1. The Music of the Spheres -- symmetry and symmetry breaking in Nature -- Stephen Lars Olsen Seoul National University

2. Johannes Kepler [1571 - 1630]

3. Symmetry & Beauty

4. Hokusai 1760-1849 24 views of Fuji View 18View 20

5. Hiroshige 1797-1858 36 views of Fuji View 4View 14

6. Temple of heaven (Beijing)

7. From a different angle

8. Seoul Arts Center 만화경

9. Snowflakes 60 0

10. Kaleidoscope 만화경

11. How it works rotate by 45 0 Start with a random pattern Use mirrors to repeat it over & over The attraction is all in the symmetry Include a reflection

12. Rotational symmetry No matter which way I turn a perfect sphere It looks identical  

13. Space translation symmetry Mid-west corn field

14. Time- translation symmetry in music repeat repeat again & again

15. Prior to Kepler, Galileo, etc God is perfect, therefore nature must be perfectly symmetric: Planetary orbits must be perfect circles Celestial objects must be perfect spheres

16. Tycho Brahe [1546 - 1601]

17. "Music of the Spheres" by Michail Spiridonov

18. Seoul Arts Center

19. Kepler: planetary orbits are ellipses; not perfect circles Kepler’s 1 st law: published in July 1609 (500 years ago)

21. Galileo & his telescope 1 st recorded observations were in July 1609 (500 years ago) Discoveries: Moons of Jupiter Saturn’s rings Phases of Venus and…

22. 1 st seen January 7, 1610 Galileo’s sketches of the Moon’s changing locations Moons of Jupiter

23. Rings of saturn Sketch of Saturn by Galileo in 1616

24. Clear evidence that Venus orbits the Sun (& not the Earth) Galileo's sketch of the phases on Venus Phases of Venus Modern photos of Venus

25. & mountains on the Moon

26. Modern photo of the Moon The Moon is not a perfect sphere

27. Symmetries of the laws of Nature

28. Newton’s laws implicitly assume that they are valid for all times in the past, present & future Processes that we see occurring in these distant Galaxies actually happened billions of years ago Newton’s laws have time-translation symmetry

29. The Bible agrees that nature is time-translation symmetric The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun Ecclesiates 1.9 이미 있던 것이 후에 다시 있겠고 이미 한 일을 후에 다시 할지라 해 아래 는새 것이 없나니 전도서 1.9

30. Newton believed that his laws apply equally well everywhere in the Universe Newton realized that the same laws that cause apples to fall from trees here on Earth, apply to planets billions of miles away from Earth. Newton’s laws have space-translation symmetry

31. rotational symmetry F F a a F = m aF = m a Same rule for all directions (no “preferred” directions in space.) Newton’s laws have rotation symmetry

32. Symmetry recovered Symmetry resides in the laws of nature, not necessarily in the solutions to these laws.

33. Conservation Laws

34. Conservation of Momentum Momentum= mass x velocity total momentum before = total momentum after

35. Finding nemo eating

36. Concept of Kinetic Energy Emilie du Châtelet (1706-1749) Brilliant mathematician One of Voltaire’s lovers K.E.= ½ MV 2

37. Conservation of energy h max E tot =mgh max E tot =1/2 m(v max ) 2 Total energy = Kinetic Energy + Potential Energy + Heat Energy = Constant

38. Energy conversion of a skier Friction: energy gets converted to heat Potential energy Potential energy  kinetic energy Total energy = Kinetic Energy + Potential Energy + Heat Energy = Constant

39. Conservation of angular momentum

40. Emmy Noether 1882 - 1935 Conserved quantities: stay the same throughout a process Symmetry: something that stays the same throughout a process Conservation laws are consequences of symmetries

41. Symmetries  Conservation laws Symmetry Conservation law Rotation  Angular momentum Space translation  Momentum Time translation  Energy

42. Atomic spectra

43. Decoding atomic spectra Mercury spectrum Mercury energy levels “quantum jump”

44. Laporte Rule even odd even oddeven odd even odd even X X

46. Even & Odd functions L  R R  L Even Function Odd Function Does not change Changes sign Parity = +1Parity = -1