Beauty as a Guiding Principle Beauty as a Guiding Principle In Search of Scientific TruthIn Search of Scientific Truth

Avshalom C. ElitzurAvshalom C. Elitzur

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Contents

2 .Classical Physics:Two Harmonies give rise to Disharmony

3. Special and General Relativity:Less Assumptions, More Explanations

4. Quantum Theory:Opposites Unite

5. A New DisharmonyWhat Comes Next?

1. Preface: The Scientific Ideal of Harmony

Pythagoras of Samos (ca. 560 – ca. 480 BC(

Are Truth and Beauty Related?

Mathematical BeautyTheorem: Every sum of consecutive odd numbers beginning with 1 is quadratic. 1+3=4=22

1+3+5=9=32

1+3+5+7=16=42 1+3+5+7+9=25=52 …

Human Beauty

Plato, 427-347 BC

Come on!

Ideas existed prior to objects!

Euclides, 365-300 AC

The Beauty in the Axiomatic System:Simplicity, Parsimony, Unity

Assumptions

Explanations

Euclides, 365-300 AC

The Beauty in the Axiomatic System:Simplicity, Parsimony, Unity

Unity Underlying Plurality

J. Kepler, 1571-1630

God must be a harmony freak…

Heliocentric(Copernicus, 1473-1543 )

Geocentric(Ptolemy, 85-165)

TWO WORLD VIEWS

Tetrahedron

Octahedron

Cube

Dodecahedron

Icosahedron

The Insight:

There are 6 planets

Hence 5 spaces between their spheres

There are also 5 perfect solids!

r1/r2 = 1/2

Mysterium Cosmographicum

I’m a genius alright!!!

T. Brahe (1546-1601)

O yeah ?

Mars deviates in 8 minutes!

?

I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

A=+B=Constant

II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.

III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes.

Newton Simplifies

“To this purpose the philosophers say, that Nature does nothing in vain, and more is in vain, when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.”

Philosophiae Naturalis Principia Mathematica (1687) Book III, Rule I

First LawAn object at rest tends to stay in rest and an object in motion tends to stay in motion in a straight line at constant speed unless acted upon by an external, unbalanced force.

Second LawThe rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.

Third LawTo every action (force applied) there is an equal and opposite reaction (equal force applied in the opposite direction).

I. Newton, 1643-1727

Newton Unifies

Newton Unifies

Revealing the underlying unity

Predicting new Phenomena

Analyzing

A Scientific Theory is Beautifulwhen its Laws are

• Few • Simple• Invariant• Comprehensive• Reveal Order beneath Randomness• Unify Different and even Opposite Phenomena• Incorporate the laws of Earlier Theories• Predict New Phenomena

“It’s the simple things thattake your breath away”

R. Descartes, 1596-1650

I. Newton, 1643-1727

G. Galilei, 1564-1642

J. C. Maxwell, 1831-1879

J. Kepler, 1571-1630

M. Faraday , 1791-1867

Classical Physics:Observational Data gives rise to Mathematical Formalism

Contents

2 .Classical Physics:Two Harmonies give rise to Disharmony

3. Special and General Relativity:Less Assumptions, More Explanations

4. Quantum Theory:Opposites Unite

5. A New DisharmonyWhat Comes Next?

1. Preface: The Scientific Ideal of Harmony

MechanicsElectromagnetism

Galilean Invariance: Natural Lawshould appear the Same for every Observer

Galilean Invariance: Natural Lawshould appear the Same for every Observer

Galilean Invariance: Natural Lawshould appear the Same for every Observer

As long as motion is inertial, David can• Build a house of cards• Perform a brain surgery• Drink tea with old English ladies• Etc.

Galilean Invariance: Natural Lawshould appear the Same for every Observer

J. C. Maxwell, 1831-1879

Maxwell gets more than he bargained for

electricitymagnetismlight

electromagnetism

radiation 300,000 Km/sec

Maxwell gets more than he bargained for

“What would you say have you been told that the man you go out with has discovered the nature of the light coming from these stars?”

• The velocity of sound can be derived from the properties of air

• The velocity of water waves can be derived from the properties of water

• The velocity of light can be derived from the properties of

• But no one knows what are the properties of aether!

aether?

E=elasticity, ρ=viscosity

What’s so special about the speed of light?

A. Einstein, 1879-1955

Einstein demands harmony (& gets it)

If Maxwell’s equations are always valid, What about Galilean invariance?

And if Galilean invariance is always valid,would Maxwell’s equation lose their validity?

Contents

2 .Classical Physics:Two Harmonies give rise to Disharmony

3. Special and General Relativity:Less Assumptions, More Explanations

4. Quantum Theory:Opposites Unite

5. A New DisharmonyWhat Comes Next?

1. Preface: The Scientific Ideal of Harmony

Einstein asks (at 16):

• What happens if David, in the moving room, will play with a light ray rather than with a rock?

• What will I see if I ride on a light ray?

In our case:

Space is absolute Time is absolute The speed of light is absolute

Let’s replace two assumptions with one:

Einstein replies (at 26):

How can any speed be absolute for all observers?!

Galileo’s velocity addition rule: V1+V2

Galileo’s velocity addition rule: V1+V2

Galileo’s velocity addition rule: V1+V2

Galileo’s velocity addition rule: V1+V2

How can any speed be absolute for all observers?!

When a frame moves at a near-light velocity, its rulers contract and its clocks slow down relative to one another, such that light velocity remains 300,000 km/sec.

Assumption: Light velocity is constant for all observers

Conclusion: rulers’ length and clock rates are not equal for all observers

Galileo’s velocity addition rule:

Einstein’s velocity addition rule:2

21

21

1cvvvv

v1+v2

When an accelerated body approaches light velocity, the addition of energy cannot turn into velocity, hence it turns into mass.

E=Mc2

Assumption: Light velocity is constant for all observers

Conclusion: Nothing can go faster than light

How can any speed be absolute for all observers?!

Why is Einstein unhappy?

I want my relativity theory to hold also for non-inertial frames!

(please, pleeeaaase…)

A few years later…

“The happiest thought of my life…”

The Equivalence Principle

David in space

David freely falling

The Equivalence Principle

Mere coincidence of profound principle?

David resisting gravity

The Equivalence Principle

David accelerates upwards in space

The Equivalence Principle

Free fall = no gravity

Resisting gravity = acceleration

The Equivalence Principle

An incoming rock draws a parabola

Acceleration=Gravity

David accelerates upwards in space

An incoming rock draws a parabola

The Equivalence Principle

David resisting gravity

Einstein’s new question:

• What would David find if he studies the acceleration=gravity equivalence with a light ray rather than with a rock? Would the principle then turn invalid?

An incoming rock draws a parabola

David accelerates upwards in space

The Equivalence Principle

An incoming light draws a Parabola! ?_______

David resisting gravity

The Equivalence Principle:Einstein’s new prediction

The Equivalence Principle:Einstein’s new prediction

"Raffiniert ist der Hergott, aber boshaft ist er nicht !"

Subtle is the Lord, but not vicious!

פיקח הוא אלוהים, אבל לא מניאק!

Spacetime

H. Minkowski, 1864-1909

x

y

t

inertia

Gravitational curvature

Gravity=InertiaSpace=Time

Mass=Energy

Pygmalion (2002) Mark Dennis

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