From Craig Hogan's paper 0706.1999: "[W]ere there no holographic uncertainty, it would be possible to find many distinguishable inward trajectories for particles [...] that would end up creating exactly indistinguishable black hole states. [...] Holographic uncertainty offers a way to resolve the contradiction in a way that respects the continuity of the trajectories of evaporated particles. The distant spacetime does not have so many independent degrees of freedom: all those apparently dierent inward traveling particle states are not actually independent states. The problem is solved for black holes of any size if the holographic limit on the number of angular states as a function of distance applies to at spacetime generally." Does one really need a modification of the usual uncertainty to avoid such a contradiction? Suppose you have a shell of particles that will be forming the black hole. How many dof can these have? Consider one particle in place (0,0,0) and the black hole would be formed in z direction, after the particle had traveled distance D (and there met with all the other particles to collapse). Thus, the particle needs to be aimed precisely enough to end up inside the Schwarzschild horizon. The uncertainty in momentum in the transverse directions thus has to be \Delta p_x / p_z < R_H/D where p_x is the momentum in x-direction etc, and a similar relation for the y-direction. (This isn't exactly right as the curves of the particles are not tangential to the Schwarzschild sphere, but actually intersect it at a shorter distance, but at distances much larger than the radius this is an arbitrarily good approximation). Plugging in the usual Heisenberg uncertainty, one finds \Delta x > D/( R_H p_z ) Squaring this, we can devide up the shell into the areas determined by this uncertainty and find that the number of patches that fit on the sphere (N_S) is N_S < D^2/Delta x^2 < R_H^2 p_z^2 Where p_z should be understood as the radial coordinate now. Now from Hogan's argument, the number of dof on the shell should not be larger than that of the black hole formed, that would be N_BH = R_H^2/l_p^2. Thus one has a problem if N_S > N_BH (*) which, putting in the above leads to p_z > m_p (where m_p = 1/ l_p is the Planck mass). However, if I have the shell with all these particles, each with momentum > m_p, then the mass (M) of the black hole I will be creating must be larger than the number of particles times at least this energy, thus M > R_H^2 p_z^3 > R_H^2 m_p^3 = M^2/m_p or m_p > M, meaning (*) only poses a problem if the mass of the black hole is below the Planck mass. That is as far as the creation of a black hole is concerned. Looking at the evaporation of a black hole, for one the question how much information could have been encoded in the radiation when measured at a very large distance doesn't change how many indeed were encoded, but besides this the average energy of the emitted particles is ~ 1/R_H which is < m_p again as long as M < m_p. Thus it seems the usual uncertainty relation is sufficient to deal with the problem Hogan is concerned about. ?