1 Symmetry and Physics
2 1.Origin 2.Greeks 3.Copernicus & Kepler 4.19th century 5.20th century
3 1. Origin of Concept of Symmetry
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6 Painting Sculpture Music Literature Architecture
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12 2. Greeks
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14 Harmony of the Spheres Dogma of the Circles
15 3. Copernicus ( ) Kepler ( )
16 Six planets: Saturn, Jupiter, Mars, Earth, Venus, Mercury
17 Mysterium Cosmographicum 1596
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19 One of the methods now to find reasons of some observed regularity:
20 (a)Choose some mathe- matical regularity resulting from symmetry require- ments. (b)Match it to observed regularity.
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22 Discussed why snow flakes are 6-sided Albertus Magnus: In China: -135
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25 But no effort to try to explain why.
th Century Groups and Crystals
27 Galois ( )
28 Concept of groups is the mathematical representation of concept of symmetry.
29 Symmetry and invariance
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33 A 90° rotation is called a 4-fold rotation.
34 It will be denoted by 4. It is an invariant element of the graph.
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41 3 dimensional 230 (1890) 2 dimensional 17 (1891) 4 dimensional4895 (~1970)
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th Century
Symmetry applied to concepts of space and time
46 Special Relativity 1905 Lorentz Symmetry
47 General Relativity 1916 Very Large Symmetry
Symmetry applied to atomic, nuclei, particle properties
49 Quantum Numbers, spin, parity
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51 Great importance in most branches of physics 1920
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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Symmetry applied to structure of interactions (forces).
58 Maxwell Equations have, beyond Lorentz Symmetry,
59 Another symmetry: Gauge Symmetry
60 In Einstein published his general relativity, making gravity a geometrical theory. He then emphasized that EM should also be geometricized.
61 H. Weyl (1885 – 1955) took up the challenge and proposed in 1918 a geometrical theory of EM.
62 Hermann Weyl ( )
63 Levi–Civita and others have developed the idea of “parallel transport”
64. A
65 On a curved surface, the parallel transported vector may not come back to its original direction.
66 Weyl asked, if so “Why not also its length?”
67 “Warum nicht auch seine Länge?”
68 A B.. Proportionalitätsfaktor
69 And pointed out that some changes in leaves his theory invariant, while the EM vector potential has similar properties.
70 So he put
71 Connecting EM with geometry
72 Masstab Invarianz Measure Invariance Calibration Invariance Gauge Invariance
73 Weyl submitted his paper to the Prussian Academy. The editors, Planck and Nernst, asked for the opinion of Einstein:
74 With his penetrating physical intuition, Einstein objected.
75 AB
76 Einstein’s postscript: “the length of a common ruler (or the speed of a common clock) would depend on its history.”
77 QM came to the rescue.
Fock, London
79 Proportionality Factor Phase Factor
80 Gauge Theory Phase Theory
81 With gauge phase, how about Einstein’s objection?
82 Phase difference at B AB
Aharonov-Bohm A B
84 Chambers used a tapered magnetic needle instead of a long solenoid and claimed he had seen the A-B effect.
85 But the leaked flux from his needle caused objection.
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 Weyl’s idea was generalized in 1954
90 Searching for a Principle for Interaction
91 First Motivation: Many new particle. How do they interact?
92 Second Motivation: “the electric charge serves as a source of electromagnetic field; an important concept in this case is gauge invariance...”
93 “We have tried to generalize this concept of gauge invariance to apply to isotopic conserva- tions.”
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 MaxwellNon Abelian Gauge Theory
96 Beautiful and Unique Generalization. But too much symmetry to agree with experiments in 1954 to late 1960s.
97 Symmetry Breaking
98 Algebraic Symmetry. But broken symmetry in observation.
99 Symmetry Dictates Interaction
100 SymmetryInvariance ———— 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. Different PhysicsSame Physics
102 Supersymmetry1973 Supergravity1976 Superstrings1984