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Wo r l d v i e w s , W r a n g l e r s , a n d t h e

Ma k i n g o f T h e o r e t i c a l P h y s i c i s t s

Image is in the public domain.

8. 225 / S T S . 042, P h y s i c s i n t h e 20t h C e n t ur y Pr of e s s or D a v i d K a i s e r , 1 4 Se pt e m be r 2 0 2 0

1. M a x w el l ’ s E qua t i ons , Th e n a n d N o w

2. T r a i ni ng C a m br i dg e Wr a n g l e r s

3. T he E l ect r om a gnet i c Wo r l d v i e w

4. I ns t i t ut i ons a nd Th e o r i s t s

Re c a p : Fa r a d a y , T h o m s o n , M a x w e l l

Mi c h a e l F a r a d a y h a d l i t t l e f o r m a l e d u c a t i o n ; h e w a s f i r s t ap p r e n t i c e d as a b o o k b i n d e r , an d t h e n as a n at u r al p h i l o s o p h e r at th e R o y a l I n s ti tu ti o n .

Pa r t l y i n s p i r e d b y h i s S a n d e m a n i a n f a i t h , h e w a s f a s c i n a t e d b y th e in t e r c o n v e r t ib il it y of f or c e s a nd a n u nd e r l y i ng uni t y o f na t ur e — a un i t y m a d e p o s s i b l e b y a n a l l - pe r v a s i v e lu m i n i f e r o u s e t h e r .

He i n t r o d u c e d li n e s o f fo r c e an d t h e n fi e ld s to c h a r a c te r i z e th e st a t e o f t h e e t h e r . In p l a c e o f N e w t o n i a n “a c t i o n a t a d i st a n c e , ”

Fa r a d a y d e l i v e r i n g Ro y a l I n s t i t u t i o n “C h r i s t ma s L ect u r e , ” 1 8 5 5

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Fa r a d a y e m p h a s i z e d l o c a l e f f e c t s . Th e b i r t h o f f i e l d t h e o r y !

Wi l l i a m T h o m s o n a n d J a m e s C l e r k M a x w e l l t r a i n e d i n m a t h e m a t i c s at C am b r i d g e U n i v e r s i t y i n t h e 1 8 4 0 s - 50s . T h e y f o r m a l i z e d m a n y o f Fa r a d a y ’ s i d e a s , a n d f o u n d ma t h e ma t i c a l a n a l o g i e s be t w e e n el ect r o m a g n et i c p h en o m en a a n d m ec h a n i cs : a “ m ec h a n i ca l w o r l dv i e w . ”

Ma x w e l l f o u n d t h a t d i s t u r b a n c e s i n t h e e t h e r p r o p a g a t e d a t t h e sp eed of l i g h t : l i g h t w a s j u s t “ t r a n s v e r s e u n d u l a t i o n s ” o f E an d B in t h e e t h e r .

Ca m b r i d g e U n i v e r s i t y , K i n g ’ s P a r a d e , c a . 1 8 7 0

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In h i s t w o - vo l u m e 1 8 7 3 Tr e a t i s e , M a x w e l l d e s c r i b e d h i s n e w th e o r y o f e le c tr ic ity a n d m a g n e tis m . H e in tr o d u c e d w h a t w e c a ll “M ax w e l l ’ s e quat i o n s , ” i n f ul l C ar t e s i an - co m p o n en t f o r m .

A l a t e r M a x w e l l i a n , O l i v e r H e a v i s i d e , in v e n te d v e c to r n o ta tio n ( E , B , d i v ,

gr a d , c u r l ) ex p r essl y to e a s e th e ma n i p u l a t i o n o f M a x w e l l ’ s h u g e Tr e a t i s e !

Mo r e t h a n j u s t d i f f e r e n c e s i n no t at i o n . T o M a x w e l l a n d h i s p e e r s , Ma x w e l l ’ s e q u a t i o n s w e r e f o u n d e d o n a f u n d a m e n t a l l y d i f f e r e n t i d e a o f wh a t t h e w o r l d i s m a d e o f th a n o u r m o d e r n v ie w s .

fu n d a m e n t a l c h a r g e - car ri ers i n m o t i o n .

