beauty … what beauty? beauty seminar, 3/16/04 – al albano

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.