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

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Geometric symmetry Linear symmetry Parthenon temple, Athens

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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

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

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Insulin molecule Rotation / reflection symmetry

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We are not mirror-symmetric!

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

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Suppose the temple of Parthenon was like this: To know the width, need to measure distance between each pair of pillars!

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Whole from Part gives rise to atomism / reductionism… part

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Atomism, with a pinch of salt

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

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

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

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

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Study of symmetry leads to puzzles and discoveries Olbers 1823

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A possible model of the night sky.

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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.

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

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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)………

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Saved!!!

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

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Symmetry between states of motion (frames of reference) Relativity

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Ever threw a ball up inside a moving train?

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

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Right! Close the windows. Can’t 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.

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

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Equally Possible

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

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

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

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Where will the gas molecules go? Another arrow of time

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What if we begin like this?

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

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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?Doesn’t this contradict T-symmetry, hence quantum mechanics? No. (Challenging questions, any takers?) Toss 10 coins at once

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

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Black holes are made of very tiny vibrating strings

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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)

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

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Time Human Evolution Darwin The final frontier: The arrow of life RightWrong (hopefully)

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E. Coli David monocellular vertebrate

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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

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DisorderOrderHHHTHHHHHHHHHHTH…… Origin of life Hot primordial soup

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http:// theory.tifr.res.in/~mandal/

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