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Role of Symmetry in the Sciences

Role of Symmetry in the Sciences. Gautam Mandal. Jai Hind College, Seminar on Symmetry, November 18, 2006. Geometric symmetry. Linear symmetry. Parthenon temple, Athens. An object has linear symmetry if it looks the same when the observer moves some distance along a line.

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Role of Symmetry in the Sciences

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  1. Role of Symmetry in the Sciences Gautam Mandal Jai Hind College, Seminar on Symmetry, November 18, 2006

  2. Geometricsymmetry Linear symmetry Parthenon temple, Athens

  3. An object has linear symmetry if it looks the same when the observer moves some distance along a line • Linear symmetry can be discrete (e.g. columns) or continuous Can also be along curves… A lonely desert road, USA

  4. Spiral / helical symmetry 54367-spitzer-M81 Helical staircase, Vatican Museum DNA double-helix

  5. Rotation / reflection symmetry Insulin molecule

  6. We are not mirror-symmetric!

  7. Uses of symmetry How wide is the Parthenon temple? 0 2 32 Total width = 16 times 2 = 32 metres

  8. Suppose the temple of Parthenon was like this: To know the width, need to measure distance between each pair of pillars! Can’t guess the whole from a part.

  9. Whole from Part part gives rise to atomism / reductionism…

  10. Atomism , with a pinch of salt

  11. Symmetry makes physical laws possible Hydrogen atom in Mumbai Hydrogen atom in Tokyo …… known to a very high accuracy (the story of e,h,c)

  12. SYMMETRIES ARE RARE…. 3 4 5 6 7 ….... 4 6 8 12 20 tetrahedron cube (hexahedron) octahedron dodecahedron icosahedron Platonic solids (Convex regular polyhedra)

  13. The fullerene C-60 buckyball C-540 Truncated icosahedron Fullerene nanotubes Icosahedral symmetry causes stability (too many bonds to break). Soot can be harder than diamond!

  14. To Cosmology Harmony of the spheres The ancient Greeks didn’t quite get it…………….

  15. Study of symmetry leads to puzzles and discoveries Olbers 1823

  16. WHY IS THE SKY DARK AT NIGHT?

  17. A possible model of the night sky.

  18. Assume that there is a uniform density of stars through all space. Farther stars are less bright but exactly that much more numerous: total luminosity same as that of the near ones!

  19. Night sky a la Olbers!!

  20. The day (the night, rather) is saved by the……………. Big Bang

  21. The universe originated a finite time ago (14 billion years), hence stars too far away can’t send us light yet! Distant stars are also receding, distant light is redshifted! (Expanding universe)………

  22. Saved!!!

  23. Linear symmetry in time (time translation symmetry) Clocks exist Hydrogen atom today = Hydrogen atom tomorrow

  24. Symmetry between states of motion (frames of reference) Relativity

  25. Ever threw a ball up inside a moving train?

  26. How about this? Train moves ahead, ball falls back. Sure? Wrong!

  27. Close the windows. Can’t figure out if the train is moving if the train does not turn or speed up or down. Right! Laws of physics are the same in all references which are in uniform motion with respect to each other.

  28. “Mirror” Symmetry between past and future!(T-symmetry) If this is possible

  29. Equally Possible

  30. T-symmetry in Quantum Mechanics Atom Atoms can absorb light (we feel hot in the Sun) Atoms can radiate light (light bulb works)

  31. Does not work for black holes! Black holes Cygnus X-1 Impossible Allowed

  32. Since Quantum mechanics is T-symmetric and black holes are not, black holes violate quantum mechanics!! Hawking 1974

  33. Another arrow of time Where will the gas molecules go?

  34. What if we begin like this?

  35. Is this what will happen? We would drop dead if this is what happens to air in this room

  36. Second law of thermodynamics Toss 10 coins at once H H H H H H H H H H H T H T T T T H H H improbable probable (ordered) (disordered) Doesn’t this contradict T-symmetry, hence quantum mechanics? Is THIS what marks the future from the past? No. (Challenging questions, any takers?)

  37. What has all that got to do with black holes? Black holes Black holes

  38. Black holes are made of very tiny vibrating strings

  39. which are bouncing about, much like air molecules in this room. Hence Hawking’s arrow is just the arrow of thermodynamics. (Dhar, Mandal, Wadia 1996)

  40. Harmony of the spheres The ancient Greeks were not too far wrong…………….

  41. The final frontier: The arrow of life Human Evolution Darwin Time Right Wrong (hopefully)

  42. monocellular vertebrate E. Coli David

  43. Origin of life Miller-Urey Experiment (simulated atmosphere of young Earth) Stanley Miller, Harold Urey, Chicago 1953 Methane, ammonia, hydrogen Amino acid But Life From the Primordial Soup is yet another cup of tea.

  44. life Origin of life Hot primordial soup Arrow of life unsolved HHHTHHHHHHHHHHTH…… Disorder Order

  45. THE END The Real Fun starts Now Thank you http:// theory.tifr.res.in/~mandal/

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