Te a c h i n g F e y n m a n ’ s To o l s :

T he Dispersion of F eynman Diag r ams in P ostw ar P h ysic s

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1. Put t i ng N e w T ool s i nt o C i r c ul a t i on

2. U s i ng N e w T ool s t o w a rd D i f f e re nt E nds

3. W h y D o S om e T ool s S t i c k ?

2

F ashioning F eynman Diag r ams into T ools

To d a y F e y n m a n d i a g r a m s h a v e be c om e r out i ne : c om put e r s c a n dr a w a nd e v a l ua t e t hous a nds of th e m in m in u te s .

No t a l w a y s t h a t w a y : e v a l u a t i n g ju s t a h a n d fu l w a s a p u b lis h a b le fe a t in th e e a r ly 1 9 5 0 s , a n d th e s tu ff o f wh i c h d o z e n s o f d i s s e r t a t i o n s w e r e ma d e .

Of t e n t h e d i a g r a ms w e r e adapt ed as t h ey w er e ado pt ed .

De s p i t e t h e d i a g r a m s ’ c e n t r a l i t y t o d a y , th er e h a d b e e n n o a tte n tio n to ho w , b y wh o m , o r wh y th e d ia g r a m s w e r e a c tu a lly

us e d i n t he 1950s a nd 1960s .

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Th e T w o M e a n i n g s o f “ D i s p e r s i o n ”

Di s p e r s e . 1 . T o d is tr ib u te fr o m a ma in so u r c e o r c e n t r e ; t o p u t i n t o c i r c u l a t i o n .

2. T o c a us e t o s e pa r a t e i n di f f e re nt di re c t i ons ; t o put i n s c a t t e re d orde r .

Qu esti o n s:

• Ho w di d t he di a g r a m s s pr e a d s o f a s t ?

• F o r wh a t we r e t h e y u s e d d u r i n g t h e 1 9 5 0 s a n d 1960s ?

• G i v e n th is v a r ie t y , wh y di d t he di a g r a m s s t i c k ?

4

Fe y n m a n a n d t h e I n t r o d u c t i o n o f t h e D i a g r a m s

Fi r s t p r e s e n t e d a t t h e 1 9 4 8 p r i v a t e P o c o n o c o n f e r e n c e , a s a to o l fo r ta c k lin g th e in fin itie s o f QE D . T h e d ia g r a ms w e r e a bo o k k e e pi n g de v i c e fo r p e r tu r b a tio n th e o r y .

NA S p l a n f o r t h e m e e t i n g : “t o gat her a gr oup cons i s t i ng of t he y ounger m en, w ho wo u l d u n d e r s t a n d e a c h ot her ’ s j ar gon . ”

Why do electrons repel each other?

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Bo h r : s p a c e tim e p ic tu r e s v io la te th e u n c e r ta in ty p r in c ip le

Im m ed i ate R ec ep ti o n

Po o r r e c e p t i o n a t Po c o n o Fo l l o w e d S c h w i n g e r ’ s 8 - hour l e c tur e Fe y n m a n w a s r e p e a t e d l y i n t e r r u p t e d :

Di r a c : d o th e y o b e y u n ita r ity ?

Dirac © Boyer/Viollet/Rex Features. Bohr, Feynman © source unknown. Schwinger © AIP Emilio Segrè Visual Archives. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/

Teller is courtesy of Lawrence Livermore National Laboratory. Used under CC BY-NC-SA.

In g e n e r a l : w h a t ru l e s go v er n t h e d i agr am s ’ u s e?

Fe y n m a n le ft th e m e e tin g d isa p p o in te d , e v e n d e p r e sse d .

6

Co n fu s i o n Li n g er ed after M eeti n g

Be t h e t o F e y n m a n , s u mme r 1 9 4 8 : “ I tr ie d to d o yo u r t h i n g , b l a h b l a h b l a h … ”

Ma r s h a k , D e c e mb e r 1 9 4 8 : “ W e a r e in d e b te d to P r o fe s s o r Fe y n m a n f o r p e r f o r m i n g t h e [ d i a g r a m m a t i c ] c a l c u l a t i o n a t o u r re q u e st . ”

Ma tth e w s to P a u l i e t a l . , F e b r u a r y 1 9 5 0 : “ W e h a v e obt ai ned bet w een us t hr ee di f f er ent ans w er s … ”

Bethe © Los Alamos

Pa u l i t o K äl l én , A u g u s t 1 9 5 2 : “ I a m m y s e lf n o t e n o u g h o f

National Laboratory. an exper t i n ‘ gr aphs ’ t o be abl e t o c hec k al l t he det ai l s … ”

Marshak © City College of

New York.

