Special Relativity(Math-426)

Description

Calculus Vector transformations Tensors for GTR. To understand why we need these two theories. For that see the problems with Galilean transformation and equivalence of inertial and gravitational mass. The most important thing to study SR is to accept geometry as the concept behind it. The math is not difficult, it's the way of thinking you have to adopt. Draw space time diagrams, something to transform to another frame of reference (Lorentz transforms are available). Keep in mind that the view in the other reference frame is just a different view of the same situation that nothing really has changed, even if it looks different on Euclidean paper. It's merely a rotation, all lengths (t²-x²) stay the same. Learn to state problems in terms of events and the lines connecting them. You can't draw diagrams without translating the problems to space time coordinates properly. Special Relativity. SR really only requires some basic geometry and algebra. It's much more concept driven with the gedanken (thought experiments) than GR which requires some basic partial differential equations, basic differential geometry, tensor calculus and the field theory formulation of Newtonian mechanics (variation formulas).

Learning Outcomes

To understand the two postulates of special relativity.
To understand how the principle of relativity leads to time dilation and length contraction.
To solve novel problems using the equations for time dilation and length contraction.
To explore relativistic energy and momentum.
To recognize the significance of Einstein’s famous equation E = mc2.

Contents

Historical background and fundamental concepts of special theory of relativity.
Galilean transformations.
Lorentz transformations (for motion along one axis).
Length contraction.
Time dilation and simultaneity.
Velocity addition formulae.3-dimensional.
Lorentz transformations.
Introduction to 4-vector formalism. Lorentz transformations in the 4-vector formalism.
The Lorentz and Poincare groups.
Introduction to classical mechanics.
Minkowski space-time and null cone, 4-velocity and 4-momentum and 4-force.
Application of special relativity to Doppler shift and Compton effect, aberration of light.
Particle scattering.
Binding energy.
Particle production and decay.
Special relativity with small acceleration.

Recommended Books

Qadir, 1989. An introduction to the Special Relativity theory. 1st ed. World scientific.
P.L. Sardesai. 2008. A Primer of Special Relativity. 2nded. Offset, Delhi.

Suggested Books

Qadir, 1989. An introduction to the Special Relativity theory. 1st ed. World scientific. https://www.scribd.com/document/335473718/Special-Relativity-1989-by-Asghar-Qadir
P.L. Sardesai. 2008. A Primer of Special Relativity. 2nded. Offset, Delhi.
D’Inverno R., 1992. Introducing Einstein’s Relativity. 1st ed. Oxford University Press.

Reserah Products / Practicals /Labs /Assignments

Exercises are given as assignments to student to check their level of understanding.

Assignments criteria

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam: 30

Final-Term Exam: 50