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Lecture Two

Lecture Two. Historical Background of Special Relativity. Principle of Relativity in Classical Mechanics. Galilean transformation Newtonian Relativity. Galilean transformation. x ' = x – v t y ' = y z ' = z t ' = t. Measurement of length. E A = ( t A , x A , y A , z A )

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Lecture Two

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  1. Lecture Two

  2. Historical BackgroundofSpecial Relativity

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

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

  5. Measurement of length EA = (tA, xA, yA, zA) marking of the left end A EB = (tB, xB, yB, zB) marking of the right end B

  6. Measurement of length simultaneous measurement tA = tB length =xB －xA

  7. tA = tBSimultaneity is crucial in length measurement of a moving rod.Otherwise …

  8. Under Galilean transformation t'A = tA t'B = tB x'A = xA – v tA x'B = xB – v tB time is absolute

  9. x'B －x'A = (xB – v tB) – (xA – v tA) = xB －xA －v (tB – tA) = 0 = xB －xA

  10. Measurement of length length = xB －xA = x'B －x'A Length is invariant.

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

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

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

  14. kinematics a' = a

  15. dynamics • mass is unaffected by the motion of the reference frame F = ma = ma' = F '

  16. 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.

  17. same means: invariant under a certain transformation

  18. Newtonian Relativity • Laws of mechanics are the same in all inertial frames of reference. namely • Laws of mechanics are invariant under the Galileantransformation.

  19. Eisteinian Relativity • Laws of mechanics are the same in all inertial frames of reference. namely • Laws of mechanics are invariant under the Lorentztransformation.

  20. Consequences of Relativity whether Newtonian or Einsteinian • 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.

  21. Example 3 Invariance of Momentum Conservation • In S: P = m1u1 + m2u2 = m1U1 + m2U2 • In S': P ' = m1u1 ' + m2u2 '= m1U1 ' + m2U2 '

  22. Example 4Invariance of Equation of Motion

  23. ElectromagnetismandNewtonian Relativity

  24. Maxwell’s Equationsare not invariantunderGalilean transformation.

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

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

  27. 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.

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

  29. Three possibilities or alternatives

  30. 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:

  31. 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

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

  33. 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.

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

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

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

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

  38. Alternative 2 But then electromagnetism is notcorrect in the Maxwell formulation.

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

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

  41. Alternative 3 and themechanics in the Newtonian form needs modification.

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

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

  44. The End

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

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