Natural Science Forum / Physics / General Physics / July 2008

From Osher Doctorow

A. M. (Mary) Selvam of the Indian Institute of Tropical Meterology
Pune India (Retired), who has many papers on arXiv through 2008, has
an especially interesting (arguably) paper:

1) "Quantum-like chaos in prime number distribution and in turbulent
fluid flows," arXiv: physics/0005067 v2 [physics.gen-ph] 10 Aug 2000.

The prime numbers turn out to be analogous to dominant eddies in the
eddy continuum in turbulent fluid flow, and the prime number frequency
spectrum appears to follow quantum-like mechanics laws.   There also
is a strong correspondence with the prime number theorem.

One of the reasons for the relative lack of interest of numerical/
combinatorics mathematicians in Causation relationships between primes
or between primes and even integer or analogous relationships in
physics is, and vice versa for physicists, in my opinion, the fact
that the Prime Number Theorem gives an approximation to the number of
primes less than or equal to a particular real number x which
approximation involves x/ln(x), giving researchers the rather
misleading focus on the relationship between x and ln(x) or even the
integral of 1/ln(x) dx from 2 (or another lower limit) to n rather
than on relationships among primes or between primes and even numbers
and so on.

There certainly is something to study in x/ln(x) and the integral of 1/
ln(x), but logarithms in other branches of mathematics have turned out
to be far less valuable than exponentials, especially in relation to
physics, and this seems to be the case here.   I will try to discuss
the Prime Number Theorem in more detail in the future.

Osher Doctorow