亚毫米范围扭秤检验牛顿反平方定律改进实验
摘要
牛顿反平方定律作为引力理论的基石之一,描述了小到日常物品大到天体间的相互作用,但在极小范围内它的正确性并没有得到足够高的验证。除此之外,自然界还存在着其他基本相互作用,趋于最朴素的想法,物理学家们致力于寻找一个统一理论去包含所有的相互作用形式。在漫漫统一路途上,出现了如等级问题、宇宙常数问题需要填补的鸿沟。由此提出的弦理论、膜世界理论、M理论等频频预言着额外维的存在,反平方定律在一定范围内将出现破缺。近些年物理学界对反平方定律的实验检验充满了关注,不断刷新的破缺上限也使人们对寻找额外维充满了期待。根据ADD理论中提出的大尺度额外维,当额外维数目n=2时,反平方定律会在亚毫米范围发生破缺,这也使得国际上众多研究小组在这个区间展开高精度的实验检验。扭秤作为极端精密测量工具,在弱力检测领域有着重要的地位,本实验室对扭秤的长期研究及使用为开展反平方定律检验提供了良好的基础。采用间距调制的原理,将扭秤作为检验质量,周期性地改变它与吸引质量之间的间距,测量非牛顿信号的大小。调制过程中,通过合理的设计补偿掉牛顿力矩变化,使实验成为一个“零”检验。本实验室于2007年,在间距176μm-343,um范围内,对检验质量与吸引质量的牛顿力矩补偿水平达到(0.2±2.1)×10-16Nm水平,在95%的置信水平上,给出反平方定律的破缺上限为|α|≤1时,λ≤66μm,能量的统一标度M*≥2.8Tev/c2,该结果非常接近国际上的最好结果。为了能在更高精度上开展实验,进行了以下几点主要改进：1)检验质量与吸引质量之间的间距变化减小到120μm-240μm,提高非牛顿力的强度；2)减少装置中的零散部件,提高定位安装精度,使牛顿力矩的补偿水平提高至10-17Nm量级；3)将调制信号的频率选取在高频区域,提高扭秤的探测灵敏度。基于上述改进,“零”实验的结果可望将当前的最好上限提高一个量级。经过两年的准备,实验于2010年底完成了整体的搭建,并进行了初步的间距调制实验,但在调制频率处实验探测到了非常明显的信号。在排除掉牛顿力矩的影响,并根据当前非牛顿力的上限排除掉它的可能性,经过大量的实验分析,得出干扰信号产生的最主要来源为静电效应。目前正在对静电屏蔽装置、地线干扰、仪器电源波动等进行相应的研究及改进,为下一阶段再次进行间距调制实验而准备。本课题为国家重点研究发展计划(批准号：2010CB832802)的资助。
The inverse-square law is a fundamental of theories of gravity, impressively demonstrated from astronomical scales to sub-millimeter scales. However, due to difficulties associated with designing sensitive short-range experiments, the range below1mm was mostly unexplored until a few years ago. Besides that, there are other three fundamental interactions. Connecting gravity with the rest of physics is clearly the central challenge of physics. In an attempt to solve some of the greatest puzzles in physics, namely, the hierarchy problem, the comsmological constant problem, many modern theories of gravity, including string, brane-world theories and M-theories, suggest the existence of extra dimensions. The gravitational force will deviate from Newtonian inverse-square law. In ADD formalism, if the number of extra dimensions is two, it is hoped to find the deviation of inverse-square law in submillmeter range.Torsion pendum as the extreme precision measuring tool in extremely weak force detection plays an important role. By using the torsion pendulum as a test mass, modulate the distance between the test mass and source mass to test the non-Newtonian force. Design a counterbalance mass to decrease the Newtonian force, and such experimental design is so-called null test for the expected signal. In the year2007, we finished experiment in the range176μm～343μm, the results disclosed that the upper limit on non-Newtonian force was λ≤66μm when|a|≤1and the uniform energy M'≥2.8Tev/c2. The net change of the Newton's torque in experimental range is (0.2±2.1)x10-16Nm. The result nearly reaches the best limit in the world.This thesis describes our improved experiment. Three main improvements have been made to elevate the sensitivity of our torsion pendulum compared with previous by one order. First, the minimal surface separation between test and source mass can be approached as close as120μm by using a thinner electrostatic shielding membrane. Second, the Newtonian gravitational perturbations, due to the modulating motions of the source mass and its supporting glass masses from120μm to240μm, are precisely balanced to the amplitude of10-17Nm. Third, the higher frequencies (than the free oscillation of torsion pendulum) are chosen for the dual modulation of both the expected signal and the calibration gravitational torque. In the latest two years, we have got the preliminary results. The amplitude of the signal is not exactly as we expecte. After lots of experiments, we suppose that the signal is due to the electrostatic effect. Now we are focusing on the improving the electrostatic shielding, decreasing the ground disturbance and the voltage fluctuations on the wires.This work is supported by the National Basic Research Program of China (No.2010CB832802).
