution com-ponent of the tilt was minimized by a feedback loop that changed the length of two of the turntable’s support legs by controlling their temperature with Peltier elements. This system nulled the periodic tilt of the level sensor to within±3nrad.At the pendulum body,1.7m be-low the feedback sensor,local vertical was di?erent by 55nrad and a correction to the data was required.We inferred this tilt by using a second tilt sensor0.2m below the pendulum.We also found the change in local verti-cal consistent with our local mass integration.The data were corrected using the tilt at the pendulum and a tilt matrix characterizing the tilt sensitivity.The tilt matrix was measured for all four pendulum mirrors by deliber-ately tilting the turntable rotation axis.The magnitude of the tilt matrix ranged from≈1%to≈7%depending on the mirror.

The largest entry in our error budget arises from sys-tematic and statistical uncertainties associated with tem-perature gradients and?uctuations.We assessed the sen-sitivity to temperature gradients by placing temperature-controlled panels on opposite sides of the apparatus to produce exaggerated thermal gradients.The quoted un-certainty is limited by sensor noise in resolving the small temperature gradients that occurred during equivalence principle data taking.By applying a magnetic?eld and

3

?eld gradients using coils,as well as strong permanent

magnets,

we

found the

magnetic coupling to be small (Table I).

FIG.2:Shown are measured di?erential accelerations to-wards North (top)and West.After the ?rst four data runs the Be and Ti test bodies were interchanged on the pendulum frame.A violation of the equivalence principle would appear as a di?erence in the means (lines)of the two data sets.The o?set acceleration is due to systematic e?ects that follow the pendulum frame but not the composition dipole.The data have been corrected for tilt and gravity gradients,but only the statistical uncertainties are shown.

TABLE I:The raw di?erential accelerations between Be and Ti towards North (N)and West (W)are shown in line 1.Lines 2to 5list corrections that were applied and the bottom line gives our corrected results.Uncertainties are 1σ.di?erential acceleration in

?a N,Be ?T i ?a W,Be ?T i (10?15m /s 2)(10?15m /s 2)

residual gravity gradients

1.6±0.20.3±1.7tilt

1.2±0.6?0.2±0.7magnetic

0±0.30±0.3temperature gradients 0

±

1.70

±

1.7

a g ⊥

=(0.3±1.8)×10?13.

(2)

Figure 3shows the limits on the strength,α,of a new

interaction (Eq.1)as a function of range λ.To estab-lish these limits we used the mass density and charge content of the environment surrounding the torsion bal-ance to create a source model.For λ=1?100m the source is dominated by a hill sloping towards the East.For λ<10km the local topography and bedrock become signi?cant.At ranges between 10km and 1000km,pre-liminary results using large scale density and composi-tion models indicate that the limit on αis better than the dashed line shown in Fig.3.A detailed description of the model and limits will be included in a future publi-cation.We used an elliptical layered Earth model[3,8,9]for λ>1000km.For this range the source mass is lo-cated towards the North.

Equivalence-principle violating interactions associated with an astronomical source are additionally modulated

4 by a solar or sidereal frequency:

?a N=cosθ ??a cos(φ?φ0)???a sin(φ?φ0) +o N,

?a W=cosθ ?a sin(φ?φ0)???a cos(φ?φ0) +o W,

withθandφbeing the altitude and azimuth of the astro-

nomical source,?a the di?erential acceleration towards

the source and??a its quadrature

component;o N and

o W are possible instrument o?sets.Figure4shows the

averaged?a N and?a W versus sidereal time.A simul-

taneous?t of?a N and?a W towards the galactic center

yields

a(Be)?a(T i)=?a=(?2.1±3.1)×10?15m/s2,

?a(Be)??a(T i)=??a=(2.7±3.1)×10?15m/s2.

Since only about a quarter of the total acceleration of the

solar system towards the center of our galaxy is caused

by galactic dark matter[10],we?ndηDM,Be?T i=(?4±

7)×10?5.

With95%con?dence we constrain space-?xed di?er-

ential accelerations in any direction to be smaller than

?a=8.8×10?15m/s2.

