I Am the Speed of Light C, You ‘See’ …..!
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Galileo and the Telescope
Galileo and the Telescope A Discussion of Galileo Galilei and the Beginning of Modern Observational Astronomy ___________________________ Billy Teets, Ph.D. Acting Director and Outreach Astronomer, Vanderbilt University Dyer Observatory Tuesday, October 20, 2020 Image Credit: Giuseppe Bertini General Outline • Telescopes/Galileo’s Telescopes • Observations of the Moon • Observations of Jupiter • Observations of Other Planets • The Milky Way • Sunspots Brief History of the Telescope – Hans Lippershey • Dutch Spectacle Maker • Invention credited to Hans Lippershey (c. 1608 - refracting telescope) • Late 1608 – Dutch gov’t: “ a device by means of which all things at a very great distance can be seen as if they were nearby” • Is said he observed two children playing with lenses • Patent not awarded Image Source: Wikipedia Galileo and the Telescope • Created his own – 3x magnification. • Similar to what was peddled in Europe. • Learned magnification depended on the ratio of lens focal lengths. • Had to learn to grind his own lenses. Image Source: Britannica.com Image Source: Wikipedia Refracting Telescopes Bend Light Refracting Telescopes Chromatic Aberration Chromatic aberration limits ability to distinguish details Dealing with Chromatic Aberration - Stop Down Aperture Galileo used cardboard rings to limit aperture – Results were dimmer views but less chromatic aberration Galileo and the Telescope • Created his own (3x, 8-9x, 20x, etc.) • Noted by many for its military advantages August 1609 Galileo and the Telescope • First observed the -
A Mathematical Derivation of the General Relativistic Schwarzschild
A Mathematical Derivation of the General Relativistic Schwarzschild Metric An Honors thesis presented to the faculty of the Departments of Physics and Mathematics East Tennessee State University In partial fulfillment of the requirements for the Honors Scholar and Honors-in-Discipline Programs for a Bachelor of Science in Physics and Mathematics by David Simpson April 2007 Robert Gardner, Ph.D. Mark Giroux, Ph.D. Keywords: differential geometry, general relativity, Schwarzschild metric, black holes ABSTRACT The Mathematical Derivation of the General Relativistic Schwarzschild Metric by David Simpson We briefly discuss some underlying principles of special and general relativity with the focus on a more geometric interpretation. We outline Einstein’s Equations which describes the geometry of spacetime due to the influence of mass, and from there derive the Schwarzschild metric. The metric relies on the curvature of spacetime to provide a means of measuring invariant spacetime intervals around an isolated, static, and spherically symmetric mass M, which could represent a star or a black hole. In the derivation, we suggest a concise mathematical line of reasoning to evaluate the large number of cumbersome equations involved which was not found elsewhere in our survey of the literature. 2 CONTENTS ABSTRACT ................................. 2 1 Introduction to Relativity ...................... 4 1.1 Minkowski Space ....................... 6 1.2 What is a black hole? ..................... 11 1.3 Geodesics and Christoffel Symbols ............. 14 2 Einstein’s Field Equations and Requirements for a Solution .17 2.1 Einstein’s Field Equations .................. 20 3 Derivation of the Schwarzschild Metric .............. 21 3.1 Evaluation of the Christoffel Symbols .......... 25 3.2 Ricci Tensor Components ................. -
1 Lecture 26
PHYS 445 Lecture 26 - Black-body radiation I 26 - 1 Lecture 26 - Black-body radiation I What's Important: · number density · energy density Text: Reif In our previous discussion of photons, we established that the mean number of photons with energy i is 1 n = (26.1) i eß i - 1 Here, the questions that we want to address about photons are: · what is their number density · what is their energy density · what is their pressure? Number density n Eq. (26.1) is written in the language of discrete states. The first thing we need to do is replace the sum by an integral over photon momentum states: 3 S i ® ò d p Of course, it isn't quite this simple because the density-of-states issue that we introduced before: for every spin state there is one phase space state for every h 3, so the proper replacement more like 3 3 3 S i ® (1/h ) ò d p ò d r The units now work: the left hand side is a number, and so is the right hand side. But this expression ignores spin - it just deals with the states in phase space. For every photon momentum, there are two ways of arranging its polarization (i.e., the orientation of its electric or magnetic field vectors): where the photon momentum vector is perpendicular to the plane. Thus, we have 3 3 3 S i ® (2/h ) ò d p ò d r. (26.2) Assuming that our system is spatially uniform, the position integral can be replaced by the volume ò d 3r = V. -
Measurement of the Speed of Gravity