The inverse-square law is a fundamental of theories of gravity, impressively demonstrated from astronomical scales to sub-millimeter scales. However, due to difficulties associated with designing sensitive short-range experiments, the range below1mm was mostly unexplored until a few years ago. Besides that, there are other three fundamental interactions. Connecting gravity with the rest of physics is clearly the central challenge of physics. In an attempt to solve some of the greatest puzzles in physics, namely, the hierarchy problem, the comsmological constant problem, many modern theories of gravity, including string, brane-world theories and M-theories, suggest the existence of extra dimensions. The gravitational force will deviate from Newtonian inverse-square law. In ADD formalism, if the number of extra dimensions is two, it is hoped to find the deviation of inverse-square law in submillmeter range.Torsion pendum as the extreme precision measuring tool in extremely weak force detection plays an important role. By using the torsion pendulum as a test mass, modulate the distance between the test mass and source mass to test the non-Newtonian force. Design a counterbalance mass to decrease the Newtonian force, and such experimental design is so-called null test for the expected signal. In the year2007, we finished experiment in the range176μm～343μm, the results disclosed that the upper limit on non-Newtonian force was λ≤66μm when|a|≤1and the uniform energy M'≥2.8Tev/c2. The net change of the Newton's torque in experimental range is (0.2±2.1)x10-16Nm. The result nearly reaches the best limit in the world.This thesis describes our improved experiment. Three main improvements have been made to elevate the sensitivity of our torsion pendulum compared with previous by one order. First, the minimal surface separation between test and source mass can be approached as close as120μm by using a thinner electrostatic shielding membrane. Second, the Newtonian gravitational perturbations, due to the modulating motions of the source mass and its supporting glass masses from120μm to240μm, are precisely balanced to the amplitude of10-17Nm. Third, the higher frequencies (than the free oscillation of torsion pendulum) are chosen for the dual modulation of both the expected signal and the calibration gravitational torque. In the latest two years, we have got the preliminary results. The amplitude of the signal is not exactly as we expecte. After lots of experiments, we suppose that the signal is due to the electrostatic effect. Now we are focusing on the improving the electrostatic shielding, decreasing the ground disturbance and the voltage fluctuations on the wires.This work is supported by the National Basic Research Program of China (No.2010CB832802).
引文
[1] Kaluza T, Sitzungsber. in Zum Unitatsproblem in der Physik. Berlin:Sitzungsber Press,1921, K1:966.
[2] Klein O. The atomicity of electricity as a quantum theory law. Nature,1926,118:516.
[3]王顺金.物理学前沿问题,第一版,成都：四川大学出版社,2005.
[4] J C Taylor.自然规律中蕴蓄的统一性.第一版.[译]暴永宁.北京,北京理工大学出版社,2004.
[5] Adelberger E G. Battat J, Currie D. and et al. et al. Opportunities for Probing Fundamental Gravity with Solar System Experiments. ar Xive:0902.3004v2.2009.