To us , M a x w e l l ’ s e q u a t i o n s d e s c r i b e t h e b e h a v i o r of f u nd a m e nt a l c ha r g e d pa r t i c l e s ( e l e c t r ons , i ons ) . El e c t r i c c h a r g e i s co n ser v ed : a f i x e d a m o u n t o f ch a r g e i s a t t a ch e d t o e a ch m i c r o s c o p i c ch a r g e - car ri er . E l ect ri c cu r r en t is n o th in g m o r e th a n

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To M a x w e l l , no ne o f t h i s w as t r ue ! (T h e e le c tr o n w a s n ’ t d is c o v e r e d f o r a n o th e r 2 0 y e a r s a f te r pu bl i c a t i on of hi s Tr e a t i s e .) T o t h e M a x w e l l i a n s , t h e w o r l d w a s a co n tin u u m , n o t a c o l l e c t i o n o f di s c r e t e p o i n t p a r t i c l e s . T h e y w e r e “ i n v e r t e d a t o m i s t s ” : “ I n s t e a d o f b u i l di n g t h e w o r l d o u t o f at o m s , t h ey b ui l t at o m s o ut o f t h e w o r l d . ” ( B uc h w al d )



 1 ,  1	 2 ,  2
 (s u r f a c e c h a r g e )

+V - V

To t h e M a x w e l l i a n s , c h a r g e c o u l d d r i f t i n a n d o u t of e x i s t e nc e , d e pe nd i ng on t he s t a t e of t he m e d i u m . It w a s a l oc a l m a ni f e st a t i on of d i ssi pa t i v e st r a i ns i n th e e th e r .

Ch a r g e a s s u r f a c e e f f e c t : t w o d i f f e r e n t m a t e r i a l s f i l l t h e sp a c e b e t w e e n t w o c o n d u c t i n g p l a t e s . T h e a p p l i e d vo l t a g e p u t s t h e u n d e r l y i n g e t h e r u n d e r te n s i o n . T h e pot e nt i a l e ne r g y s t or e d i n t he e t he r w ou l d be di s s i p a t ed a t a r a t e co n t r o l l ed b y t h e l o ca l m edi u m ’ s el a st i c c a p a c i t y [d i e l e c t r i c c o n s t a n t ] a n d co n d u ct i n g ca p a ci t y [c o n d u c t i v i t y ]. D i s s i p a t i o n r a t e :    /  .

 : h o w e a s y i s i t t o s t o r e p o t e n t i a l e n e r g y

 : h o w e a s y i s i t t o r e l e a s e t h e s t o r e d t e n s i o n



 1 ,  1	 2 ,  2
 (s u r f a c e c h a r g e )

+V - V

To t h e M a x w e l l i a n s , c h a r g e c o u l d d r i f t i n a n d o u t of e x i s t e nc e , d e pe nd i ng on t he s t a t e of t he m e d i u m . It w a s a l oc a l m a ni f e st a t i on of d i ssi pa t i v e st r a i ns i n th e e th e r .

We wo u l d s a y : b o t h m a t e r i a l s c o n s i s t o f fu n d am e n t al c h ar g e s , w h i c h c an b e m o v e d ar o u n d o r po l ar i z e d wh e n t h e v o l t a g e s a r e a p p l i e d , l e a d i n g t o a su r f a c e c h a r g e  . T h e p a r a m e t e r s  an d  ch a r a c t e r i z e h o w e a s i l y t h e f u n d a m e n t a l ch a r g e s c a n be r e a r r a ng e d .

Fo r u s , ch a r g e co m e s f i r s t . F o r t h e M a x w e l l i a n s , ch a r g e wa s a s e c o n d a r y e f f e c t o f t h e s t a t e o f t h e m e d i u m .

Ma x w e l l S u mma r y

Al t h o u g h w e s t i l l u s e “ M a x w e l l ’ s Eq u a t i o n s ” ( t h a n k y o u , Ol i v e r He a v i s i d e ! ) , t h e w a y w e in ter p r et th o s e e q u a tio n s is a lm o s t ex act l y t h e o p p o s i t e o f h o w t h e M ax w el l i an s d i d .

