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

Role of Symmetry in the Role of Symmetry in the SciencesSciences

Gautam MandalGautam Mandal

Jai Hind College, Seminar on Symmetry, November 18, 2006

Geometric

symmetry

Linear symmetryParthenon temple, Athens

•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

Spiral / helical symmetry

54367-spitzer-M81

Helical staircase, Vatican MuseumDNA double-helix

Insulin molecule

Rotation / reflection symmetry

We are not mirror-symmetric!

Total width = 16 times 2 = 32 metres

0 2

Uses of symmetry

How wide is the Parthenon temple?

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 Whole from Part

gives rise to atomism / reductionism…

part

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)

…....

4 6 8 12 20

tetrahedron cube (hexahedron) octahedron dodecahedron icosahedron

Platonic solids (Convex regular polyhedra)

3 4 5 6 7

SYMMETRIES ARE RARE….

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.

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.

Big Bang

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

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)

Hydrogen atom today = Hydrogen atom tomorrow

Clocks exist

Symmetry between states of motion(frames of reference)

Relativity

Ever threw a ball up inside a moving train?

Wrong!

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

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.

“Mirror” Symmetry

between past and future! (T-symmetry)

If this is possible

Equally Possible

Atom

Atoms can absorb light (we feel hot in the Sun)Atoms can radiate light (light bulb works)

T-symmetry in Quantum Mechanics

Black holes

Cygnus X-1

Does not work for black holes!

ImpossibleAllowed

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

Where will the gas molecules go?

Another arrow of time

What if we begin like this?

We would drop dead if this is what happens to air in this room

Is this what will happen?

Second law of thermodynamics

H H H H H H H H H H H T H T T T T H H H

improbable probable

(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

Black holes

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…………….

Time

Human Evolution

Darwin

The final frontier: The arrow of life

RightWrong (hopefully)

E. Coli

David

monocellular vertebrate

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

DisorderOrderHHHTHHHHHHHHHHTH……

Origin of life Hot primordial soup

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