### Special Relativity (MATH-426)

Special Relativity (MATH-426)

Introduction: Special Relativity, is the phsical theory of relativity formed by German physicist Albert Einstein in 1905. It is limited with the objects that are moving with respect to inertial frame of reference and is the origion of most famous equation of science E = mc^2,  which expresses the fact that mass and energy are same physical entity and can be changed into each other. However,this physical theory of space and time based on the postulates that all the laws of physics are equally valid in all frames of reference moving at a uniform velocity and that the speed of light from a uniformly moving source is always the same, regardless of how fast or slow the source or its observer is moving. The theory has as consequences the relativistic mass increase of rapidly moving objects, the Lorentz-FitzGerald contraction, time dilatation, and the principle of mass-energy equivalence.

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.

Course Content

1.  Historical background and fundamental concepts of special theory of relativity
2.  Galilean transformations
3.  Lorentz transformations (for motion along one axis)
4.  Length contraction
5.  Time dilation and simultaneity
7.  Lorentz transformations
8.  Introduction to 4-vector formalism. Lorentz transformations in the 4-vector formalism
9.  The Lorentz and Poincare groups
10.  Introduction to classical mechanics
11.  Minkowski space-time and null cone
12.   4-velocity and 4-momentum and 4-force
13.  Application of special relativity to Doppler shift and Compton effect, aberration of light
14.  Particle scattering
15.  Binding energy
16.  Particle production and decay
17. Special relativity with small acceleration.

Recommended Books:

1. Qadir. An introduction to the Special Relativity theory. 1st ed. World scientific, 1989.

2. D’Inverno  R. Introducing Einstein’s Relativity. 1st ed. Oxford University
Press, 1992.

3. Rindler W. Essential Relativity. 2nd ed.  Springer Verlag, 1977.

PPT/Handouts:

Research Products / Practicals /Labs /Assignments

Q: If Composition of Lorentz transformation is also a Lorentz transformation then show that t"=r"(t-Ux/c^2).

Q:Prove that 4-velocity and 4-momentum is invariant.

Assessment criteria

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

Mid-Term Exam:   30

Final-Term Exam: 50

### Key Dates and Time of Class Meeting

BS (Math) Ex-PPP

Teusday                                                                                   9:30 am-11:00 am

Thursday                                                                                   11:00 am-12:30 am

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020