Chapter 11. Maxwell's Equations in Special Relativity. 1
|
|
- Brenda Clarke
- 6 years ago
- Views:
Transcription
1 Vetor Spaes in Phsis 8/6/15 Chapter 11. Mawell's Equations in Speial Relativit. 1 In Chapter 6a we saw that the eletromagneti fields E and B an be onsidered as omponents of a spae-time four-tensor. This tensor, the Mawell field tensor F, transforms under relativisti "boosts" with the same oordinate-transformation matri used to arr out the Lorent transformation on the spae-time vetor. Sine then we have introdued vetor differential alulus, entered around the gradient operator. This operator, operating on the fields E and B and the potentials and A, an be used to epress the four Mawell equations, giving a omplete theor of the eletromagneti field. In this hapter we will start to put these equations into "ovariant form," epressed in terms equall valid in an Lorent frame. In Chapter 6a we introdued the position four-vetor, t the eletromagneti-field four-tensor, E E E 1 E B B F, 1 E B B 1 E B B and the Lorent transformation matri, 1 1 whih is used in the "usual tensor wa" to transform vetor and tensor indies from one rest frame to another. Contration of indies must alwas be between a upper and a lower inde, with the metri tensor One ma note fators of 1/ whih were not present in the form of the field-strength tensor introdued in Chapter 6a. This is a pesk issue of unit sstems. The form given here gives the orret onstants in the SI sstem of units. 11-1
2 Vetor Spaes in Phsis 8/6/ g g 1 1 used to raise or lower indies. Upper indies are referred to as "ontravariant" indies, and lower indies, as "ovariant" indies, referring to details of tensor analsis whih we hope to avoid disussing here. More Four-Vetors Let's just see some other ombinations of a salar and a three-vetor whih form fourvetors. E p four-momentum p, p E p p p p p four-urrent, A four-potential: A, A A A A A A 1 t 1 four-gradient:, t Note the ool salar invariants formed b ontrating ertain of these vetors with themselves. 11 -
3 Vetor Spaes in Phsis 8/6/15 t p p E p m 4 1 t The proper-time interval, invariant under Lorent trans. A partile's invariant mass-squared. The wave-equation operator, or the d'alembertian. Here we are interested in seeing what important relations of eletromagnetism an be epressed simpl in ovariant language. Here is an interesting ontration to form a foursalar: Conservation of harge. t Remember? Positive divergene of requires a derease in the harge densit. Now let's show where Mawell's equations ome from. Sine the divergene of the eletri field equals the harge, probabl the divergene of the field-strength tensor equals the four-vetor ombination of harge and urrent E E E 1 E B B F t 1 E B B 1 E B B E E E t E B B This gives a stak of four equations, t E B B t E B B t 11-3
4 Vetor Spaes in Phsis 8/6/15 1 E E B B t E B B t E B B t Or, in old Earth-bound three-vetor notation, E E B t Here we have the two most ompliated of Mawell's equations, the soure equation. And ou might notie that the famous "displaement-urrent" term, invented b Mawell to make the wave-equation work, has appeared as b magi: E displaement t. Well, that is about as muh eitement as most people an bear. But if ou are good for more nobod reall likes the url. Let's set the four-url of the field-strength tensor equal to ero. This will of ourse involve the four-dimensional version of the Levi-Civita totall anti-smmetri tensor, 1, an even permutation of 13 1, an odd permutation of 13 otherwise Then F The top line gives and the net three lines give B B B E E B 3 1 E B E 1 B E E B 11-4
5 Vetor Spaes in Phsis 8/6/15 B E t These omplete Mawell's equations. Good enough for one da
(a) We desribe physics as a sequence of events labelled by their space time coordinates: x µ = (x 0, x 1, x 2 x 3 ) = (c t, x) (12.
