# Hughes–Drever experiment

Hughes–Drever experiments (also clock comparison-, clock anisotropy-, mass isotropy-, or energy isotropy experiments) are spectroscopic tests of the isotropy of mass and space. Although originally conceived of as a test of Mach's principle, they are now understood to be an important test of Lorentz invariance. 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).

## 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 or measuring the Zeeman splitting in the excited nuclear state of $^{57}$ Fe using the Mössbauer effect.
Vernon W. Hughes et al. (1960) and Ronald Drever (1961) 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. Neither Hughes nor Drever observed any frequency shift of the energy levels, and due to their experiments' high precision, the maximal 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.

## 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 about 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 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.
Due to the fact that different frequencies ("clocks") are compared, these experiments are also denoted as clock-comparison experiments.

## 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.
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):
| Author | Year | SME constraints | SME constraints | SME constraints | Description |
| Author | Year | Proton | Neutron | Electron | Description |
| Prestage et al. | 1985 | | 10$^{−27}$ | | Comparing the nuclear spin-flip transition of $^9$ Be$^+$ (stored in a penning trap) with a hydrogen maser transition. |
| Phillips | 1987 | | | 10$^{−27}$ | Sinusoidal oscillations were investigated using a cryogenic spin-torsion pendulum carrying a transversely polarized magnet. |
| Lamoreaux et al. | 1989 | | 10$^{−29}$ | | They induced dipole and quadrupole spin polarization into a vapor of $^{201}$ Hg , by which quadrupole energy shifts can be observed. |
| Chupp et al. | 1989 | | 10$^{−27}$ | | Time-dependent quadrupole splitting of Zeeman levels is investigated. $^{21}$ Ne and $^3$ He gases are polarized by spin exchange and compared. |
| Wineland et al. | 1991 | | | 10$^{−25}$ | The anomalous dipole-monopole and dipole-dipole couplings are investigated, by examining hyperfine resonances in $^9$ Be$^+$ . |
| Wang et al. | 1993 | | | 10$^{−27}$ | A spin-torsion pendulum carrying a spin-polarized Dy–Fe mass is investigated for sidereal variations. |
| Berglund et al. | 1995 | 10$^{−27}$ | 10$^{−30}$ | 10$^{−27}$ | The frequencies of $^{199}$Hg and $^{133}$Cs are compared by applying a magnetic field. |
| Bear et al. | 2000 | | 10$^{−31}$ | | The frequencies of $^{129}$ Xe and $^3$ He Zeeman masers are compared. |
| Phillips et al. | 2000 | 10$^{−27}$ | | | The Zeeman frequency is measured using hydrogen masers. |
| Humphrey et al. | 2003 | 10$^{−27}$ | | 10$^{−27}$ | Similar to Phillips et al. (2000). |
| Hou et al. | 2003 | | | 10$^{−29}$ | Similar to Wang et al. (1993). |
| Canè et al. | 2004 | | 10$^{−32}$ | | Similar to Bear et al. (2000). |
| Wolf et al. | 2006 | 10$^{−25}$ | | | Atomic frequencies are measured using laser cooled $^{133}$ Cs atomic fountains. |
| Heckel et al. | 2006 | | | 10$^{−30}$ | They used a spin-torsion pendulum with four sections of Alnico and four sections of Sm$_5$Co. |
| Heckel et al. | 2008 | | | 10$^{−31}$ | Similar to Heckel et al. (2006). |
| Altarev et al. | 2009 | | 10$^{−29}$ | | The spin-precession frequencies in stored ultracold neutrons and $^{199}$ Hg are analyzed. |
| Brown et al. | 2010 | 10$^{−32}$ | 10$^{−33}$ | | Comparing the frequencies in a K / $^3$ He comagnetometer. |
| Gemmel et al. | 2010 | | 10$^{−32}$ | | Comparing the frequencies in a $^{129}$ Xe / $^3$ He comagnetometer. |
| Smiciklas et al. | 2011 | | 10$^{−29}$ | | Comparing the frequencies in a $^{21}$ Ne / Rb / K comagnetometer. Test of the maximal attainable velocity of neutrons. |
| Peck et al. | 2012 | 10$^{−30}$ | 10$^{−31}$ | | Similar to Berglund et al. (1995). |
| Hohensee et al. | 2013 | | | 10$^{−17}$ | Measuring the transition frequencies of two nearly degenerate states of $^{164}$ Dy and $^{162}$ Dy . Test of the maximal attainable velocity of electrons. |
| Allmendinger et al. | 2013 | | 10$^{−34}$ | | Similar to Gemmel et al. (2010). |

## Secondary sources

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* 1 2 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.
* 1 2 3 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. S2CID 119039071.
* 1 2 3 Mattingly, David (2005). "Modern Tests of Lorentz Invariance". Living Rev. Relativ. 8 (5): 5. arXiv:gr-qc/0502097. Bibcode:2005LRR.....8....5M. doi:10.12942/lrr-2005-5. PMC 5253993. PMID 28163649.
* 1 2 Pospelov, Maxim; Romalis, Michael (2004). "Lorentz Invariance on Trial" (PDF). Physics Today. 57 (7): 40–46. Bibcode:2004PhT....57g..40P. doi:10.1063/1.1784301. Archived from the original (PDF) on 2022-01-02. Retrieved 2011-05-26.
* 1 2 Walsworth, R. L. (2006). "Tests of Lorentz Symmetry in the Spin-Coupling Sector" (PDF). Special Relativity. Lecture Notes in Physics. Vol. 702. pp. 493–505. doi:10.1007/3-540-34523-X_18. ISBN 978-3-540-34522-0.
* ↑ 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.
* ↑ 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. S2CID 28211115.

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* ↑ 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.
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* ↑ 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.
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* ↑ Phillips, D. F.; Humphrey, M. A.; Mattison, E. M.; Stoner, R. E.; Vessot, R. F.; Walsworth, R. L. (2001). "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. S2CID 10665017.
* ↑ 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. S2CID 13659676.
* ↑ 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. S2CID 28211115.
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* ↑ 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. S2CID 118438569.
* ↑ 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. S2CID 17459575.
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* ↑ 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. S2CID 27090952.
* ↑ Allmendinger, F.; et al. (2014). "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. S2CID 8122573.