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### ImportantConcepts05

Course: PH 136, Spring 2002
School: Caltech
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Word Count: 728

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136 Physics Kip Thorne Important Concepts Chapters 1 through 5 Caltech Nov 3, 2002 I Frameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for a collection of particles: Chap 2 C Phase space for an ensemble of systems: Chap 3 D Relationship of Classical Theory to Quantum Theory 1 Mean occupation number as...

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136 Physics Kip Thorne Important Concepts Chapters 1 through 5 Caltech Nov 3, 2002 I Frameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for a collection of particles: Chap 2 C Phase space for an ensemble of systems: Chap 3 D Relationship of Classical Theory to Quantum Theory 1 Mean occupation number as classical distribution function: Sec. 2.3 2 Mean occupation number determines whether particles behave like a classical wave, like classical particles, or quantum mechanically: Secs. 2.3 & 2.4; Ex. 2.1; Fig. 2.5 II Physics as Geometry A Newtonian: coordinate invariance of physical laws 1 Idea Introduced: Sec. 1.2 2 Newtonian particle kinetics as an example: Sec. 1.4 B Special relativistic: frame-invariance of physical laws 1 Idea introduced: Sec. 1.2 2 Relativistic particle kinetics: Sec. 1.4 3 4-momentum conservation: Secs. 1.4 & 1.12 a Stress-energy tensor: Sec. 1.12 4 Electromagnetic theory: Sec. 1.10 a Lorentz force law: Sec. 1.4 5 Kinetic theory: Chap. 2 a Derivation of equations for macroscopic quantities as integrals over momentum space [Sec. 2.5] b Distribution function is frame-invariant and constant along fiducial trajectories [Secs. 2.2 & 2.7] C Statistical mechanics: invariance of the laws under canonical transformations (change of generalized coordinates and momenta in phase space): Sec. 3.2, Ex. 3.1 III 3+1 Splits of spacetime into space plus time, and resulting relationship between frame-invariant and frame-dependent laws of physics A Particle kinetics: Sec. 1.6 B Electromagnetic theory: Sec. 1.10 C Continuum mechanics; stress-energy tensor: Sec. 1.12 D Kinetic theory: Secs. 2.2, 2.5 & 2.7 1 Cosmic microwave radiation viewed in moving frame: Ex. 2.3 IV Spacetime diagrams A Introduced: Sec. 1.7 B Simultaneity breakdown, Lorentz contraction, time dilation: Exercise 1.11 C The nature of time; twins paradox, time travel: Sec. 1.8 D Global conservation of 4-momentum: Secs. 1.6 & 1.12 E Kinetic theory -- Momentum space: Sec. 2.2 V Statistical physics concepts A Systems and ensembles: Sec. 3.2 B Distribution function 1 For particles: Sec. 2.2 2 For photons, and its relationship to specific intensity: Sec. 2.2 3 For systems in statistical mechanics: Sec. 3.2 4 Evolution via Vlasov or Boltzmann transport equation: Sec. 2.7 a Kinetic Theory: Sec 2.7 b Statistical mechanics: Sec. 3.3 5 For random processes: hierarchy of probability distributions: Sec. 5.2 C Thermal equilibrium 1 Kinetic-theory distribution functions: Sec. 2.4 2 In statistical mechanics; general form of distribution function in terms of quantities exchanged with environment: Sec. 3.4 3 Evolution into statistical equilbrium--phase mixing and coarse graining: Secs. 3.6 and 3.8 D Representations of Thermodynamics 1 Summary: Table 4.1 2 Energy representation: Sec. 4.2 3 Free-energy representation: Sec. 4.3 4 Enthalpy representaiton: Ex. 4.3 5 Gibbs representation: Sec. 4.4 E Specific ensembles statistical-equilibrium and their uses 1 Summary: Table 4.1 2 Canonical, Gibbs, grand canonical and microcanonical defined: Sec. 3.4 3 Microcanonical: Secs. 3.5 and 4.2 4 Canonical: Sec. 4.3 5 Gibbs: Sec. 4.4 6 Grand canonical: Sec. 3.7 and Ex. 3.6 and 3.8 F Fluctuations in statistical equilibrium 1 Summary: Table 4.2 2 Particle