Mössbauer experiments in a rotating system and physical interpretation of their results

We discuss the results of modern Mössbauer experiments in a rotating system, which show the presence of an extra energy shift between the emitted and absorbed resonant radiation in addition to the relativistic energy shift of the resonant lines due to the time dilation effect in the co-rotating source and absorber with different radial coordinates. We analyse the available attempts to explain the origin of the extra energy shift, which include some extensions of special theory of relativity with hypothesis about the existence of limited acceleration in nature, with hypothesis about a so-called «time-dependent Doppler effect», as well as in the framework of the general theory of relativity under re-analysis of the metric effects in the rotating system, which is focused to the problem of correct synchronisation of clocks in a rotating system with a laboratory clock. We show that all such attempts remain unsuccessful until the moment, and we indicate possible ways of solving this problem, which should combine metric effects in rotating systems with quantum mechanical description of resonant nuclei confined in crystal cells.