2 Relativity Postulates (a) All inertial observers have the same equations of motion and the same physial laws. Relativity explains how to translate the measurements and events aording to one inertial
More informationExamples of Tensors. February 3, 2013
Examples of Tensors February 3, 2013 We will develop a number of tensors as we progress, but there are a few that we an desribe immediately. We look at two ases: (1) the spaetime tensor desription of eletromagnetism,
More informationELECTRODYNAMICS: PHYS 30441
. Relativisti Eletromagnetism. Eletromagneti Field Tensor How do E and B fields transform under a LT? They annot be 4-vetors, but what are they? We again re-write the fields in terms of the salar and vetor
More informationVector Field Theory (E&M)
Physis 4 Leture 2 Vetor Field Theory (E&M) Leture 2 Physis 4 Classial Mehanis II Otober 22nd, 2007 We now move from first-order salar field Lagrange densities to the equivalent form for a vetor field.
More informationTENSOR FORM OF SPECIAL RELATIVITY
TENSOR FORM OF SPECIAL RELATIVITY We begin by realling that the fundamental priniple of Speial Relativity is that all physial laws must look the same to all inertial observers. This is easiest done by
More informationThe Procedure of Finding the Stress-Energy. Tensor and Equations of Vector Field of Any Form
Advaned Studies in Theoretial Phsis Vol. 8, 14, no. 18, 771-779 HIKARI Ltd, www.m-hikari.om htt://d.doi.org/1.1988/ast.14.4711 The Proedure of Finding the Stress-Energ Tensor and Equations of Vetor Field
More informationParticle-wave symmetry in Quantum Mechanics And Special Relativity Theory
Partile-wave symmetry in Quantum Mehanis And Speial Relativity Theory Author one: XiaoLin Li,Chongqing,China,hidebrain@hotmail.om Corresponding author: XiaoLin Li, Chongqing,China,hidebrain@hotmail.om
More informationFour-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field
Four-dimensional equation of motion for visous ompressible substane with regard to the aeleration field, pressure field and dissipation field Sergey G. Fedosin PO box 6488, Sviazeva str. -79, Perm, Russia
More information11.1 The Special Theory of Relativity
Figure 1 Albert Einstein s ideas in phsis hanged our pereption of spae and time. 11.1 The Speial Theor of Relativit At the turn of the twentieth entur, most of the phsis ommunit enjoed a sense of aomplishment.
More informationThe homopolar generator: an analytical example
The homopolar generator: an analytial example Hendrik van Hees August 7, 214 1 Introdution It is surprising that the homopolar generator, invented in one of Faraday s ingenious experiments in 1831, still
More informationVolume Charge Density in Most General Lorentz Transformation
Publiations Aailable Online J. Si. Res. 8(), 59-65 (016) JOURNA OF SCIENTIFIC RESEARCH www.banglajol.info/inde.php/jsr Volume Charge Densit in Most General orent Transformation S. A. Bhuian *, A. R. Baiid
More informationThe Dirac Equation in a Gravitational Field
8/28/09, 8:52 PM San Franiso, p. 1 of 7 sarfatti@pabell.net The Dira Equation in a Gravitational Field Jak Sarfatti Einstein s equivalene priniple implies that Newton s gravity fore has no loal objetive
More informationChapter 26 Lecture Notes
Chapter 26 Leture Notes Physis 2424 - Strauss Formulas: t = t0 1 v L = L0 1 v m = m0 1 v E = m 0 2 + KE = m 2 KE = m 2 -m 0 2 mv 0 p= mv = 1 v E 2 = p 2 2 + m 2 0 4 v + u u = 2 1 + vu There were two revolutions
More informationSpinning Charged Bodies and the Linearized Kerr Metric. Abstract
Spinning Charged Bodies and the Linearized Kerr Metri J. Franklin Department of Physis, Reed College, Portland, OR 97202, USA. Abstrat The physis of the Kerr metri of general relativity (GR) an be understood
More informationName Solutions to Test 1 September 23, 2016
Name Solutions to Test 1 September 3, 016 This test onsists of three parts. Please note that in parts II and III, you an skip one question of those offered. Possibly useful formulas: F qequb x xvt E Evpx
More informationGeneration of EM waves
Generation of EM waves Susan Lea Spring 015 1 The Green s funtion In Lorentz gauge, we obtained the wave equation: A 4π J 1 The orresponding Green s funtion for the problem satisfies the simpler differential
More informationThe Hamiltonian in Covariant Theory of Gravitation
