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/
