In the present paper, based on Lobachevskian (hyperbolic) static geometry, we present (as an alternative to the existing Big Bang model of CMB) a geometric model of CMB in a Lobachevskian static universe as a homogene...In the present paper, based on Lobachevskian (hyperbolic) static geometry, we present (as an alternative to the existing Big Bang model of CMB) a geometric model of CMB in a Lobachevskian static universe as a homogeneous space of horospheres. It is shown that from the point of view of physics, a horosphere is an electromagnetic wavefront in Lobachevskian space. The presented model of CMB is an Lorentz invariant object, possesses observable properties of isotropy and homogeneity for all observers scattered across the Lobachevskian universe, and has a black body spectrum. The Lorentz invariance of CMB implies a mathematical equation for cosmological redshift for all z. The global picture of CMB, described solely in terms of the Lorentz group—SL(2C), is an infinite union of double sided quotient spaces (double fibration of the Lorentz group) taken over all parabolic stabilizers P⊂SL(2C). The local picture of CMB (as seen by us from Earth) is a Grassmannian space of an infinite union all horospheres containing origin o∈L3, equivalent to a projective plane RP2. The space of electromagnetic wavefronts has a natural identification with the boundary at infinity (an absolute) of Lobachevskian universe. In this way, it is possible to regard the CMB as a reference at infinity (an absolute reference) and consequently to define an absolute motion and absolute rest with respect to CMB, viewed as an infinitely remote reference.展开更多
In this work, we present our theory and principles of the mathematical foundations of Lobachevskian (hyperbolic) astrophysics and cosmology which follow from a mathematical interpretation of experimental data in a Lob...In this work, we present our theory and principles of the mathematical foundations of Lobachevskian (hyperbolic) astrophysics and cosmology which follow from a mathematical interpretation of experimental data in a Lobachevskian non-expanding Universe. Several new scientific formulas of practical significance for astrophysics, astronomy, and cosmology are presented. A new method of calculating (from experimental data) the curvature of a Lobachevskian Universe is given, resulting in an estimated curvature-K on the order of 10−52 m−2. Our model also estimates the radius of the non-expanding Lobachevskian Universe in a Poincare ball model as approximately 14.9 bly. A rigorous theoretical explanation in terms of the fixed Lobachevskian geometry of a non-expanding Universe is provided for experimental data acquired in the Supernova Project, showing an excellent agreement between experimental data and our theoretical formulas. We present new geometric equations relating brightness dimming and redshift, and employ them to fully explain the erroneous reasoning and erroneous conclusions of Perlmutter, Schmidt, Riess and the 2011 Nobel Prize Committee regarding “accelerated expansion” of the Universe. We demonstrate that experimental data acquired in deep space astrophysics when interpreted in terms of Euclidean geometry will result in illusions of space expansion: an illusion of “linear space expansion”—Hubble, and an illusion of “accelerated (non-linear) space expansion”—Perlmutter, Schmidt, Riess.展开更多
In this paper, we present a new form of “special relativity” (BSR), which is isomorphic to Einstein’s “special relativity” (ESR). This in turn proves the non-uniqueness of Einstein’s “special relativity” and i...In this paper, we present a new form of “special relativity” (BSR), which is isomorphic to Einstein’s “special relativity” (ESR). This in turn proves the non-uniqueness of Einstein’s “special relativity” and implies the inconclusiveness of so-called “relativistic physics”. This work presents new results of principal significance for the foundations of physics and practical results for high energy physics, deep space astrophysics, and cosmology as well. The entire exposition is done within the formalism of the Lorentz <em>SL</em>(2<em>C</em>) group acting via isometries on <strong>real 3-dimensional Lobachevskian (hyperbolic) spaces</strong> <em>L</em><sup>3</sup> regarded as quotients <span style="white-space:nowrap;"><em>SL</em>(2<em>C</em>)/<em>SU</em>(2)</span>. We show via direct calculations that both ESR and BSR are parametric maps from Lobachevskian into Euclidean space, namely a <strong>gnomonic</strong> (central) map in the case of ESR, and a<strong> stereographic </strong>map in the case of BSR. Such an identification allows us to link these maps to relevant models of Lobachevskian geometry. Thus, we identify ESR as the physical realization of the Beltrami-Klein (non-conformal) model, and BSR as the physical realization of the Poincare (conformal) model of Lobachevskian geometry. Although we focus our discussion on ball models of Lobachevskian geometry, our method is quite general, and for instance, may be applied to the half-space model of Lobachevskian geometry with appropriate “Lorentz group” acting via isometries on (positive) half space, resulting yet in another “special relativity” isomorphic with ESR and BSR. By using the notion of a<strong> homotopy</strong> of maps, the identification of “special relativities” as maps from Lobachevskian into Euclidean space allows us to justify the existence of an uncountable infinity of hybrid “special relativities” and consequently an uncountable infinity of “relativistic physics” built upon them. This is another new result in physics and it states that so called “relativistic physics” is unique only up to a homotopy. Finally, we show that “paradoxes” of “special relativities” in either ESR or BSR are simply common distortions of maps between non-isometric spaces. The entire exposition is kept at elementary level accessible to majority of students in physics and/or engineering.展开更多