[6] Gell-Mam M, Ramonel P and Slansky. Color embeddings, charge assignments, and proton stability in unified gauge theories. Reviews of Modern Physics.1978,50: 721-744.
[7] Riess A, Filippenko A V, Challis P, et al. Observation Evidence from Supernovae for an accelerating universe and a cosmological constant. Astronomical Journal, 1998,116:1009.
[8] Perlmutter S, Aldering G, Knop R A, et al. Measurements of Ω. and A from 42 high-redshift supernovae. Astrophysical Journal.1999.517:565.
[9] http://wmap.gsfc.nasa.gov.
[10] Antoniadis I, Arkani-Hamed N. Dimopoulos S and Dvali G. New dimensions at a millimeter to a fermi and superstrings at a TeV. Physics Letters B.1998.436: 257-263.
[11] Arkani-Hamed N. Dimopoulos S and Dvali G. The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B.1998.429:263-272.
[12] Arkani-Hamed N, Dimopoulos S and Dvali G. Phenomenology, astrophysics, and cosmology of theories with submillimeter dimensions and TeV scal quantum gravity. Physical Review D,1999.59:086004-1.
[13] Arkani-Hamed N. Dimopoulos S and Dvali. Deviations from the 1/r2 Newton law to extra dimensions. Physics Letters B,2000.472:39-44.
[14] Ederth T. Template-stripped gold surfaces with 0.4-mm rms roughness suitable for force measurements:Application to the Casimir force in the 20-200nm range. Physical Review A.2000.62:062101-1.
[15] Mohideen U and Roy A. Precision measurement of the Casimir force from 0.1 to 0.9 μm. Physical Review Letters,1998,81:4549-4552.
[16] Roy A, Yuan C and Mohideen U. Improved precision measurement of the Casimir force. Physical Review D,1999,60:111101-1.
[17] Harris B W and Mohideen U. Precision measurement of the Casimir force using gold surface. Physical Review A,2000,62:052109-1.
[18] Lamoreaus S K. Demonstration of the Caimir force in the 0.6 to 6 μm range. Physical Review Letters,1996,78:5-8.
[19] Kim W J, Sushkov A O, Dalvit D A R, et al. Measurement of the short-range attractive force between Ge plates using a torsion balance. Physical Review Letters, 2009,103:060401-1.
[20] Abele H, Bea(31er S and Westphal A. Quantum state of neutrons in the gravitational field and limits for non-Newtonian interaction in the range between 1 μm and 10 μm. arXiv:hep-ph/0301145vl,2003.
[21] Chiaverini J. Smullin S J, Geraci A A, et al. New experiment constraints on non-Newtonian forces below 100 μ.m. Physical Review Letters,2003,90:151101-1.
[22] Geraci A A, Smullin S, Weld D M, et al. Improved constraints on non-Newtonian forces at 10 micros. Physical Review D,2008,78:022002-1.
[23] Long J C, Chan H W, Churnside A B, et al. Upper limits to submillimetre-range forces from extra space-time dimensions. Nature,2003,421:922-925.
[24] Tu L C, Guan S G, Luo J, et al. Null test of Newtonian inverse-square law at submillimeter range with a dual-modulation torsion pendulum. Physical Review Letters.2007,98:201101-1.
[25] Hoyle C D. Schmidt U. Heckel B R. el al. Submillimeter test of the gravitational inverse-square law:A search for "large" extra dimensions. Physical Review Letters.2001.86:1418-1421.
[26] Kapner D J, Cook T S, Adelberger E G, et al. Tests of the gravitational inverse-square law below the dark-energy length scale. Physical Review Letters, 2007,98:021101-1.
[27] Spero R. Hoskins J K, Newman R D, et al. Test of the gracitational inverse-square law at laboratory distances. Physical Review Letters,1981.44:1645-1648.
