Transcript 無投影片標題 - 2009 Asian Science Camp/Japan

The historic achievements brought forth by
physics in the 20th
century:
1
 Man discovered, for the
first time since our
ancestors discovered fire,
the second and the vastly
stronger source of energy:
nuclear power.
2
 Man learned to manipulate electrons to create the
transistor which led to the
modern computer, thereby greatly increasing
human productivity.
3
 Man learned how to probe
into structures of atomic
dimensions which led to
the double-helix, thereby
ushering in bioengineering technology.
4
 Man take first steps on
the moon.
5
However,
from
the
viewpoint of physicists, the
most important advances
are the profound revolutions
in our understanding of the
basic concepts of physics.
6
Space
Time
Motion
Energy
Force
7
There were three themes
that, singly and together,
underlie the chief new
ideas in the 20th century
physics. We may call them:
8
Thematic Melodies of
Twentieth Century
Theoretical Physics:
Quantization
Symmetry
Phase Factor
9
1. Quantization
10
Max Planck (1858-1947)
11
12
13
Quantization
1900
Planck
1905
Einstein
1913
Bohr
14
Albert Einstein (1879-1955)
15
Niels Bohr (1885-1962)
16
It was the spring of hope,
it was the winter of despair
17
At present I am myself
most optimistic as regards
the future of the theory.
Bohr to Rutherford 1918
18
Physics is once again at a
dead end at this time. For
me, at any rate. It is much
too difficult.
Pauli to Kronig,
May 21, 1925
19
Heisenberg’s mechanics
has restored my zest for
life.
Pauli to Kronig,
October 9, 1925
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Wolftgang Pauli (1900-1958)
21
Do not enter into this
conflict, we are both much
too kind and gentle to
participate in that kind of
struggle. Both Bohr and
Heisenberg are tough, hard
nosed, uncompromising and
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indefatigable. We would
just be crushed in that
juggernaut.
Kramers to Klein 1927
Quoted in Pais’ <Genius of
Science>, p.159 (2000)
23
J.R. Oppenheimer (1904-1967)
24
It was a period of patient
work in the laboratory, of
crucial
experiments
and
daring action, of many false
starts and many untenable
conjectures. It was a time of
earnest correspondence and
25
hurried
conferences,
of
debate, criticism, and brilliant
mathematical improvisation.
For those who participated, it was a time of
creation; there was terror as
well as exaltation in their new
insight . It will probably not
26
be recorded very completely
as history. As history, its
recreation would call for an
art as high as the story of
Oedipus or the story of
Cromwell, yet in a realm
of
action so remote from
our common experience that
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it is unlikely to be known to
any poet or any historian.”
J.R. Oppenheimer
Reith Lectures 1953
28
Werner Heisenberg (1901-1976)
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P.A.M. Dirac (1902-1984)
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Erwin Schrödinger (1887-1961)
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Enrico Fermi (1901-1954)
32
Pauli
— Power
Fermi
— Solidity, Strength
Heisenberg — Deep Insight
Dirac
— Cartesian Purity
33
2. Symmetry
(= invariance)
34
The five regular solids with maximum symmetry. Reprinted
from A.V. Shubnikov and V.A. Koptsik, Symmetry in Science
and Art (Plenum, 1974).
35
Symmetry
1905
Einstein
1908
Minkowski
36
“Superfluous learnedness”
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… that the basic demand of
the special theory of relativity
(invariance of the laws under
Lorentz-transformations) is
t o o n a r r o w, i . e . t h a t a n
invariance of the laws must
be postulated also relative to
non-linear transformations of
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the coordinates in the fourdimensional continuum.
This happened in 1908.
Einstein: Autobiographical Notes
in <Albert Einstein>, ed. P.A.
Schilpp, p.67
39
With the introduction of
quantum mechanics in
1925, symmetry became
very important.
The
mathematical
language
for symmetry is groups.
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It has been rumored
that the “group pest” is
gradually being cut out
of quantum physics.
H. Weyl, Nov. 1930
41
Symmetry gradually became
the thematic melody (19271970)
 atomic, molecular physics

nuclear physics

elementary particle physics
42
A great shock created by
Prof. C. S. Wu in 1957
Parity Nonconservation
in Weak Interactions
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C.S. Wu (1912-1997)
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Now, where shall I start? It
is good that I did not make
a bet.
It would have
resulted in a heavy loss of
money (which I cannot
afford); I did make a fool of
myself, however (which I
think I can afford)
Pauli 1957
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Never before or afterward
have I seen him so excited
about physics.
Heisenberg 1978
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3. Phase Factor
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So if one asks what is the
main feature of quantum
mechanics, I feel inclined now
to say that it is not noncommutative algebra, it is the
phase.
Dirac 1972
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phase factor = e
i
  0 to 360


