## Τρίτη, 11 Απριλίου 2017

### A "Solution" to Riemann Hypothesis

Riemann hypothesis is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$". The Riemann zeta function is conventionally represented as the sum:
$\zeta \left(z\right)=\sum _{k=1}^{\infty }\frac{1}{{k}^{z}}$
Recently, I read in Peter Woit's blog that some researchers have published a paper that describes a  Hamiltonian operator H that can be used to possibly solve this problem. This operator has the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function! The paper is also available as a preprint. In a sense, this paper says that one can set up a quantum system whose evolution "solves" Riemann hypothesis. To me this is a reasonable approach to the solution of the problem. And it reminds me of the work of  Leonard Adlemam.

## Κυριακή, 22 Ιανουαρίου 2017

### Multiverse and Computation

The idea that quantum computation is a manifestation of the multiverse is not new. For example, David Deutsch believes that quantum computers can be used to test its existence. Personally I believe that the multiverse is good for scripts of scifi series (e.g., the Fringer) but that's all. But I think that something is also logically wrong with this idea.

Roughly, the multiverse is the idea that there many copies of our universe (or some universe) and each evolves differently, yet in each one of them there is a copy of me but all these copies are different pairwise. Obviously, at each moment many things happen that can have different outcomes so in one universe a spermatozoon fuses with an ovum while in another this never happens but in another universe a different spermatozoon fuses with it. Practically, this means that in the first universe person A will be born, in the second nothing will happen while in the third person B will be born. If all these things are quite possible (!), I wonder how and why a quantum computer would synchronize all these universes? In most of these universes there is no parallel of myself so who is going to participate in the computation that I just started?

In my opinion, hypercomputation is the idea that we do not know enough physics to definitely say that the Turing machine dictates what can and what cannot be computed. On the other hand, the multiverse, in general, and Deutsch's ideas, are about the certitude that
• the multiverse exists
• there are different forms of ourselves in parallel universes
• quantum computation takes place simultaneously in a number of universes
Some call this science but I call it pseudoscience!

### A "Solution" to Riemann Hypothesis

Riemann hypothesi s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex n...