On the Measurement of T*

Inspired by Stillman Drake’s definition of G&lean Units as those for which & = (g)g where g is any finite, constant acceleration measured in units of L and T, we construct a lcinematical dimensional analysis based only on two universal, dimensionless constants. For the linear relation between L and T we use Einsteinian Units 6 = (1)~. For orbiting masses negligible compared to some mass unit M, we use Keplerian Units based on his second law $ = (&)&. Then the unit for orbital angular momentum is ti, independent of the mass scale. This allows us to define dimensionless coupling constants f2 = p = i where v is the orbital velocity. We find that most of relativistic quantum mechanics requires only kinematical units. Dynamical units require a mass scale with universal significance, set by the orbital velocity v = c (or f2 = 1). In dimensional form this becomes M = (l)[g]k A ssuming baryon number conservation, the fact that the proton is the lightest stable baryon allows us to calculate fic/Gmz M 1.7 x 1O38 as the Beckenstein number of the proton-the number of bits of information lost in its formation-and connects our units to the elementary particle mass scale. Submitted to the Thirteenth Annual International Meeting of the Alternative Natural Philosophy Association Department of History and Philosophy of Science Free School Lane, Cambridge, England; 12-15 September 1991 ..-.. t *Work supported by Department of Energy contract DE-AC03-76SF00515.