Special Relativity

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Lectures

  • Lecture 0. [Invitation to Special Relativity]
  • Lecture 1. [Infamous Experiments]
  • Lecture 2. [Einstein's Postulates]
  • Lecture 3. [Lorentz Transformation]
  • Lecture 4. [Mass-Energy Equivalence]
  • Lecture 5. [Relativistic Dynamics]
  • Lecture 6. [Relativistic Energy-Momentum]
  • Lecture 7. [Collisions]
  • Lecture 8. [Four Vector Notation]
  • Lecture 9. [P.H.L.G.]
  • Lecture 10. [Minkowski Force]

Numerical Problems

Remarks

  1. Be careful about tensor indices. Practice problems from Spiegel/Arfken-Weber Book (and NOT from Kleppner-Kolenkow).
  2. When solving assignments, whenever applicable, draw neat & physical diagram of events and explain the symbols. Read the question carefully and after solving the problem, frame and write to-the-point answer asked in the question.
  3. Video-lecture on Orthogonal Transformation (OT).
  4. Video-lecture on Proper Homogeneous Lorentz Group (PHLG).
  5. Tensor Properties and application.

Topics

  1. Michelson-Morley Experiment and its outcome: Postulates of Special Theory of Relativity. Lorentz Transformations. Simultaneity and order of events. Lorentz contraction. Time dilation. Relativistic transformation of velocity. Relativistic Dynamics. Variation of mass with velocity. Massless Particles. Mass-energy Equivalence. Transformation of Energy and Momentum.
  2. A Short Introduction to Tensors: Covariant and contravariant vectors. Contraction. Covariant, contravariant, and mixed tensors of rank-2, transformation properties. The metric tensor (flat space-time only). Raising and lowering of indices with metric tensors. (Consistent use of convention → diag(1,-1,-1,-1).)
  3. Relativity in Four Vector Notation: Four-vectors, Lorentz Transformation and Invariant interval, Space-time diagrams. Proper time and Proper velocity. Relativistic energy and momentum - Four momentum. Conservation of four momentum and applications to collisions. Minkowski Force.

Study Materials

  1. Einsteinian Relativity:
    • Introduction to Special Relativity - R. Resnick (Main Book).
    • Special Relativity (MIT Introductory Physics) - A.P. French.
    • The Special Theory of Relativity - Banerji and Banerjee.
    • Modern Physics - A.Beiser/Mani-Mehta.
    • Special Theory of Relativity - J.H.Smith/D.Bohm/N.D.Mermin/D.Morin/A.Einstein.
  2. Poincarian Relativity:
    • Classical Electrodynamics - J.D. Jackson.
    • Classical Theory of Fields (Vol II) - Landau and Lifshitz.
    • Tensor Analysis - Barry Spain.
    • Mathematical Physics - Arfken-Weber/Murray Spiegel/S.D.Joglekar.