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Foundations o f Physics, Vol. 12, No . 6, 1982

Instead of Part ic les and Fie lds:

A Mic r o Re a l i s t i c Quantum

S m e a r o n T h e o r y

N i c h o l a s M a x w e l l

Rece ived May 26 , 1981

A fu lly mic ro realistic, prop ensity version of qua ntu m theory is proposed,

according to which fun dam enta l physica l ent i t ies--nei the r part ic les not

fi el ds -- ha ve phy sica l characteristics whieh determine probabilistically how they

interact w ith one another (rath er than with measuring instruments). The version

o f quantum smea ron theoo, proposed here does not modify the equations o f

ortho dox qu ant um theory: rather it gives a radically new interpretation to these

equations. It is argu ed th at (i) there are stro ng general reasons fo r preferrring

qua ntum sm earo n theory to ortho dox quantum theory; (ii) the proposed

change in phy sica l interpretation leads qua ntum smearon' theory to m ak e

experimen tal predictions subtly d if ferent fro m those of orthodox quantum theory.

So m e possible crucial experiments are eonsidered.

T h i s i s o f t en t h e w a y i t i s i n p h y s i c s - - o u r m i s t a k e is n o t t h a t w e t a k e o u r

t h e o r i e s t o o s e r i o u s l y , b u t t h a t w e d o n o t t a k e t h e m s e r i o u s l y e n o u g h . I t i s

a l w a y s h a r d t o r e a li z e t h a t t h e s e n u m b e r s a n d e q u a t i o n s w e p l a y w i th a t o u r

d e s k s h a v e s o m e t h i n g t o d o w i t h t h e re a l w o r ld . E v e n w o r s e , th e r e o f te n s e e m s

t o b e a g e n e r a l a g r e e m e n t t h a t c e r t a in p h e n o m e n a a r e j u s t n o t f it s u b j e c t s fo r

r e s p e c t a b l e t h e o r e t i c a l a n d e x p e r i m e n t a l e f f o r t . ' . - S . W e i n b e r g .

1. I N T R O D U C T I O N

I t i s w i d e l y a s s u m e d t h a t q u a n t u m m e c h a n i c s Q M ) m u s t b e i n te r p re t ed a s a

t h e o r y r e st r ic t e d t o p r e d ic t in g t h e o u t c o m e o f p e r f o r m i n g m e a s u r e m e n t s o n

q u a n t u m m e c h a n i c a l l y d e s c ri b e d m i c r o s y s t e m s . M a n y , l ik e B o h r , ~

H e i s e n b e r g , 2) B o r n , 3) D i r a c , ~4) a n d o t h e r s , h o l d t h a t m e a s u r e m e n t s o c c u r

w h e n m i c r o s y s t e m s i n t e r a c t a p p r o p r i a t e l y w i t h c l a s s i c a l l y d e s c r i b a b l e

D e p a r t m e n t o f t h e H i s t o r y a n d P h i l o s o p h y o f S c i en c e , U n i v e r s i t y C o ll e g e L o n d o n , G o w e r

S t r e e t , L o n d o n W C 1 E 6 B T , E n g l a n d .

6 0 7

0015-9018/82/0600-0607503.00/0 ~? 1982 Plenum Publishing Corporation

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608 Maxwell

m a c r o s y s t e m s . O t h e r s , l i ke L udw i g , (5) D a ne r i , L o i nge r , a nd P r o s pe r i , 16)

h o l d t h a t t h e o c c u r e n c e o f a n i r r e v e r s i b l e p r o c e s s is t h e k e y t o

m e a s u r e m e n t . T h e r e a r e e v e n s o m e w h o , l ik e B a u e r a n d L o n d o n , (7~ v o n

N e u m a n n , (8) a n d W i g n e r , (9) h o l d t h a t m e a s u r e m e n t o n l y o c c u r s w h e n a

c o n s c i o u s p e r s o n m a k e s a n o b s e r v a t i o n . O t h e r s , l ik e P o p p e r , (l)

M a r g e n a u , ( l~ ) L a nd ~ , ~2 ) Bung e , (13) D ' E s p a g na t , (14) Ba l l e n t i ne , ~15) a nd

F i ne , (16) i n va r i ou s w a ys s e e k t o de f e nd ob j e c t i ve o r r e a l i s t i c

f o r m u l a t i o n s o f Q M , a n d y e t a r e o b l ig e d t o c o n c e d e , in o n e w a y o r a n o t h e r ,

