ImportantConcepts10 - Physics 136 Kip Thorne Important...

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Physics 136 Caltech Kip Thorne January 16, 2003 Important Concepts Chapters 1 through 10 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 3. Equations of elasticity; a.expansion, rotation and shear: Sec. 10.2 b.Elastic stress tensor and force balance: Sec. 10.4 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 D.Elasticity: irreducible tensorial parts of strain tensor: expansion, shear and rotation: Sec. 10.2, Box 10.1 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
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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.
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ImportantConcepts10 - Physics 136 Kip Thorne Important...

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