The Physical Interpretation of Special Relativity - a Vindication of Hendrik Lorentz
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Explain Inertial and Noninertial Frame of Reference
Explain Inertial And Noninertial Frame Of Reference Nathanial crows unsmilingly. Grooved Sibyl harlequin, his meadow-brown add-on deletes mutely. Nacred or deputy, Sterne never soot any degeneration! In inertial frames of the air, hastening their fundamental forces on two forces must be frame and share information section i am throwing the car, there is not a severe bottleneck in What city the greatest value in flesh-seconds for this deviation. The definition of key facet having a small, polished surface have a force gem about a pretend or aspect of something. Fictitious Forces and Non-inertial Frames The Coriolis Force. Indeed, for death two particles moving anyhow, a coordinate system may be found among which saturated their trajectories are rectilinear. Inertial reference frame of inertial frames of angular momentum and explain why? This is illustrated below. Use tow of reference in as sentence Sentences YourDictionary. What working the difference between inertial frame and non inertial fr. Frames of Reference Isaac Physics. In forward though some time and explain inertial and noninertial of frame to prove your measurement problem you. This circumstance undermines a defining characteristic of inertial frames: that with respect to shame given inertial frame, the other inertial frame home in uniform rectilinear motion. The redirect does not rub at any valid page. That according to whether the thaw is inertial or non-inertial In the. This follows from what Einstein formulated as his equivalence principlewhich, in an, is inspired by the consequences of fire fall. Frame of reference synonyms Best 16 synonyms for was of. How read you govern a bleed of reference? Name we will balance in noninertial frame at its axis from another hamiltonian with each printed as explained at all. -
The Special Theory of Relativity
THE SPECIAL THEORY OF RELATIVITY Lecture Notes prepared by J D Cresser Department of Physics Macquarie University July 31, 2003 CONTENTS 1 Contents 1 Introduction: What is Relativity? 2 2 Frames of Reference 5 2.1 A Framework of Rulers and Clocks . 5 2.2 Inertial Frames of Reference and Newton’s First Law of Motion . 7 3 The Galilean Transformation 7 4 Newtonian Force and Momentum 9 4.1 Newton’s Second Law of Motion . 9 4.2 Newton’s Third Law of Motion . 10 5 Newtonian Relativity 10 6 Maxwell’s Equations and the Ether 11 7 Einstein’s Postulates 13 8 Clock Synchronization in an Inertial Frame 14 9 Lorentz Transformation 16 9.1 Length Contraction . 20 9.2 Time Dilation . 22 9.3 Simultaneity . 24 9.4 Transformation of Velocities (Addition of Velocities) . 24 10 Relativistic Dynamics 27 10.1 Relativistic Momentum . 28 10.2 Relativistic Force, Work, Kinetic Energy . 29 10.3 Total Relativistic Energy . 30 10.4 Equivalence of Mass and Energy . 33 10.5 Zero Rest Mass Particles . 34 11 Geometry of Spacetime 35 11.1 Geometrical Properties of 3 Dimensional Space . 35 11.2 Space Time Four Vectors . 38 11.3 Spacetime Diagrams . 40 11.4 Properties of Spacetime Intervals . 41 1 INTRODUCTION: WHAT IS RELATIVITY? 2 1 Introduction: What is Relativity? Until the end of the 19th century it was believed that Newton’s three Laws of Motion and the associated ideas about the properties of space and time provided a basis on which the motion of matter could be completely understood. -
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 ................. -
Relativity with a Preferred Frame. Astrophysical and Cosmological Implications Monday, 21 August 2017 15:30 (30 Minutes)
6th International Conference on New Frontiers in Physics (ICNFP2017) Contribution ID: 1095 Type: Talk Relativity with a preferred frame. Astrophysical and cosmological implications Monday, 21 August 2017 15:30 (30 minutes) The present analysis is motivated by the fact that, although the local Lorentz invariance is one of thecorner- stones of modern physics, cosmologically a preferred system of reference does exist. Modern cosmological models are based on the assumption that there exists a typical (privileged) Lorentz frame, in which the universe appear isotropic to “typical” freely falling observers. The discovery of the cosmic microwave background provided a stronger support to that assumption (it is tacitly assumed that the privileged frame, in which the universe appears isotropic, coincides with the CMB frame). The view, that there exists a preferred frame of reference, seems to unambiguously lead to the abolishmentof the basic principles of the special relativity theory: the principle of relativity and the principle of universality of the speed of light. Correspondingly, the modern versions of experimental tests of special relativity and the “test theories” of special relativity reject those principles and presume that a preferred inertial reference frame, identified with the CMB frame, is the only frame in which the two-way speed of light (the average speed from source to observer and back) is isotropic while it is anisotropic in relatively moving frames. In the present study, the existence of a preferred frame is incorporated into the framework of the special relativity, based on the relativity principle and universality of the (two-way) speed of light, at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. -
