Dr Faustus of Modern Physics - Department of Speech, Music and ...

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42 CHAPTER 8. WELLPOSED VS ILLPOSED 8.2 Causality as Wellposedness The most basic principle of science may be viewed to be causality, that a certain cause has a certain effect, or that a certain effect results from a certain cause. Causality has an essential time aspect in the sense that an effect has to come after a cause. By causality predictions can be made: If the cause is known an effect can be predicted to occur at a later time. Causality is directly connected to wellposedness: If an arbitrarily small cause can have a substantial effect, that is if the model is illposed, then causality is lost in the sense that the cause of an effect is no longer known, that is the coupling cause-effect is lost. Figure 8.1: Riding a unicycle is like balancing an inverted pendulum: An illposed problem. 8.3 Pendulum: Wellposed and Illposed The motion of a pendulum of a clock is wellposed with a period which is not sensitive to perturbations. This is why a pendulum can be used to keep track of time. On the other hand, the motion of an inverted pendulum is illposed if the pendulum reaches the top position with small velocity, in which case a small perturbation may change the direction of the motion. The illposedness is expressed as the difficulty of balancing an inverted pedndulum.
8.4. SMALL CAUSE - BIG EFFECT: ILLPOSED 43 8.4 Small Cause - Big Effect: Illposed Prandtl said that a small cause (an arbitrarily thin boundary layer) can change the global features of a flow around a body and cause substantial drag. Prandtl thus claimed that his flow problem was illposed, but insisted that his model anyway was scientifically acceptable. This was breach of the fundamental principle of wellposedness. Prandtl commited the crime in order to resolve d’Alembert’s paradox, because it appeared that it could not be solved within the laws of rational wellposed science. At the end of the book you will be invited to a wellposed scientifically lawful resolution and discover that Prandtl’s sacrifice was meaningless. But to get there you have to browse the book. Figure 8.2: Wellposed Newtonian models.
Page 1: Dr Faustus of Modern Physics Claes
Page 4 and 5: 4 CONTENTS 6.5 Quantum Leap . . . .
Page 6 and 7: 6 CONTENTS III Paradoxes and Catast
Page 8 and 9: 8 CONTENTS 37.5 Heisenberg . . . .
Page 10 and 11: 10 CONTENTS
Page 12 and 13: 2 CONTENTS Figure 1: Einstein in fr
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Page 17 and 18: Chapter 1 Deal with the Devil Newto
Page 19 and 20: 1.2. BOLTZMANN: TRAGEDY OF CLASSICA
Page 21 and 22: 1.3. PLANCK: FATHER OF MODERN PHYSI
Page 23 and 24: 1.4. BOHR: DIRECTOR OF MODERN PHYSI
Page 25 and 26: 1.5. PRANDTL: FATHER OF MODERN FLUI
Page 27 and 28: 1.7. THE FAUSTUS LEGEND 17 from the
Page 29 and 30: Chapter 2 The Sacrifice The sacrifi
Page 31 and 32: Chapter 3 The Tragical History of t
Page 33 and 34: 3.3. THE QUEST FOR MAGICS OF SCIENC
Page 35 and 36: 3.4. THE PACT WITH LUCIFER 25 devot
Page 37 and 38: 3.5. DR FAUSTUS SPEAKS 27 Figure 3.
Page 39 and 40: Chapter 4 Faust by Goethe What a ma
Page 41 and 42: Chapter 5 Oxford Faust Festival 201
Page 43 and 44: Chapter 6 Battle: Continuous vs Dis
Page 45 and 46: 6.4. DAMNED QUANTUM JUMPING 35 tion
Page 47 and 48: Chapter 7 Zeno’s Paradox Hide our
Page 49 and 50: 7.4. WHO RESOLVED ZENO’S ARROW PA
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Page 55 and 56: Chapter 9 Doped Scienctists or Scie
Page 57: Part II Modern Physics 47
Page 60 and 61: 50 CHAPTER 10. BIRTH OF MODERN PHYS
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Page 80 and 81: 70 CHAPTER 14. MYSTICISM OF MODERN
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Page 88 and 89: 78 CHAPTER 17. PHYSICS TODAY: STRIN
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Page 92 and 93: 82 CHAPTER 18. END OF PHYSICS? and
Page 94 and 95: 84 CHAPTER 19. QUANTUM FIELD MAGICS
Page 96 and 97: 86 CHAPTER 20. MAX BORN: I DID IT!