Measurement of the Speed of Gravity Yin Zhu Agriculture Department of Hubei Province, Wuhan, China Abstract From the Liénard-Wiechert potential in both the gravitational field and the electromagnetic field, it is shown that the speed of propagation of the gravitational field (waves) can be tested by comparing the measured speed of gravitational force with the measured speed of Coulomb force. PACS: 04.20.Cv; 04.30.Nk; 04.80.Cc Fomalont and Kopeikin [1] in 2002 claimed that to 20% accuracy they confirmed that the speed of gravity is equal to the speed of light in vacuum. Their work was immediately contradicted by Will [2] and other several physicists. [3-7] Fomalont and Kopeikin [1] accepted that their measurement is not sufficiently accurate to detect terms of order , which can experimentally distinguish Kopeikin interpretation from Will interpretation. Fomalont et al [8] reported their measurements in 2009 and claimed that these measurements are more accurate than the 2002 VLBA experiment [1], but did not point out whether the terms of order have been detected. Within the post-Newtonian framework, several metric theories have studied the radiation and propagation of gravitational waves. [9] For example, in the Rosen bi-metric theory, [10] the difference between the speed of gravity and the speed of light could be tested by comparing the arrival times of a gravitational wave and an electromagnetic wave from the same event: a supernova. Hulse and Taylor [11] showed the indirect evidence for gravitational radiation. However, the gravitational waves themselves have not yet been detected directly. [12] In electrodynamics the speed of electromagnetic waves appears in Maxwell equations as c = √휇0휀0, no such constant appears in any theory of gravity. -
Carbon – Science and Technology
© Applied Science Innovations Pvt. Ltd., India Carbon – Sci. Tech. 1 (2010) 139 - 143 Carbon – Science and Technology ASI ISSN 0974 – 0546 http://www.applied-science-innovations.com ARTICLE Received :29/03/2010, Accepted :02/09/2010 ----------------------------------------------------------------------------------------------------------------------------- Ablation morphologies of different types of carbon in carbon/carbon composites Jian Yin, Hongbo Zhang, Xiang Xiong, Jinlv Zuo State Key Laboratory of Powder Metallurgy, Central South University, Lushan South Road, Changsha, China. --------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction : Carbon/carbon (C/C) composites the ablation morphology and formation mechanism of combine good mechanical properties and designable each types of carbon. capabilities of composites and excellent ultrahigh temperature properties of carbon materials. They have In this study, ablation morphologies of resin-based low densities, high specific strength, good thermal carbon, carbon fibers, pyrolytic carbon with smooth stability, high thermal conductivity, low thermal laminar structure and rough laminar structure has been expansion coefficient and excellent ablation properties investigated in detail and their formation mechanisms [1]. As C/C composites show excellent characteristics were discussed. in both structural design and functional application, 2 Experimental : they have become one of the most competitive high temperature materials widely used in aviation and 2.1 Preparation of C/C composites : Bulk needled polyacrylonitrile (PAN) carbon fiber felts spacecraft industry [2 - 4]. In particular, they are were used as reinforcements. Three kinds of C/C considered to be the most suitable materials for solid composites, labeled as sample A, B and C, were rocket motor nozzles. prepared. Sample A is a C/C composite mainly with C/C composites are composed of carbon fibers and smooth laminar pyrolytic carbon, sample B is a C/C carbon matrices. -
From Relativistic Time Dilation to Psychological Time Perception
From relativistic time dilation to psychological time perception: an approach and model, driven by the theory of relativity, to combine the physical time with the time perceived while experiencing different situations. Andrea Conte1,∗ Abstract An approach, supported by a physical model driven by the theory of relativity, is presented. This approach and model tend to conciliate the relativistic view on time dilation with the current models and conclusions on time perception. The model uses energy ratios instead of geometrical transformations to express time dilation. Brain mechanisms like the arousal mechanism and the attention mechanism are interpreted and combined using the model. Matrices of order two are generated to contain the time dilation between two observers, from the point of view of a third observer. The matrices are used to transform an observer time to another observer time. Correlations with the official time dilation equations are given in the appendix. Keywords: Time dilation, Time perception, Definition of time, Lorentz factor, Relativity, Physical time, Psychological time, Psychology of time, Internal clock, Arousal, Attention, Subjective time, Internal flux, External flux, Energy system ∗Corresponding author Email address: [email protected] (Andrea Conte) 1Declarations of interest: none Preprint submitted to PsyArXiv - version 2, revision 1 June 6, 2021 Contents 1 Introduction 3 1.1 The unit of time . 4 1.2 The Lorentz factor . 6 2 Physical model 7 2.1 Energy system . 7 2.2 Internal flux . 7 2.3 Internal flux ratio . 9 2.4 Non-isolated system interaction . 10 2.5 External flux . 11 2.6 External flux ratio . 12 2.7 Total flux . -