number in a box: Ex. 3.7 3 Distribution of particles and energy inside a closed box: Sec. 4.5 4 Temperature and volume fluctuations of system interacting with a heat and volume bath: Sec. 4.5 5 Fluctuation-dissipation theorem: Sec. 5.6.1 6 Fokker-Planck equation: Sec. 5.6.2 7 Brownian motion: Sec. 5.6.3 G Entropy 1 Defined: Sec. 3.6 2 Second law (entropy increase): Secs. 3.6, 3.8 3 Entropy per particle: Secs. 3.7, 3.8, Fig. 3.4, Exs. 3.5, 3.9 4 Of systems in contact with thermalized baths: a Summary: Table 4.1 b Heat & volume bath (Gibbs): Sec. 4.4 a Phase transitions: Secs. 4.4 & 4.6, Ex. 4.4 & 4.7 b Chemical reactions: Sec. 4.4, Ex. 4.5 & 4.6 H Macroscopic properties as integrals over momentum space: 1 In kinetic theory a Number-flux vector, stress-energy tensor: Sec. 2.5 b Equations of state: Sec. 2.6 c Transport coefficients: Sec. 2.8 2 In statistical mechanics: Extensive thermodynamic variables a Grand partition function: Ex. 3.6 3 In theory of random processes: Ensemble averages: Sec. 5.2 I Random Processes: Chap 5 1 Properties of random processes a Stationarity: Sec. 5.2 b Markov: Sec. 5.2 c Gaussian: Sec. 5.2 d Ergodicity: Sec. 5.3 2 Characterization of random processes a Probability distributions: Sec. 5.2 b Correlation functions: Sec. 5.3 c Spectral densities: Sec. 5.3 a white, flicker, random-walk: Sec. 5.4 b shot noise: Sec. 5.5 3 Theorems a Central limit theorem [many influences -> Gaussian]: Sec. 5.2 a and shot noise: Sec. 5.5 b Wiener-Khintchine [correlation <-> spectral density]: Sec. 5.3 c Doobs theorem [Gaussian & Markoff -> fully characterized by mean, variance, and relaxation time: Sec. 5.3 d Effect of filter on spectral density: Sec. 5.5 e Fluctuation-dissipation theorem: Sec. 5.6.1, Ex. 5.7, 5.8, 5.10 f Fokker-Planck equation: Sec. 5.6.2 a and Brownian motion: Sec. 5.6.3, Ex. 5.6, 5.9 4 Filtering a Band-pass filter: Sec. 5.5, Ex. 5.2 b Wiener's optimal filter: Ex. 5.3 VI Computational techniques A Tensor analysis 1 Without a coordinate system, abstract notation: Secs. 1.3 and 1.9 2 Index manipulations in Euclidean 3-space and in spacetime a Tools introduced; slot-naming index notation: Sec's 1.5, 1.7 &1.9 b Used to derive standard 3-vector identities: Exercise 1.15 B Two-lengthscale expansions: Box 2.2 1 Solution of Boltzmann transport equation in diffusion approximation: Sec. 2.8 2 Semiclosed systems in statistical mechanics: Sec. 3.2 3 Statistical independence of subsystems: Sec. 3.4 C Statistical physics: 1 Computation of fundamental potentials (or partition functions) via sum over states: Secs. 3.8, 4.3; Exercise 3.6 2 Renormalization group: Sec. 4.6 3 Monte carlo: Sec. 4.7
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Caltech - PH - 136
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Caltech - PH - 136
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Caltech - PH - 136
Part II OPTICS1OpticsPrior to the opening up of the electromagnetic spectrum and the development of quantum mechanics, the study of optics was only concerned with visible light. Reection and refraction were rst described by the Greek philosophers and f
Caltech - PH - 136
Ph 136a CHAPTER 6: GEOMETRIC OPTICS Reading: Chapter 6 of Blandford and Thorne. Problems A. Do: 1. 2. B. Do: C. Do: 1. 2. D. Do: 1. 2. Exercise 6.2 Gaussian wave packet and its spreading, or Exercise 6.4 Gravitational waves from a spinning neutron star. E
Caltech - PH - 136
Physics 136 Kip Thorne Important Concepts Chapters 1 through 6 ICaltech Nov 10, 2002IIIIIIVVFrameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for
Caltech - PH - 136
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Caltech - PH - 136
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Caltech - PH - 136
Chapter 7 DiractionVersion 0207.1, 13 Nov 02 Please send comments, suggestions, and errata via email to kip@tapir.caltech.edu and to rdb@caltech.edu, or on paper to Kip Thorne, 130-33 Caltech, Pasadena CA 911257.1OverviewThe previous chapter was devot
