On Lorentz Invariance and the Minimum Length.

It was shown by Kirzhnits and Chechen, following an earlier paper by Mead, that the minimum length scale l is constrained by the Mössbauer effect, which leads to the result cm, assuming the Snyder discrete space–time and conventional nuclides. Here, we note, firstly, that some recently discussed nuclides, for example , have much narrower natural line widths, which, if excited by synchrotron radiation, could potentially decrease the limiting value to cm in future experiments. The Snyder space–time and the superstring theory are both locally Lorentz invariant, and give rise to the same form of generalized indeterminacy principle, if we set , where is the Regge slope parameter, which is thus also constrained by the Mössbauer effect. For the heterotic superstring, in particular, cm, apparently beyond experimental reach. A hadron string theory at energy ~250 MeV, however, would be ruled out, since then cm. We emphasize that these results all presuppose a de Sitter momentum space, for the alternative anti-de Sitter momentum space implies no minimum length scale, and therefore seems unphysical. [ABSTRACT FROM AUTHOR]