Some consequences of the generalised uncertainty principle: statistical mechanical, cosmological, and varying speed of light

We study the dynamical consequences of Maggiore's unique generalised uncert ainty principle (GUP). We find that it leads naturally, and generically, to novel consequences. In the high temperature limit, there is a drastic redu ction in the degrees of freedom, of the type found, for example, in strings far above the Hagedorn temperature. In view of this, the present GUP may p erhaps be taken as the new version of the Heisenberg uncertainty principle. conjectured by Atick and Witten to be responsible for such reduction. Also , the present GUP leads naturally to varying speed of light and modified di spersion relations. They are likely to have novel implications for cosmolog y and black hole physics, a few of which we discuss qualitatively. (C) 2001 Published by Elsevier Science B.V.