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Beauty in physics by Avshalom C. Elitzur

Beauty as a guiding principle in the evolution of theoretical physics

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Beauty in physics by Avshalom C. Elitzur

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  1. Beauty as a Guiding PrincipleIn Search of Scientific Truth Avshalom C. Elitzur Copyleft all rights reversed

  2. Outline 1. Preface: The Scientific Ideal of Harmony 2. Magnificent Harmony: Classical Physics 3. Harmony Upset and Regained: Special and General Relativity 4. Harmony Upset and Regained: Quantum Theory 5. A New Disharmony: Quantum vs. Relativity What Comes Next?

  3. Knowledge is Power:Archimedes (287-212 BC) overcomes might by math superiority of mind absent-mindedness disregard for life power of thought experiment

  4. Are Truth and Beauty Related? Pythagoras (560-480 BC( reveals the mathematical basis of harmony

  5. Famous Controversy Ideas existed prior to things! Here you go again! Aristotle384-322 BC Plato 427-347 BC

  6. The Platonist Triumph:Mathematical “fictions” eventually match reality! The number 1 The number 0 Negative numbers Imaginary numbers The derivative and the integral Non-Euclidian geometries Infinities

  7. Mathematical Beauty Theorem: 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 …

  8. Artistic beauty: Reality abstracted universal unique abstract Sandro Botticelli: Venus Pablo Picasso: Woman with a Flower Unknown photographer: Susan Dey, aged 17

  9. The Beauty in the Axiomatic System: Simplicity, Parsimony and Strength proofs Axioms Euclides, 365-300 AC

  10. Mathematics vs. Physics A mathematician and a physicist were asked the following question: Suppose you walked by a burning house and saw a hydrant and a hose not connected to the hydrant. What would you do? P: I would attach the hose to the hydrant, turn on the water, and put out the fire. Then they were asked this question: Suppose you walked by a house and saw a hose connected to a hydrant. What would you do? P: I would keep walking, as there is no problem to solve. M: I would disconnect the hose from the hydrant and set the house on fire, reducing the problem to a previously solved form.

  11. The Axiomatic System applied to Physics: The Miracle of Predictive Power Phenomena Explanations Assumptions

  12. The Axiomatic System applied to Physics: The Miracle of Predictive Power To hell with the data! The data doesn’t fit my beautiful theory? Phenomena well, Mendeleev Explanations Assumptions

  13. Outline 1. Preface: The Scientific Ideal of Harmony 2. Magnificent Harmony: Classical Physics 3. Harmony Upset and Regained: Special and General Relativity 4. Harmony Upset and Regained: Quantum Theory 5. A New Disharmony: Quantum vs. Relativity What Comes Next?

  14. Early Rebels against Aristotelianism Muhammad Nasir al-Din Al-Tusi (1201-1274) Abu Ali al-Ḥusayn ibn Sina (980–1037) Abu Abdallah Muḥammad al-Khwarizmi (780–850)

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

  16. What’s the advantage? Mine is nicer! ??? Too many epicycles!

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

  18. 6 Edges 4 Faces, 4 Vertices Tetrahedron The Five Platonic Solids 8 Faces, 6 Vertices 12 Edges Octahedron 6 Faces, 8 Vertices 12 Edges Cube 20 Faces, 12 Vertices 30 Edges Icosahedron 12 Faces, 20 Vertices 30 Edges Dodecahedron

  19. The Insight: r1/r2 = 1/2 There are 6 planets Hence 5 spaces between their spheres There are also 5 perfect solids!

  20. Mysterium Cosmographicum notice the thickness :-)

  21. I’m a genius alright !!!

  22. O yeah? T. Brahe (1546-1601)

  23. Mars deviates in 8 minutes! ?

  24. Where’s the error? Perhaps, God forbid, the planet’s orbit is not a circle but an ellipse? Or perhaps, God forbid, its motion is not constant? Both!

  25. Kepler’s Laws I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. A + B = Constant A B No epicycles! 

  26. Kepler’s Laws II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.

  27. Kepler’s Laws 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.

  28. The Seeds of the Revolution: One Physics Governing the Entire Universe Earth is a magnet Physicist, beware: We are going to invade your profession! No, it’s a force coming from the Sun William Gilbert (1544-1603) It’s the Sun’s soul affecting the planets

  29. Galileo makes thought experiments (פיזיקה = אמנות ההנחה וההזנחה) Galileo, 1564-1642

  30. Thought experiment 1: Heaviness has no effect on free-fall

  31. Thought experiment 1: Weight has no effect on free-fall

  32. Thought experiment 2: Motion in itself does not go down ignore friction!

  33. Thought experiment 2: Motion in itself does not go down

  34. Thought experiment 2: Motion in itself does not go down

  35. The Mathematics of the Parabola Velocity in the initial direction remains the same!

  36. 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 I. Newton, 1643-1727 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: F=ma . Third Law To every action (force applied) there is an equal and opposite reaction (equal force applied in the opposite direction): FAB=-FBA .

  37. Three Laws Turn into One 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. Redundant. The purpose was only to emphasize the contrast with Aristotle’s F=mv. 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: F=ma . Third Law To every action (force applied) there is an equal and opposite reaction (equal force applied in the opposite direction): FAB= –F BA . Modern physics’ Conservation Law Energy and momentum cannot be created or destroyed.

  38. Newton Unifies Everything attract everything!

  39. Newton Unifies Ax2+Bxy+Cy2+Dx+Ey+F=0 R. Descartes, 1596-1650 Circle! Circle! Parabola! Ellipse

  40. Newton Unifies

  41. Newton Unifies Kepler’s laws of planetary motion: Newton’s law of gravity: I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. 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’s second (first!) law of motion

  42. Philosophiae Naturalis Principia Mathematica (1687)

  43. Philosophiae Naturalis Principia Mathematica (1687) In every physical state, given the relevant law and initial conditions, it is possible to predict other states at any time in the past or future. Earth’s gravitational constant initial height time

  44. Newton’s Vision:Even errors are gold-mine for discoveries! If Uranus does not obey the law Perhaps something’s missing, say, a new planet? Urbain Jean Joseph Le Verrier (1811–77) John Couch Adams (1819–92) Hi, I am Neptune!

  45. Faraday Expands and Unifies Further Michael Faraday (1791-1867)

  46. Maxwell gets more than he bargained for magnetism light electricity radiation 300,000 Km/sec J. C. Maxwell, 1831-1879 Electromagnetism

  47. “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?”

  48. The Atom Thales of Miletus (624–546 BC) ήλεκτρον (ēlektron)

  49. Charles François du Fay(1698–1739)

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