R e t h i n k i n g L i g h t

8 . 225 / S T S . 042 , P h y s i cs in t h e 20 t h C e n t u r y P r o f e ss o r D a v id K a i se r , 30 S e p te m b e r 202 0

“ O l d Q u a n t u m T h e o r y ” ( ~ 1900 – 1924 * )

t o da y ’ s t o p i c

# S e e L e c t u r e N o t e s on “ B l a c k bo d y r a d i a t i on a n d

* d a t e s a r e a pp r o x i m a t e ! A s w e w ill s e e , p h y s i c i st s

C o m p t on s c a t t e r i n g ” de b a t e d a n d r e v i s it e d e a c h o f t h e s e t op i c s o v e r a s p a n o f y e a r s .

P h y s ikali s c h - T e c hn i s c he R e i c h s a n s t al t ( P T R ) , B e r li n , c a . 190 0

G e r m a n y b e c a m e a un i t e d c oun t r y i n 1871 , a n d ac ce l e r a t e d a p r o g r a m o f r a p i d i n d u s t r i a li za t i on . I n 1887 , a t t h e u r g i ng o f s c i e n t i s t s a nd e n g i n e e r s , t h e g o v e r n m e n t f o u nd e d t h e P h ys i ka li s c h - T e c h n i s c h e R e ic h s an s t a lt * ( P T R ) t o f o st e r r e s e a r c h a t t h e i n t e rs e c t i on s o f b a s i c s c i e n c e , a pp li e d r e s e a r c h , a nd i nd u st r i a l d e v e l op m e n t . ( A k i n t o t h e U . S . B u r e au o f S t a n d a r d s , n o w t h e N a t i on a l I n st i t u t e o f S t a n da r d s a n d T e c hno l o g y [ N I S T ]. )

E ar l y , p r e ss i n g c h a ll e n g e : e v a l u a t e c o m p e t i ng p r opo sals f o r lar g e - s c a l e e l e c t ri c st r e e t li gh t i n g .

* I m p e r i a l P h y s i c a l - T e c hn i c al I n s t i t u t e

G l o w i n g e m b e rs i n a f i r e p la c e

W h e n a n ob j e c t i s h e a t e d t o a h i g h e no ug h t e m p e r a t u r e , i t w ill g l o w . T h e c o l o r o f t h e e m it t e d li g h t s h ift s w it h t h e t e m p e rat u r e t o w h i c h t h e ob j e c t h a s b e e n h e a t e d .

edsuom

W h il e w o r k i n g on c a li b r a t i on s f o r v a r i o u s e l e c t r i c li g h t i n g p r opo s a l s , r e se a r c h e r s a t t h e P TR no t e d a “un i v e r sa l g l o w ” : t h e p a t t e r n o f li gh t e m i t t e d fr o m v a r i o u s ob j e c t s w h e n t h e y w e r e h e a t e d t o s u ff i c i e n t l y h i g h t e m p e r a t u r e s s e e m e d t o b e i nd e p e nd e n t o f t h e c o m po s i t i on o f t ho se m a t e r i a l s .

T h e y po s t u l a t e d t h a t f o r a n i d e a l “ b l a c k bod y ” — a n ob j e c t t h a t a b s o r be d

a ll li g h t t h a t f e ll u pon i t , r e f l e c t i n g none — t h e r e m i g h t e x i st a s i n g l e , u n i v e rs a l L u mme r a n d P r i ng s h e i m ,

s p e ct r u m , o r p at t e r n o f t h e i n t e n sit y o f li g h t e m it t e d at v ari ou s w a v e l e n g t h s .

b la c k bo dy s p e c t r u m , 1890 s

T h e u n i v e r s a l b l a c k bod y s p e c t r u m s e e m e d i n t e r e s t i n g f o r a t l e a s t t w o r e as on s : i t c ou l d b e u se f u l f o r i ndu s t r i a l c a l i b r a ti o n s and s t anda r d i z a ti o n , a nd it m i gh t o ff e r c l u e s a bou t f unda m e nta l inte r acti o ns b e t w e e n li gh t a n d m a t t e r .

So P TR r e s e ar c h e rs c o ll e c t e d m o r e a nd m o r e d a t a on e m i ss i on s fr o m ( n e a r) b l a c k bod i e s t h r o ug ho u t t h e 1880 s a nd 1890 s .