Caltech - PH - 136
Ph 136a CHAPTER 7: DIFFRACTION Reading: Chapter 7 of Blandford and Thorne. Problems A. Do: 1. 2. B. Do: 1. 2. C. Do: 1. 2. D. Do: Exercise 7.1 Pointillist painting, or Exercise 7.2 Thickness of a human hair Exercise 7.3 Diraction grating, or Exercise 7.5
Caltech - PH - 136
Physics 136 Kip Thorne Important Concepts Chapters 1 through 7 ICaltech Nov 15, 2002Frameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for a collectio
Caltech - PH - 136
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Caltech - PH - 136
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Caltech - PH - 136
Chapter 8 InterferenceVersion 0208.1, 20 November 2002 Please send comments, suggestions, and errata via email to kip@tapir.caltech.edu and to rdb@caltech.edu, or on paper to Kip Thorne, 130-33 Caltech, Pasadena CA 911258.1OverviewIn the last chapter,
Caltech - PH - 136
Ph 136a CHAPTER 8: INTERFERENCE Reading: Chapter 8 of Blandford and Thorne. Problems A. Do: 1. 2. B. Do: C. Do: 1. 2. D. Do: 1. 2.20 November 2002Exercise 8.2 Lateral coherence of solar radiation, or Exercise 8.4 Longituidinal coherence of heavy metal r
Caltech - PH - 136
Physics 136 Kip Thorne Important Concepts Chapters 1 through 8 ICaltech Nov 20, 2002Frameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for a collectio
Caltech - PH - 136
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Caltech - PH - 136
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %Title: ps8.dvi %Pages: 9 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips ps8 %DVIPSParameters: dpi=1200, com
Caltech - PH - 136
Chapter 9 Nonlinear OpticsVersion 0209.1, 27 Nov 02 Please send comments, suggestions, and errata via email to kip@tapir.caltech.edu and rdb@caltech.edu, or on paper to Kip Thorne, 130-33 Caltech, Pasadena CA 911259.1OverviewCommunication technology i
Caltech - PH - 136
1Ph 136: Nonlinear Optics HomeworkRead the text and try to work again through the monatomic gas calculations we went through in class. 1. Ex 9.2 In answering Part a, you may make a calculation based on Fraunhofer diraction or give a verabl argument. 2.
Caltech - PH - 136
Physics 136 Kip Thorne Important Concepts Chapters 1 through 9 ICaltech Nov 29, 2002Frameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for a collectio
Caltech - PH - 136
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Caltech - PH - 136
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Caltech - PH - 136
Part III ELASTICITY1Chapter 10 ElastostaticsVersion 0210.1, 08 January 2003 Please send comments, suggestions, and errata via email to kip@tapir.caltech.edu and rdb@caltech.edu, or on paper to Kip Thorne, 130-33 Caltech, Pasadena CA 9112510.1Introduc
Caltech - PH - 136
Ph 136a CHAPTER 10: ELASTOSTATICS Reading: Chapter 10 of Blandford and Thorne. Problems20 November 2002A. Do: Exercise 10.3, Order of Magnitude Estimates B. Do: 1. Exercise 10.1a, Connection in Cylindrical Coordinates [only part a, not part b], and ALSO
Caltech - PH - 136
Physics 136 Kip Thorne Important Concepts Chapters 1 through 10 I.Caltech January 16, 2003Frameworks for physical laws and their relationships to each other A. General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B. Phase space for a c
Caltech - PH - 136
Solution for Chapter 10(compiled by Xinkai Wu) A. 10.3 Order of magnitude estimates (i) Steel wire [C.Y.Mou/90]z=Lz=0Figure 1: Steel wire The weight of the wire creates stress inside, Tzz,z + g = 0 Tzz = gzmax The maximum stress is at z = L, Tzz = gL
ASU - MGT - 302
ASU - MGT - 302
Chapter2CountryDifferencesPoliticalSystems Systemofgovernmentinanation Politicalsystemscanbeassessed accordingtotwodimensions: CollectivismversusIndividualism DemocraticversusTotalitarianCollectivismandIndividualism CollectivismCollectivegoalsaremo
