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2009, Volume 4 Progress in Physics 2009, VOLUME 4 PROGRESS IN PHYSICS “All scientists shall have the right to present their scien- tific research results, in whole or in part, at relevant sci- entific conferences, and to publish the same in printed scientific journals, electronic archives, and any other media.” — Declaration of Academic Freedom, Article 8 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 included in the ab- stracting and indexing coverage of: Mathematical Reviews and MathSciNet (AMS, USA), DOAJ of Lund University (Sweden), Zentralblatt MATH (Germany), Scientific Commons of the University of St. Gallen (Switzerland), Open-J-Gate (India), Referativnyi Zhurnal VINITI (Russia), etc. To order printed issues of this journal, con- OCTOBER 2009 VOLUME 4 tact the Editors. Electronic version of this journal can be downloaded free of charge: http://www.ptep-online.com CONTENTS Editorial Board P.-M.Robitaille Kirchhoff’s Law of Thermal Emission: 150 Years . 3 Dmitri Rabounski (Editor-in-Chief) P.-M.Robitaille Blackbody Radiation and the Loss of Universality: Implications for [email protected] Planck’s Formulation and Boltzman’s Constant . 14 Florentin Smarandache [email protected] P.-M.Robitaille COBE: A Radiological Analysis . 17 Larissa Borissova G. C. Vezzoli Active Galactic Nuclei: the Shape of Material Around Black Holes and [email protected] the Witch of Agnesi Function. Asymmetry of Neutrino Particle Density . 43 Stephen J. Crothers [email protected] R. T. Cahill Combining NASA/JPL One-Way Optical-Fiber Light-Speed Data with Spacecraft Earth-Flyby Doppler-Shift Data to Characterise 3-Space Flow. .50 Postal address U. E. Bruchholz Geometry of Space-Time . 65 Department of Mathematics and Science, University of New Mexico, U. E. Bruchholz Derivation of Planck’s Constant from Maxwell’s Electrodynamics . 67 200 College Road, S. N. Shapovalov, I. A. Rubinstein, O. A. Troshichev, and S. E. Shnoll Changes in the Gallup, NM 87301, USA Shape of Histograms Constructed from the Results of 239Pu Alpha-Activity Meas- urements Correlate with the Deviations of the Moon from the Keplerian Orbit . 68 E. N. Chifu Astrophysically Satisfactory Solutions to Einstein’s R-33 Gravitational Field Equations Exterior/Interior to Static Homogeneous Oblate Spheroidal Masses . 73 Copyright © Progress in Physics, 2009 I. Suhendro A New Finslerian Unified Field Theory of Physical Interactions . 81 All rights reserved. The authors of the ar- ticles do hereby grant Progress in Physics E. Comay Physical Consequences of Mathematical Principles. .91 non-exclusive, worldwide, royalty-free li- cense to publish and distribute the articles in accordance with the Budapest Open Initia- tive: this means that electronic copying, dis- tribution and printing of both full-size ver- sion of the journal and the individual papers published therein for non-commercial, aca- demic or individual use can be made by any user without permission or charge. The au- thors of the articles published in Progress in Physics retain their rights to use this journal as a whole or any part of it in any other pub- lications and in any way they see fit. Any part of Progress in Physics howsoever used in other publications must include an appro- priate citation of this journal. This journal is powered by LATEX A variety of books can be downloaded free from the Digital Library of Science: http://www.gallup.unm.edu/smarandache ISSN: 1555-5534 (print) ISSN: 1555-5615 (online) Standard Address Number: 297-5092 Printed in the United States of America Information for Authors and Subscribers Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathe- matics and astronomy. All submitted papers should be professional, in good English, containing a brief review of a problem and obtained results. 