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Phase factor became
particularly important
through the proposal
of Weyl in 1918.
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Weyl introduced
gauge factor = e

51
Then London and Fock
added i  1, so that

i
e e
gauge → phase
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1918 Weyl
1927 Fock & London
*****
Gauge Theory
Flexibility of phase factor
→ electromagnetic equation
53
Gauge invariance is
a very large symmetry.
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Weyl
1918
Schrödinger
1922
London
1927
de Broglie
1923
Schrödinger
1926
Bose
1924
Einstein
1924
Fock
1927
Weyl
1929
55
Phase Factor
1918 Weyl:
 e

exp   A dx 
 

Stretch Factor
1922 Schrödinger: Bohr orbit,
h


n
exponent
 
 
“Remarkable Property”
******
  i  stretch factor = 1
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The de Broglie interpretation
of the quantum rules seems
to me to be related in some
ways to my note in the Zs. F.
Phys. 12, 13, 1922,….. The
mathematical situation is, as
far as I can see, the same,
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only from me much more
formal, less elegant and not
r e a l l y s h o w n g e n e r a l l y.
Schrödinger to Einstein,
Nov 3, 1925
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Erwin Schrödinger (1887-1961)
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The three thematic melodies
were introduced in the first
half of the century, their
developments in the next half
century were:
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Developments
Variations
Intertwinings
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Generalization of
Gauge Symmetry
p  eA  p  eB
Motives:
(1) Discovery of more and
more “strange” particles
need a general principle
for interactions through
symmetry.
62
(2) Conservation of charge
→ electromagnetic field
Conservation of energy
→ gravitational field
Why other conservation laws
do not → specific field?
63
(3) Some Conservation laws
were related to global
gauge transformation.
This is not consistent
with the spirit of the
concept of localized
fields.
64
Principle for
Interactions
Non-Abelian
Gauge Theory
Conservation
Law
Localized
Gauge
Symmetry
65
Mathematical
Language of
Symmetry: Groups
Galois (1811-1832)
Lie
(1842-1899)
66
Simplest Lie Group is
i
Phase Factors e
Non-Abelian Lie Groups
are Generalizations of this
Phase Factor
67
QM
1926
Flexibility in
Definition of
Phase
Flexibility
Generalized
phase
1929
EM is
Gauge
Theory
1954
NonAbelian
Gauge
Theory
68
Usual Symmetry
Gauge Symmetry
Equation
Sol.
Sol.
Equation
Sol.
(Different State)
Sol.
Sol.
Sol.
(Same State)
Schematic diagram illustrating the difference between usual
symmetry and gauge symmetry. The horizontal arrows
represent symmetry transformations which relate the solutions
(sol. in the diagram). For the left column, these solutions
represent different physical states. For the right column, they
represent the same physical state.
69
Non-Abelian gauge field,
which was introduced in
1954, was initially found
not
consistent
with
experimental
results.
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1960’s
Breaking of Symmetry
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Yoichiro Nambu (1921- )
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Steven Weinberg (1933- )
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Abdus Salam (1926-1996)
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Sheldon Lee Glashow (1932- )
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Standard Model
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Symmetry Dictates
Interaction
77
Propagator =
i

 exp  ( action ) d ( path )


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Richard Feynman (1918-1988)
79
The relationship between
gauge theory and 20th
century mathematics:
Fiber bundles
Topology
80
Taken in 1985. From left: Sheldon Chang, S.S. Chern, C.N. Yang.
81
Flow
of
Ideas
82
The
three
thematic
melodies of the 20th
century led to a new
understanding of the basic
concepts of physics.
83
Space
Time
Motion
Energy
Force
84
Origin of the
thematic melodies
three
85
Early concepts related to
Quantization:
Democritus (~450 bc) Atoms
Zeno
(~300 bc) Continuity
Zhuang-zhou (~300 bc) Continuity
*****
Quantization of action (not of
matter)
86
Early concepts related to
Symmetry:
Anaximander (~600 bc)
Pythagoras (~510 bc):
Harmony of the Spheres
*****
Non-Abelian Lie Groups
87
Early concepts related to
Phases:
Phases of the Moon
Cycling of four seasons
*****
Flexibility of phases determines
equations governing
fundamental forces
88
Through more than a
century of hard work by
mathematicians
and
physicists, these three
primordial and inaccurate
concepts
89
Became
the
thematic
melodies of twentieth
century theoretical physics.
90
And
these
thematic
melodies are the spirit of
today’s theoretical physics.
91
They will continue to lead
the development of physics
in the next thirty to fifty
years.
92