Fo r M a x w e l l , l i k e F a r a d a y a n d T h o m s o n , t h e e t h e r c a m e f i r s t . T h e i r s wa s a me c h a n i c a l w o r l d v i e w . C o n t i n u i t y w a s t h e k e y : a l l o f p h y s i c s c a m e do w n t o t h e b e h a v i o r o f a c o n t i n u o u s e l a s t i c m e di u m , w h i c h s u p p o r t e d co n t i g u o u s l o cal act i o n s . N o p o i n t p ar t i cl es , n o f u n d am en t al c h arg es — al l ( t i m e - va r y i n g ) s t a t e s o f t h e e t h e r .

Qu e s t i o n s ?

Mi c h a e l F a r a d a y h a d p r a c t i c a l l y n o m a t h e m a t i c a l t r a i n i n g . B y t h e m i d - 19t h cen t u r y , t h ere b eg an a m as s i v e s h i f t i n t h e tr a in in g of na t u r a l phi l os ophe r s , cen t ered at C am b ri d g e U n i v ers i t y .

Ne w s h i f t t o pape r an d wr i t t en ex a m i n a t i o n s .

St ud e n t s p r e v i o us l y h a d t o b r i n g t h e i r o w n s l a t e , ch a l k , c o m p a s s , a n d r u l e r f o r l e s s o n s i n E u c l i d — an d t h e n d i s p u t e g e o m e t r i c al p r o o fs or a l l y , i n La t i n !

Or a l d i s p u t a t i o n ( i n La t i n ) , Ca m b r i d g e , ea r l y 1 9 th cen t u r y

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In pl a c e of a pu bl i c or a l d i spu t a t i on, st u d e nt s no w t ook a

si l e n t , t i m e d p r o b l e m - so l v i n g e x a m o n p a p e r . T h e i r e n t i r e un d e r g r a d ua t e s t ud i e s c ul m i n a t e d i n a g r ue l i n g , 3 - da y w r i t t en ex a m t h a t det er m i n ed t h ei r g r a du a t i o n r a n k i n g : t h e Ma t h e m a t i c a l T r i p o s ex a m .

Wr i t t e n “ T r i p o s ” e x a m i n a t i o n a t C a m b r i d g e , m i d - 19 th cen t u r y

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Wr i t t e n “ T r i p o s ” e x a m i n a t i o n a t C a m b r i d g e , m i d - 19 th cen t u r y

Image is in the public domain.

Ra n k - or d e r e d r e s u l t s of t he T r i pos w e r e pu bl i s he d i n th e n e w s p a p e r s . T h e to p s c o r e r s w e r e c a lle d “w r an gl e r s . ” F i r s t p l ac e : “S e n i o r W r an gl e r . ” ( B o t h

Th o m s o n a n d M a x w e l l w e r e S e c o n d W r a n g l e r s . )

Ja m e s W a r d ’ s 1 8 7 5 d i a r y :

1. T o b e o u t o f b e d b y 7: 35 ( o r o n S u n d a y s 8: 45)

2. T o d o 5 h o u r s w o r k b e f o r e h a l l [ l u n c h ]

3. A t l e a s t o n e h o u r s [ a t h l e t i c ] ex er c i se aft e r h al l

4. T h r e e h o u r s w o r k a f t e r h a l l

5. F i n i s h w o r k b y 11 a n d b e i n b e d b y 11: 30 ( e x c e p t o n S a t u r d a y w h e n i t i s 12)

6. A f i n e o f 3d t o b e p a i d f o r t h e f i r s t r u l e b r o k e n o n a n y d a y a n d 1d e v e r y o t h e r ru l e b r o k e n o n t h e s a m e d a y

7. A h a l f p e n n y t o b e a l l o w e d o u t o f t h e f u n d t o e v e r y m e m b e r w a ki n g a n o t h e r be t w e e n 6 : 3 5 a nd 7 : 3 5 on w e e k d a y s a nd be t w e e n 7 : 4 5 a nd 8 : 4 5 on S u nd a y s