文摘In the present paper, based on Lobachevskian (hyperbolic) static geometry, we present (as an alternative to the existing Big Bang model of CMB) a geometric model of CMB in a Lobachevskian static universe as a homogeneous space of horospheres. It is shown that from the point of view of physics, a horosphere is an electromagnetic wavefront in Lobachevskian space. The presented model of CMB is an Lorentz invariant object, possesses observable properties of isotropy and homogeneity for all observers scattered across the Lobachevskian universe, and has a black body spectrum. The Lorentz invariance of CMB implies a mathematical equation for cosmological redshift for all z. The global picture of CMB, described solely in terms of the Lorentz group—SL(2C), is an infinite union of double sided quotient spaces (double fibration of the Lorentz group) taken over all parabolic stabilizers P⊂SL(2C). The local picture of CMB (as seen by us from Earth) is a Grassmannian space of an infinite union all horospheres containing origin o∈L3, equivalent to a projective plane RP2. The space of electromagnetic wavefronts has a natural identification with the boundary at infinity (an absolute) of Lobachevskian universe. In this way, it is possible to regard the CMB as a reference at infinity (an absolute reference) and consequently to define an absolute motion and absolute rest with respect to CMB, viewed as an infinitely remote reference.
文摘In this work, we present our theory and principles of the mathematical foundations of Lobachevskian (hyperbolic) astrophysics and cosmology which follow from a mathematical interpretation of experimental data in a Lobachevskian non-expanding Universe. Several new scientific formulas of practical significance for astrophysics, astronomy, and cosmology are presented. A new method of calculating (from experimental data) the curvature of a Lobachevskian Universe is given, resulting in an estimated curvature-K on the order of 10−52 m−2. Our model also estimates the radius of the non-expanding Lobachevskian Universe in a Poincare ball model as approximately 14.9 bly. A rigorous theoretical explanation in terms of the fixed Lobachevskian geometry of a non-expanding Universe is provided for experimental data acquired in the Supernova Project, showing an excellent agreement between experimental data and our theoretical formulas. We present new geometric equations relating brightness dimming and redshift, and employ them to fully explain the erroneous reasoning and erroneous conclusions of Perlmutter, Schmidt, Riess and the 2011 Nobel Prize Committee regarding “accelerated expansion” of the Universe. We demonstrate that experimental data acquired in deep space astrophysics when interpreted in terms of Euclidean geometry will result in illusions of space expansion: an illusion of “linear space expansion”—Hubble, and an illusion of “accelerated (non-linear) space expansion”—Perlmutter, Schmidt, Riess.
文摘In this paper, we present a new form of “special relativity” (BSR), which is isomorphic to Einstein’s “special relativity” (ESR). This in turn proves the non-uniqueness of Einstein’s “special relativity” and implies the inconclusiveness of so-called “relativistic physics”. This work presents new results of principal significance for the foundations of physics and practical results for high energy physics, deep space astrophysics, and cosmology as well. The entire exposition is done within the formalism of the Lorentz <em>SL</em>(2<em>C</em>) group acting via isometries on <strong>real 3-dimensional Lobachevskian (hyperbolic) spaces</strong> <em>L</em><sup>3</sup> regarded as quotients <span style="white-space:nowrap;"><em>SL</em>(2<em>C</em>)/<em>SU</em>(2)</span>. We show via direct calculations that both ESR and BSR are parametric maps from Lobachevskian into Euclidean space, namely a <strong>gnomonic</strong> (central) map in the case of ESR, and a<strong> stereographic </strong>map in the case of BSR. Such an identification allows us to link these maps to relevant models of Lobachevskian geometry. Thus, we identify ESR as the physical realization of the Beltrami-Klein (non-conformal) model, and BSR as the physical realization of the Poincare (conformal) model of Lobachevskian geometry. Although we focus our discussion on ball models of Lobachevskian geometry, our method is quite general, and for instance, may be applied to the half-space model of Lobachevskian geometry with appropriate “Lorentz group” acting via isometries on (positive) half space, resulting yet in another “special relativity” isomorphic with ESR and BSR. By using the notion of a<strong> homotopy</strong> of maps, the identification of “special relativities” as maps from Lobachevskian into Euclidean space allows us to justify the existence of an uncountable infinity of hybrid “special relativities” and consequently an uncountable infinity of “relativistic physics” built upon them. This is another new result in physics and it states that so called “relativistic physics” is unique only up to a homotopy. Finally, we show that “paradoxes” of “special relativities” in either ESR or BSR are simply common distortions of maps between non-isometric spaces. The entire exposition is kept at elementary level accessible to majority of students in physics and/or engineering.