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92 CHAPTER 20. MAX BORN: I DID IT!
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94 CHAPTER 21. EINSTEIN: I DID IT!
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Chapter 22 Loschmidt’s Reversibil
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Chapter 23 The Ultraviolet Catastro
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Chapter 24 The Twin Paradox Since t
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Chapter 25 Collapse of Schrödinger
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Chapter 26 D’Alembert’s Paradox
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111 to the pressure of resolving d
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Part IV Physics Tribunal 113
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116 CHAPTER 27. ACCUSATIONS Figure
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118 CHAPTER 27. ACCUSATIONS Figure
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Chapter 28 Boltzmann 28.1 Life and
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28.1. LIFE AND WORK 123 constitutio
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28.2. CONFESSION 125 source of this
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28.2. CONFESSION 127 Figure 28.2: L
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Chapter 29 Planck 29.1 Life and Wor
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29.1. LIFE AND WORK 131 Figure 29.1
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29.2. CONFESSION 133 • In order t
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Chapter 30 Einstein 30.1 Life and W
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30.2. CONFESSION 137 to philosopher
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30.2. CONFESSION 139 to the extent
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Chapter 31 Bohr 31.1 Life and Work
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31.2. CONFESSION 143 Figure 31.1: N
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31.2. CONFESSION 145 classical conc
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Chapter 32 Prandtl 32.1 Life and Wo
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32.2. CONFESSION 149 adheres to the
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Chapter 33 Motives Feeling and long
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33.1. SUMMARY OF MOTIVES 153 Figure
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Part VI Witnesses 155
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158 CHAPTER 34. STATISTICS: BOLTZMA
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160 CHAPTER 35. RADIATION: PLANCK
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162 CHAPTER 35. RADIATION: PLANCK
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164 CHAPTER 36. RELATIVITY: EINSTEI
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166 CHAPTER 36. RELATIVITY: EINSTEI
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168 CHAPTER 37. QUANTUM MECHANICS:
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178 CHAPTER 38. BOUNDARY LAYER: PRA
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180 CHAPTER 38. BOUNDARY LAYER: PRA
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Chapter 39 Nobel Prize: Planck The
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Chapter 40 Nobel Prize: Einstein +
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40.1. DOUBLE PLAY OF QUANTUM MECHAN
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Chapter 41 Atomic Bomb: Einstein +
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Chapter 42 Copenhagen Interpretatio
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193 Figure 42.1: Bohr and Einstein
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42.2. THE EPR CONTROVERSY 1935 195
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Chapter 43 Copenhagen Play Copenhag
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Chapter 44 Corruption of Climate Sc
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Chapter 45 Large Hadron Collider Ph
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Chapter 46 Mathematics as Magics
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Chapter 47 God as Mathematician or
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207 • Even if there is only one p
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Chapter 48 Penguin Logic Man has su
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211 • If we assume Heisenberg’s
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Part VIII One Mind vs Many Minds 21
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216 CHAPTER 49. GALILEO’S DIALOG
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218 CHAPTER 50. QFT AND MURDERER-VI
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220 CHAPTER 51. FINITE PRECISION CO
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222 CHAPTER 51. FINITE PRECISION CO
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224 CHAPTER 52. MANY-MINDS PHYSICS
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232 BIBLIOGRAPHY [13] A. Pais, Subt
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