! "

T 1 < T 2 < T 3

L u mm e r a n d P r i ng s h e i m , b la c k bo d y s p e c t r u m , 1890 s

Image is in the public domain.

u ( , T ) : e ne r g y d e n s it y , h o w m u c h e ne r g y w as r adi a te d pe r v ol um e pe r f r e qu e nc y .

T 3

T 2

T 1

1 2 3

As t he t e m pe r at ur e r i s e s , t he int en s it y o f t he e m it t e d light r i s e s an d t he f r e qu e nc y o f t he pe ak e m i ss ion r i s e s .

A s t h e e m p i r i c a l p a t t e r n o f t h e b l a c k bod y s p e c t r u m w as b e c o m i n g m o r e c l e a r , h o w t o e x p l a i n t h a t p a t t e r n w a s b e c o m i n g m o r e pu z z li n g .

M a x P l an c k w a s f o ll o w i n g t h e d e v e l op m e n t s a t t h e P TR c l o s e l y . H e b e c a m e t h e n e w O r d i na ri u s p r o f e ss o r o f t h e o r e t i c a l p h y s i c s i n B e r li n i n 1892 , a nd w a s a n e xp e r t i n s t a ti s tic a l m e c h an ic s .

! " In t he r m al e qu ilib r i um , e ac h de g r e e

L u mm e r a n d P r i ng s h e i m ,

“ u l t r a v i o l e t c a t as t r oph e ” !

o f f r e e do m s ho u l d h a v e a v e r ag e e ne rg y kT ( “e qu ip ar t it ion t he o re m ”) .

b l a c k bo dy s p e c t r u m , 1890 s

Image is in the public domain.

u ( , T ) : e ne r g y d e n s it y , h o w m u c h e ne r g y w as r adi a te d pe r v ol um e pe r f r e qu e nc y .

b l a c k bo d y s pe c t r u m Co m bine d w it h M ax w e ll ’ s t r e at m e nt

o f e le ct r o m a gnet ic r adi a tion , t h at y ie l de d u ( , T ) ~ kT 2 : t he e ne r g y d e n s it y s ho u l d r is e wi t h o u t li mi t as t he f r e qu e nc y o f e m it t e d light inc r e as e d!

G i v e n h i s p r o x i m i t y t o t h e P TR , P l a n c k h ad ac c e ss t o b e t t e r , m o r e u p - t o - d a t e d a t a on b l a c k bo d y s p e c t r a t h a n m o s t o f h i s c o ll e ague s . H e k n e w no t on l y t h a t t h e u ( , T ) c u r v e m u s t f a ll w it h i n c r e a s i n g ; h e h a d e m p iri c al e v i d e n c e a bou t h o w s h a r p l y t h e c u r v e ac t ua ll y f e ll . S o h e b e g an t o ti n k e r .

O n D e c e m be r 14 , 1900 , he p r e s e n t e d a p a p e r t o t he G e r m a n P h y s i c a l So c i e t y :

L u mm e r a n d P r i ng s h e i m , b l a c k bo dy s p e c t r u m , 1890 s

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h : a ne w , u n i v e rs al c on s t a nt , n o w kn o w n as “ P l an c k ’ s c on s t a nt . ”

T h e Q u a n t u m S c a l e

I n h i s 1900 t r e a t m e n t o f b l a c kbo dy r ad i a t i on , P l a n c k i n t r o d u c e d a n e w un i v e rs a l c on st a n t , h . It s e t t h e s c a l e f o r d e p a r t u r e s fr o m p h y s i c a l d e s c r i p t i on s b a s e d s o l e l y on N e w t o n ’ s o r M ax w e ll ’ s e qu at i on s .

h = 6 . 26 1 x 1 0 - 2 7 e r g - s e c on d s

O n t he s c a l e o f h u m a n - s i ze d ob j e c t s , h i s i n c r e d i b l y s m a l l :

e r g : a u nit o f e ne r g y 1 e r g = 1 g c m 2 / s 2

D r op a g r a p e fr o m 5 c m : E t ~ 1 0 2 8 h F l y b uzz i n g y o u r h e a d : | L | ~ 1 0 2 8 h

Images © sources 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/

S c i e n t i s t s t y p i c a ll y s a y t h a t P l a n c k l a u n c h e d a n e w “qu a n t u m r e v o l u t i on” w i t h h i s w o r k i n 1900 . I n m o d e r n d e r i v a t i on s , w e a r r i v e a t P l a n c k ’ s e x p r e ss i on f o r u ( , T ) b y st i p u l a t i n g t h a t t he e ne r g y e x c h a n g e d b e t w e e n m a t t e r a n d r ad i a t i on m u s t b e quan ti z e d , i n un it s E = h , rat h e r t h a n t r e a t e d a s c on t i n u o u s . I s t h a t w h a t P l an c k t h ou g h t h e w a s do i n g?