Advanes in Natural Siene Vol 5 No 4 pp 55-75 DOI:3968/jans75787543 ISSN 75-786 [PRINT] ISSN 75-787 [ONLINE] wwwsanadanet wwwsanadaorg The Hamiltonian in Covariant Theor of Gravitation Serge G Fedosin [a]*
More informationLagrangian Formulation of the Combined-Field Form of the Maxwell Equations
Physis Notes Note 9 Marh 009 Lagrangian Formulation of the Combined-Field Form of the Maxwell Equations Carl E. Baum University of New Mexio Department of Eletrial and Computer Engineering Albuquerque
More informationDynamics of the Electromagnetic Fields
Chapter 3 Dynamis of the Eletromagneti Fields 3.1 Maxwell Displaement Current In the early 1860s (during the Amerian ivil war!) eletriity inluding indution was well established experimentally. A big row
More informationRelativistic Dynamics
Chapter 7 Relativisti Dynamis 7.1 General Priniples of Dynamis 7.2 Relativisti Ation As stated in Setion A.2, all of dynamis is derived from the priniple of least ation. Thus it is our hore to find a suitable
More informationELECTROMAGNETIC WAVES WITH NONLINEAR DISPERSION LAW. P. М. Меdnis
ELECTROMAGNETIC WAVES WITH NONLINEAR DISPERSION LAW P. М. Меdnis Novosibirs State Pedagogial University, Chair of the General and Theoretial Physis, Russia, 636, Novosibirs,Viljujsy, 8 e-mail: pmednis@inbox.ru
More informationDirac s equation We construct relativistically covariant equation that takes into account also the spin. The kinetic energy operator is
Dira s equation We onstrut relativistially ovariant equation that takes into aount also the spin The kineti energy operator is H KE p Previously we derived for Pauli spin matries the relation so we an
More informationThe concept of the general force vector field
The onept of the general fore vetor field Sergey G. Fedosin PO box 61488, Sviazeva str. 22-79, Perm, Russia E-mail: intelli@list.ru A hypothesis is suggested that the lassial eletromagneti and gravitational
More informationElectrodynamics in Uniformly Rotating Frames as Viewed from an Inertial Frame
letrodnamis in Uniforml Rotating Frames as Viewed from an Inertial Frame Adrian Sfarti Universit of California, 387 Soda Hall, UC erele, California, USA egas@paell.net (Reeived 3 rd Feruar, 7; Aepted 3
More informationAdvanced Computational Fluid Dynamics AA215A Lecture 4
Advaned Computational Fluid Dynamis AA5A Leture 4 Antony Jameson Winter Quarter,, Stanford, CA Abstrat Leture 4 overs analysis of the equations of gas dynamis Contents Analysis of the equations of gas
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non-relativisti ase January 2019 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials are (Notes 1 eqns 43 and 44): 1 2 A 2 2 2 A = µ 0
More information1 sin 2 r = 1 n 2 sin 2 i
Physis 505 Fall 005 Homework Assignment #11 Solutions Textbook problems: Ch. 7: 7.3, 7.5, 7.8, 7.16 7.3 Two plane semi-infinite slabs of the same uniform, isotropi, nonpermeable, lossless dieletri with
More information1 The beginnings of relativity
Physis 46 Fall 26 Susan M. Lea The beginnings of relativity The priniple of relativity was first expressed by Galileo in the 7th entury: If tworeferenefranes moveat onstant relative veloitywith respet
More informationn n=1 (air) n 1 sin 2 r =
Physis 55 Fall 7 Homework Assignment #11 Solutions Textbook problems: Ch. 7: 7.3, 7.4, 7.6, 7.8 7.3 Two plane semi-infinite slabs of the same uniform, isotropi, nonpermeable, lossless dieletri with index
More informationHamiltonian with z as the Independent Variable
Hamiltonian with z as the Independent Variable 1 Problem Kirk T. MDonald Joseph Henry Laboratories, Prineton University, Prineton, NJ 08544 Marh 19, 2011; updated June 19, 2015) Dedue the form of the Hamiltonian
More information1 Summary of Electrostatics
1 Summary of Eletrostatis Classial eletrodynamis is a theory of eletri and magneti fields aused by marosopi distributions of eletri harges and urrents. In these letures, we reapitulate the basi onepts
More informationFinal Review. A Puzzle... Special Relativity. Direction of the Force. Moving at the Speed of Light
Final Review A Puzzle... Diretion of the Fore A point harge q is loated a fixed height h above an infinite horizontal onduting plane. Another point harge q is loated a height z (with z > h) above the plane.
