THE CONCEPT OF TIME IN 2D GRAVITY

We show that the ''time'' t(s) defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension d(h)(s) = 6 o f space-time at the critical point, as advocated by Ishibashi and Kawa i. In the unmagnetized phase, however, this definition of Hausdorff di mension breaks down. Numerical measurements are consistent with these results. The same definition leads to d(h)(s) = 16 at the critical poi nt when applied to at space. The fractal dimension d(h)(s) is in disag reement with both analytical prediction and numerical determination of the fractal dimension d(h)(g), which is based on the use of the geode sic distance t(g) as ''proper time''. There seems to be no simple rela tion of the kind t(s) = t(g)(dh(g)/dh(s)), as expected by dimensional reasons.