Wave Extraction in Numerical Relativity
Doctoral Dissertation Wave Extraction in Numerical Relativity Dissertation zur Erlangung des naturwissenschaftlichen Doktorgrades der Bayrischen Julius-Maximilians-Universitat¨ Wurzburg¨ vorgelegt von Oliver Elbracht aus Warendorf Institut fur¨ Theoretische Physik und Astrophysik Fakultat¨ fur¨ Physik und Astronomie Julius-Maximilians-Universitat¨ Wurzburg¨ Wurzburg,¨ August 2009 Eingereicht am: 27. August 2009 bei der Fakultat¨ fur¨ Physik und Astronomie 1. Gutachter:Prof.Dr.Karl Mannheim 2. Gutachter:Prof.Dr.Thomas Trefzger 3. Gutachter:- der Dissertation. 1. Prufer¨ :Prof.Dr.Karl Mannheim 2. Prufer¨ :Prof.Dr.Thomas Trefzger 3. Prufer¨ :Prof.Dr.Thorsten Ohl im Promotionskolloquium. Tag des Promotionskolloquiums: 26. November 2009 Doktorurkunde ausgehandigt¨ am: Gewidmet meinen Eltern, Gertrud und Peter, f¨urall ihre Liebe und Unterst¨utzung. To my parents Gertrud and Peter, for all their love, encouragement and support. Wave Extraction in Numerical Relativity Abstract This work focuses on a fundamental problem in modern numerical rela- tivity: Extracting gravitational waves in a coordinate and gauge independent way to nourish a unique and physically meaningful expression. We adopt a new procedure to extract the physically relevant quantities from the numerically evolved space-time. We introduce a general canonical form for the Weyl scalars in terms of fundamental space-time invariants, and demonstrate how this ap- proach supersedes the explicit definition of a particular null tetrad. As a second objective, we further characterize a particular sub-class of tetrads in the Newman-Penrose formalism: the transverse frames. We establish a new connection between the two major frames for wave extraction: namely the Gram-Schmidt frame, and the quasi-Kinnersley frame. Finally, we study how the expressions for the Weyl scalars depend on the tetrad we choose, in a space-time containing distorted black holes. -
Einstein's Mistakes
Einstein’s Mistakes Einstein was the greatest genius of the Twentieth Century, but his discoveries were blighted with mistakes. The Human Failing of Genius. 1 PART 1 An evaluation of the man Here, Einstein grows up, his thinking evolves, and many quotations from him are listed. Albert Einstein (1879-1955) Einstein at 14 Einstein at 26 Einstein at 42 3 Albert Einstein (1879-1955) Einstein at age 61 (1940) 4 Albert Einstein (1879-1955) Born in Ulm, Swabian region of Southern Germany. From a Jewish merchant family. Had a sister Maja. Family rejected Jewish customs. Did not inherit any mathematical talent. Inherited stubbornness, Inherited a roguish sense of humor, An inclination to mysticism, And a habit of grüblen or protracted, agonizing “brooding” over whatever was on its mind. Leading to the thought experiment. 5 Portrait in 1947 – age 68, and his habit of agonizing brooding over whatever was on its mind. He was in Princeton, NJ, USA. 6 Einstein the mystic •“Everyone who is seriously involved in pursuit of science becomes convinced that a spirit is manifest in the laws of the universe, one that is vastly superior to that of man..” •“When I assess a theory, I ask myself, if I was God, would I have arranged the universe that way?” •His roguish sense of humor was always there. •When asked what will be his reactions to observational evidence against the bending of light predicted by his general theory of relativity, he said: •”Then I would feel sorry for the Good Lord. The theory is correct anyway.” 7 Einstein: Mathematics •More quotations from Einstein: •“How it is possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” •Questions asked by many people and Einstein: •“Is God a mathematician?” •His conclusion: •“ The Lord is cunning, but not malicious.” 8 Einstein the Stubborn Mystic “What interests me is whether God had any choice in the creation of the world” Some broadcasters expunged the comment from the soundtrack because they thought it was blasphemous. -
The Sagnac Effect: Does It Contradict Relativity?