Matthews, Schiff © source

unknown. Sc hi f f t o T el l er , M a y 1 9 5 3 : M y s tu d e n t do e s

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Th e d i a g r a m s w e r e n o t a u t o m a t i c o r o b v i o u s a t f i r s t s i g h t .

[a n d y e t … ] 7

Ev id e n c e o f Dis p e r s io n

Nu mb e r o f a r t i c l e s i n t h e P h y s ic a l R e v ie w

co n t ai n i n g F eyn m an d i agr am s , 1 9 4 9 - 1954

Th r e e s h a r e d t r a i t s : yo u n g , th e o r i s ts , a n d in c o n t a c t wi t h e a c h o t h e r

37% of f i r s t - time u s e r s w e r e g r a du a t e s t u de n t s

45% of f i r s t - time u s e r s w e r e po s t do c s

Ne a r l y a l l t h e r e s t we r e f e we r t h a n 7 y e a r s p a s t t h e i r P h . D . s

8

Dyson as Diag r ammatic Ambassador

Co r n e l l g r a d u a t e s tu d e n t , fr ie n d o f F e y n ma n ’ s .

Th e y d r o v e f r o m O h i o t o A l b u q u e r q u e d u r i n g s u m m e r 1948; F J D a t t e nde d S c hw i ng e r ’ s l e c t ur e s a t A nn A r bor su m m e r sc h o o l ; t h e n h e a r r i v e d a t I A S i n f a l l 1 9 4 8 .

Su b m i t t e d t w o ar t i cl e s t o P R o n di a g r a m s i n f a l l 1948 .

Publ i s he d be fo re Fe y n m a n ’ s o w n ar t i cl es ; c ite d mo r e o f t e n t h a n F e y n ma n ’ s .

De r i v e d r u le s fo r d ia g r a m s ’ u s e ; pr e s e nt e d “ ho w - to ” g u id e .

De mo n s t r a t e d e q u i v a le n c e of Fe y n m a n , S c h w i n g e r , a n d T o m o n a g a me t h o d s .

O ppe n h e i m e r : “ N o lo c o n te n d e r e , ” N o v e mb e r 1 9 4 8 , a fte r

Be t h e ’ s i n t e r v e n t i o n . Dyson © source unknown. All rights reserved. This content is excluded

from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/

New Institution: P ostdoc tor al T r aining

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Po s t d o c p o s i t i o n s w e r e des i gn ed to fo s te r ta c it kn o w l ed ge: m ean t t o s u p p l em en t “ b o o k l ear n i n g” o f th e P h . D . T r a v e l to n e w p la c e s to le a r n “ h a n d s o n , ” an d t h en car r y t h e n ew s ki l l s t o an o t h er p l ace t o be g i n t e a c hi ng . A l l a bout ci r cu l at i o n .

10

Domestic T r aining

Af t e r W o r l d W a r I I , n e w e m p h a s i s o n do m es t i c tr a in in g fo r th e o r i s ts . M o s t im p o r ta n t p la c e : th e In s titu te fo r A d v a n c e d S tu d y (IA S ), o n c e O p p e n h e im e r a r r i v e d in 1 9 4 7 . O v e r o b je c tio n s , h e in c r e a s e d th e o r is t - pos t doc e nr ol l m e nt s b y 60% i n hi s f i r s t y e a r (b e g in n in g 1 9 4 8 - 49) .

1 1

IAS : A F ac tory of F eynman Diag r ams

Fa l l 1 9 4 8 : n e w I A S b u i l d i n g n o t co m p l et ed ; al l t h eo r y p o s t d o cs s h ar ed one bi g of f i c e , j us t a s D y s on a r r i v e d.

