Hughes–Drever experiment

7Li-NMR spectrum of LiCl (1M) in D2O. The sharp, unsplit NMR line of this isotope of lithium is evidence for the isotropy of mass and space.

Hughes–Drever experiments (also clock comparison-, clock anisotropy-, mass isotropy-, or energy isotropy experiments) are spectroscopic tests of the isotropy of mass and space. As in Michelson–Morley experiments, the existence of a preferred frame of reference or other deviations from Lorentz invariance can be tested, which also affects the validity of the equivalence principle. Thus these experiments concern fundamental aspects of both special and general relativity. Unlike Michelson–Morley type experiments, Hughes–Drever experiments test the isotropy of the interactions of matter itself, that is, of protons, neutrons, and electrons. The accuracy achieved makes this kind of experiment one of the most accurate confirmations of relativity (see also Tests of special relativity).[A 1] [A 2] [A 3] [A 4] [A 5] [A 6]

Experiments by Hughes and Drever

Giuseppe Cocconi and Edwin Ernest Salpeter (1958) theorized that inertia depends on the surrounding masses according to Mach's principle. Nonuniform distribution of matter thus would lead to anisotropy of inertia in different directions. Heuristic arguments led them to believe that any inertial anisotropy, if one existed, would be dominated by mass contributions from the center of our Milky Way galaxy. They argued that this anisotropy might be observed in two ways: Measuring the Zeeman splitting in an atom,[1] or measuring the Zeeman splitting in the excited nuclear state of 57Fe using the Mössbauer effect. [2]

Vernon W. Hughes et al. (1960)[3] and Ronald Drever (1961)[4] independently conducted similar spectroscopic experiments to test Mach's principle. However, they didn't use the Mössbauer effect but made magnetic resonance measurements of the nucleus of lithium-7, whose ground state possesses a spin of 3⁄2. The ground state is split into four equally spaced magnetic energy levels when measured in a magnetic field in accordance with its allowed magnetic quantum number. The nuclear wave functions for the different energy levels have different spatial distributions relative to the magnetic field, and thus have different directional properties. If mass isotropy is satisfied, each transition between a pair of adjacent levels should emit a photon of equal frequency, resulting in a single, sharp spectral line. On the other hand, if inertia has a directional dependence, a triplet or broadened resonance line should be observed. During the 24-hour course of Drever's version of the experiment, the Earth turned, and the magnetic field axis swept different sections of the sky. Drever paid particular attention to the behavior of the spectral line as the magnetic field crossed the center of the galaxy.[A 7] Neither Hughes nor Drever observed any frequency shift of the energy levels, and due to their experiments' high precision, the maximum anisotropy could be limited to 0.04 Hz = 10−25 GeV.

Regarding the consequences of the null result for Mach's principle, it was shown by Robert H. Dicke (1961) that it is in agreement with this principle, as long as the spatial anisotropy is the same for all particles. Thus the null result is rather showing that inertial anisotropy effects are, if they exist, universal for all particles and locally unobservable.[5][6]

Modern interpretation

While the motivation for this experiment was to test Mach's principle, it has since become recognized as an important test of Lorentz invariance and thus special relativity. This is because anisotropy effects also occur in the presence of a preferred and Lorentz-violating frame of reference – usually identified with the CMBR-rest frame as some sort of luminiferous aether (relative velocity ca. 368 km/s). Therefore, the negative results of the Hughes–Drever experiments (as well as the Michelson–Morley experiments) rule out the existence of such a frame. In particular, Hughes-Drever tests of Lorentz violations are often described by a test theory of special relativity put forward by Mark P. Haugan and Clifford Will. According to this model, Lorentz violations in the presence of preferred frames can lead to differences between the maximal attainable velocity of massive particles and the speed of light. If they were different, the properties and frequencies of matter interactions would change as well. In addition, it is a fundamental consequence of the equivalence principle of general relativity that Lorentz invariance locally holds in freely moving reference frames = local Lorentz invariance (LLI). This means that the results of this experiment concern both special and general relativity.[A 1][A 2]

Due to the fact that different frequencies ("clocks") are compared, these experiments are also denoted as clock-comparison experiments.[A 3][A 4]