More informationHidden Momentum in a Spinning Sphere
Hidden Momentum in a Spinning Sphere 1 Problem Kirk T. MDonald Joseph Henry Laboratories, Prineton University, Prineton, NJ 8544 (August 16, 212; updated June 3, 217 A spinning sphere at rest has zero
More informationRelativity in Classical Physics
Relativity in Classial Physis Main Points Introdution Galilean (Newtonian) Relativity Relativity & Eletromagnetism Mihelson-Morley Experiment Introdution The theory of relativity deals with the study of
More informationThe concept of the general force vector field
OALib Journal, Vol. 3, P. 1-15 (16). http://dx.doi.org/1.436/oalib.11459 The onept of the general fore vetor field Sergey G. Fedosin PO box 61488, Sviazeva str. -79, Perm, Russia E-mail: intelli@list.ru
More informationPHY 396 T: SUSY Solutions for problem set #12.
PHY 396 T: SUSY Solutions or problem set #. Problem a: In priniple the non-perturbative superpotential o the theory may depend on the dual quark and antiquark ields q and q as well as the singlets Φ but
More informationAn Elucidation of the Symmetry of Length Contraction Predicted by the Special Theory of Relativity
pplied Phsis Researh; Vol 9, No 3; 07 ISSN 96-9639 E-ISSN 96-9647 Published b Canadian Center of Siene and Eduation n Eluidation of the Smmetr of ength Contration Predited b the Speial Theor of Relativit
More informationQUANTUM MECHANICS II PHYS 517. Solutions to Problem Set # 1
QUANTUM MECHANICS II PHYS 57 Solutions to Problem Set #. The hamiltonian for a lassial harmoni osillator an be written in many different forms, suh as use ω = k/m H = p m + kx H = P + Q hω a. Find a anonial
More informationarxiv: v1 [physics.gen-ph] 5 Jan 2018
The Real Quaternion Relativity Viktor Ariel arxiv:1801.03393v1 [physis.gen-ph] 5 Jan 2018 In this work, we use real quaternions and the basi onept of the final speed of light in an attempt to enhane the
More informationTheory of Dynamic Gravitational. Electromagnetism
Adv. Studies Theor. Phys., Vol. 6, 0, no. 7, 339-354 Theory of Dynami Gravitational Eletromagnetism Shubhen Biswas G.P.S.H.Shool, P.O.Alaipur, Pin.-7445(W.B), India shubhen3@gmail.om Abstrat The hange
More informationVirtual Work for Frames. Virtual Work for Frames. Virtual Work for Frames. Virtual Work for Frames. Virtual Work for Frames. Virtual Work for Frames
IL 32 /9 ppling the virtual work equations to a frame struture is as simple as separating the frame into a series of beams and summing the virtual work for eah setion. In addition, when evaluating the
More informationCHAPTER 26 The Special Theory of Relativity
CHAPTER 6 The Speial Theory of Relativity Units Galilean-Newtonian Relativity Postulates of the Speial Theory of Relativity Simultaneity Time Dilation and the Twin Paradox Length Contration Four-Dimensional
More information[Khalid, 5(3): March 2018] ISSN DOI /zenodo Impact Factor
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES LORENZ TRANSFORMATION FOR FREE SPACE AND FIELDS USING MAXWELL S EQUATIONS AND NEWTON'S LAWS Nuha Abdelrahman Khalid*, Mubarak Dirar Abdallah, Zoalnoon
More informationNew Chapter 3 The Universal Constants
New Chapter 3 The Universal Constants 3. Our Set of Universal Constants The ten dimensionless universal onstants to be used here have already been listed at the beginning of.. In this hapter we desribe
More informationIn this case it might be instructive to present all three components of the current density:
Momentum, on the other hand, presents us with a me ompliated ase sine we have to deal with a vetial quantity. The problem is simplified if we treat eah of the omponents of the vet independently. s you
More informationF = F x x + F y. y + F z
ECTION 6: etor Calulus MATH20411 You met vetors in the first year. etor alulus is essentially alulus on vetors. We will need to differentiate vetors and perform integrals involving vetors. In partiular,
More informationPhysics 6C. Special Relativity. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Physis 6C Speial Relatiity Two Main Ideas The Postulates of Speial Relatiity Light traels at the same speed in all inertial referene frames. Laws of physis yield idential results in all inertial referene
More informationA EUCLIDEAN ALTERNATIVE TO MINKOWSKI SPACETIME DIAGRAM.