K uh n : I n P la n c k ’ s 1900 d e r i v at i on , h e fi x e d t h e t o t a l e n e rg y o f t h e s ys t e m t o b e a n i n t e g e r n u m b e r o f un i t s o f h ,

bu t h e d i d n o t r e qu i r e E i = h . I n fa c t , i n P la n c k ’ s d e s c ri p t i on , t h e e n e r g i e s f o r s u b - s y s t e m s f e ll “ i n t h e r an g e ( E i , E i + E i ) . ” P l a n c k u s e d b i n s o f s i ze = h f o r h i s ac c o u n t i n g , b u t t h e n c oun t e d h o w m a n y o s c illat o rs o f c o n ti nu o u s e n e r g y f e ll w it h i n b i n s [ 0 , ] , [ , 2 ] , a nd s o on .

I n h i s 1906 l e c t u r e s , P l a n c k s ti l l s po k e o f c on t i n u o u s ( r a t h e r t h a n qua n t i ze d ) e n e r g y e x c h a n g e .

( T h e d e b a t e c on t i n u e s : s e e M . N a u e nb e rg , A m e r i c an J o u r na l o f P h y s i c s 84 ( 2016 ) : 70 9 - 720 . )

bu t h e d i d n o t r e qu i r e E i = h . I n fa c t , i n P la n c k ’ s d e s c ri p t i on , t h e e n e r g i e s f o r s u b - s y s t e m s f e ll “ i n t h e r an g e ( E i , E i + E i ) . ” P l a n c k u s e d b i n s o f s i ze = h f o r h i s ac c o u n t i n g , b u t t h e n c oun t e d h o w m a n y o s c illat o rs o f c o n ti nu o u s e n e r g y f e ll w it h i n b i n s [ 0 , ] , [ , 2 ] , a nd s o on .

I n h i s 1906 l e c t u r e s , P l a n c k s ti l l s po k e o f c on t i n u o u s ( r a t h e r t h a n qua n t i ze d ) e n e r g y e x c h a n g e .

( T h e d e b a t e c on t i n u e s : s e e M . N a u e nb e rg , A m e r i c an J o u r na l o f P h y s i c s 84 ( 2016 ) : 70 9 - 720 . )

Q ue s ti ons ?

I n 1900 , P l a n c k h ad b e e n c on c e r n e d w i t h t h e i n t e r a cti o n b e t w e e n li gh t a nd m a t t e r , no t t he p r op a g a t i on o f li g h t on i t s o w n . I n 1905 , E i n st e i n b e g a n t o t h i nk a bou t t h e n a t u r e o f li gh t i t se l f .

E i n s t e i n a t t h e P a t e n t O ff i c e , I n p a r t i c u l a r , h e w a s t r y i ng t o m a k e s e n s e o f r e c e n t e x p e r i m e n t a l

190 5

r e s u l t s ( 1902 ) fr o m P h ili pp L e na r d on t h e e j e c t i on o f e l e c t r on s fr o m a m e t a l p l a t e , w h e n h i g h - e n e r g y ra d iat i on s h i n e s on it .

e -

V

A

In h i s e x p e ri m e n t s , Le n a r d a pp li e d a t u n a b l e v o l t a g e V a c r o ss

c on d u c t i n g p la t e s . W he n one o f t he p la t e s w a s i r r a d ia t e d w i t h u lt r a vi o l e t li g h t ( U V ) , e l e c t r on s w e r e e j e c t e d a n d t r a v e l e d t o t he o t he r p l a t e , c o m p l e t i n g a c i r c u i t ( he nc e c u r r e n t w a s m e a s u r e d i n t h e a mm e t e r A ) . B y a d j u s t i n g t h e v o l t a g e , Le n a r d c o u l d m e a s u r e h o w m u c h e n e r g y t h e e l e c t r ons h a d u pon b e i n g e j e c t e d fr o m t h e p l a t e ( “st opp i n g v o l t a g e ”) , a nd c o m p a r e t h a t w i t h t he f r e qu e n c y o f t h e r a d i a t i on t h a t h a d shon e on t o t h e p l a t e .

