Symmetry and Physics

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Marjorie Franklin
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1 Symmetry and Physics 1

2 1. Origin 2. Greeks 3. Copernicus & Kepler 4. 19th century 5. 20th century 2

3 1. Origin of Concept of Symmetry 3

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6 Painting Sculpture Music Literature Architecture 6

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12 2. Greeks 12

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14 Harmony of the Spheres Dogma of the Circles 14

15 3. Copernicus ( ) Kepler ( ) 15

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

17 Mysterium Cosmographicum

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

20 (a) Choose some mathematical regularity resulting from symmetry requirements. (b) Match it to observed regularity. 20

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22 Discussed why snow flakes are 6-sided Albertus Magnus: In China:

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25 But no effort to try to explain why. 25

26 4. 19th Century Groups and Crystals 26

27 Galois ( ) 27

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

29 Symmetry and invariance 29

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

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

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41 3 dimensional 230 (1890) 2 dimensional 17 (1891) 4 dimensional 4895 (~1970) 41

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44 5. 20th Century 44

45 5.1 Symmetry applied to concepts of space and time 45

46 Special Relativity 1905 Lorentz Symmetry 46

47 General Relativity 1916 Very Large Symmetry 47

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

49 Quantum Numbers, spin, parity 49

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51 Great importance in most branches of physics

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

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

58 Maxwell Equations have, beyond Lorentz Symmetry, 58

59 Another symmetry: Gauge Symmetry 59

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

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

62 Hermann Weyl ( ) 62

63 Levi Civita and others have developed the idea of parallel transport 63

64 A. 64

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

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

67 Warum nicht auch seine Länge? 67

68 exp B A ϕ d μ x μ. B A. Proportionalitätsfaktor 68

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

70 So he put ϕ μ = ea μ 70

71 Connecting EM with geometry 71

72 Masstab Invarianz Measure Invariance Calibration Invariance Gauge Invariance 72

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

74 With his penetrating physical intuition, Einstein objected. 74

75 A B 75

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

77 QM came to the rescue. 77

78 Fock, London exp Adx exp ( iadx) 78

79 Proportionality Factor Phase Factor 79

80 Gauge Theory Phase Theory 80

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

82 A B Phase difference at B 82

83 1959 Aharonov-Bohm A B 83

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

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

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

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89 Weyl s idea was generalized in

90 Searching for a Principle for Interaction 90

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

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

93 We have tried to generalize this concept of gauge invariance to apply to isotopic conservations. 93

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. 94

95 Maxwell Non Abelian Gauge Theory F μν = bμ, ν bμ, ν F i μν = b i μ, ν b i ν, μ c i jk b j μ b k ν F μν, ν = J μ F i i j k i μν, ν + c jkbνfμν = Jμ 95

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

97 Symmetry Breaking 97

98 Algebraic Symmetry. But broken symmetry in observation. 98

99 Symmetry Dictates Interaction 99

100 100 Symmetry Invariance Conservation Laws Gauge Symmetry Symmetry Dictates Interaction Other Consequences Quantum Numbers Selection Rules Strong Force Electromagnetic Force Weak Force Gravity Force

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

102 Supersymmetry 1973 Supergravity 1976 Superstrings

Conceptual Origins of Maxwell Equations and of Gauge Theory of Interactions

Conceptual Origins of Maxwell Equations and of Gauge Theory of Interactions 1 It is usually said that Coulomb, Gauss, Ampere and Faraday discovered 4 laws experimentally, and Maxwell wrote them into equations