Recent experiments

Besides Lorentz violations due to a preferred frame or influences based on Mach's principle, spontaneous violations of Lorentz invariance and CPT symmetry are also being searched for, motivated by the predictions of various quantum gravity models that suggest their existence. Modern updates of the Hughes–Drever experiments have been conducted studying possible Lorentz and CPT violation in neutrons and protons. Using spin-polarized systems and co-magnetometers (to suppress magnetic influences), the accuracy and sensitivity of these experiments have been greatly increased. In addition, by using spin-polarized torsion balances, the electron sector has also been tested.[A 5][A 6]

All of these experiments have thus far given negative results, so there is still no sign of the existence of a preferred frame or any other form of Lorentz violation. The values of the following table are related to the coefficients given by the Standard-Model Extension (SME), an often used effective field theory to assess possible Lorentz violations (see also other Test theories of special relativity). From that, any deviation of Lorentz invariance can be connected with specific coefficients. Since a series of coefficients are tested in those experiments, only the value of maximal sensitivity is given (for precise data, see the individual articles):[A 3][A 8][A 4]

Author Year SME constraints Description
ProtonNeutronElectron
Prestage et al.[7]1985 10−27 Comparing the nuclear spin-flip transition of 9Be+ (stored in a penning trap) with a hydrogen maser transition.
Phillips[8]1987 10−27Sinusoidal oscillations were investigated using a cryogenic spin-torsion pendulum carrying a transversely polarized magnet.
Lamoreaux et al.[9]1989 10−29 They induced dipole and quadrupole spin polarization into a vapor of 201Hg, by which quadrupole energy shifts can be observed.
Chupp et al.[10]1989 10−27 Time-dependent quadrupole splitting of Zeeman levels is investigated. 21Ne and 3He gases are polarized by spin exchange and compared.
Wineland et al.[11]1991 10−25 The anomalous dipole-monopole and dipole-dipole couplings are investigated, by examining hyperfine resonances in 9Be+.
Wang et al.[12]1993 10−27 A spin-torsion pendulum carrying a spin-polarized 6Dy–23Fe mass is investigated for sidereal variations.
Berglund et al.[13]199510−2710−3010−27 The frequencies of 199Hg and 133Cs are compared by applying a magnetic field.
Bear et al.[14]2000 10−31 The frequencies of 129Xe and 3He Zeeman masers are compared.
Phillips et al.[15]200010−27 The Zeeman frequency is measured using hydrogen masers.
Humphrey et al.[16]200310−27 10−27 See Phillips et al. (2000).
Hou et al.[17]2003 10−29 See Wang et al. (1993).
Canè et al.[18]2004 10−32 See Bear et al. (2000).
Wolf et al.[19]200610−25 Atomic frequencies are measured using laser cooled 133Cs atomic fountains.
Heckel et al.[20]2006 10−30 They used a spin-torsion pendulum with four sections of Alnico and four sections of Sm5Co.
Heckel et al.[21]2008 10−31 See Heckel et al. (2006).
Altarev et al.[22]2009 10−29 The spin-precession frequencies in stored ultracold neutrons and 199Hg are analyzed.
Brown et al.[23]201010−32 10−33 Comparing the frequencies in a K / 3He comagnetometer.
Gemmel et al.[24]2010 10−32 Comparing the frequencies in a 129Xe / 3He comagnetometer.
Smiciklas et al.[25]2011 10−29 Comparing the frequencies in a 21Ne / Rb / K comagnetometer. Test of the maximal attainable velocity of neutrons.
Peck et al.[26]201210−3010−31 Similar to Berglund et al. (1995).
Hohensee et al.[27]201310−17 Measuring the transition frequencies of two nearly degenerate states of 164Dy and 162Dy. Test of the maximal attainable velocity of electrons.
Allmendinger et al.[28]201310−34 See Gemmel et al. (2010).