8. W o r k b e f o r e 8a m m a y c o u n t e i t h e r f o r m o r n i n g o r e v e n i n g w o r k o f t h e d a y

9. T i m e s p e n t a t C h u r c h S o c i e t y m e e t i n g c o u n t s f o r h a l f t h e s a m e t i m e ’ s w o r k a n d al s o al l o w s t h e m e m b e r at t e n d i n g t o w o r k t i l l 1 1 : 3 0 an d s t a y u p t i l l 1 2

10. T h e s e r u l e s b i n d i n g t i l l f u r t h e r n o t i c e a n d a n y a l t e r a t i o n o f t h e m r e q u i r e s

un a n i m i t y .

L “n at ur al f r e que n c y ”:

 2 = g / L

“S i m p l e h ar m o n i c o s c i l l at o r ”:

L ( t )

If t h e l en g t h o f t h e p en d u l u m c h a n g es p eri o d i ca l l y , th e n w e m u s t s o lv e th e Ma t h i e u E q u a t i o n :

pe nd u l u m of

va r y i n g l e n g t h

Co m p l i c a t e d b e h a v i o r : p e r i o d i c o s c i l l a t i o n s fo r so m e v a l u e s o f t h e p a r a m e t e r s; e x p o n e n t i a l in s ta b ilitie s f o r o th e r v a lu e s . . .

Tr a i n i n g C a m b r i d g e W r a n g l e r s

Th i s i n t e n s e m a t h e m a t i c a l t r a i n i n g w a s n o t o n l y f o r w o u l d - be ph y s i c i s t s ; i t wa s c o n s i d e r e d a n i d e a l wa y t o d i s c i p l i n e t h e m i n d fo r e v e r y o n e ! A s t h e B r i t i s h Em p i r e e x p a n d e d r a p i d l y , t h e r e w a s a n e e d f o r l a r g e n u m b e r s o f d i s c i p l i n e d ci v i l s er v an t s . If t h ey co u l d m as t er t h e M at h i eu eq u at i o n o n a t i m ed ex am , th e y c o u ld h a n d le c o m p le x p r o b le m s o f e c o n o m ic s , g o v e r n a n c e , lo g is tic s . . .

As a sid e ef f ect , a c r i t i c a l m a s s g r e w o f T r i p o s - tr a in e d sc h o l a rs w h o a c t u a l l y so u g h t a sc i e n t i fi c c a re e r . T h e Ma x w e l l i a n s c a m e m o s t l y f r o m t h i s C a m b r i d g e T r i p o s tr a d itio n .

Th e p r o f e s s i o n a l i z a t i o n o f m a t h e m a t i c a l l y t r a i n e d ph y s i c i s t s i n Br i t a i n w a s d r i v e n i n pa r t b y t he d e m a nd s of em p ir e : s u p p l y i n g r e s e a r c h p r o b l e m s ( l i k e t e l e g r a p h y ) an d p r i o r i t i zi n g an el i t e ed ucat i o n al i n f r as t r uct ur e .

Wr i t t e n “ T r i p o s ” e x a m i n a t i o n a t C a m b r i d g e , m i d - 19 th cen t u r y

Image is in the public domain.

Qu e s t i o n s ?

He i n r i c h He r t z ’ s 1 8 8 8 a p p a r a t u s , d e m o n s t r a t i n g M a x w e l l i a n w a v e s

Ma x w e l l ’ s e l e c t r o m a g n e t i c t h e o r y b e c a m e popu l a r on t he C ont i ne nt , e s pe c i a l l y i n t he l a t e 1880s , af t e r H e i n r i c h H e r t z s uc c e s s f ul l y g e n e r at e d an d d et ect ed “M ax w el l w a v es ” i n w h at w e w o ul d no w c a l l t he r a d i o por t i on of t he s pe c t r u m .

Ye t i n G e r m a n y , m o s t p h y s i c i s t s d i d n o t in te r p r e t M a x w e ll ’ s e q u a tio n s th e s a m e w a y th a t th e B r itis h M a x w e llia n s d id — an o t h er d i vi d e o v er Ma x w e l l ’ s e q u a t i o n s , t h i s t i m e a c r o s s s p a c e a n d n o t ju s t o v e r tim e .

