the music of the spheres -- symmetry and symmetry breaking in nature -- stephen lars olsen seoul...
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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