Emerging Complexity in Physics

1. Emerging Complexity in Physics How does Physical Complexity arise from Basic Particles and Simple Principles? Ronald Westra Dep. Mathematics Maastricht UniversityNovember, 2005

2. Part 2a The Character of Physical Laws and the Structure of Space and Time

3. Emergent Complexity in Physics UCM Course LS213 –2005/2006

4. The History of Modern Physics Thomas Kuhn (1922-1996 ) The Structure of Scientific Revolutions(~1962 )

5. Thomas Kuhn (1922-1996 ) The Structure of Scientific Revolutions (SSR) (1962) Central idea : Science does not evolve gradually toward truth, but instead undergoes periodic revolutions which he calls "paradigm shifts."

6. The role of Observations and Experiments

7. St. Augustinus All truth follows directly from the Holy Scriptures. (De Civitate Dei, 5th century a.D.)

8. René Descartes 1596-1650 Meditationes de Prima Philosophia (1641): The exist Unchanceable Laws of Nature in space and time that govern all elementary building stones of Nature.

9. René Descartes 1596-1650 These natural laws are completely rational and can be induced by logical reasoning using the language of mathematics Therefore it is not necessary to validate these laws experimentally.

10. René Descartes 1596-1650 Descartes proceeds to construct a system of knowledge, discardingperception as unreliableand instead admittingonly deductionas a method.

11. Blaise Pascal 1623 - 1662 The first formulation Of the scientific methode:

12. Blaise Pascal “In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity.” Communication with Estienne Noel (1648)

13. Blaise Pascal His insistence on the existence of the vacuum also led to conflict with a number of other prominent scientists, including Descartes.

14. The Scientific Method

15. The Scientific Method (Mathematical) Theory Experiment / Observation

16. Isaac Newton (1642-1727)

17. Example: Gravity Experimentspendulum, falling apples Observationscelestial orbits (Mathematical) Theory

18. Newton sets the standard T * Absolute space and time * derived quantities: velocity, accelaration, momentum (=impuls) ·   * abstraction of the point mass * abstract quantities: force, energy · * dependance on position in space and time

19. Newton sets the standard T * The law of Nature as principle: [1] the rate of change of the momentum of a point mass equals the resultant force acting on it ·[2] the force of gravity of a mass M acting on a point mass of mass m is proportional to the inverse of the square of their relative distance

20. According to Newton T time t place x momentum p force F

21. According to Newton T

22. N After Newton T * mathematisation of Physics ·   * Extention of abstract quantities: · * E.g.: Electro-Magentism : Maxwell

23. N James Clerk Maxwell (1831-1879) T Electro- Magentism

24. NMichael Faraday (1791-1867) T Experimental findings and principles: the law of Faraday

25. N James Clerk Maxwell The laws of Electro-Magnetisme

26. HHendrik Lorentz Max Planck (

27. Towards the end of the 19th Century Lord Kelvin had warned of two small clouds on the horizon of Newtonian Physics: • 1. Ultraviolet catastrophe, photo-electric effect • 2. Michelson-Morley and aether-theory • (3. Brownian Motion)

28. Ultraviolet catastrophe • TThe ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power. As observation showed this to be clearly false, it was one of the first clear indications of problems with classical physics.

29. Michelson-Morley experiment • Velocity of light does not depend on own velocity

30. Michelson-Morley experiment

31. Brownian Motion • Molecules wiggle in fluid

33. Albert Einstein Special Relativity (1905) solves MM’exp Photoelectrisch effect (1905)  QM Brownian Motion (1905)  Chaos Theory

35. EINSTEIN and RELATIVITY

36. EINSTEINs Blackboard in 1905: How Einstein REALY discovered relativity:

37. Michelson-Morley experiment • Velocity of light does not depend on own velocity

38. Michelson-Morley experiment

39. Special Relativity • In all inertial frames the velocity of light • has the same value. • Direct mathematical consequences: • time-intervals and lengths differ for • different observers • Energy and mass are related as: E = mc2

40. Special Relativity E E = mc2 TThis is probably the most-well known equation in Physics LLet us here take a simple course towards special relativity only involving the law of Pythagoras:

41. Special Relativity

42. SSpecial Relativity BASIC PRINCIPLE: The Postulates of special relativity 1. First postulate (principle of relativity) The laws of electrodynamics and optics will be valid for all frames of reference in which the laws of mechanics hold good (non-accelerating frames). In other words: Every physical theory should look the same mathematically to every inertial observer; the laws of physics are independent of the state of inertial motion.

43. SSpecial Relativity 2. Second postulate (invariance of c) Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body; here the velocity of light c is defined as the two-way velocity, determined with a single clock. In other words: The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, and does not depend on the velocity of the object emitting the light.

44. Special Relativity in rest moving

45. Speciale Relativity Length of path according to fixed observer: This also equals the velocity of light times the duration

46. Special Relativity This is the well-known expression of Einstein for time dilatation: A moving clock ticks slower than a fixed clock. How much faster depends on the velocity v. If v increases towards the velocity of light c, than T becomes infinitely large. When v = c the time of the moving clock is observed to be stopped … … has time stopped also?

48. Special Relativity - Dali

49. Einstein By Train