gill1109 wrote:I think you are forgetting Pearle's equation (22) for the probability density of r and equation (4) relating beta and r. He has a sphere of random radius r < 1 in his story. One has to translate it into a story with a fixed radius 1 by projecting the smaller sphere outward to the bigger 1. As I read him, formula (23) for g is *derived* from the other choices. So it's (22) which needs to be programmed, not (23).
B****y hard paper to read!
Phil's paper is not all that difficult to understand. Apart from some details, his logic is quite straightforward and easy to follow.
I have not forgotten his eq. (22), which is an explicit expression for the probability density
as a function of
. But this probability density is integrated out to obtain the solution (23) he is after. It is only the fraction
that appears on the LHS of eq. (5) for quantum probabilities. Once an explicit solution for the fraction
is found---as he does in eq. (23)---there is no need to worry about
anymore, because it has been integrated out to obtain
. The only
ad hoc choice he makes in deriving the fraction is that of
, but even this choice is rendered irrelevant by normalization. He does note, however, that "the fraction of undetected events can be reduced somewhat by a different choice of
; the extent of this reduction is an open question." So his solution is not all that "unique" after all.