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.ÿþPhysics 136 CaltechKip Thorne Oct 16, 2002Important ConceptsChapters 1 through 3I Frameworks for physical laws and their relationships to each otherA General Relativity, Special Relativity and Newtonian Physics: Sec.1.1B Phase space for a collection of particles: Chap 2C Phase space for an ensemble of systems: Chap 3D Relationship of Classical Theory to Quantum Theory1 Mean occupation number as classical distribution function: Sec.2.32 Mean occupation number determines whether particles behave likea classical wave, like classical particles, or quantum mechanically:Secs.2.3 & 2.4; Ex.2.1; Fig.2.5II Physics as GeometryA Newtonian: coordinate invariance of physical laws1 Idea Introduced: Sec.1.22 Newtonian particle kinetics as an example: Sec.1.4B Special relativistic: frame-invariance of physical laws1 Idea introduced: Sec.1.22 Relativistic particle kinetics: Sec.1.43 4-momentum conservation: Secs.1.4 & 1.12a Stress-energy tensor: Sec.1.124 Electromagnetic theory: Sec.1.10a Lorentz force law: Sec.1.45 Kinetic theory: Chap.2a Derivation of equations for macroscopic quantities as integralsover momentum space [Sec.2.5]b Distribution function is frame-invariant and constant along fiducialtrajectories [Secs.2.2 & 2.7]C Statistical mechanics: invariance of the laws under canonicaltransformations (change of generalized coordinates and momenta inphase space): Sec.3.2, Ex.3.1III 3+1 Splits of spacetime into space plus time, and resulting relationshipbetween frame-invariant and frame-dependent laws of physicsA Particle kinetics: Sec.1.6B Electromagnetic theory: Sec.1.10C Continuum mechanics; stress-energy tensor: Sec.1.12D Kinetic theory: Secs.2.2, 2.5 & 2.71 Cosmic microwave radiation viewed in moving frame: Ex.2.3IV Spacetime diagramsA Introduced: Sec.1.7B Simultaneity breakdown, Lorentz contraction, time dilation: Exercise1.11C The nature of time; twins paradox, time travel: Sec.1.8D Global conservation of 4-momentum: Secs.1.6 & 1.12E Kinetic theory -- Momentum space: Sec.2.2 V Statistical physics conceptsA Systems and ensembles: Sec.3.2B Distribution function1 For particles: Sec.2.22 For photons, and its relationship to specific intensity: Sec.2.23 For systems in statistical mechanics: Sec.3.24 Evolution via Vlasov or Boltzmann transport equation: Sec.2.7a Kinetic Theory: Sec 2.7b Statistical mechanics: Sec.3.3C Thermal equilibrium1 Distribution functions: Sec.2.42 In statistical mechanics; general form of distribution function in termsof quantities exchanged with environment: Sec.3.43 Evolution into statistical equilbrium--phase mixing and coarsegraining: Secs.3.6 and 3.9D Specific statistical-equilibrium ensembles and their uses1 Canonical, Gibbs, grand canonical and microcanonical defined: Sec.3.42 Microcanonical: Sec.3.5 and Ex.3.83 grand canonical: Sec.3.8 and Ex.3.6E Fluctuations in statistical equilibrium1 Particle number in a box: Ex.3.7F Entropy1 Defined: Sec.3.62 Second law (entropy increase): Secs.3.6, 3.93 Entropy per particle: Secs.3.8, 3.9, Fig.3.4, Exs.3.5, 3.9G Macroscopic properties as integrals over momentum space:1 In kinetic theorya Number-flux vector, stress-energy tensor: Sec.2.5b Equations of state: Sec.2.6c Transport coefficients: Sec.2.82 In statistical mechanics: Extensive thermodynamic variablesa Grand partition function: Ex.3.6VI Computational techniquesA Tensor analysis1 Without a coordinate system, abstract notation: Secs.1.3 and 1.92 Index manipulations in Euclidean 3-space and in spacetimea Tools introduced; slot-naming index notation: Sec's 1.5, 1.7 &1.9b Used to derive standard 3-vector identities: Exercise 1.15B Two-lengthscale expansions: Box 2.21 Solution of Boltzmann transport equation in diffusion approximation:Sec.2.82 Semiclosed systems in statistical mechanics: Sec.3.23 Statistical independence of subsystems: Sec.3.4
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