Identifying the Elastic Isotropy of Architectured Materials Based On
Identifying the elastic isotropy of architectured materials based on deep learning method Anran Wei a, Jie Xiong b, Weidong Yang c, Fenglin Guo a, d, * a Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China b Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China c School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China d State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China * Corresponding author, E-mail: [email protected] Abstract: With the achievement on the additive manufacturing, the mechanical properties of architectured materials can be precisely designed by tailoring microstructures. As one of the primary design objectives, the elastic isotropy is of great significance for many engineering applications. However, the prevailing experimental and numerical methods are normally too costly and time-consuming to determine the elastic isotropy of architectured materials with tens of thousands of possible microstructures in design space. The quick mechanical characterization is thus desired for the advanced design of architectured materials. Here, a deep learning-based approach is developed as a portable and efficient tool to identify the elastic isotropy of architectured materials directly from the images of their representative microstructures with arbitrary component distributions. The measure of elastic isotropy for architectured materials is derived firstly in this paper to construct a database with associated images of microstructures. Then a convolutional neural network is trained with the database. It is found that the convolutional neural network shows good performance on the isotropy identification. -
Hypercomplex Algebras and Their Application to the Mathematical
Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory Torsten Hertig I1, Philip H¨ohmann II2, Ralf Otte I3 I tecData AG Bahnhofsstrasse 114, CH-9240 Uzwil, Schweiz 1 [email protected] 3 [email protected] II info-key GmbH & Co. KG Heinz-Fangman-Straße 2, DE-42287 Wuppertal, Deutschland 2 [email protected] March 31, 2014 Abstract Quantum theory (QT) which is one of the basic theories of physics, namely in terms of ERWIN SCHRODINGER¨ ’s 1926 wave functions in general requires the field C of the complex numbers to be formulated. However, even the complex-valued description soon turned out to be insufficient. Incorporating EINSTEIN’s theory of Special Relativity (SR) (SCHRODINGER¨ , OSKAR KLEIN, WALTER GORDON, 1926, PAUL DIRAC 1928) leads to an equation which requires some coefficients which can neither be real nor complex but rather must be hypercomplex. It is conventional to write down the DIRAC equation using pairwise anti-commuting matrices. However, a unitary ring of square matrices is a hypercomplex algebra by definition, namely an associative one. However, it is the algebraic properties of the elements and their relations to one another, rather than their precise form as matrices which is important. This encourages us to replace the matrix formulation by a more symbolic one of the single elements as linear combinations of some basis elements. In the case of the DIRAC equation, these elements are called biquaternions, also known as quaternions over the complex numbers. As an algebra over R, the biquaternions are eight-dimensional; as subalgebras, this algebra contains the division ring H of the quaternions at one hand and the algebra C ⊗ C of the bicomplex numbers at the other, the latter being commutative in contrast to H. -
Autobiography of Sir George Biddell Airy by George Biddell Airy 1
Autobiography of Sir George Biddell Airy by George Biddell Airy 1 CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. Autobiography of Sir George Biddell Airy by George Biddell Airy The Project Gutenberg EBook of Autobiography of Sir George Biddell Airy by George Biddell Airy This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg Autobiography of Sir George Biddell Airy by George Biddell Airy 2 License included with this eBook or online at www.gutenberg.net Title: Autobiography of Sir George Biddell Airy Author: George Biddell Airy Release Date: January 9, 2004 [EBook #10655] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK SIR GEORGE AIRY *** Produced by Joseph Myers and PG Distributed Proofreaders AUTOBIOGRAPHY OF SIR GEORGE BIDDELL AIRY, K.C.B., M.A., LL.D., D.C.L., F.R.S., F.R.A.S., HONORARY FELLOW OF TRINITY COLLEGE, CAMBRIDGE, ASTRONOMER ROYAL FROM 1836 TO 1881. EDITED BY WILFRID AIRY, B.A., M.Inst.C.E. 1896 PREFACE. The life of Airy was essentially that of a hard-working, business man, and differed from that of other hard-working people only in the quality and variety of his work. It was not an exciting life, but it was full of interest, and his work brought him into close relations with many scientific men, and with many men high in the State. -
