The Music of the Spheres-- symmetry and symmetry breaking in Nature --

Stephen Lars OlsenSeoul National University

Johannes Kepler [1571 - 1630]

Symmetry & Beauty

Hokusai 1760-1849

24 views of Fuji

View 18 View 20

Hiroshige 1797-1858

36 views of Fuji

View 4 View 14

Temple of heaven (Beijing)

From a different angle

Seoul Arts Center

만화경

Snowflakes

600

Kaleidoscope 만화경

How it works

rota

te

by 450

Start with a random pattern

Use mirrorsto repeat itover & over

The attraction

is all in thesymmetry

Include a reflection

Rotational symmetry

No matter which way I turn a perfect sphereIt looks identical

Space translation symmetry

Mid-west corn field

Time-translation symmetry in music

repeat

repeat a

gain

& 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 [1546 - 1601]

"Music of the Spheres" by Michail Spiridonov

Seoul Arts Center

Kepler: planetary orbits are ellipses; not perfect circles

Kepler’s 1st law: published inJuly 1609 (500 years ago)

Galileo & his telescope

1st recorded observations were in July 1609 (500 years ago)

Discoveries:

• Moons of Jupiter• Saturn’s rings• Phases of Venus• and…

1st seen January 7, 1610

Galileo’s sketches of theMoon’s changing locations

Moons of Jupiter

Rings of saturn

Sketch of Saturn by Galileo in 1616

Clear evidence that Venusorbits 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 nota 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

symmetricThe thing that hath been, it is that which shall be; and that which is doneis that which shall be done: and there is no new thingunder 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

aF = m aSame rule forall 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 nemoeating

Concept of Kinetic Energy

Emilie du Châtelet (1706-1749)

Brilliant mathematician

One of Voltaire’s lovers

K.E.= ½ MV2

Conservation of energy

hmax

Etot=mghmaxEtot=mghmax

Etot=1/2 m(vmax)2

Total energy = Kinetic Energy + Potential Energy + Heat Energy = Constant

Energy conversion of a skier

Friction: energy gets converted to heat

Potential energy

Potential energykinetic energy

Total energy = Kinetic Energy + Potential Energy + Heat Energy = Constant

Conservation of angular momentum

Emmy Noether

1882 - 1935

Conserved quantities:

stay the same

throughout a

process

Symmetry: something that stays the same

throughout a

process

Conservation laws are consequenc

es of symmetries

Symmetries Conservation laws

Symmetry Conservation law

Rotation Angular momentum

Space translation Momentum

Time translation Energy

Atomic spectra

Decoding atomic spectra Mercuryspectrum

Mercury energy levels

“quantum jump”

Laporte Rule

even

even

even

even

od

d

od

d

od

d

od

d

odd even

oddeven

odd

even

odd

even X

X

Even & Odd functions

LR RL LR RL

Even Function Odd Function

Does not changeChanges sign

Parity = +1 Parity = -1