[28] Hoskins J K, Newman R D, Spero R, et al. Experimental tests of the gravitational
inverse-square law for mass separations from 2 to 105 cm. Physical Review D.1985, 32:3084-3095.
[29] Yang S Q. Zhan B F. Wang Q L, et al. Test of the gravitational inverse square law at millimeter ranges. Physical Review Letters,2012.108:081101-1.
[30] Antoniadis I, Dimopoulos S and Dvali G. Millimetre-range forces in superstring theories with weak-scale compactification. Nuclear Physics B.1998,516:70-82.
[31] Moody J E and Wilezek F. New macroscopic force? Physical Review D,1984,30: 130-138.
[32] Hagiwara K (Particle Data Group). Review of particle properties. Physical Review D.2002.66:010001(R)-1.
[33] Mostepanenko V M and Novello M. Constraints on non-Newtonian gravity from the Casimir force measurements between two crossed cylinders. Physical Review D. 2001.63:115003-1.
[34] Fischbach E. Krause D E. Mostepanenko V M. et al. New constraints on ultrashort-ranged Yukawa interactions from atomic force microscopy. Physical Review D,2001,64:075010-1.
[35] Long J C, Chan H W and Price J. Experimental status of gravitational-strength force in the sub-centimeter regime. Nuclear Physics B,1999.539:23-34.
[36] Cornaz A. Hubler B. and Kundig W. Determination of the gravitational constant at an effective interaction distance of 122m. Physical Review Letters.1994.72: 1152-1155.
[37] Romaides A J and Sands R W. Final results from the WABG tower gravity experiment. Physical Review D.1997,55:4532-4536.
[38] Talmadge C L and Fischbach E. in The Search for Non-Newtonian Gravity. Berlin: Springer Verlag,1998.
[39] Shirata A, Shiromizu T. Yoshida N, and et al. Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales. Physical Review D. 2005.71:064030-1.
[40] Adelberger E G, Heckel B R and Nelson A E. Test of the gravitational inverse-square law. Annual Review of Nuclear and Particle Science.2003. 53:77-121.
[41]张雅婷.测G和牛顿反平方检验实验中的数学建模：[硕士学位论文].武汉：华
中科技大学,2009.
[42]国家重点基础研究发展计划(973)计划.课题任务书,2010,编号：2010CB832802.
[43]官盛果.亚毫米范围牛顿反平方定律的实验检验：[博士学位论文].武汉：华中科技大学,2009.
[44]范相东.地面振动对测G实验的影响与扭秤“反常”模式的研究：[硕士学位论文].武汉：华中科技大学,2007.
[45]涂英.周期法测G中高精度周期拟合方法与“反常模式”研究：[硕士学位论文].武汉：华中科技大学,2004.
[46]刘淇.基于双球体吸引质量的扭秤周期法测量牛顿引力常数G：[博士学位论文].武汉：华中科技大学,2009.
[47]刘林霞.测G实验中几种相关效应的影响分析：[博士学位论文].武汉：华中科技大学,2009.
[48]谭栓斌,郭让民,刘建章等.钨的冶金及其加工技术.中国钨业,2007,22：51-53.
[49]占必富.毫米范围引力反平方定律的实验检验：[博士学位论文].武汉：华中科技大学,2012.
[50]黄友锐,曲立国.PID控制器参数整定与实现.第一版,北京：科学出版社,2010.
[51]邓木生.基于参数实时最优整定的智能PID控制器研究.计算机测量与控制,2011,19：1629-1632.
[52] Brown R. A brief account of microscopical observations made in the months of June. July and August,1827, on the particles contained in the pollen of plants; and on the gengral existence of active molecules in organic and inorganic bodies. Philosophical Magazine,1828,4:161-173.
[53] Brown R. Annual Review of Physical Chemistry.1828,14:294.
[54] Einstein A. in Investigations on the Theory of the Brownian Movement. New York: Dover,1956.
[55] Reif F. in Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hill.1965.
