Natural Science Forum / Physics / General Physics / July 2008

From Osher Doctorow

Pigod Nicolini of U. Trieste and INFN Trieste Italy, the paper
reviewed by J.C.A. Miller-Jones of NRAO (National Radio Astronomy
Observatory Headquarters Charlottesville Virginia USA - the latter
himself has 28 papers in arXiv starting from Oxford to Netherlands to
NRAO), 47 pages, arXiv: 0807.1939 v1 [hep-th] 11 Jul 2008,
"Noncommutative black holes, the final appeal to quantum gravity: a
review," raises some questions that arguably go beyond his own
questions and even his own conjectures.

The most deep question that I can find is: What exactly is generating
the research into Noncommutativity (NC for short)?   On the surface,
it looks like NC is a "natural" outcome of problems not solved by
other methods, and this is what the above paper indicates.  But like
most NC papers that I have read, this paper lacks clear summaries or
even comprehensive conclusions.  We know that Noncommutativity (NC)
began in earnest in France via Alain Connes, itself during a period
when France itself was rather difficult for USA people to relate to
(to say the least) at least in politics.  Connes appears to be unable
to clearly summarize his theory, so perhaps France is awaiting its
popularizers like Briane Greene and M. Kaku and even Sir Roger
Penrose, although it would be somewhat more "respectable" for arXiv to
have a clear and concise summary of Connes' and his physics
successors'/collaborators' theories.

The outcome of the Nicolini paper is even more curious.  It may be a
coincidence, but the key equations that he obtains in the first 21
pages of his 77 pages paper involve prominently two special gamma
functions called "lower incomplete gamma functions", namely:

1) g(1/2, r^2/4 theta) = I dt t^(-1/2) exp(-t), I...dt integral from 0
to r^2/4theta
2) g(3/2, r^2/ 4theta) = I dt t^(1/2) exp(-t)

unless I have made a typographical error on the (1/2) in the right
hand side of (2).

But gamma functions only come from Probable Causation/Influence
maximum entropy, not from any other type of maximum entropy.  So
either the paper has these equations as coincidence with Probable
Causation/Influence (PI), or PI is a much simpler way to derive its
results, or I should be overjoyed to find that PI and Noncommutative
Theory overlaps so well with black hole Quantum Gravity despite the
fact that the latter theorists seem to be unable to summarize anything
even remotely as simple as PI.  Readers will have to read the Nicolini
paper to see for themselves.  Even the physics/astrophysics and
physical/astrophysical assumptions of the paper seem to lack
reasonable length summaries, so it might be a long reading session.

Osher Doctorow