Post on 13-Jun-2020
The Strangest Man - Dirac
John Anderson
The Academy Class “The Ghost Particle”
mi
His view that fundamental
physics could be gleaned
from elegant mathematics
now permeates a whole
field of inquiry into the
reality of nature, string
theory.
•Swiss father, Charles, taught French at
English School - well regarded teacher
•Mother, Flo, was English - 12 years
younger (and Methodist)
•Father wanted Paul to speak only
French (Paul would stay silent)
•One sister, Betty, one brother, Felix
• Father a bit of a charlatan
X - Lied on resume
X - Hid large amounts of income
X - Had long term secret affair
X - Lied to Paul about financial aid
Early Life
Paul
Family in 1907
Charles later on.
•Rivalry between older brothers - would
pass in streets without speaking
•Wanted to go into medicine. No money
so mech. eng. at local tech college
•Took a dull job as draftsman in
Wolverhampton
•Took up Buddhism, found a guru, had a
girlfriend (family split on meeting her)
•Suicide 1925, two months after quitting
•Ravaged family, especially father
•Paul resolved never to take his own life
Brother Felix
Felix
1921
“My parents were terribly distressed. I
didn’t know they cared so much…
I never knew that parents ought to care
for their children, but from then on I
knew.” P. Dirac
•Extrovert from Hungary. Wigner’s sister
•Divorced with 2 children. (Judith,
Gabriel)
•Met in Princeton lunch counter, 1934
•They had 2 daughters (Mary Elizabeth
and Florence Monica)
Wife - Margit Wigner
Manci 1963
When asked by Manci what
he would say if she left, the
sweet-talking Paul said “I
would say good-bye dear.” Judy,
MIA
•Honeymoon at the shore, conventional Brighton.
Family Photos
Education
• Starts out slow. Scholarship exam
success at Bishop Road School
• Outshines brother in high school,
college, relationship strained
• Completes degree at Bristol, only bad
mark in OJT internship at factory
•Studies general relativity
•J.S. Mill’s philosophy of science
• Applies to Cambridge - Needs money
• More study at Bristol - Projective
geometry, Q.M., Hamiltonian mechanics
• British citizenship in 1919
• Cambridge - Re-applies. Gets
money
• In the big time now
Education Bristol
• Merchant Venturers’ Technical
College in Bristol
• Grade school with Archibald Leach
Cambridge Education
•Terse cards home to mother
•Cavendish Lab connections
•Patrick Blackett - (cosmic rays,
cloud chambers, Nobel 1948)
•Pyotr Kapitza (Soviet Ideology,
super-fluidity, Nobel 1978)
• Dirac is a passive listener
• Ralph Fowler urges Dirac to
publish
•Dirac stories begin in earnest.
•“It is not now raining.”
• Brother Felix commits suicide
•Paul sees parents grief (Paul’s
emotional blindness)
• Heisenberg, Bohr speak at Kapitza
club
•Early work: 5 good papers, and then,
• Kapitsa at Cambridge educates Dirac on
Soviet ideology
• Kapitsa club at Cambridge (Bohr guest)
• Climbed Mt. Elbrus in Caucasus mountains
• Attended conferences in Soviet Union
• Gets roughed up at border, held 3 days
• No MI-5 file
Russian Affinity
Peter Kapitsa
1894-1984 Nobel 1978
Mt. Elbrus, 18,510 ft. Tough climb.
Igor Tamm
1895-1971 Nobel 1958
Making a Name
•First Really Major Paper - 1925
•Born astonished:
“This was -- I remember well -- one of the
greatest surprises of my scientific life. For the
name Dirac was completely unknown to me, the
author appeared to be a youngster, yet
everything was perfect in its way and admirable.”
•Niels Bohr in Copenhagen - 1926
• Next Born in Göttingen, then Leiden,
then Brussels for Solvay Conference of
1927.
European Tour
Quantum Revolution Over - 1927
First row: I. Langmuir, M. Planck, M. Curie, H. A. Lorentz, A. Einstein, P. Langevin, C. E. Guye, C. T. R. Wilson,
O. W. Richardson.
Second row, left to right: P. Debye, M. Knudsen, W. L. Bragg, H. A. Kramers, P. A. M. Dirac, A. H. Compton,
L. V. de Broglie, M. Born, N. Bohr.
Standing: A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, T. De Donder, E. Schroedinger, E. Verschaffelt,
W. Pauli, W. Heisenberg, R. H. Fowler, L. Brillouin.
Fifth Solvay Conference – Changing of the Guard
P. A. M. Dirac
How to incorporate Special
Relativity into Quantum Mechanics
Dirac has recalled a conversation with Bohr during the 1927 Solvay
conference.
Bohr: ‘What are you working on?’
Dirac: ‘I’m trying to get a relativistic theory of the electron.’