Po s t d o c s c i r c u l a t e d t h r o u g h t h e I A S “i n t e l l e c t u a l h o t e l ” f o r t w o - ye a r s t a y s ; Dy s o n c o o rd i n a t e d g ro u p c a l c u l a t i o n s .

Th e p o s t d o c s n e x t t o o k j o b s e l s e w h e r e : 80% of a l l t he Ph y s i c a l Re v i e w ar t i cl es t h at u s ed F eyn m an d i agr am s b et w een 1 9 4 9 - 54 ar o s e f r o m t h es e I A S po s t do c cas cades .

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Po s t d o c C a s c a d e s

Th e d i s p e r s e d p o s t d o c s d r i l l e d t h e i r o w n g r a d u a t e s t u d e n t s in th e d ia g r a ms (p r o b le m s e ts , e x a ms , d is s e r ta tio n s ); o th e r st u d e n t s d i d n o t u se t h e m .

Dy s o n at I A S, U K , Co r n e l l ; K r o ll to Co l u m b i a ; R o h r lic h to Co r n e l l , P r i n c e t o n , Io w a ; W a ts o n to Be r k e l e y a nd M a di s on; K a r p lu s to H a rv a rd a n d Be r k e l e y …

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G e ll- Ma n n to Ch i c a g o ; Lo w to Ur b a n a ; Br ue c k ne r to In d ia n a ; Ja u c h to Io w a ; Y e n n ie to St an f o r d …

1 3

In ter n ati o n al D i s p er s i o n

UK : D y s o n me n to r e d s tu d e n ts in h is o w n fo r me r a d v is o r ’ s g r o u p a t Ca m b r i d g e , a n d t a u g h t a t Bi r m i n g h a m , 1 9 4 9 - 1951.

Ja p a n : To m o n a g a S i n - itir o ’ s g r o u p w a s al r ead y w or ki ng on s i m i l ar di agr am m at i c te c h n iq u e s fo r p e r tu r b a ti v e c a lc u la tio n s .

Th e T o k y o g r o u p r e c e i v e d n e w s a n d Dy s o n ’ s p r e p r i n t s f r o m Y u k a w a Hi d e k i , th e n a t IA S . A fte r mo n th s of car ef ul s t ud y , th e y b e g a n to u s e F e y n ma n d ia g r a ms .

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1949 G H Q decr ee: expand J apanes e uni v er s i t y s ys t em te n f o l d .

Me mb e r s o f T o mo n a g a ’ s g r o u p g o t j o b s a t Os a k a a n d e l s e w h e r e ; t h e y wo r k e d w i t h p h y s i c i s t s t h r o u g h o u t J a p a n .

14

“Natur al E x periment”: Diag r ams in US S R

Co l d W a r : N o p o s s i b i l i t y f o r p e r s o n a l c o n t a c t , c a . 1 9 4 8 - 1954.

No F e y n ma n d i a g r a ms p u b l i s h e d i n So vi et j o u r n al s u n t i l 1 9 5 2 .

Be t w e e n 1952 - 54, onl y 12 F d pa pe r s publ i s he d i n S o v i e t j our na l s .

S ix of t he s e w e r e b y t he s a m e a ut hor ! ( T o p - se c r e t H - bom b a s s i g nm e nt : l e a r n to c a lc u la te c o rre c tio n s to C o m p to n sc a t t e r i n g . T o o k a f u l l y e a r o f st u d y i n g Fe y n m a n ’ s a n d D y s o n ’ s p a p e r s . )

All “c o o k b o o k ” D y s o n - rul e s f or pe rt urba t i v e QE D .

Dy s o n , 1 9 4 9

Al e k s e i G a l a n i n , 1 9 5 2 15

Que st i ons?

1 6

Q u es t i o n 2 : W h at i s i t t h at ’ s d i s p er s i n g ?

Th e c a s c a d e m o d e l m i s s e s t h e r i c h he t e rog e ne i t y of di a g r a m us a g e : pi c t o r i a l fo r ms , re l a t i ons wi t h o t h e r e l e m e n t s o f fo r ma lis m, a n d calcu lat io n al r o les .

