1. EPPT M2 INTRODUCTION TO RELATIVITY K Young, Physics Department, CUHK  The Chinese University of Hong Kong

2. Chapter 1 INTRODUCTION

3. Questions of interest in relativity  Behavior of particles at high speeds   Energy / momentum of particles at high speeds; their interactions  Twin paradox; length contraction  Black holes  Cosmology; expansions of universe

4. Common Theme  How does the same phenomenon appear to different observers?  How is the same phenomenon described in different coordinate systems?

5. Example v

6. Objectives  Physics independent of coordinates  Rotation of coordinates  Principle of relativity  Experimental basis  Applications

7. Physics Independent of Coordinates

8. Physics independent of coordinates  Physics is absolute  Coordinates are arbitrary  Physics independent of coordinates

9. Coordinate Transformations

10.  Rotation leads to vectors x y x' y'

11. Moving coordinates leads to Special Relativity V

12. General transformation leads to General Relativity

13. Rotation of coordinates  Linear relationship  Vectors and matrices  Rotation matrix

14. 3D notation bold Cartesian

15. Coordinates are relative Study coordinate transformations x' y' L  x y L End point = r

16.  r y x y' r '' x' 

18. Properties of rotation matrices Addition theorem for sin, cos

19. Addition theorem

20. Principle of Relativity

21. Physical law: different observers  Variables covariant  Equation invariant  Depends on linear transformation

22. Physical law: different observers a F

23. Principle of relativity  All valid laws of physics should take the same form in different coordinates systems invariance  All terms in valid equation must transform in the same way covariance  How do they transform?

24. Experimental basis  SR: Michelson-Morley experiment: The speed of light is the same for all observers  GR: All objects fall at the same acceleration in a gravitational field  Both known to great precision  Thought to be exact

25. Order of magnitude of effect  Particle moving at speed v  Speed of light c  Dimensionless ratio v c 

26. Order of magnitude of effect   Sign of does not matter

27. Another expression

28. Order of magnitude of effect  Gravity important in GR

29. Example What is clock error (seconds/day) due to  speed  height 3 km 1000 km/hr

30. Applications

31.  Relativistic kinematics and dynamics — collisions  Mass-energy equivalence  Relation between E & M  Theory of gravity

32. Applications  Astrophysics  Cosmology  Global Positioning System (GPS)  Constraining other laws of physics

33. Relativistic kinematics & dynamics Only need to do this once and for all SS'

34. Mass-energy equivalence From relativistic kinematics & dynamics, new concept of E, P, m Important for nuclear physics & high energy physics

35. High energy physics  What is matter made of ?  How do the constituents interact ? To study experimentally  Accelerate to high energy/speed  Let them collide  To probe short distance

36. Quantum Field Theory  When E > E 0 =mc 2, particles can be created / destroyed  Theoretical description requires relativistic quantum field theory

37. S B Electricity Magnetism q v S' q

39. Gravity =If a o = g, cannot tell apart =If we understand transformation to an accelerating frame, then we understand gravity?? SS' aoao g

40. BUT

41. Astrophysics — gravity important

42. Black hole — heuristic derivation M m R Escape?

43. Black hole — heuristic derivation Escape? M m R Max speed = c

44. Black hole — heuristic derivation Escape M m R Cannot Escape

45. Black hole — heuristic derivation M m R

46. Mixture of Newtonian + relativistic Not really legitimate OK for order-of -magnitude estimate

47. Global Positioning System (GPS)

48. GPS Accuracy ~ 10 m

49. GPS

50. Cosmology =Depends on gravity =In detail: Einstein's theory

51. Constraining other laws of physics =Laws must be invariant =Limited possibilities

52. Objectives =Physics independent of coordinates =Rotation of coordinates =Principle of relativity =Experimental basis =Applications

53. Acknowledgment =I thank Miss HY Shik and Mr HT Fung for design