Kepler, Newton, and Einstein:

“Wrong” Theories and the Progress of Science

Rob Knop aka. Prospero Frobozzthe Meta-Institute of Computational Astrophysics

Second Life2008-06-06

   

...starting well before Kepler

The Ptolemaic UniverseThe Ptolemaic Universe

• Earth is at the center

• Other planets are on “celestial spheres” about Earth

• The “fixed stars” are on the outermost sphere

• Sub-circles on the spheres rotate in “epicycles” to make it all work... (and epicycles on epicycles...)

• Immensely complicated, but it works.

   

Ptolemaic Universe is based onAristotle's Physics

• The Heavens and the Earth are separate realms.

• The Heavens are “perfect”; crystalline spheres, all motion is uniform circular motion.

• Everything has a natural place. Heavier objects are naturally “lower” (closer to the center of the Earth) than lighter objects.

• Things seek their place. The more out of place they are, the harder the seek it.

• Everything is naturally at rest.

• Ptolemy's model is based on and fits with this physics.

   

One Philosophy of Science

We are all model builders: no more, no less.

The measure of a scientific theory is its predictive power within the realm where the theory applies.

Occam's Razor: where two theories possess equivalent equivalent predictive power, prefer the simpler.

“Archaeology is the search for fact... not truth. If it's truth you're looking for, Dr. Tyree's philosophy class is right down the hall.

   

Copernicus Universe

• Sun at center

• Planets orbit in circles

   

Successes and Failures ofthe Copernican Model

(ignoring heresy for the time being)

Successes• Far simpler than Ptolemy's model.

• Naturally explains retrograde motion

• ...today, we recognize it is far closer to the true nature of reality

Failures• Ad hoc: no physics behind it.

• Does not predict planetary positions as well as Ptolemy's model!

Which is the better theory?Which, if any, is “right”, or “wrong”?

   

Kepler's LawsA tuning-up of Copernicus that finally surpasses Ptolemy in predictive power.

1. Planets orbit the Sun in ellipses with the Sun at one focus.

2. Larger orbits have longer periods (mathematical relationship).

3. Planets move faster when closer to the Sun than when farther from the Sun (mathematical relationship).

   

Newtons Laws of Motionand

Newton's Theory of Universal Gravitation

Describe how things move-- inertia, change of motion with force, action/reaction.

Provide a physics of gravity that explain Kepler's laws.

Kepler's laws can be mathematically derived from Newton's theory of motion and gravity!

F = m a F =G M m

d2

   

Newton's laws unify the heavens and the Earth

F = m aF =

G M md2

   

Ptolemy's Universe is the archetype of a discarded physical theory.

The model doesn't even include e.g. the moons of Jupiter (stuff not going around the Earth)

It is horrendously complicated, and Kepler's laws predict planetary positions as well or better.

Newton's Laws explain a huge range of physical phenomena, including but not limited to planetary orbits.

But are we even allowed to say that it's “wrong”? Or must we be pedantic and indicate that it's a “less powerful theory” or a “less usefully predictive theory”?

(Me, I say it's WRONG.)

   

REMEMBER AND NOTICE

The path from Ptolemy to Kepler goes through Copernicus...

...but Copernicus' model was not as good at predicting as was Ptolemy's!

By some measures, it is not as good a physical model.

But, we describe the view of the Solar System we have today as a “Copernican” view.

   Fact

Experimental Result

Individual observation or piece of data

Results of an experimentor observing program

via processing/analysis/interpretation of data, understanding uncertainties, etc.

Model

Experiments test models, or models explain experiments

ExperimentalDesign

“Truth” The ultimate (unattainable?) goal: What is nature?

Truth

When is a model enough to be called a theory?

When do we consider a theory “right?”

THEORY : a quantitative and descriptive framework that explains a set of natural phenomena and successfully describes the results of experiments or observations about the natural world.

   

Newton was WRONGWRONG

Newton's GravityPrediction(Kepler 1)

Observed

Mercury's OrbitAround the Sun

(Ellipticity, precessionexaggerated.)

   

Newton's Gravity is Inconsistentwith Special Relativity (SR)

SR : no signal travels faster than the speed of light.

F =G M m

d2

Implies a signal – how much force of gravity there should be for a given mass – that travels instantaneously.

   

General RelativityGeneral Relativityour modern theory of Gravity

Predicts the precession of Mercury's orbit

Gets gravitationallensing right

Needed forprecision gravitationalcalculations (e.g. GPS)

   

Was Newton Wrong?

Yes General Relativity gives us a deeper understanding of gravity consistent with other laws of Physics, borne out by experiment.

No Newton's Gravity is exactly what General Relativity gives you if things aren't moving too close to the speed of light and there isn't too much mass in too small a volume. We still use Newton's Law of Universal Gravitation all the time!!!

Newton Was Incomplete

   

Einstein Was WRONGWRONG

Quantum Mechanics : the physics of the very small, of atoms, molecules, electrons, quarks, etc.

Quantum Mechanics and Special Relativity are fully compatible.

Quantum Mechanics and General Relativity are not compatible...! ☹

A working theory of Quantum Gravity is a (the?) holy grail of modern theoretical physics.

The Elegant Universe by Brian Greene (book & Nova Special)

   

Einstein Was Right

GR is very well tested; any deeper theory will incorporate it, just as GR incorporates Newtonian gravity.

Challenges to Relativity

• Quantum Gravity

• Variable Speed of Light (early universe or only tiny variations over billions of years)

• Push experiments further to test General Relativity's predictions, look for cracks

• ...and more nutty things ☺

   

Things to take away

• We do not have absolute knowledge of The Truth... but we do know something! Ptolemy's view is wrong, even if not useless.

• One view is that it's not even meaningful to call theories “right” or “wrong”... they are measured only by how useful they are in predicting...

• ...but some of us still like to think the progress of science points us to deeper and deeper understanding, and that we're not just doing a better job at being Kepler. (Can be a trap!)

• Good theories are usually not “wrong”, even when superseded... they are incomplete.