A EUCLIDEAN ALTERNATIVE TO MINKOWSKI SPACETIME DIAGRAM. S. Kanagaraj Eulidean Relativity s.kana.raj@gmail.om (1 August 009) Abstrat By re-interpreting the speial relativity (SR) postulates based on Eulidean
More informationHOW TO FACTOR. Next you reason that if it factors, then the factorization will look something like,
HOW TO FACTOR ax bx I now want to talk a bit about how to fator ax bx where all the oeffiients a, b, and are integers. The method that most people are taught these days in high shool (assuming you go to
More informationThe gravitational phenomena without the curved spacetime
The gravitational phenomena without the urved spaetime Mirosław J. Kubiak Abstrat: In this paper was presented a desription of the gravitational phenomena in the new medium, different than the urved spaetime,
More informationThe First Principle of Thermodynamics under Relativistic Conditions and Temperature
New Horizons in Mathematial Physis, Vol., No., September 7 https://dx.doi.org/.66/nhmp.7. 37 he First Priniple of hermodynamis under Relativisti Conditions and emperature Emil Veitsman Independent Researher
More informationThe Electromagnetic Radiation and Gravity
International Journal of Theoretial and Mathematial Physis 016, 6(3): 93-98 DOI: 10.593/j.ijtmp.0160603.01 The Eletromagneti Radiation and Gravity Bratianu Daniel Str. Teiului Nr. 16, Ploiesti, Romania
More informationHigh Energy Astrophysics
High Energ Astrophsis Essentials Giampaolo Pisano Jodrell Bank Centre for Astrophsis - Uniersit of Manhester giampaolo.pisano@manhester.a.uk - http://www.jb.man.a.uk/~gp/ Februar 01 Essentials - Eletromagneti
More informationEinstein s Three Mistakes in Special Relativity Revealed. Copyright Joseph A. Rybczyk
Einstein s Three Mistakes in Speial Relativity Revealed Copyright Joseph A. Rybzyk Abstrat When the evidene supported priniples of eletromagneti propagation are properly applied, the derived theory is
More informationClassical Field Theory
Preprint typeset in JHEP style - HYPER VERSION Classial Field Theory Gleb Arutyunov a a Institute for Theoretial Physis and Spinoza Institute, Utreht University, 3508 TD Utreht, The Netherlands Abstrat:
More informationAn Effective Photon Momentum in a Dielectric Medium: A Relativistic Approach. Abstract
An Effetive Photon Momentum in a Dieletri Medium: A Relativisti Approah Bradley W. Carroll, Farhang Amiri, and J. Ronald Galli Department of Physis, Weber State University, Ogden, UT 84408 Dated: August
More informationELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES.
ELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES. All systems with interation of some type have normal modes. One may desribe them as solutions in absene of soures; they are exitations of the system
More informationProperties of Quarks
PHY04 Partile Physis 9 Dr C N Booth Properties of Quarks In the earlier part of this ourse, we have disussed three families of leptons but prinipally onentrated on one doublet of quarks, the u and d. We
More informationApplication of Bi-Quaternions in Physics
Appliation of Bi-Quaternions in Physis André Waser * First issued: 9.7. Last update: 6.5.7 This paper introdues a new bi-quaternion notation and applies this notation to eletrodynamis. A set of extended
More informationChapter 35. Special Theory of Relativity (1905)
Chapter 35 Speial Theory of Relatiity (1905) 1. Postulates of the Speial Theory of Relatiity: A. The laws of physis are the same in all oordinate systems either at rest or moing at onstant eloity with
More informationModes are solutions, of Maxwell s equation applied to a specific device.
