We consider briefly the problem of increasing the accuracy of observation of the effects of displacement energy gamma rays in nuclear gamma-resonance. Set out the reasons for the need for repeated experiments, described the theory of relativity and gravity on Earth at a higher level of accuracy (above 1 %). The method of detecting nuclear gamma-resonance spectra of rotating objects with high accuracy was proposed. The evaluation of the experimental results obtained under different conditions was carried out. The possibility of experimental verification of a brand new approach to relativistic phenomena description was considered. It is the extended relativistic theory that predicts the existence of the maximum acceleration.

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