B o h r ' s c r u c i a l p o i n t t h a t Q M m u s t , i n a n e s s e n t i a l w a y , p r e s u p p o s e s o m e

p a r t o f c la s s ic a l p h y s i c s f o r a d e s c r ip t i o n o f p r e p a r a t i o n a n d m e a s u r i n g

de v i c e s . A l l , i n s ho r t , a s s um e t ha t i t i s no t pos s i b l e t o f o r m u l a t e a v i a b l e

f u l ly m i c r o r e a l i s ti c v e r s i o n o f Q M , a v e r s i o n o f Q M w h i c h i s, in t h e fi r st

i n s t a n c e , e x c l u s i v e l y a b o u t h o w m i c r o s y s t e m s p h y s i c a l l y e v o l v e a n d i n t e r a c t

w i th o n e a n o t h e r , th e f u n d a m e n t a l p o s t u l a te s o f t h e t h e o r y m a k i n g n o

r e f e r e n c e t o o b s e r v a b l e s , t o m e a s u r e m e n t o r c l a s s i c a l p h y s i c s w h a t s o e v e r . I t

i s t r ue t ha t s om e , l i ke de Br og l i e , ( i v ) S c h r 6 d i nge r , ~ l s) Bo hm , (19) a nd

V i g ie r (2 ) h a v e d e f e n d e d m i c r o r e a l i s m in t h is s t r o n g s e n s e, o r h a v e s o u g h t t o

d e v e l o p m i c r o r e a l is t ic v e r s i o n s o f Q M ; h o w e v e r , th e s e a t t e m p t s h a v e n o t y e t

m e t w i t h s u c c e s s . I t w a s p e r h a p s a b o v e a ll E i n s t e in w h o u n d e r s t o o d a n d

d e p l o r e d t h e r i s k y g a m e t h a t t h e o r t h o d o x in t e r p r et a ti o n o f Q M is

p l a y i n g w i t h r e a l i t y . (21) E i n s t e i n ' s p o s i t i v e i d e a f o r a m i c r o r e a l is t ic t h e o r y

t h a t m a d e n o e s s e n t i a l r e f e r e n c e t o m e a s u r e m e n t o r c l a s s i c a l p h y s i c s w a s ,

h o w e v e r , t e n t a t i v e l y a n d s k e p t i c a l l y , a d e t e r m i n i s t i c u n i f i e d f i e l d t h e o r y , f r o m

w h i c h Q M w o u l d b e d e r i v e d a s a n a p p r o x i m a t i o n . T h i s a p p r o a c h h a s n o t

m e t w i t h s u c c e s s e i th e r , a n d a s E i n s t ei n h i m s e l f r e m a r k e d : O n e c a n g i v e

g o o d r e a s o n s w h y r e a l i t y c a n n o t a t a l l b e r e p r e s e n t e d b y a c o n t i n u o u s f i e l d .

F r o m t h e q u a n t u m p h e n o m e n a i t a p p e a r s t o f o l l o w w i t h c e r t a i n t y t h a t a

f in i te s y s t e m o f fi n it e e n e r g y c a n b e c o m p l e t e l y d e s c r i b e d b y a f in i te s e t o f

n u m b e r s ( q u a n t u m n u m b e r s ) . T h i s d o e s n o t s e e m to b e in a c c o r d a n c e w i t h a

c o n t i n uu m t he o r y . ''122 )

T h i s f i f t y y e a r l o n g d i s c u s s i o n a b o u t w h a t Q M t e l l s u s a b o u t p h y s i c a l

r e a l i t y s e e m s , h o w e v e r , t o h a v e o v e r l o o k e d o n e p o s s i b i l i t y : t o d e v e l o p a f u l l y

m i c r o r e a l is t ic p r o p e n s i t y v e r s i o n o f Q M , w h i c h is a b o u t , n o t p a r t i c l e o r

f ie ld o r m e a s u r e m e n t , b u t r a t h e r a n e w k i n d o f p h y s c i a l e n t it y , c a ll e d h e r e

t he s m e a r o n , z h a v i n g p h y s i c a l p r o p e r t i e s t h a t d i ff er r a d ic a l l y f r o m b o t h

c l a s s i c a l pa r t i c l e a nd c l a s s i c a l f ie l d. 3

z Alternative possible terms: quant on , propensitron , or waviclon .

3 This muc h neglected approa ch has been advocated in two earlier publications ~23'24) where

further details of the micro realistic, propensity idea are to be found: a somewhat similar

approach has been advocated by Bedford and Wang. (25'26)

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610 Maxwetl

In an at tempt to establ ish this point , I make the fol lowing six remarks,

and spell out a general argu me nt in sec. 2 below:

1. A ma jor t rad i t ional objec t ion to regard ing the wav e pack ets of

QM as physica l ly real i s tha t the wave mot ion of n in terac t ing qu an tum

entangled par t ic les cann ot be represented in three d imensional , physica l ly

rea l space , bu t only in 3n d imensional configura t ion space . This has been

take to exclude the poss ib i l i ty o f in terpre t ing wave pac kets as physica l ly rea l

for n >/2. Th is object io n is, perhap s, fatal for Schr 6dinge r 's original w ave

packet in terpre ta t ion of h is wave mech anics : i t does not , however , a t a l l

underm ine the propensi ty , sme aron vers ion of QM propo sed here . A system

consis ting of two qua ntu m entang led par t ic les physica l ly ex ist s in space

and evolves in t ime: w hat ex ist s and evolves i s the propen si ty of the system

to in terac t in a probabi l i s t ic way, as two par t ic les , should the appropria te

physica l condi t ions to do so ar i se . In order to represent the evolu t ion of th is

propensi ty in physica l space and t ime i t may be convenient to resor t to the

mathe mat ica l f ic t ion of a wav e pac ket in s ix d imensional configura t ion

space: but , according to the smearon view, this must be interpreted as

descr ib ing the evolu t ion of the physica l ly rea l propensi ty of the qua ntum

entangled s tem in physica l space and t ime. Smearon theory in terpre ts the

quantum s ta te of an n par t ic le quantum entangled system as a t t r ibu t ing to

any n poin ts in a reg ion o f space a def in i te probab i l i ty tha t the n par t ic les

wi l l in terac t a t these n poin ts , should the appropria te physica l condi t ions to

do so arise.