The Sagnac Effect: Does it Contradict Relativity? By Doug Marett 2012 A number of authors have suggested that the Sagnac effect contradicts the original postulates of Special Relativity, since the postulate of the constancy of the speed of light is violated in rotating systems. [1,2,3] Sagnac himself designed the experiment of 1913 to prove the existence of the aether [4]. Other authors have attempted to explain the effect within the theoretical framework of relativity, even going as far as calling the effect “relativistic”.[5] However, we seek in this paper to show how the Sagnac effect contravenes in principle the concept of the relativity of time and motion. To understand how this happens and its wider implications, it is necessary to look first at the concept of absolute vs. relative motion, what the Sagnac effect implies about these motions, and what follows logically about the broader notions of space and time. Early Ideas Regarding Rotation and Absolute Motion: The fundamental distinction between translational and rotational motion was first pointed out by Sir Isaac Newton, and emphasized later by the work of Ernest Mach and Heinrich Hertz. One of the first experiments on the subject was Newton’s bucket experiment of 1689. It was an experiment to demonstrate that true rotational motion cannot be defined as relative rotation of a body with respect to surrounding bodies – that true motion and rest should be defined relative to absolute space instead. In Newton’s experiment, a bucket is filled with water and hung by a rope. If the rope is twisted around and around until it is tight and then released, the bucket begins to spin rapidly, not only with respect to the observers watching it, but also with respect to the water in the bucket, which at first doesn’t move and remains flat on its surface. -
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. -
Von Richthofen, Einstein and the AGA Estimating Achievement from Fame
Von Richthofen, Einstein and the AGA Estimating achievement from fame Every schoolboy has heard of Einstein; fewer have heard of Antoine Becquerel; almost nobody has heard of Nils Dalén. Yet they all won Nobel Prizes for Physics. Can we gauge a scientist’s achievements by his or her fame? If so, how? And how do fighter pilots help? Mikhail Simkin and Vwani Roychowdhury look for the linkages. “It was a famous victory.” We instinctively rank the had published. However, in 2001–2002 popular French achievements of great men and women by how famous TV presenters Igor and Grichka Bogdanoff published they are. But is instinct enough? And how exactly does a great man’s fame relate to the greatness of his achieve- ment? Some achievements are easy to quantify. Such is the case with fighter pilots of the First World War. Their achievements can be easily measured and ranked, in terms of their victories – the number of enemy planes they shot down. These aces achieved varying degrees of fame, which have lasted down to the internet age. A few years ago we compared1 the fame of First World War fighter pilot aces (measured in Google hits) with their achievement (measured in victories); and we found that We can estimate fame grows exponentially with achievement. fame from Google; Is the same true in other areas of excellence? Bagrow et al. have studied the relationship between can this tell us 2 achievement and fame for physicists . The relationship Manfred von Richthofen (in cockpit) with members of his so- about actual they found was linear. -
Evolution of Mathematics: a Brief Sketch
Open Access Journal of Mathematical and Theoretical Physics Mini Review Open Access Evolution of mathematics: a brief sketch Ancient beginnings: numbers and figures Volume 1 Issue 6 - 2018 It is no exaggeration that Mathematics is ubiquitously Sujit K Bose present in our everyday life, be it in our school, play ground, SN Bose National Center for Basic Sciences, Kolkata mobile number and so on. But was that the case in prehistoric times, before the dawn of civilization? Necessity is the mother Correspondence: Sujit K Bose, Professor of Mathematics (retired), SN Bose National Center for Basic Sciences, Kolkata, of invenp tion or discovery and evolution in this case. So India, Email mathematical concepts must have been seen through or created by those who could, and use that to derive benefit from the Received: October 12, 2018 | Published: December 18, 2018 discovery. The creative process of discovery and later putting that to