Secondary sources

  1. ↑ 1.0 1.1 Will, C. M. (2006). "The Confrontation between General Relativity and Experiment". Living Reviews in Relativity 9 (3). Retrieved June 23, 2011.
  2. ↑ 2.0 2.1 Will, C. M. (1995). "Stable clocks and general relativity". Proceedings of the 30th Rencontres de Moriond: 417. arXiv:gr-qc/9504017. Bibcode:1995dmcc.conf..417W.
  3. ↑ 3.0 3.1 3.2 Kostelecký, V. Alan; Lane, Charles D. (1999). "Constraints on Lorentz violation from clock-comparison experiments". Physical Review D 60 (11): 116010. arXiv:hep-ph/9908504. Bibcode:1999PhRvD..60k6010K. doi:10.1103/PhysRevD.60.116010.
  4. ↑ 4.0 4.1 4.2 Mattingly, David (2005). "Modern Tests of Lorentz Invariance". Living Rev. Relativity 8 (5): 5. arXiv:gr-qc/0502097. Bibcode:2005LRR.....8....5M. doi:10.12942/lrr-2005-5.
  5. ↑ 5.0 5.1 Pospelov, Maxim; Romalis, Michael (2004). "Lorentz Invariance on Trial". Physics Today 57 (7): 40–46. Bibcode:2004PhT....57g..40P. doi:10.1063/1.1784301.
  6. ↑ 6.0 6.1 Walsworth, R.L. (2006). "Tests of Lorentz Symmetry in the Spin-Coupling Sector". Lecture Notes in Physics. Lecture Notes in Physics 702: 493–505. doi:10.1007/3-540-34523-X_18. ISBN 978-3-540-34522-0.
  7. ↑ Bartusiak, Marcia (2003). Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time. Joseph Henry Press. pp. 96–97. ISBN 0425186202. Retrieved 15 Jul 2012. 'I watched that line over a 24-hour period as the Earth rotated. As the axis of the field swung past the center of the galaxy and other directions, I looked for a change,' recalls Drever.
  8. ↑ Hou, Li-Shing; Ni, Wei-Tou; Li, Yu-Chu M. (2003). "Test of Cosmic Spatial Isotropy for Polarized Electrons Using a Rotatable Torsion Balance". Physical Review Letters 90 (20): 201101. arXiv:physics/0009012. Bibcode:2003PhRvL..90t1101H. doi:10.1103/PhysRevLett.90.201101. PMID 12785879.

