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

Dec 14, 2015



  • Slide 1

Role of Symmetry in the Sciences Gautam Mandal Jai Hind College, Seminar on Symmetry, November 18, 2006 Slide 2 Geometric symmetry Linear symmetry Parthenon temple, Athens Slide 3 An object has linear symmetry if it looks the same when the observer moves some distance along a line A lonely desert road, USA Linear symmetry can be discrete (e.g. columns) Can also be along curves or continuous Slide 4 Spiral / helical symmetry 54367-spitzer-M81 Helical staircase, Vatican Museum DNA double-helix Slide 5 Insulin molecule Rotation / reflection symmetry Slide 6 We are not mirror-symmetric! Slide 7 Total width = 16 times 2 = 32 metres 0 2 Uses of symmetry How wide is the Parthenon temple? 32 Slide 8 Suppose the temple of Parthenon was like this: To know the width, need to measure distance between each pair of pillars! Slide 9 Whole from Part gives rise to atomism / reductionism part Slide 10 Atomism, with a pinch of salt Slide 11 Symmetry makes physical laws possible Hydrogen atom in MumbaiHydrogen atom in Tokyo known to a very high accuracy (the story of e,h,c) Slide 12 .... 4 6 8 12 20 tetrahedron cube (hexahedron) octahedron dodecahedron icosahedron Platonic solids (Convex regular polyhedra) 3 4 5 6 7 SYMMETRIES ARE RARE. Slide 13 The fullerene C-60 buckyballC-540 Truncated icosahedronFullerene nanotubes Icosahedral symmetry causes stability (too many bonds to break). Soot can be harder than diamond! Slide 14 Harmony of the spheres The ancient Greeks didnt quite get it. Slide 15 Study of symmetry leads to puzzles and discoveries Olbers 1823 Slide 16 Slide 17 A possible model of the night sky. Slide 18 Farther stars are less bright but exactly that much more numerous: total luminosity same as that of the near ones! Assume that there is a uniform density of stars through all space. Slide 19 Slide 20 Big Bang The day (the night, rather) is saved by the. Slide 21 The universe originated a finite time ago (14 billion years), hence stars too far away cant send us light yet! Distant stars are also receding, distant light is redshifted! (Expanding universe) Slide 22 Saved!!! Slide 23 Linear symmetry in time (time translation symmetry) Hydrogen atom today = Hydrogen atom tomorrow Clocks exist Slide 24 Symmetry between states of motion (frames of reference) Relativity Slide 25 Ever threw a ball up inside a moving train? Slide 26 Slide 27 Wrong! How about this? Train moves ahead, ball falls back. Sure? Slide 28 Right! Close the windows. Cant figure out if the train is moving if the train does not turn or speed up or down. Laws of physics are the same in all references which are in uniform motion with respect to each other. Slide 29 Mirror Symmetry between past and future ! (T-symmetry) If this is possible Slide 30 Equally Possible Slide 31 Atom Atoms can absorb light (we feel hot in the Sun)Atoms can radiate light (light bulb works) T-symmetry in Quantum Mechanics Slide 32 Black holes Cygnus X-1 Does not work for black holes! Impossible Allowed Slide 33 Since Quantum mechanics is T-symmetric and black holes are not, black holes violate quantum mechanics!! Slide 34 Where will the gas molecules go? Another arrow of time Slide 35 What if we begin like this? Slide 36 We would drop dead if this is what happens to air in this room Is this what will happen? Slide 37 Second law of thermodynamics H H H H H H T H T T T T H H H improbableprobable (ordered)(disordered) Is THIS what marks the future from the past?Doesnt this contradict T-symmetry, hence quantum mechanics? No. (Challenging questions, any takers?) Toss 10 coins at once Slide 38 Black holes What has all that got to do with black holes? Black holes Slide 39 Black holes are made of very tiny vibrating strings Slide 40 which are bouncing about, much like air molecules in this room. Hence Hawkings arrow is just the arrow of thermodynamics. (Dhar, Mandal, Wadia 1996) Slide 41 Harmony of the spheres The ancient Greeks were not too far wrong. Slide 42 Time Human Evolution Darwin The final frontier: The arrow of life RightWrong (hopefully) Slide 43 E. Coli David monocellular vertebrate Slide 44 Miller-Urey Experiment Methane, ammonia, hydrogen Amino acid Origin of life But Life From the Primordial Soup is yet another cup of tea. (simulated atmosphere of young Earth) Stanley Miller, Harold Urey, Chicago 1953 Slide 45 DisorderOrderHHHTHHHHHHHHHHTH Origin of life Hot primordial soup Slide 46 http://