Download Symmetry in Science

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-M81
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
6
cube (hexahedron)
8
octahedron
12
dodecahedron
Platonic solids (Convex regular polyhedra)
20
icosahedron
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
Atom
Atoms can absorb
radiatelight
light(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
HHHHHHHHHH
HTHTTTTHHH
improbable
probable
(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
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
HHHTHHHHHHHHHHTH……
Order
Disorder
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