Primary sources

  1. ↑ Cocconi, G.; Salpeter E. (1958). "A search for anisotropy of inertia". Il Nuovo Cimento 10 (4): 646–651. doi:10.1007/BF02859800.
  2. ↑ Cocconi, G.; Salpeter E. (1960). "Upper Limit for the Anisotropy of Inertia from the Mössbauer Effect". Physical Review Letters 4 (4): 176–177. Bibcode:1960PhRvL...4..176C. doi:10.1103/PhysRevLett.4.176.
  3. ↑ Hughes, V. W.; Robinson, H. G.; Beltran-Lopez, V. (1960). "Upper Limit for the Anisotropy of Inertial Mass from Nuclear Resonance Experiments". Physical Review Letters 4 (7): 342–344. Bibcode:1960PhRvL...4..342H. doi:10.1103/PhysRevLett.4.342.
  4. ↑ Drever, R. W. P. (1961). "A search for anisotropy of inertial mass using a free precession technique". Philosophical Magazine 6 (65): 683–687. Bibcode:1961PMag....6..683D. doi:10.1080/14786436108244418.
  5. ↑ Dicke, R. H. (1961). "Experimental Tests of Mach's Principle". Physical Review Letter 7 (9): 359–360. Bibcode:1961PhRvL...7..359D. doi:10.1103/PhysRevLett.7.359.
  6. ↑ Dicke, R. H. (1964). The Theoretical Significance of Experimental Relativity. Gordon and Breach.
  7. ↑ Prestage, J. D.; Bollinger, J. J.; Itano, W. M.; Wineland, D. J. (1985). "Limits for spatial anisotropy by use of nuclear-spin-polarized Be-9(+) ions". Physical Review Letters 54 (22): 2387–2390. Bibcode:1985PhRvL..54.2387P. doi:10.1103/PhysRevLett.54.2387. PMID 10031329.
  8. ↑ Phillips, P. R. (1987). "Test of spatial isotropy using a cryogenic spin-torsion pendulum". Physical Review Letters 59 (5): 1784–1787. Bibcode:1987PhRvL..59.1784P. doi:10.1103/PhysRevLett.59.1784.
  9. ↑ Lamoreaux, S. K.; Jacobs, J. P.; Heckel, B. R.; Raab, F. J.; Fortson, E. N. (1989). "Optical pumping technique for measuring small nuclear quadrupole shifts in 1S(0) atoms and testing spatial isotropy". Physical Review A 39 (3): 1082–1111. Bibcode:1989PhRvA..39.1082L. doi:10.1103/PhysRevA.39.1082. PMID 9901347.
  10. ↑ Chupp, T. E.; Hoare, R. J.; Loveman, R. A.; Oteiza, E. R.; Richardson, J. M.; Wagshul, M. E.; Thompson, A. K. (1989). "Results of a new test of local Lorentz invariance: A search for mass anisotropy in 21Ne". Physical Review Letters 63 (15): 1541–1545. Bibcode:1989PhRvL..63.1541C. doi:10.1103/PhysRevLett.63.1541. PMID 10040606.
  11. ↑ Wineland, D. J.; Bollinger, J. J.; Heinzen, D. J.; Itano, W. M.; Raizen, M. G. (1991). "Search for anomalous spin-dependent forces using stored-ion spectroscopy". Physical Review Letters 67 (13): 1735–1738. Bibcode:1991PhRvL..67.1735W. doi:10.1103/PhysRevLett.67.1735. PMID 10044234.
  12. ↑ Wang, Shih-Liang; Ni, Wei-Tou; Pan, Sheau-Shi (1993). "New Experimental Limit on the Spatial Anisotropy for Polarized Electrons". Modern Physics Letters A 8 (39): 3715–3725. Bibcode:1993MPLA....8.3715W. doi:10.1142/S0217732393003445.
  13. ↑ Berglund, C. J.; Hunter, L. R.; Krause, D., Jr.; Prigge, E. O.; Ronfeldt, M. S.; Lamoreaux, S. K. (1995). "New Limits on Local Lorentz Invariance from Hg and Cs Magnetometers". Physical Review Letters 75 (10): 1879–1882. Bibcode:1995PhRvL..75.1879B. doi:10.1103/PhysRevLett.75.1879. PMID 10059152.
  14. ↑ Bear, D.; Stoner, R. E.; Walsworth, R. L.; Kostelecký, V. Alan; Lane, Charles D. (2000). "Limit on Lorentz and CPT Violation of the Neutron Using a Two-Species Noble-Gas Maser". Physical Review Letters 85 (24): 5038–5041. arXiv:physics/0007049. Bibcode:2000PhRvL..85.5038B. doi:10.1103/PhysRevLett.85.5038. PMID 11102181.
  15. ↑ Phillips, D. F.; Humphrey, M. A.; Mattison, E. M.; Stoner, R. E.; Vessot, R. F.; Walsworth, R. L. (2000). "Limit on Lorentz and CPT violation of the proton using a hydrogen maser". Physical Review D 63 (11): 111101. arXiv:physics/0008230. Bibcode:2001PhRvD..63k1101P. doi:10.1103/PhysRevD.63.111101.