FIG.3:New upper limits on Yukawa interactions coupled to

baryon number with95%con?dence.The uncertainties in

the source integration is not included in this plot.The num-

bers indicate references.The shaded region is experimentally

excluded.Preliminary models for10km<λ<1000km

indicate that the limit onαis smaller than the dashed line.

We have substantially improved the limits on the

strength of an equivalence-principle violating,long-range

interaction.We are currently broadening our search by

using other test-body materials and improving the sensi-

tivity of our torsion balance.

This work was supported by NSF Grants PHY0355012,

PHY0653863and by NASA Grant NNC04GB03G,and

DOE funding for the CENPA laboratory.Blayne Heckel,

Stephen Merkowitz,Erik Swanson,Phil Williams,Ulrich

FIG.4:The averaged di?erential acceleration of Be and

Ti towards North and West as a function of sidereal time.

The dashed line represents a hypothetical signal of20×

10?15m/s2.The solid line is the best?t toward the galactic

center(?a=(?2.1±3.1)×10?15m/s2).

Schmidt,Tom Butler and Chris Spitzer have contributed

to the apparatus development.

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2. 终端驱动安装 终端通过USB连接PC后,设备管理器将检测到多个未知端口,右键选择更新驱动,并选择驱动存放路径即可,需注意每个未知端口都要完成更新。 1、终端连接PC后,设备管理器显示未知端口: 2、驱动安装后,Diag Port及Modem已识别:

3. 关停终端的LOG采集 终端与CDS、鼎利、QXDM等软件对接时,需关停终端内部的Log采集,否则软件无法抓取终端信令,可在“应用程序→HTC SSD Test Tool→QXDM Logger”中关停(终端每次重启后都必须进行如下操作): 点击Disable DQ: 去掉图中红圈内的小勾:

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r_tmnl_run这张表,在r_tmnl_run表中对终端进行配置,然后将r_tmnl_run这张表单表下装。在界面中查询到终端是否下装到缓存中,输入终端对应的资产号(资产号从下面第二步r_tmnl_run中取得)。查询到有此终端地址的记录表示终端可以准备测试了。 下面介绍知道了某个具体的终端地址,可以将该终端添加到左边树中,之后在网页上对终端测试。如测试某个终端的地址为‘07550001’ 第一步查询得到将终端下挂的地市的代码 select * from o_org o where https://www.sodocs.net/doc/4913718312.html,_name like'景德镇%'----36402 得到景德镇的区域代码为“36402” 第二步配置r_tmnl_run表 因为知道要测试的终端地址(可以通过手工的方法调试查看终端参数) 此时,需要修改r_tmnl_run表中的参数。 select * from r_tmnl_run run where run.terminal_addr='07550001' 如果未做修改,在查询该表的时候,这行记录为空。 此时,需要使用下面的SQL语句 select * from r_tmnl_run run for update 可以选择到某一行,直接复制到要更新的一行中,打开编辑的

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English song-as long as you love me英文经典脍炙人口歌曲歌词解析

歌名:As Long As You Love Me 歌手:Justin Bieber 所属专辑:Believe Acoustic 作曲 : Persson Svensson 作词 : Persson Svensson As long as you love me yeah 只要你爱我就好 I'm under pressure, seven billion people in the world trying to fit in 我们在压力下跟着全世界70亿人适应这个社会 Keep it together, smile on your face even though your heart is frowning 紧紧相依,你心有困懑却面带笑容 But hey now, you know girl, we both know it's a cruel world 但是现在,宝贝你知道,我们都知道世界多么残酷 But I will take my chances 但我愿意(搏一搏)抓住我的机会 As long as you love me, we could be starving, 只要你爱我,我们可以挨饿(饥肠辘辘) We could be homeless, we could be broke 可以流离失所,也可以支离破碎 As long as you love me I'll be your platinum, I'll be your silver, i'll be your gold 只要你爱我,我是你的铂金,我是你的银,我是你的财富(我会不离不弃,无坚不摧,所向披靡)

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