Mirowave Integrated Ciruits Prof. Jayanta Mukherjee Department of Eletrial Engineering Indian Institute of Tehnology, Bombay Mod 01, Le 06 Mirowave omponents Welome to another module of this NPTEL mok
More informationSimple Considerations on the Cosmological Redshift
Apeiron, Vol. 5, No. 3, July 8 35 Simple Considerations on the Cosmologial Redshift José Franiso Garía Juliá C/ Dr. Maro Mereniano, 65, 5. 465 Valenia (Spain) E-mail: jose.garia@dival.es Generally, the
More informationElectromagnetic radiation
5584 5585 8 Eletromagneti radiation 5586 5587 5588 5589 8. Solution of Maxwell equations with external urrent The eletromagneti field generated by an external (expliitly given) four-urrent J µ (x) is given
More informationClassical Trajectories in Rindler Space and Restricted Structure of Phase Space with PT-Symmetric Hamiltonian. Abstract
Classial Trajetories in Rindler Spae and Restrited Struture of Phase Spae with PT-Symmetri Hamiltonian Soma Mitra 1 and Somenath Chakrabarty 2 Department of Physis, Visva-Bharati, Santiniketan 731 235,
More informationChapter Outline The Relativity of Time and Time Dilation The Relativistic Addition of Velocities Relativistic Energy and E= mc 2
Chapter 9 Relativeity Chapter Outline 9-1 The Postulate t of Speial Relativity it 9- The Relativity of Time and Time Dilation 9-3 The Relativity of Length and Length Contration 9-4 The Relativisti Addition
More informationModule 5: Red Recedes, Blue Approaches. UNC-TFA H.S. Astronomy Collaboration, Copyright 2012
Objetives/Key Points Module 5: Red Reedes, Blue Approahes UNC-TFA H.S. Astronomy Collaboration, Copyright 2012 Students will be able to: 1. math the diretion of motion of a soure (approahing or reeding)
More informationarxiv:gr-qc/ v7 14 Dec 2003
Propagation of light in non-inertial referene frames Vesselin Petkov Siene College, Conordia University 1455 De Maisonneuve Boulevard West Montreal, Quebe, Canada H3G 1M8 vpetkov@alor.onordia.a arxiv:gr-q/9909081v7
More informationTransverse momentum as a source of gravitoelectromagnetism
Transverse momentum as a soure of gravitoeletromagnetism D. H. Delphenih Spring Valley, OH 45370 USA Abstrat: Momentum an be regarded as a mass urrent that an be used as the soure of the gravitoeletromagneti
More informationElectromagnetic Theory Prof. Ruiz, UNC Asheville, doctorphys on YouTube Chapter B Notes. Special Relativity. B1. The Rotation Matrix
Eletromagneti Theory Prof. Ruiz, UNC Asheille, dotorphys on YouTube Chapter B Notes. Speial Relatiity B1. The Rotation Matrix There are two pairs of axes below. The prime axes are rotated with respet to
More informationTime Domain Method of Moments
Time Domain Method of Moments Massahusetts Institute of Tehnology 6.635 leture notes 1 Introdution The Method of Moments (MoM) introdued in the previous leture is widely used for solving integral equations
More informationVelocity Addition in Space/Time David Barwacz 4/23/
Veloity Addition in Spae/Time 003 David arwaz 4/3/003 daveb@triton.net http://members.triton.net/daveb Abstrat Using the spae/time geometry developed in the previous paper ( Non-orthogonal Spae- Time geometry,
More informationLecture 15 (Nov. 1, 2017)
Leture 5 8.3 Quantum Theor I, Fall 07 74 Leture 5 (Nov., 07 5. Charged Partile in a Uniform Magneti Field Last time, we disussed the quantum mehanis of a harged partile moving in a uniform magneti field
More informationECE507 - Plasma Physics and Applications
ECE57 - Plasma Phsis and Appliations Leture 4 Prof. Jorge Roa and Dr. Fernando Tomasel Department of Eletrial and Computer Engineering Constant, uniform Let s align with the -ais, so = k. Then we an write
More informationarxiv: v1 [physics.class-ph] 12 Mar 2012
Relativisti Dynamis of a Charged Partile in an Eletrosalar Field D.V. Podgainy 1, O.A. Zaimidoroga 2 arxiv:1203.2490v1 [physis.lass-ph] 12 Mar 2012 Joint Institute for Nulear Researh 141980, Dubna, Russia
More informationCS420/ S-04 Intro to 3D Math 1
CS420/686-2016S-04 Intro to 3D Math 1 04-0: Right-Handed vs. Left-Handed Hold out our left hand (reall, do it!): Thum to the right Inde finder up Middle finger straight ahead This forms a asis for a 3D
More informationSURFACE WAVES OF NON-RAYLEIGH TYPE
SURFACE WAVES OF NON-RAYLEIGH TYPE by SERGEY V. KUZNETSOV Institute for Problems in Mehanis Prosp. Vernadskogo, 0, Mosow, 75 Russia e-mail: sv@kuznetsov.msk.ru Abstrat. Existene of surfae waves of non-rayleigh
More informationInternational Journal of Thermodynamics, Vol. 18, No. 1, P (2015). Sergey G.
