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

Johannes Kepler [ ]

Symmetry & Beauty

Hokusai views of Fuji View 18View 20

Hiroshige views of Fuji View 4View 14

Temple of heaven (Beijing)

From a different angle

Seoul Arts Center 만화경

Snowflakes 60 0

Kaleidoscope 만화경

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

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

Space translation symmetry Mid-west corn field

Time- translation symmetry in music repeat repeat again & again

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

Tycho Brahe [ ]

"Music of the Spheres" by Michail Spiridonov

Seoul Arts Center

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

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…

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

Rings of saturn Sketch of Saturn by Galileo in 1616

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

& mountains on the Moon

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

Symmetries of the laws of Nature

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

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

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

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

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

Conservation Laws

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

Finding nemo eating

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

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

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

Conservation of angular momentum

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

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

Atomic spectra

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

Laporte Rule even odd even oddeven odd even odd even X X

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