use must have been arduous and slow. I try to look back from my limited Indian perspective, and reflect up on what might have been the course taken up by mathematics during 10, 11, 12, 13, etc., giving place value to each digit. The barrier the long journey, since ancient times. of writing very large numbers was thus broken. For instance, the numbers mentioned in Yajur Veda could easily be represented A very early method necessitated for counting of objects as Dasha 10, Shata (102), Sahsra (103), Ayuta (104), Niuta (enumeration) was the Tally Marks used in the late Stone Age. In (105), Prayuta (106), ArA bud (107), Nyarbud (108), Samudra some parts of Europe, Africa and Australia the system consisted (109), Madhya (1010), Anta (1011) and Parartha (1012). -
Henry Andrews Bumstead 1870-1920
NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA BIOGRAPHICAL MEMOIRS VOLUME XIII SECOND MEMOIR BIOGRAPHICAL MEMOIR OF HENRY ANDREWS BUMSTEAD 1870-1920 BY LEIGH PAGE PRESENTED TO THE ACADEMY AT THE ANNUAL MEETING, 1929 HENRY ANDREWS BUMSTEAD BY LIUGH PAGE Henry Andrews Bumstead was born in the small town of Pekin, Illinois, on March 12th, 1870, son of Samuel Josiah Bumstead and Sarah Ellen Seiwell. His father, who was a physician of considerable local prominence, had graduated from the medical school in Philadelphia and was one of the first American students of medicine to go to Vienna to complete his studies. While the family was in Vienna, Bumstead, then a child three years of age, learned to speak German as fluently as he spoke English, an accomplishment which was to prove valuable to him in his subsequent career. Bumstead was descended from an old New England family which traces its origin to Thomas Bumstead, a native of Eng- land, who settled in Boston, Massachusetts, about 1640. Many of his ancestors were engaged in the professions, his paternal grandfather, the Reverend Samuel Andrews Bumstead, being a graduate of Princeton Theological Seminary and a minister in active service. From them he inherited a keen mind and an unusually retentive memory. It is related that long before he had learned to read, his Sunday school teacher surprised his mother by complimenting her on the ease with which her son had rendered the Sunday lesson. It turned out that his mother made a habit of reading the lesson to Bumstead before he left for school, and the child's remarkable performance there was due to his ability to hold in his memory every word of the lesson after hearing it read to him a single time. -
JOHN EARMAN* and CLARK GL YMUURT the GRAVITATIONAL RED SHIFT AS a TEST of GENERAL RELATIVITY: HISTORY and ANALYSIS
JOHN EARMAN* and CLARK GL YMUURT THE GRAVITATIONAL RED SHIFT AS A TEST OF GENERAL RELATIVITY: HISTORY AND ANALYSIS CHARLES St. John, who was in 1921 the most widely respected student of the Fraunhofer lines in the solar spectra, began his contribution to a symposium in Nncure on Einstein’s theories of relativity with the following statement: The agreement of the observed advance of Mercury’s perihelion and of the eclipse results of the British expeditions of 1919 with the deductions from the Einstein law of gravitation gives an increased importance to the observations on the displacements of the absorption lines in the solar spectrum relative to terrestrial sources, as the evidence on this deduction from the Einstein theory is at present contradictory. Particular interest, moreover, attaches to such observations, inasmuch as the mathematical physicists are not in agreement as to the validity of this deduction, and solar observations must eventually furnish the criterion.’ St. John’s statement touches on some of the reasons why the history of the red shift provides such a fascinating case study for those interested in the scientific reception of Einstein’s general theory of relativity. In contrast to the other two ‘classical tests’, the weight of the early observations was not in favor of Einstein’s red shift formula, and the reaction of the scientific community to the threat of disconfirmation reveals much more about the contemporary scientific views of Einstein’s theory. The last sentence of St. John’s statement points to another factor that both complicates and heightens the interest of the situation: in contrast to Einstein’s deductions of the advance of Mercury’s perihelion and of the bending of light, considerable doubt existed as to whether or not the general theory did entail a red shift for the solar spectrum.