International Journal of Therodynais Vol. 8 No. P. 3-4 (5). http://dx.doi.org/.554/ijot.5343 Four-diensional equation of otion for visous opressible and harged fluid with regard to the aeleration field
More informationarxiv:physics/ v1 [physics.class-ph] 8 Aug 2003
arxiv:physis/0308036v1 [physis.lass-ph] 8 Aug 003 On the meaning of Lorentz ovariane Lszl E. Szab Theoretial Physis Researh Group of the Hungarian Aademy of Sienes Department of History and Philosophy
More informationGUIDELINES FOR A SPACE PROPULSION DEVICE BASED ON HEIM'S QUANTUM THEORY
GUIDELINES FOR A SPACE PROPULSION DEVICE BASED ON HEIM'S QUANUM HEORY Walter Drösher 1, Johem Häuser 1,2 1 Institut für Grenzgebiete der Wissenshaft (IGW), Leopold - Franzens Universität Innsbruk, Innsbruk,
More informationInstitut für Grenzgebiete der Wissenschaft (IGW), Leopold - Franzens Universität Innsbruck, Innsbruck, Austria
GUIDELINES FOR A AIAA 2004-3700 SPACE PROPULSION DEVICE BASED ON HEIM'S QUANUM HEORY Walter Drösher 1, Johem Häuser 1,2 1 Institut für Grenzgebiete der Wissenshaft (IGW), Leopold - Franzens Universität
More informationThe Unified Geometrical Theory of Fields and Particles
Applied Mathematis, 014, 5, 347-351 Published Online February 014 (http://www.sirp.org/journal/am) http://dx.doi.org/10.436/am.014.53036 The Unified Geometrial Theory of Fields and Partiles Amagh Nduka
More information8.022 (E&M) Lecture 11
8.0 (E&M) Leture Topis: Introdution to Speial Relatiit Length ontration and Time dilation Lorentz transformations Veloit transformation Speial relatiit Read for the hallenge? Speial relatiit seems eas
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non relativisti ase 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials in Lorentz Gauge Gaussian units are: r 2 A 1 2 A 2 t = 4π 2 j
More informationAharonov-Bohm effect. Dan Solomon.
Aharonov-Bohm effet. Dan Solomon. In the figure the magneti field is onfined to a solenoid of radius r 0 and is direted in the z- diretion, out of the paper. The solenoid is surrounded by a barrier that
More informationFig 1: Variables in constant (1+1)D acceleration. speed of time. p-velocity & c-time. velocities (e.g. v/c) & times (e.g.
Proper veloity and frame-invariant aeleration in speial relativity P. Fraundorf Department of Physis & Astronomy University of Missouri-StL, St. Louis MO (November, 99) We examine here a possible endpoint
More informationTowards an Absolute Cosmic Distance Gauge by using Redshift Spectra from Light Fatigue.