Fe y n m a n - Dy s o n s p l i t : “in tu iti v e p ic tu r e s ” v e r s u s “me r e ly gr ap h s o n p ap e r . ”

Di a g r a m s m o s t o f t e n a p p l i e d t o str o n g n u c l e a r f o r c e , fo r wh i c h p e r t u r b a t i o n t h e o r y br o k e do w n .

e 2 ~ 1 / 1 3 7 g 2 ~ 1 5

+ … + … + …

e 2 e 4 e 10

Pi c tori a l F orms

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“F e y n m a n d i a g r a m s” i n t h e P h y s ic a l R e v ie w , 1 9 4 9 - 1954 1 8

“ F amily Resemblanc es”: Loc al T r aditions

R o c h e s te r

me s o n s c a t t e r i n g

C o r n e ll C o lu m b ia

pe r t ur ba t i on book k e e pe r s

O x b r id g e

re n o rm a liz a tio n

C h ic a g o Ur b a n a

bound - st a t e p r o b l e m s

Men t o r s an d s t u d en t s cr af t ed d i agr am s f o r d i f f er en t p u r p o s es

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G eoffrey Chew and “Nuc lear Democ r ac y”

Fa c e d w i t h t h e b r e a k d o w n o f pe r t ur ba t i v e m e t hods ( l a r g e g 2 ), a n d th e “ z o o ” o f u n a n tic ip a te d p a r tic le s , Ch e w i n t r o d u c e d r a d i c a l c h a n g e s i n pa r t i c l e t he or y .

He d e c l a re d t h a t Q F T i s “ s t e ri l e ” f o r nuc l e a r f or c e s , “ de s t i ne d not t o di e but j us t t o f a de a w a y . ” ( 1961)

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2 0

“Nu c l ear Demo c r ac y”

D a i l y C a l c a r t o o n , c a . 1 9 4 9

Above © Lawrence Berkeley National Laboratory. Top right

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2 1

Diag r ammatic Democ r ac y

 exc hanged as fo r c e - car r yi ng par t i cl e.

 pr oduced as bound - st a t e com pos i t e , w h ic h th e n d e c a y s in to tw o pi ons .

 as “ el em ent ar y ” par t i cl e, s cat t er i ng wi t h o t h e r p a r t i c l e s .

22

Th e B o o t s t r a p

Ch e w a n d h is s tu d e n ts p r e s s e d fu r th e r : W h a t if e v e r y nuc l e a r pa rt i c l e “ pul l e d i t s e l f up b y i t s o w n boot s t r a ps , ” gen er at i n g t h e for c e s th a t w o u ld le a d to its o w n cr e a t i o n ?

St e p 1 : A  produc e s a n at t r ac t i v e f o r c e be t w e e n t w o pi ons , c a us i ng t he m t o a pproa c h eac h o t h er : F fo r c e ( m  , g ) .

St e p 2 : U p o n c o llid in g , th e tw o p io n s produc e a ne w co m p o s i t e pa rt i c l e , t he  : F re s ( m  , g ) .

Tw o e q u a t i o n s f o r t w o unk no w ns ! S ol v e f or s e l f - co n s i s t en t p ar am et er s .

23

Que st i ons?

2 4

Question 3: W h y Did the Diag r ams S tic k?

Wi t h i n pe r t u r ba t i o n t h e o r y , th e d ia g r a ms ’ a d v a n ta g e w a s ob v i ous .

Bu t t h i s can ’ t be t he w hol e s t or y , be c a us e mo s t ph y s i c s t s we r e not us i ng t he di a g r a m s f or pe rt urba t i v e c a l c ul a t i ons !

2 5

Learning to S ee

Ar t h i s t o r i a n Er n s t G o m b r i c h : th e r e is n o “ in n o c e n t e y e ” ; a r tis ts be g i n w i t h “ a g ue s s c ondi t i one d b y ha bi t a nd t r a di t i on . ” Ar t a n d I l l u s i o n , 1 9 6 9

Image is in the public domain.

Fi a l e t t i , Ey es , 1 6 0 8

So , t o o , f o r s ci en t i f i c i m ages : p r i o r h ab i t s or t r a di t i ons c a n ha v e a l ong i nf l ue nc e on ho w s c i e nt i s t s s e e t he w or l d.