ISSUE 2006 PROGRESS IN PHYSICS VOLUME 4 ISSN 1555-5534 The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESS IN PHYSICS A quarterly issue scientific journal, registered with the Library of Congress (DC, USA). This journal is peer reviewed and includedinthe abstracting and indexing coverage of: Mathematical Reviews and MathSciNet (AMS, USA), DOAJ of Lund University (Sweden), Zentralblatt MATH (Germany), Referativnyi Zhurnal VINITI (Russia), etc. Electronic version of this journal: OCTOBER 2006 VOLUME 4 http://www.ptep-online.com http://www.geocities.com/ptep_online CONTENTS To order printed issues of this journal, con- tact the Editor in Chief. D. Rabounski New Effect of General Relativity: Thomson Dispersion of Light in Stars as a Machine Producing Stellar Energy. .3 Chief Editor A. N. Mina and A. H. Phillips Frequency Resolved Detection over a Large Dmitri Rabounski Frequency Range of the Fluctuations in an Array of Quantum Dots . 11 [email protected] C. Y. Lo Completing Einstein’s Proof of E = mc2 ..........................14 Associate Editors Prof. Florentin Smarandache D. Rabounski A Source of Energy for Any Kind of Star . 19 [email protected] Dr. Larissa Borissova J. Dunning-Davies The Thermodynamics Associated with Santilli’s Hadronic [email protected] Mechanics . 24 Stephen J. Crothers F. Smarandache and V.Christianto A Note on Geometric and Information [email protected] Fusion Interpretation of Bell’s Theorem and Quantum Measurement . 27 Department of Mathematics, University of J. X. Zheng-Johansson and P.-I. Johansson Developing de Broglie Wave . 32 New Mexico, 200 College Road, Gallup, NM 87301, USA The Classical Theory of Fields Revision Project (CTFRP): Collected Papers Treating of Corrections to the Book “The Classical Theory of Fields” by L. Landau and E. Lifshitz . 36 Copyright c Progress in Physics, 2006 F. Smarandache and V.Christianto Plausible Explanation of Quantization of All rights reserved. Any part of Progress in Physics howsoever used in other publica- Intrinsic Redshift from Hall Effect and Weyl Quantization . 37 tions must include an appropriate citation J. R. Claycomb and R.K. Chu Geometrical Dynamics in a Transitioning Su- of this journal. perconducting Sphere . 41 Authors of articles published in Progress in Physics retain their rights to use their own R. T. Cahill Black Holes and Quantum Theory: The Fine Structure Constant articles in any other publications and in any way they see fit. Connection. .44 L. Borissova Preferred Spatial Directions in the Universe: a General Relativity This journal is powered by LATEX Approach . 51 L. Borissova Preferred Spatial Directions in the Universe. Part II. 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October, 2006 PROGRESS IN PHYSICS Volume 4 New Effect of General Relativity: Thomson Dispersion of Light inStars as a Machine Producing Stellar Energy Dmitri Rabounski E-mail: [email protected] Given a non-holonomic space, time lines are non-orthogonal to the spatial section therein, which manifests as the three-dimensional space rotation. It is shown herein that a global non-holonomity of the background space is an experimentally verifiable fact revealing itself by two fundamental fields: a field of linear drift at 348 km/sec, and a field of rotation at 2,188 km/sec. Any local rotation or oscillation perturbs theback- ground non-holonomity. In such a case the equations of motion show additional energy flow and force, produced by the non-holonomic background, in order to compensate the perturbation in it. Given the radiant transportation of energy in stars, an additional factor is expected in relation to Thomson dispersion of light in free electrons, and pro- vides the same energy radiated in the wide range of physical conditions from dwarfs to super-giants. It works like a machine where the production of stellar energy is regu- lated by radiation from the surface. This result, from General Relativity, accounts for stellar energy by processes different to thermonuclear reactions, and coincides with data of observational astrophysics. The theory leads to practical applications of new energy sources working much more effectively and safely than nuclear energy. 