Testing the time-invariance of fundamental constants using cold and not-so-cold molecules

The equivalence principle of general relativity postulates that the outcome of any non-gravitational experiment is independent of position and time. At a first glance, the equivalence principle seems a bare minimum for a selfconsistent theory, but in fact, many theories that attempt to unify gravity with other fundamental forces violate this principle. The Kaluza-Klein theories from the 1920s as well as modern string theories, for instance, introduce additional compactified dimensions, and the size of these – yet unobserved – dimensions determines the strength of the fundamental forces. If the size of these dimensions should happen to change over time, the strength of the forces in four-dimensional space-time would change as well. Such a change would manifest itself as a change of the coupling constants and particle masses [1]. Therefore, by monitoring the time-invariance of these constants one might hope to get a glance of physics beyond the standard model. With this motivation, many studies have been, and are being, performed to search for variations of fundamental constants. Interestingly, two recent astrophysical studies by Murphy et al. [2] and by Reinhold et al. [3] have reported a small but significant time-variation of – the fine structure constant representing the strength of the electro-weak force – and the proton-electron mass ratio, =mp/me – which is a measure for the strength of the strong force. Murphy et al. have looked at absorptions of various atoms in the spectra of distant quasars. They make use of the fact that due to relativistic contributions the hyperfine-splitting in atoms depends on Z , with Z being the atomic number. By comparing different atomic species they infer both the red shift due to the expansion of the universe (which is used to calculate the look-back time) and z/ 0, where z is the fine-structure constant at the epoch when the light was absorbed, and 0 is the present value of the fine structure constant. Their results suggest that has changed by 1 part in 100 thousand over the last ten billion years, corresponding to a change of 10/yr if one assumes a linear cosmologic expansion model. Reinhold et al. have looked at absorption of molecular hydrogen in quasar systems. The spectra of molecules depend both on and on the proton-to-electron mass ratio, . Reinhold et al. found an indication that has changed by two parts in 10 over cosmological time. If one assumes that the constants change linearly over time, this implies a fractional change on the order of 10 per year. To test the time-variation of fundamental constants in the current epoch, frequency standards based on different atomic and molecular transitions are being compared as a function of time. As these standards have in general a different dependence on and , a possible time-variation of and/or will lead to a frequency shift. The sensitivity of an experiment looking for an effect due to a linear change of a fundamental constant, X, can be expressed as;