Pitkänen, Matti
(2010)
*A Possible Explanation for Shnoll Effect.*
Prespacetime Journal, 1
(10).
pp. 1545-1561.
ISSN 2153-8301
(Unpublished)

Preview |
PDF
492kB |

## Abstract

Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.

These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.

The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II_1 (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(n| λ<sub>i</sub>) for a positive integer valued variable n characterized by rational-valued parameters λ<sub>i</sub> is obtained by replacing n and the integers characterizing λ<sub>i</sub> with so called quantum integers depending on the quantum phase q<sub>m</sub>=exp(i2π/m). Quantum integer n<sub>q</sub> must be defined as the product of quantum counterparts p<sub>q</sub> of the primes p appearing in the prime decomposition of n. One has p<sub>q</sub>= sin(2π p/m)/sin(2π/m) for p ≠ P and p<sub>q</sub>=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.

The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers P<sup>n</sup> to P<sup>-n</sup> and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ P<sub>n</sub>)=∑ I(P<sub>n</sub>). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n<sup>+</sup>n<sup>-</sup>, n<sup>+</sup><sub>q</sub>>0 with fixed n<sup>-</sup><sub>q</sub>< 0.

The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ k<sub>p</sub>Δ R/R and Δ m/m≈ k<sub>m</sub>Δ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.

Item Type: | Article |
---|---|

Subjects: | Q Science > QC Physics > QC01 Quantum mechanics |

References: | [15] S. E. Shnoll et al (1998), Realization of discrete uctuations in macroscopic processes. Physics- Uspekhi 41 (10), pp. 1025-1035 (1998). http://home.t01.itscom.net/allais/blackprior/ shnoll/shnoll-1.pdf.
[16] V. A. Panchelyuga and S. E. Shnoll (2007) , On the Dependence of a Local-Time Eect on Spatial Direction. Progress in Physics Vol 3, pp. 51-54. http://www.ptep online.com/index_files/ 2007/PP-10-11.PDF. [17] V. A. Panchelyuga and S. E. Shnoll (2007) , On the Dependence of a Local-Time Eect on Moving Sources of Fluctuations. Progress in Physics Vol 3, pp. 55-56. http://www.ptep-online.com/ index_files/2007/PP-10-12.PDF. [18] S. E. Shnoll et al (2005), Experiments with rotating collimators cutting out pencil of -particle at radiactive decay of 239 Pu evidence sharp anisotropy of space. Progress in Physics Vol 1. pp. 81-83. http://www.ptep-online.com/index_files/2005/PP-01-11.PDF. [19] S. E. Shnoll and V. A. Panchelyuga (2008), The Palindrome Eect, Progress in Physics Vol. 2, pp. 151-153. http://www.ptep-online.com/index_files/2008/PP-13-20.PDF. [20] S. E. Shnoll et al (2008), Fine structure of histograms of alpha-activity measurements depends on direction of alpha particles ow and the Earth rotation: experiments with collimators. http://www.cifa-icef.org/shnoll.pdf. [21] V. H. van Zyl (2007), Searching for Histogram Patterns due to Macroscopic Fluctuations in Financial Time Series. Thesis (MSComm(Business-Management))-University of Stellenbosch. https://scholar.sun.ac.za/handle/10019.1/3078. [22] V. Jones (2003), In and around the origin of quantum groups. arXiv:math.OA/0309199. C. Kassel (1995), Quantum Groups. Springer Verlag. C. Gomez, M. Ruiz-Altaba, G. Sierra (1996), Quantum Groups and Two-Dimensional Physics. Cambridge University Press. [23] F. Q. Gouv^ea (1997), p-adic Numbers: An Introduction. Springer. See also p-Adic numbers. http://en.wikipedia.org/wiki/P-adic_number. [24] A. Yu. Khrennikov(1992), p-Adic Probability and Statistics. Dokl. Akad Nauk, vol 433 , No 6 [25] A. Khrennikov, M. Klein, T.Mor (2010), QUANTUMTHEORY: Reconsideration of Foundations- 5. AIP Conference Proceedings, Vol.e1232, pp. 299-305. http://adsabs.harvard.edu/abs/ 2010AIPC.1232..299K. [26] L. H. Kaumann and S. J. Lomonaco Jr. (2004), Braiding operations are universal quantum gates, arxiv.org/quant ph/0401090. [27] S. Sawin (1995), Links, Quantum Groups, and TQFT's. q alg/9506002. [28] Finsler Geometry. http://en.wikipedia.org/wiki/Finsler_geometry. [29] D. Da Roacha and L. Nottale (2003), Gravitational Structure Formation in Scale Relativity. astro-ph/0310036. [30] M. Pitk�anen (2010), Article series about Topological Geometrodynamics in Prespacetime Journal Vol 1, Issue 4. http://www.prespacetime.com/file/PSTJ_V1(4).pdf. [31] M. Pitk�anen (2010), TGD Inspired Theory of Consciousness. Journal of Consciousness Explo- ration & Research, March 2010, Vol. 1, Issue 2, pp. 135-152. http://www.jcer.com/file/JCER_ V1(2).pdf. [32] M. Pitk�anen (2010), Quantum Mind in TGD Universe, Journal of of Consciousness Exploration & Research| November 2010, Vol 1, Issue 8, pp. 971-991. Quantum Dream Inc.. http://www.jcer.com/file/JCER_V1(8).pdf. [33] M. Pitk�anen (2010), Quantum Mind, Magnetic Body, and Biological Body, Journal of of Con- sciousness Exploration & Research, November 2010, Vol 1, Issue 8, pp. pp. 992-1026. Quantum Dream Inc.. http://www.jcer.com/file/JCER_V1(8).pdf. |

ID Code: | 159 |

Deposited By: | Dr Matti Pitkänen |

Deposited On: | 08 Dec 2010 07:43 |

Last Modified: | 06 Feb 2021 14:41 |

Repository Staff Only: item control page