On the matter of proving Euclidean fifth postulate and the origin of non-Euclidean geometries

2019 ◽  
Vol 950 (8) ◽  
pp. 2-11
Author(s):  
S.A. Tolchelnikova ◽  
K.N. Naumov

The Euclidean geometry was developed as a mathematical system due to generalizing thousands years of measurements on the plane and spherical surfaces. The development of celestial mechanics and stellar astronomy confirmed its validity as mathematical principles of natural philosophy, in particular for studying the Solar System bodies’ and Galaxy stars motions. In the non-Euclidean geometries by Lobachevsky and Riemann, the third axiom of modern geometry manuals is substituted. We show that the third axiom of these manuals is a corollary of the Fifth Euclidean postulate. The idea of spherical, Riemannian space of the Universe and local curvatures of space, depending on body mass, was inculcated into celestial mechanics, astronomy and geodesy along with the theory of relativity. The mathematical apparatus of the relativity theory was created from immeasurable quantities

2020 ◽  
Vol 2 (1) ◽  
pp. 97-111
Author(s):  
Horst Fritsch ◽  
Eberhard Schluecker

The asymmetric cosmic time is a logical consequence of the General Theory of Relativity (GR), if one demands that it should apply to the entire cosmos. From the simplest cosmological model that is consistent with the ART (Einstein-de Sitter model) thus follows the < Cosmic Time Hypothesis > (CTH), which offers solutions for many unsolved problems of cosmology that the current standard model of cosmology (ɅCDM model) cannot explain. According to the CTH, space, time and matter form a unit and develop evolutionarily according to identical, time-dependent laws. According to the CTH time has neither beginning nor end. The "big bang" disappears into the infinite past, which is why the universe manages without inflation. The accelerated expansion of the universe is also unlikely to occur if the SN-Ia measurement results are interpreted using the CTH. The cosmological constant Ʌ can then be omitted (Ʌ=0) and consequently no "dark energy" is needed. In addition, the CTH also provides interesting results on the topics: Initial conditions for hypotheses, stability of the expanding, flat universe (Ω=1), cosmic energy balance (is there negative energy ?), theory of earth expansion, unification of natural forces, Mach's principle. Should the CTH receive broad experimental confirmation, the GR could be extended to the "Universal Relativity Theory" (UR).


Lightspeed ◽  
2019 ◽  
pp. 144-158
Author(s):  
John C. H. Spence

The confused state of theoretical physics in 1900 and the great unresolved issues are summarized, one of which led to the birth of quantum mechanics, and the other to relativity. How it seemed impossible to reconcile Bradley’s measurements of the speed of light with Fresnel’s Aether drag hypothesis, which was well supported by Fizeau’s measurements in Paris of the speed of light in a moving medium (flowing water). Maxwell’s equations predicted a constant speed of light, suggesting an absolute frame of reference in the universe, but did not “transform” in the same way as Newton’s equations from one moving observer to another. How Einstein made sense of all these rival theories and experimental results with his unifying theory of relativity, based on two assumptions. His life and work is discussed, and a simple explanation given of his relativity theory. How the failure of this search for an absolute frame of reference in our universe led him inexorably to perhaps the most famous equation in physics E = mc2, giving the energy release from nuclear explosions and the stars.


2019 ◽  
Author(s):  
Vitaly Kuyukov

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.


Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 101
Author(s):  
Maxim Eingorn ◽  
Andrew McLaughlin ◽  
Ezgi Canay ◽  
Maksym Brilenkov ◽  
Alexander Zhuk

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.


Philosophies ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 30 ◽  
Author(s):  
Abir Igamberdiev

Relational ideas for our description of the natural world can be traced to the concept of Anaxagoras on the multiplicity of basic particles, later called “homoiomeroi” by Aristotle, that constitute the Universe and have the same nature as the whole world. Leibniz viewed the Universe as an infinite set of embodied logical essences called monads, which possess inner view, compute their own programs and perform mathematical transformations of their qualities, independently of all other monads. In this paradigm, space appears as a relational order of co-existences and time as a relational order of sequences. The relational paradigm was recognized in physics as a dependence of the spatiotemporal structure and its actualization on the observer. In the foundations of mathematics, the basic logical principles are united with the basic geometrical principles that are generic to the unfolding of internal logic. These principles appear as universal topological structures (“geometric atoms”) shaping the world. The decision-making system performs internal quantum reduction which is described by external observers via the probability function. In biology, individual systems operate as separate relational domains. The wave function superposition is restricted within a single domain and does not expand outside it, which corresponds to the statement of Leibniz that “monads have no windows”.


2021 ◽  
Vol 11 (3) ◽  
pp. 43-49
Author(s):  
Hamdoon A. Khan ◽  

With the consideration of the light which carries the photon particles, the Lorentz transformation was constructed with an impressive mathematical approach. But the generalization of that equation for all the velocities of the universe is direct enforcement on other things not to travel faster than light. It has created serious issues in every scientific research that was done in the last century based on the special theory of relativity. This paper replaces the velocity of light with some other velocities and shows us the possible consequences and highlights the issues of special relativity. If I travel through my past or future and was able to see another me there, who would be the real Hamdoon I or the one I see there in the past or future! If the real one is only me, the one I saw, is not me, so, I could not travel through my or someone else's past or future. Therefore, no one can travel through time. If both of us are the same, can the key of personal identity be duplicated or be separated into two or more parts? These are some of the fundamental philosophical arguments that annihilate the concept of time travel which is one of the sequels of special relativity.


