1 / 48

Symmetry...

Symmetry. Fascinating and fundamental: Construction principle of nature. NUR DU GUDRUN (ONLY YOU GUDRUN). Palindrome:. NURDUGUDRUN. Symmetry: Reversal of reading direction Symmetry: Reversal of time flow direction. Thomas Lohse Humboldt-Universität zu Berlin. Symmetry.

norris
Download Presentation

Symmetry...

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Symmetry... Fascinating and fundamental: Construction principle of nature NUR DU GUDRUN (ONLY YOU GUDRUN) Palindrome: NURDUGUDRUN • Symmetry: Reversal of reading direction • Symmetry: Reversal of time flow direction Thomas Lohse Humboldt-Universität zu Berlin

  2. Symmetry... • Meaning in colloquial language: • harmony, beauty, „Ebenmaß“ • balance, order • geometrical mirror symmetry Influences since antiquity • everyday life • arts, arcitecture, engineering • music, language, linguistics • mathematics (Weyl, Wigner) • transformation groups • representation theory • natural sciences • physics, chemistry, biology

  3. eagle-men, grape picking mirror/rotation symmetry with defects silver vase of King Entemena mirror symmetry Sumerian Art (2700 B.C.)

  4. Cyprian shoulder figure Mirror symmetry Early Bronze Age (2000-1850 B.C.)

  5. Jewelry of Sat-Hathor (Cairo, Egyptian Museum) (almost)mirror symmetric Middle Empire, 12th Dynasty (Time of Sestorius III, 1887-1842 b. Chr.)

  6. creative power: breaking of mirror symmetry symmetry breaking emphasis of symmetry principle absence of symmetry disorder, chaos Etruscan Tomb (3rd Century B.C.)

  7. Triangle Triangle Rotation R.P. Feynman: An object is called symmetric, if one can do something with it, without, at the end, when one is finished with the procedure, having changed it. Mathematical Concept of Symmetry(Hermann Weyl) Toolbox: Transformation groups

  8. Finite symmetry group: Rotations & Reflections, which map a certain geometrical body onto itself Mathematical Concept of Symmetry Special case: Point groups of regular polyhedra

  9. Echinoderms (Ophiodea, Schlangensterne) 5th order rotary symmetry Ernst Haeckel: „Kunstformen der Natur“

  10. Snow flakes 6th order rotary symmetry & self similarity (fractal symmetry)

  11. mirror symmetry rotary symmetry translatory symmetry Architecture (1)

  12. Staggered translatory symmetry Staggered rotary symmetry in 6 levels Architecture (2) Baptisterium in Pisa Palace of the doges inVenice

  13. The art of M.C. Escher (1) Symmetries: • Translation • Reflection& • Translation & • Black/White-Flip

  14. The art of M.C. Escher (2) Symmetries: • Translation • Translation & Colour Rotation • Translation & Reflection & Colour Flip • Translation & Reflection & Colour Flip

  15. The art of M.C. Escher (3) Symmetries: • Translation • Translation & Colour Rotation • Rotation (3rd order) • Rotation (3rd order) & Colour Rotation • Rotation (6th order) & Colour Rotation

  16. The art of M.C. Escher (4) • 3-dimensional Translatory Symmetry • Rotation & Mirror Symmetry of the cube (Octaedral Group)

  17. Symmetry in Physics • Simplification of problem solutions Example: The double pendulum • Recognition of system properties Example: Conserved quantities and invariances • Classification Examples: Crystals, Elementary Particles, Theories • Unification of the fundamental forces Example: Electro-Magnetism, Grand Unification Symmetry = fundamental law of nature !!??

  18. pendulum initial excursion x time x 0 Problem Solution: Double Pendulum „simple“ oscillation

  19. initial excursion in x x y double pendulum time time initial excursion in y 0 x 0 y Symmetry of the system: x y Problem Solution: Double Pendulum complicated oscillation

  20. initial excursion in x double pendulum x y time time initial excursion in y 0 x y 0 symmetrical excursion same side: Problem Solution: Double Pendulum simple oscillation

  21. initial excursion in x initial excursion in y double pendulum x y time time 0 x y 0 symmetrical excursion opposite side: Problem Solution: Double Pendulum simple oscillation

  22. = + L/2 L/2 L/2 L L/2 = complicated non-symmetric oscillation sum of simple symmetric oscillations Double Pendulum Symmetry Trick

  23. origin of time axis energy conseravtion origin of spatial axes momentum conseravtion orientation of spatial axes angular mom. conserv. The Noether-Theorem Symmetry Conservation Law Emmi Noether (1882-1935) Laws of physics are independent of...

