An investigation of the entangled photon walk-off compensation generated by a fiber ring resonator

There are two basic number sequences which play a major role in the prime number distribution. The first Number Sequence SQ1 contains all prime numbers of the form 6n+5 and the second Number Sequence SQ2 contains all prime numbers of the form 6n+1. All existing prime numbers seem to be contained in these two number sequences, except of the prime numbers 2 and 3. Riemanns Zeta Function also seems to indicate, that there is a logical connection between the mentioned number sequences and the distribution of prime numbers. This connection is indicated by lines in the diagram of the Zeta Function, which are formed by the points s where the Zeta Function is real. Another key role in the distribution of the prime numbers plays the number 5 and its periodic occurrence in the two number sequences SQ1 and SQ2. All non-prime numbers in SQ1 and SQ2 are caused by recurrences of these two number sequences with increasing wave-lengths in themselves, in a similar fashion as Overtones (harmonics) or Undertones derive from a fundamental frequency. On the contrary prime numbers represent spots in these two basic Number Sequences SQ1 and SQ2 where there is no interference caused by these recurring number sequences. The distribution of the non-prime numbers and prime numbers can be described in a graphical way with a -Wave Model- (or Interference Model) -- see Table 2.

/pdf/about-the-logic-of-the-prime-number-distribution-4pcgx01o1e.pdf

About the Logic of the Prime Number Distribution

Completely entangled quantum states are shown to factorize into tensor products of entangled states whose dimensions are powers of prime numbers. The entangled states of each prime-power dimension transform among themselves under a finite Heisenberg group. We are thus led to examine processes in which factors are exchanged between entangled states and so consider canonical ensembles in which these processes occur. It is shown that the Riemann zeta function is the appropriate partition function and that the Riemann hypothesis makes a prediction about the high temperature contribution of modes of large dimension.

The prime factorization property of entangled quantum states

It is shown that the violation of Bell's inequality allowed by quantum mechanics and the related Bell's theorem without inequalities is accounted for by local commutations of operators representing single-particle observables. It is argued that the idea of nonlocal influencing of one particle on another when they are in spacelike separated regions clearly has neither empirical nor theoretical support.

Locality and Bell's Theorem

Prime numbers, and their distribution in the sequence of natural numbers, are of interest for fundamental as well as practical reasons. The authors introduce a stochastic model based on a network representation that closely matches some statistical properties of the prime numbers, and that can be useful as a tool in the study of the distribution of primes.

/pdf/complex-architecture-of-primes-and-natural-numbers-gd33gxnwnr.pdf

Complex architecture of primes and natural numbers.

It is shown that the algebraic structure of finite Heisenberg groups associated with the tensor product of two Hilbert spaces leads to a simple demonstration valid in all Hilbert space dimensions of the impossibility of non-contextual hidden variables.

Proof of the Impossibility of Non-Contextual Hidden Variables in All Hilbert Space Dimensions

An ambiguity is pointed out in J.S. Bell's argument that the distinction between quantum mechanics and hidden variable theories cannot be found in the behavior of single-particle beams. Within the context of theories for which states are unambiguously defined it is shown that the question of whether quantum mechanics or a locally realistic theory is valid may indeed be answered by single-particle beam measurements. It is argued that two-particle correlation experiments are required to answer the more fundamental question of whether or not the notion of a state can be unambiguously defined. As a byproduct of the discussion the general form of completely entangled states is deduced.

Implications of an Ambiguity in J.S. Bell's Analysis of the Einstein-Podolsky-Rosen Problem

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The prime factorization property of entangled quantum states

Proof of the Impossibility of Non-Contextual Hidden Variables in All Hilbert Space Dimensions

Implications of an Ambiguity in J.S. Bell's Analysis of the Einstein-Podolsky-Rosen Problem