Class Notes Introduction to Modern Physics Physics 321 Plan II Under Construction

Transcription

1 Class Notes Introduction to Modern Physics Physics 321 Plan II Under Construction Austin M. Gleeson 1 Department of Physics University of Texas at Austin Austin, TX January 15, gleeson@physics.utexas.edu

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3 Contents 1 Introduction Purpose of This Course Physics that you should know Introduction Kinematics Dynamics The Role of Mathematics Mathematics and Symbols That You Should Know First Day Handout Fermi Problems Things Everyone Should Know Order of Magnitude Estimates Home Experiments Review Syllabus Text What is Physics? Range of Phenomena Reductionism and General Principles Problems Measurement The Role of Measurement Measurability Role of Standards The Story of Length Accuracy and Precision of Standards Quantities of Physics Dimensional Analysis Uses of Dimensional Analysis

4 4 CONTENTS Scaling Laws Fundamental Dimensional Constants Sizes Modern Standards Problems Pre 19th Century Physics Introduction Least Time Formulation of Light Propagation Speculation on the form of Fermat s Theory Applications of Fermat s Principle Light Travels in Straight Lines Refraction & Snell s Law Lenses Total Internal Reflection Rays in a General Inhomogeneous Space and Mirages Reflection and Mirrors Mathematical Digression Newton and Color Fresnel/Young/Huygens Theory Recapitulation of Fermat s Least time principal Problems with Fermat s Least Time Huygens Thomas Young and Interference Detail of the Analysis of Interference for the Double Slit Phasers Example of Three Slits and More The Theory of How Light Or Any Other Wavelike Disturbance Propagates How do we get least time from Fresnel s Theory? Polarization The Field th Century Physics Action at a Distance and Field Dynamics Action at a Distance Local Field Theory The Stretched String Maxwell s Theory of Electromagnetism Dynamics and Action

5 CONTENTS Background on Formulation of Action Introduction to Action Definition of Action Trajectory of a Free Particle Proof that the Least Action Reproduces Newtonian Physics Examples of action gravitation near a flat earth Same Example done another way Digression on averages and slicing More Examples of Actions Basic Principles of Physics Symmetry The Nature of Symmetry in Physics Discrete Transformations Continuous Transformations Identity Transformation Examples of symmetry in situations like physics Physics transformations: Examples of Symmetry in physics Physics transformations: Symmetry and Action Introduction Galilean invariance More on Symmetry and Action Noether s Theorem Special Classical Physical Systems Introduction The Harmonic Oscillator Importance Dynamics Examples of harmonic oscillator systems Normal Modes The Stretched String Revisited Distributed Systems Concluding Remarks

6 6 CONTENTS 7 The Special Theory of Relativity Pre-History of concepts about light Galilean Invariance Implications of and for Maxwell s Equations Pursuit of a special frame Michelson-Morley Experiment Kinematics of special relativity Special Relativity Principles of Relativity Harry and Sally and Space Time Diagrams Introduction The Paradox of Harry and Sally The Relativity of Simultaneity Harry and Sally s Movements in a Diagram The Nature of Space-Time The Problem of Coordinates The Lorentz Transformations The Relatively Moving Clock Derivation of the Lorentz Transformation Details of the Derivation of the Lorentz Transformations Using Lorentz Transformations Time Dilation Length contraction The Doppler Effect Addition of velocities Time for Different Travelers Visual Appearence of Rapidly Moving Objects Events, Worldlines, Intervals Introduction Place and Path in the Two Dimensional Plane Minkowski Space-time Future, Past, and Elsewhere Causality and Trajectories The Hyperbolic Hangle The same result directly using calculus Four Vectors and Invariants Harry, Dorothy, and Sally Revisited

7 CONTENTS 7 11 Paradoxes of Relativity The Twin Paradox The Problem The Solution The Boy in the Barn The Problem The Solution The Bandits and the Bullet Train Uniform Acceleration Events at the same proper distance from some event Uniformly accelerated motion Details of the calculation of the acceleration The proper time along the trajectory Timelike Trajectories and Accelerated Motion Examples using accelerated motion Deceleration Accelerated Rocket John Bell s Problem The Accelerated Reference Frame Relativistic Dynamics Relativistic Action The Action for a Free Particle Energy and momentum of a single free particle Mass Kinetic Energy of a Single Particle Transformations of Momentum and Energy The Energy, Momentum, and Mass of Light Interactions Multi-particle Systems Rest energy of composite and elementary systems Applications of Energy Momentum Introduction to General Relativity The Problem Free Fall Observers and the Equivalence Principle The Equivalence Principle The Monkey and the Hunter Direct Effects from the Equivalence Principle

8 8 CONTENTS Universality and Eötvös Dicke Bending of Light Rays Clocks and Accelerations in Towers Intrinsic Effects of Gravity Distortion of Elastic Bodies Gravitation and Tidal Forces Geometry and Gravitation Introduction to Geometry Gaussian Curvature Example of negative curvature: the Pringle Curvature and Geodesics The Theorema Egregium and the Line Element Geometry in Four or More Dimensions Coordinate Labels in General Relativity Einstein Equations Effects of Gravitation Curvature around a Massive Body The Universe Background Ideas Copernican Principle Olber s Paradox Hubble Expansion The Age of the Universe Models of Expanding Universes Inflationary Cosmology The Space Time Structure Black Body Background Problems with the Expanding Universe The Cosmological Constant The Standard Model of the Universe Interface of Large Scale and Micro-physics Structure in the Universe The Inflationary Universe String Theory

9 CONTENTS 9 18 Introduction to Quantum Theory Introduction Blackbody Radiation Thermodynamics Radiation in a Cavity Attempts to explain the spectrum Planck s Explanation of the Spectrum Photo-Electric Effect Young s Double Slit Experiment Revisited Action and Quantum Mechanics Constructing the Amplitude A Mathematical Aside The Population Equation The Exponential Function Even more on phasers The Uncertainty Relations The Uncertainty Principle and the Quantum Mechanical Harmonic Oscillator Oscillator Ground State Wavefunction An Aside on the Particle in the Box Returning to the Oscillator The Time Development of Quantum Systems Motion in Quantum Mechanics Relation between the Quantum and the Classical Oscillator Classical Motion of the Quantum Oscillator An Aside on the Poisson Distribution A Return to Classical Motion of the Quantum Oscillator Quantum Measurement and Bell s Theorem A Two Level System More on polarized light as a two level system More on Bell s Theorem What is a particle and what is the field? Quantum Field Theory Introduction The Many Photon State The Stretched String Revisited Again The Quantum Stretched String The field

10 10 CONTENTS 20.6 Elementary Particles Fundamental Processes