Bohr: ‘But Klein has already solved that problem.’
Dirac disagreed.
Ingredients to Build QFT
Quantum Mechanics
Strong Force
Electroweak
Force
Einstein’s Relativity
Principle Locality (no action at a
distance – emission and
absorption of particles)
QFT
Classical
Field
Theory
Dirac
merges
The Dirac Equation - 1928
0
xmxeA
xi
Dirac gets first order equation
mi Feynman slash notation
No electromagnetic field
In Westminster Abbey Plaque
Shorthand
yields
concise
equation
“Our
equations
are smarter
than we are.”
4x4 matrices,
way to factor
equations
Electron matter field.
Special Relativity - Results
•Dirac succeeds in adding Relativity to Quantum Mechanics.
•Coefficients are really matrices not numbers.
•Two positive energy solutions
•Correct magnetic moment Wow!
•Correct Thomas factor in Coulomb field
•Ordinary Schrödinger Eq. if E<<mc2
•What is negative energy solution
Spin!
Antimatter!
Golden Years Timeline
Graduates High School - 1918 at 16
Graduates Bristol Univ. 1921,
Engineer
Bristol Univ. for 2 More Years,1923
• Advanced math and physics
Enters Cambridge. PhD 1926.
• Ceremony in Latin. Paul doesn’t
understand.
Lucasian Professor - 1932 - 1968
• Finally earning some money
Nobel Prize - 1933
• Shared with Schrödinger
Dirac, Heisenberg and Schrödinger
in Stockholm
Early Builders of QFT
Wolfgang Pauli
1929- Team w/Heisenberg
Lagrangian formulation of
QFT.
1928 – w/Jordan shows
relativity compatible with
QED time commutators.
J. Robert Oppenheimer
1929 – 3rd part of Heisenberg-
Pauli paper (Coulomb Gauge
precursor) in Göttingen,
Germany.
Werner Heisenberg
1929- Team w/Pauli
Lagrangian formulation of
QFT.
1932 – First to apply QM
principles to nucleus.
Builders - Continuity Post War
Feynman picked up Dirac’s Lagrangian
approach and developed path integrals in PhD
thesis (1942).
In Warsaw, Poland 1962
Relativity Conference
Particle and Field Concepts Evolve
Phase I - Classical View
“Your old fashioned ideas are no
damn good.” Feynman
Phase II – Quantum Mechanics
1. Particle spreads like wave
2. Particle impacts like classical particle
3. It carries its own probability info about
where it is likely to impact
Phase III – Quantum Field Theory
1. Particle is a quantum of the permanent field
2. Forces via exchange of particles
3. Fields are fundamental - particles
secondary!!!
“Duality”
D
i
s
t
i
n
c
t
Quantum
of Field
Point Particle
Wave/Field
Field/Particle
Particle/Field
Each fundamental
particle has a
corresponding field.
•The unit of the “Dirac” = 1 word per hour
•“It is not now raining.”
•“Isn’t ‘in any form” redundant in that sentence?”
• “I was taught never to start a sentence without knowing how to end it.”
to Bohr
• “But Heisenberg, how do you know beforehand the girls will be nice?”
• “I don’t understand that equation.” - “That is not a question.”
Dirac Stories
Dirac’s Verbal Style 1. Verbal economy
2. Literal mindedness
3. Mathematical precision
4. Otherworldliness
With Bohr at Copenhagen gallery
• “This boat looks as if it was not
finished.”
• “I like that because the degree of
inaccuracy is the same all over.”
Dirac - on Art
French Impressionism
is outside Paul’s
comfort zone…
On walk with Oppenheimer
• “I don’t see how you can work on physics and write
poetry at the same time. In science, you want to say
something nobody knew before, in words everyone can
understand. In poetry, you are bound to say something
that everyone knows already in words nobody can
understand.” (Rephrased by Oppie.)
Declines a Oppenheimer’s 2 gift books
• “It interferes with thought.”
Dirac - on Poetry
• Train only ran every 3 days.
• Took extra sheep train, missed bus to Mesa
Verde. Never asked conductor to call ahead.
• Picked up as suspected vagrant in Durango
• “This would not be the last time Americans
would mistake the Lucasian Professor for a
vagrant.”
Colorado Tramp - 1934
J.H. Van Vleck
Dirac’s Hiking Partner
1899-1980 Nobel 1977
Durango, CO.
•Send live alligator to George Gamow (bite)
•Pushed doctoral student, Kurşunoğlu, out of a
boat in Everglades
•Nominated Heisenberg as foreign
correspondent to the Royal Society after WWII
• Adopted Manci’s children
Nasty and Nice
Doctoral advisor to: 1. H. Bhabba,
2. H. C. Mehta
3. Dennis Sciama (Hawking’s advisor)
4. Fred Hoyle, (Great cosmologist)
5. B. Kurşunoğlu
6. John Polkinghorne (Anglican priest)
7. Freeman Dyson undergrad student
Ethics advice to daughter:
“Think about yourself first.
