Friday, October 31, 2008

Prime Numbers and Quantum Mechanics

The more I hear about mathematics and about physics the more I think that they are the same. It's strange and surprising to me that the most obscure studies of maths seem to bear the closest relationship to the real world. To me, chaos theory and quantum mechanics in particular seem to connect.

Chaos theory is about stability and turbulence. Chaos is a rather inaccurate term for the pseudo-random turbulence that can occur in any stable system, because it implies a total lack of structure and negative human ideas like futility or panic. Chaotic turbulence might be uncontrollable, and unpredictable on a local level, but it is not random and is predictable, and controllable, on a global statistical level.

I became aware that the world is full of periods of stability then a period of chaos. Financial systems are well cited examples of systems where a long period of steady stability is interspersed with other periods of chaotic activity which eventually results in a new steady state. I began to see that this occurs in many systems, including politics, societies, people's lives, and thought patterns.

I began to think of the quantum world, the sub-atomic world where local events can be fundamentally unpredictable but global events are highly predictable in terms of probability. I thought that this too was a representation of stability and chaos. Then I thought of the number line. Some numbers are more stable than others. I thought that irrational numbers were chaotic, and rational numbers more stable. Prime numbers seemed more stable still.

I began to wonder if quantum certainty could be a prime number and uncertainty be an irrational number, and then began to consider the statistical relationship of prime to irrational numbers.

Then I began to think that the certainty and predictability of prime numbers, which like quantum events are individually unpredictable but statistically highly predictable. I began to think that quantum physics was pointing towards some problems in mathematics relating to primes, such as the Riemann hypothesis and Goldbach's conjecture.

If this is correct then the matrix mathematics of the Heisenberg uncertainty principle that explains the fundamental unpredictability of atoms can also prove the fundamental unpredictability of prime numbers, and can also prove the statistical probabilities of primes in the same way. If proved, then any problem dependent on the predictability of prime numbers can also be shown to be unprovable, but statistically likely.

No comments :