1 Introduction. The mathematical basis to his reference body (bi = 0), the projections of a vector α α Q0 i α i Q are b Qα = and hαQ = Q , while for a tensor of We aim to study the effects produced on a particle, if the √g00 the 2nd rank Qαβ we have the projections bαb βQ = Q00 , αβ g00 space is non-holonomic. We then apply the result to the par- Qi hiαb βQ = 0 , hi hk Qαβ =Qik. Such projections are in- ticles of the gaseous constitution of stars. αβ √g00 α β To do this we shall study the equations of motion. To variant with respect to the transformation of time in the spa- obtain a result applicable to real experiment, we express tial section: they are chronometrically invariant quantities. the equations in terms of physically observable quantities. In the observer’s spatial section the chr.inv.-tensor Mathematical methods for calculating observable quantities g0i g0k in General Relativity were invented by A. Zelmanov, in the hik = gik + bi bk = gik + , (1) − − g00 1940’s [1, 2, 3]. We now present a brief account thereof. possesses all the properties of the fundamental metric tensor A regular observer perceives four-dimensional space as g . Furthermore, the spatial projection of it is hαhβg = the three-dimensional spatial section x0 = const, pierced at αβ i k αβ = h . Therefore h is the observable metric tensor. each point by time lines xi = const. Therefore, physical ik ik ∗ −The chr.inv.-differential operators quantities perceived by an observer are actually projections of four-dimensional quantities onto his own time line and ∗∂ 1 ∂ ∗∂ ∂ g0i ∂ (2) = , i = i 0 , spatial section. The spatial section is determined by a three- ∂t √g00 ∂t ∂x ∂x − g00 ∂x dimensional coordinate net spanning a real reference body. are different to the usual differential operators, and arenon- Time lines are determined by clocks at those points where 2 2 2 2 commutative: ∗∂ ∗∂ = 1 F ∗∂ and ∗∂ ∗∂ = the clocks are located. If time lines are everywhere orthog- ∂xi∂t − ∂t ∂xi c2 i ∂t ∂xi∂xk − ∂xk∂xi 2 ∗∂ . The non-commutativity determines the chr.inv.- onal to the spatial section, the space is known as holonomic. = c2 Aik ∂t If not, there is a field of the space non-holonomity — the non- vector for the gravitational inertial force Fi and the chr.inv.- orthogonality of time lines to the spatial section, manifest as tensor of angular velocities of the space rotation Aik a three-dimensional rotation of the reference body’s space. 1 ∂w ∂vi w Such a space is said to be non-holonomic. Fi = , √g00 = 1 , (3) √g ∂xi − ∂t − c2 By mathematical means, four-dimensional quantities can 00 be projected onto an observer’s time line and spatial section α 1 ∂vk ∂vi 1 by the projecting operators: bα = dx , the observer’s four- Aik = + Fi vk Fk vi , (4) ds 2 ∂xi − ∂xk 2c2 − dimensional velocity vector tangential to his world-line, and g0i h = g + b b . For a real observer at rest with respect where w is the gravitational potential, and vi = c is αβ − αβ α β − √g00 the linear velocity of the space rotation†. Other observable ∗Greek suffixes are the space-time indices 0, 1, 2, 3, Latin ones are the 2 α β i 0i 2 i k spatial indices 1, 2, 3. So the space-time interval is ds = g dx dx . Its contravariant component is v = cg √g00, so v = h v v . αβ † − ik D. Rabounski. Thomson Dispersion of Light in Stars as a Generator of Stellar Energy 3 Volume 4 PROGRESS IN PHYSICS October, 2006 properties of the reference space are presented with the chr. symmetric system, which can be considered as a topological inv.-tensor of the rates of the space deformations spread mapped into the spherical space Rn” [5]. Given the spread Rn, di Bartini studied “sequences of 1 ∂hik 1 ∗∂hik Dik = = (5) stochastic transitions between different dimension spreads as 2√g00 ∂t 2 ∂t stochastic vector quantities, i.