1. Lecture Two

2. Historical Background of Special Relativity

3. Principle of Relativity in Classical Mechanics Galilean transformation Newtonian Relativity

5. Galilean transformation x' = x – v t y' = y z' = z t' = t

7. Measurement of length E A = (t A, x A, y A, z A ) marking of the left end A E B = (t B, x B, y B, z B ) marking of the right end B

8. Measurement of length simultaneous measurement t A = t B length = x B － x A

9. t A = t B Simultaneity is crucial in length measurement of a moving rod. Otherwise …

11. Under Galilean transformation t' A = t A t' B = t B x' A = x A – v t A x' B = x B – v t B time is absolute

12. x' B － x' A = (x B – v t B ) – (x A – v t A ) = x B － x A － v (t B – t A ) = 0 = x B － x A

13. Measurement of length length = x B － x A = x' B － x' A Length is invariant.

14. So much about measurement process Now physics: kinematics dynamics

15. Notation v : relative velocity between inertial frames of reference u : velocity of object

16. kinematics u' = u － v (classical velocity addition theorem)

18. kinematics a' = a

19. dynamics mass is unaffected by the motion of the reference frame F = m a = m a ' = F '

20. Principle of Relativity Laws of mechanics are the same in all inertial frames of reference. namely Laws of mechanics are invariant under a certain transformation.

21. same means: invariant under a certain transformation

22. Newtonian Relativity Laws of mechanics are the same in all inertial frames of reference. namely Laws of mechanics are invariant under the Galilean transformation.

23. Eisteinian Relativity Laws of mechanics are the same in all inertial frames of reference. namely Laws of mechanics are invariant under the Lorentz transformation.

24. Consequences of Relativity No mechanical experiments carried out entirely in one inertial frame can tell the observer what the motion of that frame is with respect to any other inertial frame. There is no way at all of determining the absolute velocity of an inertial frame. No inertial frame is preferred over any other. whether Newtonian or Einsteinian

25. Example 3 Invariance of Momentum Conservation In S: P = m 1 u 1 + m 2 u 2 = m 1 U 1 + m 2 U 2 In S': P ' = m 1 u 1 ' + m 2 u 2 ' = m 1 U 1 ' + m 2 U 2 '

26. Example 4 Invariance of Equation of Motion

27. Electromagnetism and Newtonian Relativity

28. Maxwell’s Equations are not invariant under Galilean transformation.

29. Maxwell’s Electrodynamical Laws are not the same in all inertial frames of reference.

30. “Ether” frame the inertial frame of reference in which the measured speed of light is exactly c = (  0  0 ) -½ = 299792458 m/sec

31. In a frame of reference moving at a constant speed v with respect to the “ether” frame, the measured speed of light would range from c － v to c ＋ v.

32. Newtonian relativity holds for Newtonian mechanics but not for Maxwell’s laws of electromagnetism.

33. Three possibilities or alternatives

34. Arguments following Panofsky and Phillips Insisting the existence of Relativity Principle Fact: Incompatibility of Maxwell electrodynamics and Newtonian relativity Two choices of Relativity: Newtonian or new one Then there are only three alternatives:

35. Diagrammatic N: Newtonian mechanics N' : new mechanics M: Maxwell electrodynamics M' : new electrodynamics G: relativity under Galilean transformation G' : new relativity principle : compatible : incompatible, preferred frame

36. G N M G N M ' G ' N ' M preferred ether frame No other alternatives

37. First alternative: without any modification and sacrifice the relativity of electrodynamics. Second alternative: maintain Newtonian mechanics and insist Newtonian relativity of electrodynamics but give up Maxwell theory. Third alternative: maintain Maxwell electrodynamics and relativity but give up Newtonian mechanics and relativity.

38. Alternative 1 Both Newtonian mechanics and Maxwell’s electrodynamics are correct.

39. Alternative 1 Then since Newtonian relativity holds for Newtonian mechanics but not for Maxwell’s electromagnetism,

40. Alternative 1 there must be a preferred absolute “ether” frame for electrodynamics.

41. Alternative 2 Newtonian relativity holds for both mechanics and electrodynamics.

42. Alternative 2 But then electromagnetism is not correct in the Maxwell formulation.

43. Alternative 3 Relativity Principle holds for both mechanics and Maxwell’s electrodynamics.

44. Alternative 3 But then the Relativity Principle is not Newtonian, the transformation is not Galilean,

45. Alternative 3 and the mechanics in the Newtonian form needs modification.

46. Alternatives 1 and 2 was ruled out by experiments of Michelson and Morley. (Next lecture)

47. Alternative 3 was realized by Einstein’s Special Relativity. (Fourth lecture)

48. The End

49. http://www.scu.edu.tw/physics/teacher/rency/