Wh e r e a s t h e B r i t i s h c o n s i d e r e d e l e c t r o m a g n e t i c e f f e c t s t o b e g r o u n d e d i n a me c h a n i c a l et h er , to th e G e r m a n s , e le c tr o m a g n e tic e f f e c ts c a m e to s e e m tr u ly f u n d a m e n ta l: p e r h a p s me c h a n i c s its e lf w a s n o th in g b u t a p p lie d e le c tr o m a g n e tis m . A n El e c t r o ma g n e t i c W o r l d v i e w .

Co n s i d e r t h e o r i g i n o f ma s s . I n s t e a d o f a s s u m i n g t h a t o b j e c t s h a v e s o m e m a s s ( b a s e d o n th e ir m e c h a n ic a l c o m p o s itio n ), w h a t if m a s s its e lf a r o s e f r o m e le c tr o m a g n e tic in te r a c tio n s ?

A h y d r o d y n a m i c a l a n a l o g y : t h e k i n e t i c e n e r g y T of a bod y of ma s s m 0 mo v i n g w i t h v e l o c i t y v th r o u g h a n in c o m p r e s s ib le f lu id (lik e d r a g g in g a b e a c h b a ll u n d e r w a te r ).

ou t s i d e t he m e d i u m wi t h i n t h e m e d i u m

Wi t h i n t h e m e d i u m , t h e b a l l ’ s m o t i o n m a y b e d e s c r i b e d b y a n ef f ecti v e m a ss , m ef f = m 0 + m ’ , wh e r e m ’ is th e m a s s o f th e d is p la c e d f lu id .

q

No w c o n s i d e r a n e l e c t r i c a l l y c h a r g e d o b j e c t i n mo t i o n , i n t e r a c t i n g wi t h i t s ow n e l e c t r i c a n d m a g n e t i c f i e l d s . T h e s e l f - fi e l d e ffe c t s a c t l i k e a f l u i d , g e n e r a t i n g resi st a n ce t o c h a n g es i n t h e o b j ect ’ s m o t i o n .

Ef f e c t i v e m a s s :

 = m a g n e t i c p e r m e a b i l i t y o f t h e m e d i u m

a = r a d i u s o f t h e c h a r g e d o b j e c t

Bu t u nl i k e t he be a c h ba l l , a n e l e c t r i c c ha r g e c a n ne v e r be “ ou t s i d e ” of i t s “ m e d i u m ” ( i t s se l f - fi e l d ) . S o w h a t i f m 0 = 0 , a n d al l ma s s a r o s e f r o m e l e c t r o ma g n e t i c e f f e c t s ?

El e c t r o m a g n e t i c W o r l dv i e w

No w c o n s i d e r a n e l e c t r i c a l l y c h a r g e d o b j e c t i n mo t i o n , i n t e r a c t i n g wi t h i t s ow n e l e c t r i c a n d m a g n e t i c f i e l d s . T h e s e l f - fi e l d e ffe c t s a c t l i k e a f l u i d , g e n e r a t i n g resi st a n ce t o c h a n g es i n t h e o b j ect ’ s m o t i o n .

Wi l h e l m Wi e n , 1 9 0 0 : “ t h e p o s s i b i l i t y o f a n

el ect r o m a gn et i c f o u n d a t i o n f o r m ec h a n i cs ”

q

Ef f e c t i v e m a s s :

 = m a g n e t i c p e r m e a b i l i t y o f t h e m e d i u m

a = r a d i u s o f t h e c h a r g e d o b j e c t

Bu t u nl i k e t he be a c h ba l l , a n e l e c t r i c c ha r g e c a n ne v e r be “ ou t s i d e ” of i t s “ m e d i u m ” ( i t s se l f - fi e l d ) . S o w h a t i f m 0 = 0 , a n d al l ma s s a r o s e f r o m e l e c t r o ma g n e t i c e f f e c t s ?

Qu e s t i o n s ?