[56] Callen H B and Welton T A. Irreversibility and Generalized Noise. Physical Review. 1951,83:34-40.
[57] Callen H B and Greene R F. On a theorem of irreversible thermodynamics. Physical Review,1952,86:702-710.
[58] Saulson P. Thermal noise in mechanical experiments. Physical Review D,1990.42: 2437-2445.
[59] 卞春花.残余气体对扭秤Q值的影响研究：[硕士学位论文].武汉：华中科技大学,2007.
[60] Nowick A S and Berry B S. in Anelastic Relaxation in Crystalline Soilds. New York: Academic,1971.
[61] Saulson P R. in Fundamentals of Interferometric Gravitational Wave Detectors. London:Word Scientific,1994.
[62] 汪志诚.热力学·统计物理.第三版,北京：高等教育出版社,2003.
[63] 方俊鑫,陆栋.固体物理学.第一版,上海：上海科学技术出版社,1980.
[64] Baikie I D, Venderbosch E, Meyer J A and et al. Analysis of stray capacitance in the Kelvin method. Review of Scientific Instruments.62:725-735.
[65] Kim J S. Lagel B, Moons E and et al. Kelvin probe and ultraviolet photoemission measurements of indium tin oxide work function:a comparison. Synthetic Metals. 2000,111(1):311-314.
[66] Pollack S E, Schlamminger S. and Gundlach J H. Temporal extent of surface potentials between closely spaced metals. Physical Review Letters.2008.101: 071101-1.
[67] Young R D and Clark E. Effect of surface patch fields on field-emission work-function determinations. Physical Review Letters,1966.17:351-353.
[68] Hoyle C D. Kapner D J, Heckel B R. and et al. Submillimeter tests of the gravitational inverse-square law. Physical Review D,2004.70:042004-1.
[2] Klein O. The atomicity of electricity as a quantum theory law. Nature,1926,118:516.
[3]王顺金.物理学前沿问题,第一版,成都：四川大学出版社,2005.
[4] J C Taylor.自然规律中蕴蓄的统一性.第一版.[译]暴永宁.北京,北京理工大学出版社,2004.
[5] Adelberger E G. Battat J, Currie D. and et al. et al. Opportunities for Probing Fundamental Gravity with Solar System Experiments. ar Xive:0902.3004v2.2009.
[6] Gell-Mam M, Ramonel P and Slansky. Color embeddings, charge assignments, and proton stability in unified gauge theories. Reviews of Modern Physics.1978,50: 721-744.
[7] Riess A, Filippenko A V, Challis P, et al. Observation Evidence from Supernovae for an accelerating universe and a cosmological constant. Astronomical Journal, 1998,116:1009.
[8] Perlmutter S, Aldering G, Knop R A, et al. Measurements of Ω. and A from 42 high-redshift supernovae. Astrophysical Journal.1999.517:565.
[9] http://wmap.gsfc.nasa.gov.
[10] Antoniadis I, Arkani-Hamed N. Dimopoulos S and Dvali G. New dimensions at a millimeter to a fermi and superstrings at a TeV. Physics Letters B.1998.436: 257-263.
[11] Arkani-Hamed N. Dimopoulos S and Dvali G. The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B.1998.429:263-272.
[12] Arkani-Hamed N, Dimopoulos S and Dvali G. Phenomenology, astrophysics, and cosmology of theories with submillimeter dimensions and TeV scal quantum gravity. Physical Review D,1999.59:086004-1.
[13] Arkani-Hamed N. Dimopoulos S and Dvali. Deviations from the 1/r2 Newton law to extra dimensions. Physics Letters B,2000.472:39-44.
[14] Ederth T. Template-stripped gold surfaces with 0.4-mm rms roughness suitable for force measurements:Application to the Casimir force in the 20-200nm range. Physical Review A.2000.62:062101-1.
[15] Mohideen U and Roy A. Precision measurement of the Casimir force from 0.1 to 0.9 μm. Physical Review Letters,1998,81:4549-4552.
