Science > Physics > Quantum Gravity 87.2: Re Prime Variables and Prime Numbers
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
05 Feb 2007 10:19:33 PM |
| Object: |
Quantum Gravity 87.2: Re Prime Variables and Prime Numbers |
From Osher Doctorow
It turns out that not only is it probably true that:
1) p = p1 + p2 + ... + pn
for any prime p, some primes p1 + p2 + ... + pn, n > 1
integer, but also that via the very likely Strong and
Weak Goldbach Conjectures (Christian Goldbach,
1690-1764, an associate of Euler), that:
2) k = p1 + p2 + p3
for any positive integer k > 1. See Wikipedia's "Prime
Numbers" and references therein for more on this and
also for the reasons why most mathematicians consider
the Strong and Weak Goldbach Conjectures to probably
be true (probability is involved in it).
There is also another Conjecture, the Weak Polignac's
Conjecture:
3) 2k = p1 - p2
which says that every even integer is the difference of two
primes.
When we compare these results with the well-known
factorization of integers into products of primes to
various powers (a unique factorization up to order of
factors), we see that the division of integers into sums
of at most 3 primes (and for even integers, the difference
of at most two primes) simplifies representations by
typically many orders of magnitude.
Can it be that the same thing holds in physics for
"prime" observable variables, that is to say that if a
variable p represents an observable and is not the
product of two other observables or their representations,
then we have (with p1, p2, p3 some prime observables):
1.1) p = p1 + p2 + p3 (all pi different from p, i = 1 to 3)
As I pointed out earlier in this thread, we really don't need
to be that strict, and it would be good enough to show:
2.1) p = p1 + p2 + p3 + ... + pn
But (1.1) is interesting because there are three spatial
dimensions and one time dimension, so that if we add
a fourth variable p4 on the right hand side of (1.1)
instead of (1.1), we would arguably have a (3 + 1)-
dimensional representation of observables. Of course,
with (2.1) we might have for n = 10 or 11 a corresponding
Superstring representation of observables.
It is true that real numbers and real-valued functions do
not have just the properties of integers, but it is also true
that integers are among the most intuitive numbers
because they are counting numbers or their negatives,
and counting n objects is arguably the most fundamental
mathematical operation or process both theoretically and
intuitively, and practically.
Beyond this, a corresponding result can arguably be expected for
any physical variable, whether observable or not, namely
that such a variable v is the sum of "prime" observables
or their representations.
The picture that emerges from the simple equation
P(A-->B) = 1 + y - x in Probable Influence/Causation has
taken us into a fundamental sum/difference representation
of observables or their representations or at least its
well-motivated possibility. This doesn't destroy
multiplication or division, but it makes addition and
subtraction much more plausibly alternatives to the use
of the former two operations throughout physics and
mathematics.
Osher Doctorow
where n is an integer > 1.
Yet (1)
.
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