Introduction to Modern Physics By Charles W Fay Introduction to Modern Physics: Physics 311 Lecture Notes Ferris State University unpublished supplement to the text Department of Physical Science 2011 Table of Contents I The Birth of Modern Physics 1 1 What is Physics 2 1.1 Classical Physics and Modern Physics . 2 1.2 Assumptions of Science . 3 2 Classical Mechanics 5 2.1 Physics Before the 19th Century . 5 2.2 Experiment and Observables . 6 2.3 Inertial Reference Frames (IRF) . 9 2.3.1 Symmetries . 9 3 Classical Electro-Magnetism 10 3.1 Maxwell and Electro-Magnetism . 10 3.1.1 Maxwell's Equations in the integral form . 10 3.1.2 Maxwell's Equations in the derivative form . 10 3.2 Reference Frames? . 12 3.3 Implications of the Speed of Light . 12 3.4 Vector Calculus . 12 3.5 EM and Optics . 13 II Relativity 14 4 Special Relativity I 15 4.1 Two Postulates . 15 4.1.1 Simultaneity . 16 4.1.2 Measurement of Length . 16 4.1.3 Simultaneity in moving frames . 17 4.2 Building a suitable transformation: Taken from Relativity by Einstein . 17 4.3 Length Contraction . 20 4.3.1 Example: Length Contraction . 21 4.4 Time Dilation . 21 4.4.1 Example: Time Dilation . 21 4.4.2 Graphical derivation of Time Dilation . 22 4.4.3 Proper length and proper time . 22 4.4.4 Time discrepancy of an event synchronized in K as viewed in K0 sepa- rated by x2 − x1 ......................... 23 4.4.5 Time discrepancy of events separated by ∆t and ∆x in K as viewed by K0.................................. 23 ii 4.5 Doppler Effect . 23 4.5.1 Example: Doppler Effect . 25 4.6 Twin Paradox . 25 5 Special Relativity II 26 5.1 Velocity Transformations . 26 5.1.1 Example: transforming the velocity of an object moving at the speed of light . 27 5.1.2 Transformation of the angle of a light ray . 28 5.2 Transformation of the Energy of Light Rays . 28 5.3 Does the Inertia of a Body depend upon its Energy-content? . 29 5.4 Momentum . 30 6 Four vectors and Lorentz invariance 33 6.1 Momentum . 33 6.1.1 Invariant interval . 34 6.1.2 four-velocity . 37 6.1.3 Four-momentum . 37 6.1.4 Conservation of Momentum . 38 6.1.5 Classical momentum conservation under a Galilean transformation . 38 6.1.6 Relativistic Momentum Conservation . 39 6.1.7 Particles of zero mass . 41 6.2 Mechanical Laws . 42 6.2.1 Motion under a constant force . 43 6.2.2 Cyclotron Motion . 43 6.3 Proper Force . 44 7 General Relativity 45 7.1 Absolute Acceleration? . 45 7.2 2 principles of General Relativity . 45 7.2.1 Principle of Covarience . 46 7.2.2 Results of a transforming rotation in S.R. 46 7.2.3 Principle of Equivalence . 47 7.3 Experimental support for General Relativity . 48 7.3.1 Black Holes . 48 III Origins of Quantum Mechanics 50 8 QMI: Quantum Hypothesis 51 8.1 The energy density . 53 8.1.1 number density of modes in a cavity . 54 8.1.2 Solution by Micro-canonical Ensemble . 55 iii 8.1.3 Solution by canonical ensemble . 57 8.2 Einstein and the Photoelectric Effect . 59 8.2.1 The Photoelectric Effect . 60 9 QMII: The Atom 65 9.1 The Electron . 65 9.1.1 J.J. Thomson discovers the electron . 65 9.1.2 Fundamental Charge: Robert Millikin . 69 9.1.3 Measuring M by terminal speed . 70 9.2 The Nucleus: Rutherford . 71 9.2.1 The Rutherford Formula . 72 9.3 The Bohr Model . 75 9.3.1 The Bohr radius . 76 9.3.2 The energy of the Bohr atom . 77 9.3.3 Generalizing the Bohr Model . 79 9.4 The Neutron . 80 10 QM III: Elements of Quantum Theory 81 10.1 Compton Scattering . 81 10.1.1 Example: Compton Scattering . 83 10.2 de Broglie . 84 10.2.1 Example: de Broglie wavelength . 84 10.2.2 Quantization of angular momentum . 85 10.3 Wave-particle duality . 85 10.3.1 Young's Double slit Experiment . 85 10.4 Probability Waves . 86 10.4.1 Example: Probability density . 87 10.5 Electron wave packets . 87 10.5.1 Heisenberg Uncertainty . 89 10.5.2 Schroedinger's Equation . 90 10.5.3 Particle in a one-dimensional box . 91 10.5.4 Tunneling . 93 10.6 Spin . 93 10.7 The Copenhagen Interpretation . 94 11 QM IV: Atomic Structure 95 11.1 Multi-electron Atoms . 96 11.1.1 Pauli Exclusion Principle . 96 11.2 Periodic Table . 96 11.3 Heisenberg Uncertainty . 97 11.4 Relativistic Quantum Mechanics . 98 11.5 Nuclear Structure . 98 11.5.1 Nuclear Force . 99 iv 11.6 Nuclear Notation . 99 11.7 The Laser . 100 11.7.1 Absorption and Spontaneous Emission . 100 11.7.2 Holography . 100 12 QM V: Radiation 101 12.1 Radioactivity . 101 12.1.1 Alpha Decay . 101 12.1.2 Example . 102 12.1.3 Beta Decay . 102 12.1.4 Gamma Decay . 104 12.1.5 Example . 105 12.1.6 Radiation Penetration . 105 12.2 Half-life . 106 12.2.1 Example: Sr-90 . 106 12.2.2 Radioactive Dating . 107 12.2.3 Example: Carbon 14 dating . 108 12.3 Nuclear Stability . 108 12.3.1 Binding Energy . 110 12.4 Radiation Detection.