L e n a r d ’ s d a t a i nd i c a t e d t h a t t he r e w a s s o m e t h r e s h o l d f r e qu e n c y , be l o w w h i c h no e l e c t r on s w e r e e j e c t e d . A b o v e t h a t f r e qu e nc y , t he e l e c t r on s ’ e ne r g y r o s e l i n e a r l y

E o f e j e c t e d e l e c t r on s

w i t h t he fr e qu e ncy o f i nc i de n t l i g h t , b u t w a s

i n d e p e n d e n t o f t he i n t e n s i ty o f t he li g h t . 0 o f i nc i d e n t li g h t

W h y w e r e L e n a r d ’ s r e s u l t s p uzz li n g ?

E o f A c c o r d i n g t o M a x w e ll ’ s w o r k , t h e e n e rg y c a r ri e d b y a

e l e c t r on s li g h t w a v e i s p r opo r t i on a l t o i t s i n t e n s it y :

o f i n c i de n t li g h t

So w h y c o u l d n ’ t L e n ar d ’ s d e v i c e e j e c t e l e c t r on s w it h

0 h ig h - i n t e n s it y li g h t o f l o w f r e que n c y ? I f li g h t ac t e d li k e M a x w e lli a n w a v e s , t h e r e s hou l d b e n o t h r e s h o l d f r e qu e n c y 0 i n t h e pho t o e l e c t r i c e xp e r i m e n t s .

L i k e w i s e , ac c o r d i ng t o M ax w e ll ’ s w o r k , t h e e n e r g y i m p a r t e d t o t h e e l e c t r on s t h a t w e r e e j e c t e d s hou l d h a v e b e e n p r opo r t i on al t o t h e li gh t w a v e ’ s i n t e n s it y , w it h no p a r t i c u lar d e p e n d e n c e on t h e li g h t ’ s f r e que n c y .

I n w h a t h e c on s i de r e d t h e “ m o st r ad i c a l ” o f h i s p a p e rs o f 1905 , E i n s t e i n o ff e r e d a “h e u r i s t i c ” * e x p l a n a t i on o f t h e pho t o e l e c t r i c e ff e c t : W h a t i f li g h t its e l f w e r e quan ti z e d ?

* h e u r i s t i c m e a n s “ s u g g e s t i v e , ” w o r t h c on s i d e r i n g , no t d e fi n i t i v e .

s l op e : h

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o f i n c i d e n t li g h t

E o f e j e c t e d e l e c t r on s

w a s v e r y c l o s e t o P l a n c k ’ s n e w c on s t a n t , h .

I f e a c h li g h t qua n t u m c a r r i e d e n e r g y

t h e n f o ll o w i n g a c o lli s i on w i t h a n e l e c t r on i n t h e m e t a l p l a t e , t h e e l e c t r on w o u l d ac qu i r e e n e r g y

w h e r e ( t h e “ w o r k f u n c t i on ” o f t h e m e t a l ) c h a r ac t e r i ze d h o w t i g h t l y e l e c t r on s w e r e bo u nd t o t h e i r a t o m s i n t h e p l a t e .

T h e t h r e s ho l d f r e que n c y w a s t h e n g i v e n b y 0 = / h : on l y w h e n e a c h i n c o m i n g li g h t qua n t u m h a d s u ff i c i e n t e n e r g y w o u l d e l e c t r on s o v e r c o m e t h e w o r k f u n c t i on a nd b e e j e c t e d .

P ho t o e l e c t r i c E ffe c t

E i n s t e i n s u g g e s t e d : t h e li g h t s h i n i n g on t h e m e t a l p l a t e w a s n o t li k e a n e x t e nd e d , c on t i n uou s w a v e w as h i ng up on s ho r e , bu t li k e a s h o w e r o f m a r b l e s , e a c h o f w h i c h c o u l d c o lli d e w it h e l e c t r on s i n t h e m e t al .

s l op e : h

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o f i n c i d e n t li g h t

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