The Optical Thin-Film Model: Part 2
qM qMqM Previous Page | Contents |Zoom in | Zoom out | Front Cover | Search Issue | Next Page qMqM Qmags THE WORLD’S NEWSSTAND® The Optical Thin-Film Model: Part 2 Angus Macleod Thin Film Center, Inc., Tucson, AZ Contributed Original Article n part 1 of this account [1] we covered the early attempts to topics but for our present account it is his assembly of electricity Iunderstand the phenomenon of light but heavily weighted and magnetism into a coherent connected theory culminating in towards the optics of thin ilms. Acceptance of the wave theory the prediction of a wave combining electric and magnetic ields and followed the great contributions of Young and Fresnel. We found traveling at the speed of light that most interests us. an almost completely modern account of the fundamentals of Maxwell’s ideas of electromagnetism were much inluenced by optics in Airy’s Mathematical Tracts but omitting any ideas of Michael Faraday (1791-1867). Faraday was born in the south of absorption loss. hus, by the 1830’s multiple beam interference in England to a family with few resources and was essentially self single ilms was well organized with expressions that could be used educated. His apprenticeship with a local bookbinder allowed for accurate calculation in dielectrics. Lacking in all this, however, him access to books and he read voraciously and developed an was an appreciation of the real nature of the light wave. At this interest in science, nourished by his attendance at lectures in the stage the models were mechanical with Fresnel’s ideas of an array Royal Institution of Great Britain. -
Visualising Special Relativity
Visualising Special Relativity C.M. Savage1 and A.C. Searle2 Department of Physics and Theoretical Physics, Australian National University ACT 0200, Australia Abstract We describe a graphics package we have developed for producing photo-realistic images of relativistically moving objects. The physics of relativistic images is outlined. INTRODUCTION Since Einstein’s first paper on relativity3 physicists have wondered how things would look at relativistic speeds. However it is only in the last forty years that the physics of relativistic images has become clear. The pioneering studies of Penrose4, Terrell5, and Weisskopf6 showed that there is more to relativistic images than length contraction. At relativistic speeds a rich visual environment is produced by the combined effects of the finite speed of light, aberration, the Doppler effect, time dilation, and length contraction. Computers allow us to use relativistic physics to construct realistic images of relativistic scenes. There have been two approaches to generating relativistic images: ray tracing7,8 and polygon rendering9,10,11. Ray tracing is slow but accurate, while polygon rendering is fast enough to work in real time11, but unsuitable for incorporating the full complexity of everyday scenes, such as shadows. One of us (A.S.) has developed a ray tracer, called “Backlight”12, which maximises realism and flexibility. Relativity is difficult, at least in part, because it challenges our fundamental notions of space and time in a disturbing way. Nevertheless, relativistic images, such as Figure 1, are dramatic but comprehensible. It is part of most people’s experience that curved mirrors and the like can produce strange optical distortions. -
HOW FAST IS RF? by RON HRANAC
Originally appeared in the September 2008 issue of Communications Technology. HOW FAST IS RF? By RON HRANAC Maybe a better question is, "What's the speed of an electromagnetic signal in a vacuum?" After all, what we call RF refers to signals in the lower frequency or longer wavelength part of the electromagnetic spectrum. Light is an electromagnetic signal, too, existing in the higher frequency or shorter wavelength part of the electromagnetic spectrum. One way to look at it is to assume that RF is nothing more than really, really low frequency light, or that light is really, really high frequency RF. As you might imagine, the numbers involved in describing RF and light can be very large or very small. For more on this, see my June 2007 CT column, "Big Numbers, Small Numbers" (www.cable360.net/ct/operations/techtalk/23783.html). According to the National Institute of Standards and Technology, the speed of light in a vacuum, c0, is 299,792,458 meters per second (http://physics.nist.gov/cgi-bin/cuu/Value?c). The designation c0 is one that NIST uses to reference the speed of light in a vacuum, while c is occasionally used to reference the speed of light in some other medium. Most of the time the subscript zero is dropped, with c being a generic designation for the speed of light. Let's put c0 in terms that may be more familiar. You probably recall from junior high or high school science class that the speed of light is 186,000 miles per second.