Towards an Absolute Cosmi Distane Gauge by using Redshift Spetra from Light Fatigue. Desribed by using the Maxwell Analogy for Gravitation. T. De Mees - thierrydemees @ pandora.be Abstrat Light is an eletromagneti
More informationMotion through a velocity selector analyzed using a galilean transformation
Motion through a veloit seletor analzed using a galilean transformation Doug Bradle-Huthison Phsis Department, Sinlair Communit College, 444 W. 3 rd St., Daton, OH 4540. E-mail: douglas.bradle-hut@sinlair.edu
More informationQ2. [40 points] Bishop-Hill Model: Calculation of Taylor Factors for Multiple Slip
27-750, A.D. Rollett Due: 20 th Ot., 2011. Homework 5, Volume Frations, Single and Multiple Slip Crystal Plastiity Note the 2 extra redit questions (at the end). Q1. [40 points] Single Slip: Calulating
More informationThe Special Theory of Relativity
The Speial Theory of Relatiity Galilean Newtonian Relatiity Galileo Galilei Isaa Newton Definition of an inertial referene frame: One in whih Newton s first law is alid. onstant if F0 Earth is rotating
More information). In accordance with the Lorentz transformations for the space-time coordinates of the same event, the space coordinates become
Relativity and quantum mehanis: Jorgensen 1 revisited 1. Introdution Bernhard Rothenstein, Politehnia University of Timisoara, Physis Department, Timisoara, Romania. brothenstein@gmail.om Abstrat. We first
More informationWe wrote down the Boltzmann equation for photons last time; it is:
1 Objetives In this leture we will take the photon multipole equations derived last time, and onvert them into Fourier-multipole spae. This will be onvenient for linear perturbation theory, sine eah Fourier
More informationLecture 3 - Lorentz Transformations
Leture - Lorentz Transformations A Puzzle... Example A ruler is positioned perpendiular to a wall. A stik of length L flies by at speed v. It travels in front of the ruler, so that it obsures part of the
More informationVector Analysis in Three Dimensions
Appendix 1 etor Analysis in Three Dimensions MULTIPLICATIE RELATIONHIP a (b ) = (a b) = b ( a) (A1.1) a (b ) = b(a ) (a b) (A1.2) a (b ) (b a) = b (a ) (A1.3) (a b) ( d) = (a )(b d) (a d)(b ) (A1.4) a
More informationThe Hanging Chain. John McCuan. January 19, 2006
The Hanging Chain John MCuan January 19, 2006 1 Introdution We onsider a hain of length L attahed to two points (a, u a and (b, u b in the plane. It is assumed that the hain hangs in the plane under a
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nulear and Partile Physis (5110) Marh 7, 009 Relativisti Kinematis 3/7/009 1 Relativisti Kinematis Review! Wherever you studied this before, look at it again, e.g. Tipler (Modern Physis), Hyperphysis
More information4. (12) Write out an equation for Poynting s theorem in differential form. Explain in words what each term means physically.
Eletrodynamis I Exam 3 - Part A - Closed Book KSU 205/2/8 Name Eletrodynami Sore = 24 / 24 points Instrutions: Use SI units. Where appropriate, define all variables or symbols you use, in words. Try to
More informationarxiv:physics/ v4 [physics.gen-ph] 9 Oct 2006
The simplest derivation of the Lorentz transformation J.-M. Lévy Laboratoire de Physique Nuléaire et de Hautes Energies, CNRS - IN2P3 - Universités Paris VI et Paris VII, Paris. Email: jmlevy@in2p3.fr
More informationLet s move to Bound States
Let s move to Bound States When we disuss bound states of two objets in entral-fore potential, kineti energy and potential energy are ~the same. How does this ompare to the rest energy of the objets? Hydrogen
More informationINTRODUCTION TO QUANTUM MECHANICS
A. La Rosa Letre Notes PSU-Physis PH 45 INTRODUCTION TO QUANTUM MECHANICS PART-I TRANSITION from CLASSICAL to QUANTUM PHYSICS CHAPTER CLASSICAL PHYSICS ELECTROMAGNETISM and RELATIITY REIEW,. ELECTROMAGNETISM..A
More informationPhysics 523, General Relativity Homework 4 Due Wednesday, 25 th October 2006
Physis 523, General Relativity Homework 4 Due Wednesday, 25 th Otober 2006 Jaob Lewis Bourjaily Problem Reall that the worldline of a ontinuously aelerated observer in flat spae relative to some inertial
More information