  24. parquetting, 2-dimensional lattice (crystal) Classification Problems • Rotations & Reflections... • molecules: shapes & oscillations • crystals: elementary cells • ... and in addition Translations • lattices (crystals etc.) • properties of condensed matter

  25. The Mysterious World of Elementary Particles • Fundamental Forces of Nature • Mirror Symmetries • Gauge Symmetry as Law of Nature • Grand Unification of Forces

  26. Isaac Newton (1642-1727) Albert Einstein (1879-1955) Gravitational Force • Motion of planets, stars, galaxies • Infinite range • Theory: Newton, Einstein (General Relativity) • Quantum theory: Not yet included!!

  27. Electromagnetic Force • Light, Microwaves, Radiowaves, X-rays, Gamma-rays ...

  28. Electromagnetic Force • Light, Microwaves, Radiowaves, X-rays, Gamma-rays ... • Atomic structure, Chemistry • Properties of materials (Rigidity, Conductivity, ...) • Infinite range • Theory of Maxwell (quantum theorie: Feynman et. al.) J.C. Maxwell (1831-1879)

  29. M. Gell-Mann H. Fritzsch Strong Force • Binding of atomic nuclei, nuclear power • Internal structure of the proton (quarks) • Subatomic range (< radius of proton) • Theory: Quantum-Chromodynamics (Gell-Mann, Fritzsch)

  30. E. Fermi (1901-1954) Weak Force • Radioactivity (beta decay) • Burning of the sun • Sub-nuclear range (nuclear radius/1000) • Theory: • Foundations: Enrico Fermi • Electro-weak force: Glashow, Weinberg, Salam

  31. Hadrons Neutrinos Electromagnetic Force Strong Force Weak Force Forces and Elementary Particles

  32. Spatial Reflection P - Parity P-reflected neutrino not realised in nature!!

  33. Time Reversal T - Parity But: T-reversed weak processes not exactly at equal rate!!

  34. Charge Conjugation C - Parity C-conjugated neutrino not realised in nature!!

  35. Symmetry Violation of Weak Force ? Weak Force: mysterious symmetry violations => universe made of matter while no antimatter is left

  36. - electric charge electric force-field + Current moving electric charge electric current Unification of the ForcesElectro-Magnetic Force (1) +

  37. magneticbodies magneticforce-field N S electric current magneticfield Unification of the ForcesElectro-Magnetic Force (2) Iron Iron

  38. varying magnetic fieldelectric force-field N S varying electric fields varying magnetic fields electromagnetic waves Unification of the ForcesElectro-Magnetic Force (3)

  39. global re-gauging to 100000 Volts lokal re-gauging to 100000 Volts e.m.-field, current pulse Unification of the ForcesElectro-Magnetic Gauge Symmetry Gauge Symmetry: electric ground potential is arbitrary 100000 Volts Ground: 0 Volts

  40. Deep Insight Nature possesses a localgauge symmetry The complete theory of electromagnetic forces is a necessary consequence of this localgauge symmetry ! ! The localgauge symmetry is a fundamental law of nature

  41. Unification of the ForcesThe Electro-Weak Force electromagn. force gauge symmetry: weak force gauge symmetry: ????? electroweak force gauge symmetry:

  42. Deep Insight The electromagnetic und weak forces are just two aspects of a more fundamental force of nature, the electroweak force The complete theory of the electroweak force is a necessary consequence of an extended localgauge symmetry This extended localgauge symmetry is a yet more fundamental law of nature

  43. Electroweak Force in Experiment (at big particle accelerators...) DESY (Hamburg) CERN (Geneva )

  44. Electroweak Force in Experiment (... observed in particle detectors) discovery of field quantumW ALEPH: precision measurement of properties of weak field quantaZ,W

  45. The Grand Unification of Forcesthe electro-weak-strong force electroweak force gauge symmetry: strong force gauge symmetry: electroweakstrong force gauge symmetry: ?

  46. The Unification of all Forcesthe theory of everything electroweakstrong force gauge symmetry: gravitational force gauge symmetry: Poincaré-group gauge theory of all forces supersymmetry ?? superstring theories ??

  47. Conclusion: How Symmetric is Nature? • natural phenomena are only partially symmetric (including human products) • asymmetries are often hints for deeper (and more beautiful) structures, and not just signs of disorder • the deepest basis of the laws of nature seems to be a perfect and magnificent Symmetry

More Related