  16. ↑ Humphrey, M. A.; Phillips, D. F.; Mattison, E. M.; Vessot, R. F.; Stoner, R. E.; Walsworth, R. L. (2003). "Testing CPT and Lorentz symmetry with hydrogen masers". Physical Review A 68 (6): 063807. arXiv:physics/0103068. Bibcode:2003PhRvA..68f3807H. doi:10.1103/PhysRevA.68.063807.
  17. ↑ Hou, Li-Shing; Ni, Wei-Tou; Li, Yu-Chu M. (2003). "Test of Cosmic Spatial Isotropy for Polarized Electrons Using a Rotatable Torsion Balance". Physical Review Letters 90 (20): 201101. arXiv:physics/0009012. Bibcode:2003PhRvL..90t1101H. doi:10.1103/PhysRevLett.90.201101. PMID 12785879.
  18. ↑ Canè, F.; Bear, D.; Phillips, D. F.; Rosen, M. S.; Smallwood, C. L.; Stoner, R. E.; Walsworth, R. L.; Kostelecký, V. Alan (2004). "Bound on Lorentz and CPT Violating Boost Effects for the Neutron". Physical Review Letters 93 (23): 230801. arXiv:physics/0309070. Bibcode:2004PhRvL..93w0801C. doi:10.1103/PhysRevLett.93.230801. PMID 15601138.
  19. ↑ Wolf, P.; Chapelet, F.; Bize, S.; Clairon, A. (2006). "Cold Atom Clock Test of Lorentz Invariance in the Matter Sector". Physical Review Letters 96 (6): 060801. arXiv:hep-ph/0601024. Bibcode:2006PhRvL..96f0801W. doi:10.1103/PhysRevLett.96.060801. PMID 16605978.
  20. ↑ Heckel, B. R.; Cramer, C. E.; Cook, T. S.; Adelberger, E. G.; Schlamminger, S.; Schmidt, U. (2006). "New CP-Violation and Preferred-Frame Tests with Polarized Electrons". Physical Review Letters 97 (2): 021603. arXiv:hep-ph/0606218. Bibcode:2006PhRvL..97b1603H. doi:10.1103/PhysRevLett.97.021603. PMID 16907432.
  21. ↑ Heckel, B. R.; Adelberger, E. G.; Cramer, C. E.; Cook, T. S.; Schlamminger, S.; Schmidt, U. (2008). "Preferred-frame and CP-violation tests with polarized electrons". Physical Review D 78 (9): 092006. arXiv:0808.2673. Bibcode:2008PhRvD..78i2006H. doi:10.1103/PhysRevD.78.092006.
  22. ↑ Altarev, I. et al. (2009). "Test of Lorentz Invariance with Spin Precession of Ultracold Neutrons". Physical Review Letters 103 (8): 081602. arXiv:0905.3221. Bibcode:2009PhRvL.103h1602A. doi:10.1103/PhysRevLett.103.081602. PMID 19792714.
  23. ↑ Brown, J. M.; Smullin, S. J.; Kornack, T. W.; Romalis, M. V. (2010). "New Limit on Lorentz- and CPT-Violating Neutron Spin Interactions". Physical Review Letters 105 (15): 151604. arXiv:1006.5425. Bibcode:2010PhRvL.105o1604B. doi:10.1103/PhysRevLett.105.151604. PMID 21230893.
  24. ↑ Gemmel, C.; Heil, W.; Karpuk, S.; Lenz, K.; Sobolev, Yu.; Tullney, K.; Burghoff, M.; Kilian, W.; Knappe-Grüneberg, S.; Müller, W.; Schnabel, A.; Seifert, F.; Trahms, L.; Schmidt, U. (2010). "Limit on Lorentz and CPT violation of the bound neutron using a free precession He3/Xe129 comagnetometer". Physical Review D 82 (11): 111901. arXiv:1011.2143. Bibcode:2010PhRvD..82k1901G. doi:10.1103/PhysRevD.82.111901.
  25. ↑ M. Smiciklas et al. (2011). "New Test of Local Lorentz Invariance Using a 21Ne-Rb-K Comagnetometer". Physical Review Letters 107 (17): 171604. arXiv:1106.0738. Bibcode:2011PhRvL.107q1604S. doi:10.1103/PhysRevLett.107.171604. PMID 22107506.
  26. ↑ Peck, S.K. et al. (2012). "New Limits on Local Lorentz Invariance in Mercury and Cesium". Physical Review A 86 (1): 012109. arXiv:1205.5022. Bibcode:2012PhRvA..86a2109P. doi:10.1103/PhysRevA.86.012109.
  27. ↑ Hohensee, M.A. et al. (2013). "Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium". Physical Review Letters 111 (5): 050401. arXiv:1303.2747. Bibcode:2013PhRvL.111e0401H. doi:10.1103/PhysRevLett.111.050401. PMID 23952369.
  28. ↑ Allmendinger, F. et al. (2013). "New limit on Lorentz and CPT violating neutron spin interactions using a free precession 3He-129Xe co-magnetometer". Physical Review Letters 112 (11): 110801. arXiv:1312.3225. Bibcode:2014PhRvL.112k0801A. doi:10.1103/PhysRevLett.112.110801. PMID 24702343.

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