Clock hypothesis of relativity theory, maximal acceleration, and Mössbauer spectroscopy

Results obtained several years ago using the high-resolution 93.3 keV Mössbauer resonance in ⁶⁷ZnO and β^′-brass have been reanalyzed with the notion that the clock hypothesis of Special Relativity Theory is not sufficient, but that a maximal acceleration a_m exists and that an acceleration a contributes to the temperature dependence of the center shift by a term ±(1/2)(a/a_m)². The significance of the sign of this term is discussed in detail. For both substances a lower limit of a_m>1.5⋅10²¹m/s ² is inferred which is more than two orders of magnitude larger than - and thus excludes - the value a_m=1⋅10¹⁹m/s ² suggested by ⁵⁷Fe rotor experiments.