Ga l i l e o

New t o n

Ma x w e l l

“m a th e m a ti c i a n , ” “p h i l o so p h e r ”

“m a th e m a ti c i a n , ” “a str o n o m e r ”

“p h y si c i st”

La g r a n g e

La p l a c e

1600s 1700s 1800s

Images are in the public domain.

Kr u p p S t eel w o r k s

Rö n t g e n l a b o r a t o r y , W ü r t z b e r g

Ge r ma n u n i v e r s i t y s y s t e m: a s i n g l e “ O r d i n a r i u s ” p r o f e s s o r i n a gi v en f i el d . I n p h ys i cs , t h e o r d i n ar i us w as i n c h ar g e o f al l ex p eri m en t al ap p arat u s f o r t h e d e p ar t m en t .

Af t e r G e r m a n u n i f i c a t i o n i n 1 8 7 1 , th e c o u n tr y u n d e r w e n t r a p i d in d u s t r ia liz a t io n …

… wh i c h c a l l e d f o r t h e r a p i d tr a i n i n g o f n e w p h y s i c s te a c h e r s fo r s e c o n d ar y s c h o o l s .

Na t u r a l Sci en ce s l ect u r e h a l l , 1 8 7 6

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Ra p i d g r o w t h o f j u n i o r - fac u l t y ra n k s ( “ e x t ra o rd i n a ri u s ” pr of e s s or s ) t o t e a c h t he ne w cl a s s es .

Bu t t h e e x t r a o r d i n a r i u s fac u l t y on l y ha d a c c e s s t o pe nc i l a nd pa pe r .

D u r in g t h e 1 8 8 0 s a n d 1 8 9 0 s , “t he or e t i c a l ph y s i c i s t ” be c a m e a r e c o g n iz e d s p e c ia lt y , a n d jo b t it le .

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Ki r c h h o f f

Rö n t g e n l a b o r a t o r y , W ü r t z b e r g

Ge r ma n u n i v e r s i t y s y s t e m: a s i n g l e “ O r d i n a r i u s ” p r o f e s s o r i n a gi v en f i el d . I n p h ys i cs , t h e o r d i n ar i us w as i n c h ar g e o f al l ex p eri m en t al ap p arat u s f o r t h e d e p ar t m en t .

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Ei ns t e i n ’ s Zü r i c h not e book , 1 9 1 2

Na t u r a l Sci en ce s l ect u r e h a l l , 1 8 7 6

24

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Pl a n c k

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In p l a ce o f B ri t i s h em p i re - bu i l d i ng a s one m a i n r ou t e t o bu i l d i ng u p a co m m u n i t y o f m at h em at i cal l y t rai n ed t h eo ret i cal p h ys i ci s t s ( T ri p o s ex am ! ) , i n Ge r ma n y t h e f i e l d o f t h e o r e t i c a l p h y s i c s t o o k r o o t i n a v e r y d i f f e r e n t i n s t i t u t i o n a l co n t ex t : a s t at e - ru n u n i v e r s i t y s y s t e m w i t h a t i g h t l i m i t o n t h e h i g h e s t - ra n k i n g pos i t i ons .

Ch a n g i n g i n d u s t r i a l i z a t i o n p r i o r i t i e s a n d a d r a m a t i c p o p u l a t i o n i n c r e a s e d u r i n g th e m id - 19t h c e n t ur y c r e at e d a b ul g e o f l o w e r - ra n k ed , y o u n g er sc h o l a rs w h o h a d no a c c e s s t o e x pe r i m e nt a l e q u i pm e nt .

Wi t h i n a g e n e r a t i o n , t h e y h a d c r e a t e d t h e i r o w n r e s e a r c h j o u r n a l s a n d i n s t i t u t e s , an d ev en ( b y t h e 1890s ) t h e f i r s t Or d i n a r i u s pr of e s s or s hi ps i n “ t he or e t i c a l ph y s i c s . ”

It w a s w i t h i n t h i s i n s t i t u t i o n a l co n t ex t i n w h i c h m u c h o f m o d er n p h ys i cs — rel a t i v i t y a n d q u a n t u m t h eo r y — wa s c r a f t e d .

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