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It is printed from pri- vate donations. (Look for the current author fee in the online version of the journal.) October, 2009 PROGRESS IN PHYSICS Volume 4 Kirchhoff’s Law of Thermal Emission: 150 Years Pierre-Marie Robitaille Department of Radiology, The Ohio State University, 395 W. 12th Ave, Suite 302, Columbus, Ohio 43210, USA E-mail: [email protected] In this work, Kirchhoff’s law (Kirchhoff G. Monatsberichte der Akademie der Wis- senschaften zu Berlin, sessions of Dec. 1859, 1860, 783–787) is being revisited not only to mark its 150th anniversary but, most importantly, to highlight serious overreaching in its formulation. At the onset, Kirchhoff’s law correctly outlines the equivalence be- tween emission and absorption for an opaque object under thermal equilibrium. This same conclusion had been established earlier by Balfour Stewart (Stewart B. Trans. Royal Soc. Edinburgh, 1858, v. 22(1), 1–20). However, Kirchhoff extends the treatment beyond his counterpart, stating that cavity radiation must always be black, or normal: depending only on the temperature and the frequency of observation. This universal aspect of Kirchhoff’s law is without proper basis and constitutes a grave distortion of experimental reality. It is readily apparent that cavities made from arbitrary materials (" < 1) are never black. Their approach to such behavior is being driven either by the blackness of the detector, or by black materials placed near the cavity. Ample evidence exists that radiation in arbitrary cavities is sensitive to the relative position of the de- tectors. In order to fully address these issues, cavity radiation and the generalization of Kirchhoff’s law are discussed. An example is then taken from electromagnetics, at microwave frequencies, to link results in the resonant cavity with those inferred from the consequences of generalization. 1 Introduction e=a = f (T; ), then Stewart’s would be e=a = f 0 (T; ; N), where N represents all factors linked to the nature of the Kirchhoff’s law is one of the simplest and most misunder- emitter itself and f 0 is not universal. Like Kirchhoff, Stew- stood in thermodynamics [1, 2]. It is widely considered to art based his ideas on Prevost’s´ theory of exchanges [9, 10], be the first of the laws of thermal emission [3–7]. In sim- which was ultimately linked to the study of radiation within ple mathematical terms, Kirchhoff’s law can take on several enclosures. The distinctions between Stewart’s formulation formulations, which stem from the equivalence between the and Kirchhoff’s are profound [11, 12]. Kirchhoff’s ideas ad- coefficients of emission, ", and absorption, , at thermal equi- vocate a universal function [5]. Stewart’s do not [6, 11, 12]. librium. The most general expression of Kirchhoff’s law for Today, 150 years after its formulation [1, 2], the foun- opaque objects is, in fact, a statement of Stewart’s law [6], dation of Kirchhoff’s law still rests on condensed matter namely, " = 1 , where corresponds to the coefficient of physics. Blackbodies continue to be highly specialized ob- reflection. However, Kirchhoff’s law [1, 2] is much farther jects [13–25] constructed from absorbers which are nearly reaching than Stewart’s [6], in requiring that radiation within perfect over the frequency range of interest. Yet, if Kirch- an enclosure, or cavity, must always be black, or normal [5]. hoff was correct about the nature of radiation within cavities, Kirchhoff conceives that the ratio of emissive power, e, to it should be possible to assemble a blackbody from any mate- absorptive power, a, of all bodies can be described by a uni- rial. Surely, the presence of the universal function, f, dictates versal function, f, common to all radiation within enclosures: that cavity radiation must always be black, or normal [5]. All e=a = f (T; ). Furthermore, this must be the case in a man- that should be theoretically required is thermal equilibrium ner which is independent of the nature and shape of the enclo- with the walls of an enclosure. The attributes of the walls, sure, and which depends only on the temperature, T , of the or its contents, should be inconsequential. However, the body system and the wavelength, , of observation [1, 2, 5, 7]. of experimental knowledge, relative to the assembly of black- Kirchhoff’s law constitutes an attempt to summarize the bodies in the laboratory, stands firmly opposed to this concept state of knowledge in radiative heat transfer during the mid- [13–25]. True blackbodies [13–25] are extremely difficult to 1800’s. At the time, physicists created blackbodies from produce and testify against Kirchhoff’s universal formulation graphite plates, by lining the interior of cavities with soot, [1, 2, 5]. Stewart’s law [6] alone, not Kirchhoff’s [1, 2], is or by coating objects with black paint containing soot [8].
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