2021 ◽  
Vol 58 (4) ◽  
pp. 175-195
Author(s):  
Vladimir P. Vizgin ◽  

The article is based on the concepts of epistemic virtues and epistemic vices and explores A. Einstein’s contribution to the creation of fundamental physical theories, namely the special theory of relativity and general theory of relativity, as well as to the development of a unified field theory on the basis of the geometric field program, which never led to success. Among the main epistemic virtues that led Einstein to success in the construction of the special theory of relativity are the following: a unique physical intuition based on the method of thought experiment and the need for an experimental justification of space-time concepts; striving for simplicity and elegance of theory; scientific courage, rebelliousness, signifying the readiness to engage in confrontation with scientific conventional dogmas and authorities. In the creation of general theory of relativity, another intellectual virtue was added to these virtues: the belief in the heuristic power of the mathematical aspect of physics. At the same time, he had to overcome his initial underestimation of the H. Minkowski’s four-dimensional concept of space and time, which has manifested in a distinctive flexibility of thinking typical for Einstein in his early years. The creative role of Einstein’s mistakes on the way to general relativity was emphasized. These mistakes were mostly related to the difficulties of harmonizing the mathematical and physical aspects of theory, less so to epistemic vices. The ambivalence of the concept of epistemic virtues, which can be transformed into epistemic vices, is noted. This transformation happened in the second half of Einstein’s life, when he for more than thirty years unsuccessfully tried to build a unified geometric field theory and to find an alternative to quantum mechanics with their probabilistic and Copenhagen interpretation In this case, we can talk about the following epistemic vices: the revaluation of mathematical aspect and underestimation of experimentally – empirical aspect of the theory; adopting the concepts general relativity is based on (continualism, classical causality, geometric nature of fundamental interactions) as fundamental; unprecedented persistence in defending the GFP (geometrical field program), despite its failures, and a certain loss of the flexibility of thinking. A cosmological history that is associated both with the application of GTR (general theory of relativity) to the structure of the Universe, and with the missed possibility of discovering the theory of the expanding Universe is intermediate in relation to Einstein’s epistemic virtues and vices. This opportunity was realized by A.A. Friedmann, who defeated Einstein in the dispute about if the Universe was stationary or nonstationary. In this dispute some of Einstein’s vices were revealed, which Friedman did not have. The connection between epistemic virtues and the methodological principles of physics and also with the “fallibilist” concept of scientific knowledge development has been noted.


Traditio ◽  
2012 ◽  
Vol 67 ◽  
pp. 235-276
Author(s):  
Barbara Obrist

TheLiber de orbe, attributed to Māshā'allāh (fl. 762–ca. 815) in the list of Gerard of Cremona's translations, stands out as one of the few identifiable sources for the indirect knowledge of Peripatetic physics and cosmology at the very time Aristotle's works on natural philosophy themselves were translated into Latin, from the 1130s onward. This physics is expounded in an opening series of chapters on the bodily constitution of the universe, while the central section of the treatise covers astronomical subjects, and the remaining parts deal with meteorology and the vegetal realm. Assuming that Gerard of Cremona's translation of theLiber de orbecorresponds to the twenty-seven chapter version that circulated especially during the thirteenth and fourteenth centuries, it was, however, not this version, but a forty-chapter expansion thereof that became influential as early as the 1140s. It may have originated in Spain, as indicated, among others, by a reference to the difference of visibility of a lunar eclipse between Spain and Mecca. Unlike the twenty-seven chapterLiber de orbe, this expanded and also partly modified text remains in manuscript, and none of the three copies known so far gives a title or mentions Māshā'allāh as an author. Instead, the thirteenth-century witness that is now in New York attributes the work to an Alcantarus:Explicit liber Alcantari Caldeorum philosophi. While no Arabic original of the twenty-seven chapterLiber de orbehas come to light yet, Taro Mimura of the University of Manchester recently identified a manuscript that partly corresponds to the forty-chapter Latin text, as well as a shorter version thereof.


2020 ◽  
Author(s):  
Douglas Michael Snyder

Though Einstein and other physicists recognized the importance of an observer being at rest in an inertial reference frame for the special theory of relativity, the supporting psychological structures were not discussed much by physicists. On the other hand, Rock wrote of the factors involved in the perception of motion, including one’s own motion. Rock thus came to discuss issues of significance to relativity theory, apparently without any significant understanding of how his theory might be related to relativity theory. In this paper, connections between Rock’s theory on the perception of one’s own motion, as well as empirical work supporting it, and relativity theory are explored. Paper available at: https://arxiv.org/abs/physics/9908025v1 .


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