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Beauty as a Guiding Principle In Search of Scientific Truth Avshalom C. Elitzur © Everyone 2007 © Everyone 2007 Permission is granted to everyone to copy and/or use this work or any part of it.

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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 Disharmony What Comes Next? 1. Preface: The Scientific Ideal of Harmony

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Pythagoras of Samos (ca. 560 – ca. 480 BC( Are Truth and Beauty Related?

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Mathematical Beauty Theorem: Every sum of consecutive odd numbers beginning with 1 is quadratic. 1+3=4=2 2 1+3+5=9=3 2 1+3+5+7=16=4 2 1+3+5+7+9=25=5 2 …

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Human Beauty

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Plato, 427-347 BC Come on! Ideas existed prior to objects!

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Euclides, 365-300 AC The Beauty in the Axiomatic System: Simplicity, Parsimony, Unity Assumptions Explanations

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Euclides, 365-300 AC The Beauty in the Axiomatic System: Simplicity, Parsimony, Unity

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Unity Underlying Plurality

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J. Kepler, 1571-1630 God must be a harmony freak…

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Heliocentric (Copernicus, 1473-1543 ) Geocentric (Ptolemy, 85-165) TWO WORLD VIEWS

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Tetrahedron Octahedron Cube

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Dodecahedron Icosahedron

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The Insight: There are 6 planets Hence 5 spaces between their spheres There are also 5 perfect solids! r 1 /r 2 = 1/2

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Mysterium Cosmographicum

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Im a genius alright !!!

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T. Brahe (1546-1601) O yeah?

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Mars deviates in 8 minutes! ?

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I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. A=+B=Constant

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

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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.

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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 Law An 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 Law The 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 Law To every action (force applied) there is an equal and opposite reaction (equal force applied in the opposite direction). I. Newton, 1643-1727

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Newton Unifies

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Revealing the underlying unity Predicting new Phenomena Analyzing

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A Scientific Theory is Beautiful when 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 Its the simple things that take your breath away

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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

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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 Disharmony What Comes Next? 1. Preface: The Scientific Ideal of Harmony

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Mechanics Electromagnetism

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Galilean Invariance: Natural Law should appear the Same for every Observer

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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 Law should appear the Same for every Observer

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J. C. Maxwell, 1831-1879 Maxwell gets more than he bargained for

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electricity magnetism light electromagnetism radiation 300,000 Km/sec Maxwell gets more than he bargained for

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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?

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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 Whats so special about the speed of light?

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A. Einstein, 1879-1955 Einstein demands harmony (& gets it)

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If Maxwells equations are always valid, What about Galilean invariance? And if Galilean invariance is always valid, would Maxwells equation lose their validity?

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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 Disharmony What Comes Next? 1. Preface: The Scientific Ideal of Harmony

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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:

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Space is absolute Time is absolute The speed of light is absolute Lets replace two assumptions with one: Einstein replies (at 26):

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How can any speed be absolute for all observers?!

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Galileos velocity addition rule: V 1 +V 2

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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

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Galileos velocity addition rule: Einsteins velocity addition rule: v 1 +v 2

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When an accelerated body approaches light velocity, the addition of energy cannot turn into velocity, hence it turns into mass. E=Mc 2 Assumption: Light velocity is constant for all observers Conclusion: Nothing can go faster than light How can any speed be absolute for all observers?!

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Why is Einstein unhappy? I want my relativity theory to hold also for non-inertial frames! (please, pleeeaaase…) A few years later…

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The happiest thought of my life…

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The Equivalence Principle David in space

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David freely falling The Equivalence Principle

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Mere coincidence of profound principle?

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David resisting gravity The Equivalence Principle

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David accelerates upwards in space The Equivalence Principle

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Free fall = no gravity Resisting gravity = acceleration The Equivalence Principle

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An incoming rock draws a parabola Acceleration=Gravity David accelerates upwards in space

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An incoming rock draws a parabola The Equivalence Principle David resisting gravity

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Einsteins 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?

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An incoming rock draws a parabola David accelerates upwards in space The Equivalence Principle

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An incoming light draws a Parabola! ?_______ David resisting gravity The Equivalence Principle: Einsteins new prediction

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"Raffiniert ist der Hergott, aber boshaft ist er nicht !" Subtle is the Lord, but not vicious! פיקח הוא אלוהים, אבל לא מניאק!

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Spacetime H. Minkowski, 1864-1909 x y t inertia

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Gravitational curvature Gravity=Inertia Space=Time Mass=Energy

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Pygmalion (2002) Mark Dennis

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במקום בו יש אוהב ואשר אותו יאהב הינו פחות-ערך יפחת ערך האוהב בהגיע האוהב לאשר יאהב שם ינוח וכאשר הדבר הכבד נעצר שם ינוח שם ינוח Canzone di Leonardo מילים: לאונארדו דא וינצ'י לחן: ? ביצוע: אורנלה ואנוני

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