I have already earlier mentioned the work of Russian scientist Shnoll concerning random fluctuations. This work spans four decades and has finally started to gain recognition also in west. By a good luck I found from web an article of Shnoll about strange regularities of what should be random fluctuations. Then Dainis Zeps provided me with a whole collection of similar articles! Thank you Dainis!
The findings of Shnoll led within few days to a considerable progress in the understanding of the relation between p-adic and real probability concepts, the relationship between p-adic physics and quantum groups emerging naturally in TGD based view about finite measurement resolution, the relationship of the hierarchy of Planck constants (in particular the gigantic gravitational Planck constant assignable to the space-time sheets mediating gravitation) and small-p p-adicity, and also with the understanding of the experimental implications of many-sheetedness of space-time in concrete measurement situations in which the measurement apparatus also means non-trivial topology of the space-time.
The most important conclusion is that basic vision about TGD Universe seems manifest itself directly in quantum fluctuations due to quantum coherence in astrophysical scales in practically all kinds of experiments- even in the distributions of financial variables! Needless to tell how far reaching the implications are for quantum gravity. This is one of the biggest surprises of my un-paid professional life which outshines even the repeated surprises caused by the incredibly unintelligent response of most colleagues to my work! I glue below an abstract of a brand new preprint titled A possible Explanation of Shnoll Effect. I attach below the 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 II1 (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| λi) for a positive integer valued variable n characterized by rational-valued parameters λi is obtained by replacing n and the integers characterizing λi with so called quantum integers depending on the quantum phase qm=exp(i2π/m). Quantum integer nq must be defined as the product of quantum counterparts pq of the primes p appearing in the prime decomposition of n. One has pq= sin(2π p/m)/sin(2π/m) for p ≠ P and pq=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 Pn to P-n 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(∑ Pn)=∑ I(Pn). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n+n-, n+q>0 with fixed n-q< 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≈ kpΔ R/R and Δ m/m≈ kmΔ 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.
For detals see the new chapter A Possible Explanation of Shnoll Effect.