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