ImportantConcepts09

ImportantConcepts09 - Physics 136 Kip Thorne Important...

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Physics 136 Caltech Kip Thorne Nov 29, 2002 Important Concepts Chapters 1 through 9 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 3 Geometric optics of a classical wave is particle mechanics of the wave's quanta: Sec. 6.3 4 Geometric optics limit of Schrodinger equation is classical particle mechanics: Ex. 6.6 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 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 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 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 E Kinetic theory -- Momentum space: Sec. 2.2
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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
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ImportantConcepts09 - Physics 136 Kip Thorne Important...

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