MAX PRINCIPLE AND UNIVERSAL SPECTRUM OF PERIODS: COMPLEMENTARY FRACTAL DISTRIBUTIONS AS CONSEQUENCE OF RATIONAL AND IRRATIONAL RELATIONS BETWEEN PARTS OF THE WHOLE SYSTEM

The paper discusses the assumption that Mach principle should result in existence of a universal spectrum of periods. It is shown that fragments of such a spectrum were found in time series of fluctuations of various processes. A general approach is considered that demonstrates the emergence of discrete states in the spectra of periods, which is based on two basic concepts: resonance and roughness of a physical system. This approach leads to the existence of two complementary fractal distributions associated with sets of rational and irrational relations between the elements of the whole system. A brief review of works that also consider universal spectra of periods is given.

MACH PRINCIPLE AND PRINCIPLE OF RELATIVITY

The article considers the “many-faced” Mach principle and the principle of relativity, which are organically related due to the unity of nature, and provides a brief historical overview of the primary sources of these principles. Ernst Mach formulated his principle by criticizing Newtonian mechanics in his book [1] in 1896. A. Einstein, first using the term “Mach principle” in 1918, wrote that the general theory of relativity is based on three main points, one of which was the Mach principle [2. P. 613]. Currently, Mach principle is used as one of the three main provisions of the relational theory of Yu.S. Vladimirov [3]. The article also describes A. Einstein’s thought experiment from the article “Is there a gravitational effect similar to electrodynamic induction?” [2. P. 223] and about numerous experiments based on various physical principles, with the aim of checking Mach principle.

FROM GEORG CANTOR TO ERNST MACH

In the review, in the context of the ideas of E. Mach, one of the key problems of modern natural science is touched upon: the correlation of “reductionism” and “holism”. If the idea of reductionism was unprecedentedly developed in the framework of the theory of sets and the Bourbaki program, then the Mach principle, as well as other ideas of the philosopher, are only on the rise. Nevertheless, there is a clear realization that the future lies behind these ideas and the book under review in this context seems extremely important.

MACH PRINCIPLE AND SPACE-TIME METRIC

There are five arguments in favor of the statement that the metric (the concepts of lengths, intervals, time intervals) is determined by the influences of the entire surrounding world on the properties of the observed objects: 1) logical consequences of recognizing the relational nature of classical space-time and describing interactions based on the concept of long-range, 2) sequential relational interpretation of the Feynman - Wheeler absorber theory, 3) comparison of electromagnetic radiation densities and “scattering” galaxies, 4) mathematicians changing the axiom of Archimedes, 5) keeping the ideas of “metaphysics of light”.

Mach principle based explanation for the ‘cosmological red-shift’ and it’s evidence

<p>We first find here that the ratio of: (loss in energy of cosmologically red-shifting photon) and (loss in electrostatic potential-energy of an electron at the same distance <em>D</em>) remains equal to the famous ratio (G m_em_p) / e² leading us towards a possibility that ‘cosmological red-shift’ may be due to gravitational effect. Also the ratio <em>h H₀ / m_e c²= (G m_em_p) / e²</em>. Starting with Mach’s principle, that ‘mass’ of an object is because of its ‘cosmic gravitational potential energy’, we arrive at a possibility that every moving chunk of matter and energy should experience a fixed value of acceleration <em>H₀c</em>. For the purpose of comparison, we express the ‘cosmological red shift’ as deceleration of the photon, and find that the deceleration experienced by the photon matches perfectly with the expected value. Then it is argued that if such a deceleration is true for a chunk of energy called photon, then it must be true for every particle of matter too. Strikingly, the decelerations experienced by the space-probes Pioneer-10, Pioneer-11, Galileo and Ulysses, as carefully measured by Anderson J.D. ET. Al. Match perfectly with the deceleration of the ‘cosmologically red-shifting photons’; thus providing supportive evidence for the new explanation proposed here.</p>