[16] Roy A, Yuan C and Mohideen U. Improved precision measurement of the Casimir force. Physical Review D,1999,60:111101-1.
[17] Harris B W and Mohideen U. Precision measurement of the Casimir force using gold surface. Physical Review A,2000,62:052109-1.
[18] Lamoreaus S K. Demonstration of the Caimir force in the 0.6 to 6 μm range. Physical Review Letters,1996,78:5-8.
[19] Kim W J, Sushkov A O, Dalvit D A R, et al. Measurement of the short-range attractive force between Ge plates using a torsion balance. Physical Review Letters, 2009,103:060401-1.
[20] Abele H, Bea(31er S and Westphal A. Quantum state of neutrons in the gravitational field and limits for non-Newtonian interaction in the range between 1 μm and 10 μm. arXiv:hep-ph/0301145vl,2003.
[21] Chiaverini J. Smullin S J, Geraci A A, et al. New experiment constraints on non-Newtonian forces below 100 μ.m. Physical Review Letters,2003,90:151101-1.
[22] Geraci A A, Smullin S, Weld D M, et al. Improved constraints on non-Newtonian forces at 10 micros. Physical Review D,2008,78:022002-1.
[23] Long J C, Chan H W, Churnside A B, et al. Upper limits to submillimetre-range forces from extra space-time dimensions. Nature,2003,421:922-925.
[24] Tu L C, Guan S G, Luo J, et al. Null test of Newtonian inverse-square law at submillimeter range with a dual-modulation torsion pendulum. Physical Review Letters.2007,98:201101-1.
[25] Hoyle C D. Schmidt U. Heckel B R. el al. Submillimeter test of the gravitational inverse-square law:A search for "large" extra dimensions. Physical Review Letters.2001.86:1418-1421.
[26] Kapner D J, Cook T S, Adelberger E G, et al. Tests of the gravitational inverse-square law below the dark-energy length scale. Physical Review Letters, 2007,98:021101-1.
[27] Spero R. Hoskins J K, Newman R D, et al. Test of the gracitational inverse-square law at laboratory distances. Physical Review Letters,1981.44:1645-1648.
[28] Hoskins J K, Newman R D, Spero R, et al. Experimental tests of the gravitational
inverse-square law for mass separations from 2 to 105 cm. Physical Review D.1985, 32:3084-3095.
[29] Yang S Q. Zhan B F. Wang Q L, et al. Test of the gravitational inverse square law at millimeter ranges. Physical Review Letters,2012.108:081101-1.
[30] Antoniadis I, Dimopoulos S and Dvali G. Millimetre-range forces in superstring theories with weak-scale compactification. Nuclear Physics B.1998,516:70-82.
[31] Moody J E and Wilezek F. New macroscopic force? Physical Review D,1984,30: 130-138.
[32] Hagiwara K (Particle Data Group). Review of particle properties. Physical Review D.2002.66:010001(R)-1.
[33] Mostepanenko V M and Novello M. Constraints on non-Newtonian gravity from the Casimir force measurements between two crossed cylinders. Physical Review D. 2001.63:115003-1.
[34] Fischbach E. Krause D E. Mostepanenko V M. et al. New constraints on ultrashort-ranged Yukawa interactions from atomic force microscopy. Physical Review D,2001,64:075010-1.
[35] Long J C, Chan H W and Price J. Experimental status of gravitational-strength force in the sub-centimeter regime. Nuclear Physics B,1999.539:23-34.
[36] Cornaz A. Hubler B. and Kundig W. Determination of the gravitational constant at an effective interaction distance of 122m. Physical Review Letters.1994.72: 1152-1155.
[37] Romaides A J and Sands R W. Final results from the WABG tower gravity experiment. Physical Review D.1997,55:4532-4536.
[38] Talmadge C L and Fischbach E. in The Search for Non-Newtonian Gravity. Berlin: Springer Verlag,1998.