ASU - MGT - 302
ASU - MGT - 302
ASU - MGT - 302
ChapterEightRegionalEconomic IntegrationKeyConcepts Formsofregionaleconomicintegration Theincreasingimportanceofregional economicintegration ThestructureoftheEuropeanUnionand currentchallengesRegionalEconomicIntegration Regionaleconomicintegrationref
ASU - MGT - 302
Chapter 3Differences in CultureWhat is Culture? Culture is that complex whole which includes knowledge, belief, art, morals, law, custom, and other capabilities acquired by man as a member of society. A system of values and norms that are shared among
ASU - MGT - 302
Chapter NineThe Foreign Exchange MarketKey Concepts: The factors that impact exchange rates The micro and macro implications of exchange rate changes Approaches for forecasting exchange rates Techniques to protect against exchange rate riskExchange Ra
ASU - MGT - 302
Chapter10TheInternationalMonetary SystemKeyTerms: InternationalMonetarySystem: institutionalarrangementscountries adopttogovernexchangeratesFloatingExchangeRate Systems BenefitsofFloatingExchangeRate Systems Maintainmonetarypolicyautonomy Allowcurre
ASU - MGT - 302
TheGlobalCapitalMarketChapter11 Advancesininformationtechnology DeregulationbygovernmentsGrowthoftheGlobalCapitalMarketFinancialGlobalization BenefitsofFinancialGlobalization LowerCostofCapital PortfolioDiversification DangersofFinancialGlobalizati
ASU - MGT - 302
ASU - MGT - 302
Chapter13TheOrganizationofInternational BusinessOrganizationalArchitecture OrganizationalStructure ControlSystems Incentives Processes OrganizationalCulture PeopleOrganizationalArchitectureRequirementsforEffective OrganizationalArchitecture Thediffer
ASU - MGT - 302
ASU - MGT - 302
ASU - MGT - 302
Chapter 15Exporting, Importing, and CountertradeExporting Information Sources U.S. Department of Commerce Small Business Administration Trade Commissions Financial InstitutionsExport Strategy Hire experts Focus on a few markets Enter on a small scale
ASU - MGT - 302
Chapter16GlobalProduction, Outsourcing,andLogisticsMainChapterConcepts Thefactorsthatinfluencewhere productionactivitiesshouldbelocated. Thefactorsthatinfluencethenumberof locationsthatshouldbeusedtoperform productionactivities. Thefactorsthatinfluence
ASU - ACC - 241
ACC 241 Chapter 13 Continued Please pick up handout in the back of the room.Copyright 2010 School of Accountancy, Arizona State UniversityCost Concepts Review-From Wednesday Cost Object Direct vs Indirect Costs Product Costs (Manufacturing/Inventoriabl
ASU - ACC - 241
WELCOME TO ACC241Copyright 2010 School of Accountancy, Arizona State University8:35 Class Breakout InstructorSLN DAYS 8:35 AM 8:35 AM 8:35 AM 8:35 AM TIME 9:25 AM 9:25 AM 9:25 AM 9:25 AM ROOM BAC209 BA358 BA359 BAC324 INSTRUCTOR Brandon Danny Lorenzo R
ASU - ACC - 241
Chapter 16Job Costing Please pick up handoutCopyright 2010 School of Accountancy, Arizona State UniversityDeveloping a Costing SystemWhen developing a product-costing system, there are three choices that must be made: Cost accumulation method (i.e.,
ASU - ACC - 241
Chapter 16 Appendix A Job Costing Continued Recording TransactionsCopyright 2009 School of Accountancy, Arizona State UniversityCost Flow for Job Cost ComponentsThe jobs cost becomes the basis for valuing inventory and cost of goods soldMaterialsIndi
ASU - ACC - 241
Job-Order Costing: Overview Job-order industries produce a wide variety of products or jobs that are distinct. Costs are accumulated by job in a job-order costing system. Each job is documented on a job-order cost sheet. Some firms produce identical uni
ASU - ACC - 241
Chapter 18, continuedCopyright 2009, School of Accountancy, Arizona State UniversityActivity-Based Customer Costing Customers are cost objects of fundamental interest. Customer management can produce significant gains in profit. Customers can consume c
