1. 1 Symmetry and Physics

2. 2 1.Origin 2.Greeks 3.Copernicus & Kepler 4.19th century 5.20th century

3. 3 1. Origin of Concept of Symmetry

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6. 6 Painting Sculpture Music Literature Architecture

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12. 12 2. Greeks

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14. 14 Harmony of the Spheres Dogma of the Circles

15. 15 3. Copernicus (1473-1543) Kepler (1571-1630)

16. 16 Six planets: Saturn, Jupiter, Mars, Earth, Venus, Mercury

17. 17 Mysterium Cosmographicum 1596

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19. 19 One of the methods now to find reasons of some observed regularity:

20. 20 (a)Choose some mathe- matical regularity resulting from symmetry require- ments. (b)Match it to observed regularity.

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22. 22 Discussed why snow flakes are 6-sided Albertus Magnus: +1260 In China: -135

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25. 25 But no effort to try to explain why.

26. 26 4. 19th Century Groups and Crystals

27. 27 Galois (1811-1832)

28. 28 Concept of groups is the mathematical representation of concept of symmetry.

29. 29 Symmetry and invariance

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33. 33 A 90° rotation is called a 4-fold rotation.

34. 34 It will be denoted by 4. It is an invariant element of the graph.

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41. 41 3 dimensional 230 (1890) 2 dimensional 17 (1891) 4 dimensional4895 (~1970)

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44. 44 5. 20th Century

45. 45 5.1 Symmetry applied to concepts of space and time

46. 46 Special Relativity 1905 Lorentz Symmetry

47. 47 General Relativity 1916 Very Large Symmetry

48. 48 5.2 Symmetry applied to atomic, nuclei, particle properties

49. 49 Quantum Numbers, spin, parity

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51. 51 Great importance in most branches of physics 1920

52. 52 Symmetry = Invariance Conservation Laws (Except for discrete symmetry in classical mechanics) Other Consequences Quantum Numbers Selection Rules (In quantum mechanics only)

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57. 57 5.3 Symmetry applied to structure of interactions (forces).

58. 58 Maxwell Equations have, beyond Lorentz Symmetry,

59. 59 Another symmetry: Gauge Symmetry

60. 60 In 1915-1916 Einstein published his general relativity, making gravity a geometrical theory. He then emphasized that EM should also be geometricized.

61. 61 H. Weyl (1885 – 1955) took up the challenge and proposed in 1918 a geometrical theory of EM.

62. 62 Hermann Weyl (1885-1955)

63. 63 Levi–Civita and others have developed the idea of “parallel transport”

64. 64. A

65. 65 On a curved surface, the parallel transported vector may not come back to its original direction.

66. 66 Weyl asked, if so “Why not also its length?”

67. 67 “Warum nicht auch seine Länge?”

68. 68 A B.. Proportionalitätsfaktor

69. 69 And pointed out that some changes in leaves his theory invariant, while the EM vector potential has similar properties.

70. 70 So he put

71. 71 Connecting EM with geometry

72. 72 Masstab Invarianz Measure Invariance Calibration Invariance Gauge Invariance

73. 73 Weyl submitted his paper to the Prussian Academy. The editors, Planck and Nernst, asked for the opinion of Einstein:

74. 74 With his penetrating physical intuition, Einstein objected.

75. 75 AB

76. 76 Einstein’s postscript: “the length of a common ruler (or the speed of a common clock) would depend on its history.”

77. 77 QM came to the rescue.

78. 78 1926-1927 Fock, London

79. 79 Proportionality Factor Phase Factor

80. 80 Gauge Theory Phase Theory

81. 81 With gauge phase, how about Einstein’s objection?

82. 82 Phase difference at B AB

83. 83 1959 Aharonov-Bohm A B

84. 84 Chambers used a tapered magnetic needle instead of a long solenoid and claimed he had seen the A-B effect.

85. 85 But the leaked flux from his needle caused objection.

86. 86 Finally in the mid 1980s, Tonomura et. al. quantitatively proved the A-B effect. Thus introducing experimentally topology into fundamental physics.

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89. 89 Weyl’s idea was generalized in 1954

90. 90 Searching for a Principle for Interaction

91. 91 First Motivation: Many new particle. How do they interact?

92. 92 Second Motivation: “the electric charge serves as a source of electromagnetic field; an important concept in this case is gauge invariance...”

93. 93 “We have tried to generalize this concept of gauge invariance to apply to isotopic conserva- tions.”

94. 94 Third Motivation: “It is pointed out that the usual principle of invariance under isotopic spin rotation is not consistent with the concept of localized fields.”

95. 95 MaxwellNon Abelian Gauge Theory

96. 96 Beautiful and Unique Generalization. But too much symmetry to agree with experiments in 1954 to late 1960s.

97. 97 Symmetry Breaking

98. 98 Algebraic Symmetry. But broken symmetry in observation.

99. 99 Symmetry Dictates Interaction

100. 100 SymmetryInvariance ———— Conservation Laws Gauge Symmetry Symmetry Dictates Interaction Other Consequences Quantum Numbers Selection Rules Strong Force ︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴ ︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴︴ Electromagnetic Force Weak Force Gravity Force

101. 101 Usual Symmetry Gauge Symmetry Equation Equation Sol. Sol. Sol. Different PhysicsSame Physics

102. 102 Supersymmetry1973 Supergravity1976 Superstrings1984