Role of Symmetry in the Sciences Gautam Mandal

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 • Linear symmetry can be discrete (e. g. columns) or continuous Can also be along curves… A lonely desert road, USA

Spiral / helical symmetry 54367 -spitzer-M 81 Helical staircase, Vatican Museum DNA double-helix

Rotation / reflection symmetry Insulin molecule

We are not mirror-symmetric!

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

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

Whole from Part part gives rise to atomism / reductionism…

Atomism , with a pinch of salt

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)

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

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!

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

Study of symmetry leads to puzzles and discoveries Olbers 1823

A possible model of the night sky.

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!

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

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)………

Saved!!!

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

Symmetry between states of motion (frames of reference) Relativity

Ever threw a ball up inside a moving train?

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

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.

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

Equally Possible

T-symmetry in Quantum Mechanics Atoms can absorb radiatelight(we (light feel bulb hotworks) in the Sun)

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

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

Another arrow of time Where will the gas molecules go?

What if we begin like this?

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

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

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

Black holes are made of very tiny vibrating strings

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)

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

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

monocellular vertebrate E. Coli David

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

Origin of life Hot primordial soup HHHTHHHHHTH…… Order Disorder

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