Physics 139

Outline of Topics

for Prof. Smoot's class

Physics 139 - Spring Semester 1998

University of California, Berkeley

THE SPECIAL THEORY OF RELATIVITY

Space and time of Newtonian mechanics and of the ether theory

• Bradley--aberration of starlight
• Lodge--ether drag
• Fresnel, Fizeau--drag coefficient
• Airy--water-filled telescope

Postulates of special relativity and their tests

• Michelson-Morley--ether drift
• Hamar--obstruction of ether flow
• Trouton-Noble--torque on a capacitor
• Kennedy-Thorndike--time contraction
• Forms of the emission theory and their tests

Comparisons of meter sticks and clocks; setting of clocks

Lorentz transformation

• Derivation, history, group property
• Four-dimensional space-time of Minkowski
• Einstein's velocity addition law
• Accelerations and their transformation
• Velocity of a causal impulse
• Speed of light in a moving medium
• Speed of light as a maximum
• Aberration
• Doppler effect

Particle dynamics

• Postulates
• Longitudinal and transverse mass
• "internal" mass
• Transformations of mass and force
• Work and kinetic energy.
• E = mc^2
• Association of momentum with motion of energy
• Relation between force and acceleration
• Motion of charged particles in E and B fields

Transitions, collisions, reactions

• Conservation of energy and momentum
• Nuclear reactions
• Solar energy
• Fission
• Light pressure
• Compton effect
• Pair production and annihilation

Matrices in four-space

• Forward and backward light cones
• Time-like, space-like, and singular intervals
• Proper time, proper length

The principle of covariance

• Importance of tensors
• Character of tensor equations
• Line elements for special relativity
• Geodesics

Tensor analysis for special relativity

• Ranks, dimensions; linear homogeneous coordinate transformations
• Definition of a tensor
• Rotations, inversions
• Orthogonal matrices
• Tensor algebra; contraction
• Construction of scalar invariants Metric tensors
• Discussion of four-vectors; position, velocity, acceleration, momentum, force, "quad " operator (the 4-D version of " del "= --)

Electrodynamics in four-space

• Charge-current, Lorentz four-potential
• Conservation of charge, gauge invariance
• Electromagnetic field tensor, dual tensor
• Maxwell stress tensor
• Four-space equation of motion for a charged particle

Collisions and Reactions Momentum space

• Distribution functions
• Jacobian determinants
• Differential and total cross-sections; transformations, invariants
• Dynamics of a system of particles
• Conservation of energy-momentum
• Techniques of calculation; radiative transitions, two-photon final states, photon-induced reactions; one, two and more final-state particles
• Thresholds
• Momentum transfer and "cross-momentum transfer"
• Inelastic scattering
• Applications (e.g., threshold for proton-antiproton production, colliding beams)

Radiation from accelerated charges

• Vector and scalar potentials for a charge
• Retarded times; Lienard-Wiechert potentials
• Near-zone and far-zone fields
• Radiated power; Larmor's formula
• Multipole radiation (especially electric and magnetic dipole radiation)
• Relativistic modifications of angular and energy spectra and of total power radiated
• Coherence

THE GENERAL THEORY OF RELATIVITY

The equivalence principle

• Natural coordinates
• Simple consequences (e.g., proportionality of weight to mass)
• Eotvos, Dicke
• Paths of particles and light rays
• Effect of gravitational potential on clock rates
• Gravitational red shift
• Clocks on a rotating platform
• Twin paradox
• Geodesics

Tensor analysis for general relativity

• General transformations of coordinates; equation for interval
• Transformations of tensors; algebra of tensors
• Properties of the metric tensor
• Pseudo-tensors; tensor densities and tensor capacities; invariants
• Christoffel symbols
• Covariant derivatives
• Tensor forms for vector operations (grad, div. curl)
• Riemann-Christoffel tensor
• Ricci tensor
• Equation for a geodesic

Principle of Covariance; discussion

Summary of the relativity theory of gravitation

• Einstein's field equations Gravitational field in free space
• Weak-field approximation to Einstein's field equations
• Discussion of the Schwarzschild solution
• Planetary orbits
• Gravitational deflection of light
• Gravitational shift of spectral lines Black holes
• Gravitational Waves
• Cosmology