[39] Shirata A, Shiromizu T. Yoshida N, and et al. Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales. Physical Review D. 2005.71:064030-1.
[40] Adelberger E G, Heckel B R and Nelson A E. Test of the gravitational inverse-square law. Annual Review of Nuclear and Particle Science.2003. 53:77-121.
[41]张雅婷.测G和牛顿反平方检验实验中的数学建模：[硕士学位论文].武汉：华
中科技大学,2009.
[42]国家重点基础研究发展计划(973)计划.课题任务书,2010,编号：2010CB832802.
[43]官盛果.亚毫米范围牛顿反平方定律的实验检验：[博士学位论文].武汉：华中科技大学,2009.
[44]范相东.地面振动对测G实验的影响与扭秤“反常”模式的研究：[硕士学位论文].武汉：华中科技大学,2007.
[45]涂英.周期法测G中高精度周期拟合方法与“反常模式”研究：[硕士学位论文].武汉：华中科技大学,2004.
[46]刘淇.基于双球体吸引质量的扭秤周期法测量牛顿引力常数G：[博士学位论文].武汉：华中科技大学,2009.
[47]刘林霞.测G实验中几种相关效应的影响分析：[博士学位论文].武汉：华中科技大学,2009.
[48]谭栓斌,郭让民,刘建章等.钨的冶金及其加工技术.中国钨业,2007,22：51-53.
[49]占必富.毫米范围引力反平方定律的实验检验：[博士学位论文].武汉：华中科技大学,2012.
[50]黄友锐,曲立国.PID控制器参数整定与实现.第一版,北京：科学出版社,2010.
[51]邓木生.基于参数实时最优整定的智能PID控制器研究.计算机测量与控制,2011,19：1629-1632.
[52] Brown R. A brief account of microscopical observations made in the months of June. July and August,1827, on the particles contained in the pollen of plants; and on the gengral existence of active molecules in organic and inorganic bodies. Philosophical Magazine,1828,4:161-173.
[53] Brown R. Annual Review of Physical Chemistry.1828,14:294.
[54] Einstein A. in Investigations on the Theory of the Brownian Movement. New York: Dover,1956.
[55] Reif F. in Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hill.1965.
[56] Callen H B and Welton T A. Irreversibility and Generalized Noise. Physical Review. 1951,83:34-40.
[57] Callen H B and Greene R F. On a theorem of irreversible thermodynamics. Physical Review,1952,86:702-710.
[58] Saulson P. Thermal noise in mechanical experiments. Physical Review D,1990.42: 2437-2445.
[59] 卞春花.残余气体对扭秤Q值的影响研究：[硕士学位论文].武汉：华中科技大学,2007.
[60] Nowick A S and Berry B S. in Anelastic Relaxation in Crystalline Soilds. New York: Academic,1971.
[61] Saulson P R. in Fundamentals of Interferometric Gravitational Wave Detectors. London:Word Scientific,1994.
[62] 汪志诚.热力学·统计物理.第三版,北京：高等教育出版社,2003.
[63] 方俊鑫,陆栋.固体物理学.第一版,上海：上海科学技术出版社,1980.
[64] Baikie I D, Venderbosch E, Meyer J A and et al. Analysis of stray capacitance in the Kelvin method. Review of Scientific Instruments.62:725-735.
[65] Kim J S. Lagel B, Moons E and et al. Kelvin probe and ultraviolet photoemission measurements of indium tin oxide work function:a comparison. Synthetic Metals. 2000,111(1):311-314.
[66] Pollack S E, Schlamminger S. and Gundlach J H. Temporal extent of surface potentials between closely spaced metals. Physical Review Letters.2008.101: 071101-1.
[67] Young R D and Clark E. Effect of surface patch fields on field-emission work-function determinations. Physical Review Letters,1966.17:351-353.
[68] Hoyle C D. Kapner D J, Heckel B R. and et al. Submillimeter tests of the gravitational inverse-square law. Physical Review D,2004.70:042004-1.