Wednesday, October 17, 2012
Riemann Hypothesis and The Hypergeometrical Universe
Our love for knowledge and beauty has always driven us to find the most sublime analogies to represent what we are seeing in the Universe. Einstein wanted to read God's Mind. The Hypothetical Higgs Boson has been named by some as the God Particle. I equated the steps of my Lightspeed Expanding Hyperspherical Universe as being somewhat similar to the Pendulum of Brahma. At each cycle we see ourselves changed by that Universal Operator.
Mathematics is always the Golden Standard of beauty. We always hope to find a nicely fitting mathematical equation to describe the whole Universe. Mathematicians (String Theorists) are especially hopeful..:). Of course, after all, that would be redemption to their endeavor of creating the least physical (most mathematical) theory in history.
Euler's Beta Function relationship to the Strong Force model was immediately recognized as the sign we are on the right track, after all, for a theory to be correct it has to be aesthetically beautiful….:) Form over content…very typical of our Mankind always driven by superficial calculations….:)
It just happens that there isn't any indication that physics doesn't matter, that is, there isn't any indication that at the end of all, we will have everything described by a simple mathematical equations that overrules all physical properties.
For example, there is the wave equation which describes all waves as long as they have a natural velocity or one knows the elasticity of the medium where those waves propagate. This means that even though we have the knowledge of an equation which would describe such a general phenomena as waves, the physics is still there in the form of a pesky constant.. :)
This does not demerit the scientists who found those beautiful equations, it just serves as a reminder that there might be a limit on what mathematical abstraction can achieve.
It has been said with some understated deepness that the Riemann Hypothesis might be the solution to the Theory of Everything, that is, something, some force, some string might be represented somehow by the zeros of the Zeta function along the critical line. The details are fuzzy since this is just a wild (albeit educated..:) guess...:)
Scientists look down to Horoscopists all their lives…:) It is well know that vague statements can always find resonance within some fraction of the population and thus keep the readers happy and aware of their daily best options…
One might say that the same happens in Science. There is a difference. Since we are a much more educated bunch than the average person, our guesses are better educated..:) that is, there is something deep in the number theory applied to Primes..:)
Of course, this is just because people doesn't know how to think about numbers and one should expect that if the zeros of an equation are primes, most likely the logic behind the construction of the equation is such that only certain primes will be zeros..:)
It is like being surprised that f(x)=(x-1)*(x-2) has zeros equal to 1 and 2.
Number theory is just not developed enough to see the underlying logic behind the Riemann Hypothesis and the Zeta Function (or Eta Function on the Analytic Continuation).
As usual, the statement that the Riemann Hypothesis should be relevant to our understanding of the Universe can be decomposed into the simpler statement that Primes will be relevant..:) I am a simple minded man, so I will cut to the chase and explore this proposition..:)
Nobody bothered to think about Primes because nothing in Physics looks like Primes. If a poor string theorist looks around and think about making Primes to be some property of strings them we might end up with 10^500000000000000 possible Universes with different string theories explaining each one of them..:)
A Standard Model Physicist is not in much better position. Let say that zero are electromagnetic waves, the ONE is… The next basic particles are electron and Proton … Neutron might be TWO but that does not solve the problem. Electrons and Protons are certainly not equal in the Standard Model and the analogy dies there…:)
Of course, that is not the case in the Hypergeometrical Universe.
Posted by Marco Pereira at 11:30 AM