Hughes–Drever experiments (alsoclock comparison-,clock anisotropy-,mass isotropy-, orenergy isotropy experiments) arespectroscopic tests of theisotropy ofmass andspace. Although originally conceived of as a test ofMach's principle, they are now understood to be an important test ofLorentz invariance. As inMichelson–Morley experiments, the existence of apreferred frame of reference or other deviations from Lorentz invariance can be tested, which also affects the validity of theequivalence principle. Thus these experiments concern fundamental aspects of bothspecial andgeneral relativity. Unlike Michelson–Morley type experiments, Hughes–Drever experiments test the isotropy of the interactions of matter itself, that is, ofprotons,neutrons, andelectrons. The accuracy achieved makes this kind of experiment one of the most accurate confirmations of relativity (see alsoTests of special relativity).^{[1][2][3][4][5][6]}

Giuseppe Cocconi andEdwin Ernest Salpeter (1958) theorized thatinertia depends on the surrounding masses according toMach's principle. Nonuniform distribution of matter thus would lead toanisotropy 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 ourMilky Way galaxy. They argued that this anisotropy might be observed in two ways: measuring theZeeman splitting in an atom^[7] or measuring the Zeeman splitting in theexcited nuclear state of⁵⁷
Fe using theMössbauer effect.^[8]

Vernon W. Hugheset al. (1960)^[9] andRonald Drever (1961)^[10] independently conducted similarspectroscopic experiments to test Mach's principle. However, they didn't use the Mössbauer effect but mademagnetic resonance measurements of thenucleus oflithium-7, whoseground state possesses aspin of3⁄2. The ground state is split into four equally spaced magneticenergy levels when measured in a magnetic field in accordance with its allowedmagnetic 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.^[11] 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 byRobert 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.^[12][13]

While the motivation for this experiment was to test Mach's principle, it has since become recognized as an important test ofLorentz invariance and thusspecial relativity. This is because anisotropy effects also occur in the presence of apreferred and Lorentz-violating frame of reference – usually identified with theCMBR rest frame as some sort ofluminiferous aether (relative velocity about 368 km/s). Therefore, the negative results of the Hughes–Drever experiments (as well as theMichelson–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 byClifford 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 theequivalence principle ofgeneral 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.^[1][2]

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

Besides Lorentz violations due to a preferred frame or influences based on Mach's principle, spontaneous violations of Lorentz invariance andCPT symmetry are also being searched for, motivated by the predictions of variousquantum gravity models that suggest their existence. Modern updates of the Hughes–Drever experiments have been conducted studying possible Lorentz and CPT violation inneutrons andprotons. Usingspin-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-polarizedtorsion balances, theelectron sector has also been tested.^[5][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 theStandard-Model Extension (SME), an often usedeffective field theory to assess possible Lorentz violations (see also otherTest 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):^[3][14][4]

• T. Roberts (2007) & S. Schleif, Relativity FAQ,What is the experimental basis of Special Relativity?

• Tests of special relativity
• Tests of general relativity