Beauty …
what beauty?
Beauty Seminar, 3/16/04 – Al Albano
… there’s visual impact …
Cartwheel Galaxy
Eagle Nebula
Eskimo nebula
Tesselation of the triangle group
… then, there’s the beauty of a physical theory …
“ A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data…”
Dirac
What makes a theory beautiful?
A historical example: the motions of heavenly bodies.
Circumpolar stars seen from Yellowstone Park
It started with the ancients …
From Peter Apian, Cosmographia (1524)
An earth-centered universe
Retrograde motion of Mars
A problem …
A solution … epicycles
… Mars moves on a circle, the epicycle, whose center moves on another circle, the deferent.
There is a point inside the deferent, called the equant, not necessarily at the center of the deferent, such that the line from the equant to the center of the epicycle rotates with constant speed.
The earth is located on the same diameter as the equant, but not necessarily at the center of the deferent …
Check out http://www.jimloy.com/cindy/ptolemy.htm
deferent
epicycle
Mars
Earth
“If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.” Alfonso the Wise
King of Castille (13th c.)
It must be simple.
Enter Copernicus …
A sun-centered universe. But it’s still all circles …
Close … but not quite right.
Brahe
Kepler says it’s ellipses …
Kepler describes the observations, but he does not explain anything.
…ditto for GalileoAnd they did not seem to realize that they were dealing with the same phenomenon.
It must explain.
It must explain.
Version 2: It must tell a story.
Enter Newton
There’s a force.
It’s the same force that makes apples fall,
And tides rise, and holds galaxies
Together.
It must be universal.
It must be universal.
Version 2: It must explain more phenomena than those used to construct it.
… and it must be mathematically elegant.
2̂MmGrm=−=FrFa
Nature and nature's laws lay hid in night,God said, "Let Newton be," and all was light. -- Alexander Pope
Nature and nature's laws lay hid in night,God said, "Let Newton be," and all was light. -- Alexander Pope
It did not last; the devil howling "Ho!Let Einstein be!" restored the status quo. -- Sir John Collings Squire
It’s not a force.
Mass warps space and time.
Apples and planets and galaxies
Just move along paths
Of least resistance.182abababRRgGTπ−=
Mercury does not move on an ellipse; it moves on a rosette.
Massive objects bend starlight
Black holes exist
Same size as solar system.
Weighs as much as 1.2 billion suns!
Problems:
• Einstein’s theory does not work inside black holes.
• It does not work right after the big bang, either.
Verdict:
Einstein’s story does not explain enough – we don’t have a beautiful theory yet.