If nobody gets hurt, do it.”
Algebra- Factorization
iyxiyxyx
yxyxyx
22
22
Matrices needed for
higher order expressions.
Simple factorization:
pppp
expression term-3 So
AAAA
vector one to applied Theorem
AABA
:need weTheorem
,
222
10
01,
0
0
01
10
zyx
zyx
ppp
i
i
i
BB
Factorization:
Pauli Matrices: generators of
3-dimensional rotations.
2
Terms
3
Terms
Relativity - Quantum Ingredients
•Relativity’s Famous Equation
•Set c = 1 for QFT
•Basic Hamiltonian
•The Energy-momentum 4-vector ),(),( pEppEp
0))((
))((
22222
mpEpEpp
pEpE
ppE pppEpp zyx
where
21
22H mp
22222
42222
mpppEpp
cmcpE
zyx
Relativistic wave equation
for massless fermions.
Two component wave function
Factorization:
4
Terms
Dirac Equation
0
0222222
xmi
mpmp
mpppEmpp zyx
•Dirac invents new 4 x 4 matrices
•Quantum mechanical operator
Factorization:
x-iip or
Four component wave
function of the Dirac eq.
5
Terms
Mathematics - Trust
“A great deal of my work
is just playing with
equations and seeing
what they give.”
“God used beautiful
mathematics in creating
the world.”
“I learnt to distrust all physical concepts as the basis
for a theory. Instead one should put one's trust in a
mathematical scheme, even if the scheme does not
appear at first sight to be connected with physics. One
should concentrate on getting interesting
mathematics.”
“I think it is a peculiarity
of myself that I like to
play about with
equations, just looking
for beautiful
mathematical relations
which maybe don’t have
any physical meaning at
all. Sometimes they do.”
Dirac’s Textbook
First edition 1930 - a scientific
success
His lectures consisted of reading it!
Fourth edition 1958, (revised 1967)
• Includes Dirac’s Bra-ket notation
invented in 1939
Book is still in print.
A Classic
Dirac Notation - ‘Bra-ket’
Develops succinct notation
“Bra-ket” term from bracket
Still widely used
Examples: Feynman Lectures Vol. III
squared)(Length
negative-non real, is
*
ff
fggf
numbercomplex )( )(*
gfxgxfdx
ionSuperposit
cc 21
Probability of measuring qn =
| < fn | Ψ > |2 for a discrete spectrum
Simplify matrix representation.
operatoran of valueAvg
ˆˆˆ * QQdxQ
Dirac Delta Function
Useful ‘functional’
Used to enforce conservation of momentum, etc.
Like Heaviside impulse function from electricity
Shocks mathematicians
The Dirac delta
function as the limit
(in the sense
of distributions)
of the sequence of
zero-centered
normal
distributions
as a -> 0
Magnetic Monopoles
Similar to an electric charge
Big Bang should have created many
None observed. (Maxwell’s Equation)
Inflation diluted them to near zero
The Standard Model - Pithy
"Matter particles (quarks and
leptons) interact with one
another by various forces, each
of which is mediated by the
exchange of force particles
(photons, gravitons(?), gluons,
W's, and Z's) in accordance
with various conservation laws."
- Sheldon Glashow
Nobel Prize 1979
Note: Need to add the Higgs Field/Particle to this description.
Say
what?
Dirac at Florida State
o What if the English department could
hire Shakespeare?
o Near Manci’s daughter, Mary
o Wanted to stay in England
1971 - 1984
•Liked Sonny and Cher
•Could not fathom “Peanuts”
Dirac on Religion
o Well, our friend Dirac, too, has a religion, and its guiding
principle is "God does not exist and Dirac is His prophet. “ - Pauli, 1927 at Solvay conference
o “One could perhaps describe the situation by saying that God
is a mathematician of a very high order, and He used very
advanced mathematics in constructing the universe.”
o In 1971 in Lindau. “Is there a God?” One of the 5 most
important questions in contemporary physics. “A physicist
would need to make this question precise by understanding
what is meant by a universe with a God and what is a universe
without a God, having a clear distinction between the two
types of universes, and then looking at the actual universe and
seeing which class it belongs to.” (i.e. If future scientists
demonstrated that the creation of life is overwhelmingly
unlikely.)
o Dirac’s pantheism was an aesthetic faith: that observations on
nature at the most fundamental level will be described
perfectly by theories whose mathematical beauty is also
perfect. If he had a religion, this was it.
Dirac’s Matrices
0
0
0
00
k
kk
I
I
and
pppp
g
that so 2 This is four-dimensional
analogue to the
three-dimensional theorem.
10
01,
0
0 ,
01
10 zyx
i
i