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