ASU - ACC - 241
Chapter 18 Activity Based Costing Please pick up handoutCopyright 2010, School of Accountancy, Arizona State UniversityVolume-based (traditional) Cost Systems Volume-based systems/Traditional (unitlevel)Based on volume measures, such asDirect labor
It cannot be denied that the way ANZ implements some useful policies for the staff has had positive impact on the improvement of employee satisfaction .Within only four years(2000-2004), staff satisfaction in ANZ has increased by 35%.They acknowledge that
FIU - CHM - 2210
Organic Chemistry 2210; Sec1 Dr. Stanislaw F WnukOctober 25, 2008Homework/Problem Set #8Chapter 8 Alkenes. Addition Reactions An alkene adds hydrogen in the presence of a catalyst to give 3,4-dimethylhexane. Ozonolysis of 1 the alkene followed by treat
UCSC - LINGUISTIC - 117
Lecture notes: 1.1 June 23, 2009 1 What is linguistics?The goal of linguistics: Describe and understand the structure of human languages; Discover the ways in which all languages are alike and the ways in which they may dier. Develop a better understandi
UCSC - LINGUISTIC - 117
Lecture notes: 1.2 June 23, 2009 1 An introduction to phonetics (At least) two things: (1) a. b. How to produce the sounds of their language. How to interpret them, i.e. how to associate a sound wave with the letters of their alphabet.Q: What do speaker
UCSC - LINGUISTIC - 117
Lecture notes: 2.1 June 25, 2009 1 The hyoid boneOn Tuesday someone mentioned the hyoid bone as part of human speech. It turns out to be a very interesting bone: (1) Hyoid bone: http:/people.ucsc.edu/~ kirchner/classes/intro/files/hyoid.jpgPart of the e
UCSC - LINGUISTIC - 117
Lecture notes: 2.2 June 25, 2009 11.1Consonants continuedPalatoalveolar and palatal consonantsNo very clear-cut distinction between the two. Usually a language uses only one of these two positions for a certain type of consonant. So in English, we hav
UCSC - LINGUISTIC - 117
Lecture notes: 3.1 June 30, 2009 1 AnnouncementsHomework postponed: Homework 2 will be assigned on Thursday, due next Tuesday. Thanks to Peter, who has put up a version of our textbook cd with correct links and le. You can see it here: http:/abcruzww.com
UCSC - LINGUISTIC - 117
Lecture notes: 3.2 June 30, 2009 1 SuprasegmentalsThe suprasegmental features of a language are variations larger than individual segments. They are overlaid upon a word, phrase, or sentence. The two important suprasegmental features of English: (1) a. b
UCSC - LINGUISTIC - 117
Lecture notes: 4.1 July 2, 2009 1 AllophonyOn Tuesday we saw how our two classes of stops (voiceless and voiced) dont tell the whole story about whats going on phonetically. We actually have three classes in terms of VOT voiced, voiceless unaspirated, an
UCSC - LINGUISTIC - 117
Lecture notes: 4.2 July 2, 2009 1 TranscriptionSo, why do we need a phonetic alphabet? Why dont we just use English orthography for phonetics? Our English spelling system often fails to represent in an unambiguous way the sounds of the words. Dierent vow
UCSC - LINGUISTIC - 117
Lecture notes: 5.1 July 7, 2009 1 Features and natural classesIn the homework assignment, we found that [i] and [e] are allophones of the same phoneme, as are [u] and [o]. We can write rules for their distribution that look like this: (1) a. b. /i/ [e] b
UCSC - LINGUISTIC - 117
Lecture notes: 5.2 July 7, 2009 1 Phonology problemsLets look at a problem we saw (if we did the reading for today) Mokilese. Mokilese is an Austronesian language of the Malayo-Polynesian family, spoken in Micronesia. We want to explain the distribution
UCSC - LINGUISTIC - 117
Lecture notes: 6.1 July 9, 2009 11.1More phonology problemsKimatuumbiCan the distinction between implosive and plain voiced consonants in Kimatuumbi (Bantu; Tanzania) be predicted by rule?1 (1) Kimatuumbi alaaNga OOmba likUUNgwa kjaaNgi kiUla OlOja li