2 . Ano ther t rad i tional objec t ion to regard ing the wave packet of QM

as physica l ly rea l i s tha t th is requi res tha t we in terpre t the ins tan taneous

col lapse of the wave pa cket w henever a posi t ion measu rem ent is ma de as a

physica l ly rea l process . This postu la te of wave packet co l lapse seems

however en t i re ly

ad hoe

and inexpl icable ; and tha t i t should occur ins tan-

taneously seems physical ly implausible. Once again, this is perhaps a

powerfu l objec t ion to Schr6dinger 's or ig inal wa ve pac ket in terpre ta t ion of

QM , b ut i t i s en t i re ly harmless when d i rec ted against the sm earon vers ion of

QM prop osed here. I t is o f the essence of the sm earon idea tha t smearons

in terac t probabi l i s t ica l ly wi th one another . Indeed , the fundamenta l

dist inct ion between the classical part icle and field, and the quantum

mech anica l smearon , i s jus t tha t w hereas the physica l propert ies of the

part ic le or f ie ld de termine how these physica l en t i t ies in terac t or evolve

determinis t ica l ly , the physica l propert ies or propensi t ies of the sm earon

de te rmine how smearons in t e rac t probabilistically. 24) Dete rmin i s t i c

equat ions of s ta te evolu t ion mere ly speci fy how propensi t ies evolve when no

probabi l is t ic in terac t ions occur . A prec ise formula t ion of sme aron QM must

include a postulate which specifies the precise physical (smearon) condit ions

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Instead of Particles and Fields: A Micro Re alist ic Qu antu m 'Smearon' The ory

611

f o r p r o b a b i l i s t i c i n t e r a c t i o n s t o o c c u r . F r o m t h e s m e a r o n s t a n d p o i n t , t h e r e

n e e d b e n o t h i n g a d h o e a b o u t th i s p o s t u la t e w h a t s o e v e r . W h e t h e r o r n o t s u c h

a pos tu l a t e i s a d h o c w i l l d e p e n d o n t h e e x t e n t t o w h i c h i t c o h e r e s n a t u r a l l y

wi th bas i c p r i nc ip l es o f phy s i cs , such as spec i a l r e l a t i v i t y and t he ba s i c

q u a n t u m i d e a. I f s u c h a p o s t u l a t e is n o n ad hoc i n t h i s w a y , t h e n , f r o m t h e

s m e a r o n s t a n d p o i n t , n o s p e c i a l p r o b l e m r e m a i n s t o p r o v i d e a n e x p l a n a t i o n

o r m e c h a n i s m f o r p r o b a b i l i s t i c i n t e r a c t i o n s . T h e i d e a t h a t a n e x p l a n a t i o n o r

m e c h a n i s m m u s t b e p r o v i d e d f o r p r o b a b i l i s t i c i n t e r a c t i o n s r e s t s o n n o t h i n g

m o r e t h a n t h e r e f u s a l t o t o l e r a t e t h e i d e a t h a t p r o p e n s i t i e s m i g h t b e

f u n d a m e n t a l p h y s i c a l p r o p e r t i e s , t h a t t h e u n i v e r s e m i g h t b e f u n d a m e n t a l l y

probabilis t ic r a t h e r t h a n determinis t ic.

( 3 ) A f u n d a m e n t a l c o n c e p t u a l p r o b l e m t h a t c o n f r o n t e d c l a s s ic a l

p h y s i c s is t h e p r o b l e m o f h o w t h e c o n t i n u o u s ( e l e c t ro m a g n e t i c ) f ie l d c a n

in t e rac t w i th d i s c re t e ( cha rged ) po in t pa r t ic l e s o f ma t t e r . I t was an aspec t o f

t h i s p r o b l e m - - i n a n e m p i r i c a l g u i s e - - t h a t P l a n c k t a c k l e d i n d e v e l o p i n g h i s

e m p i r i c a l l aw o f b l a c k b o d y r a d i a t i o n , a n d i n a t t e m p t i n g to p r o v i d e a

t h e o r e t i c a l d e r i v a t i o n o f t h i s l a w , t h e s t e p t h a t f i r s t i n t r o d u c e d t h e q u a n t u m

o f a c t i o n i n t o p h y s i c s. E i n s t e i n 's 1 90 5 p h o t o n h y p o t h e s i s p a p e r f r o m t h e

ou t se t , qu i t e exp l i c i t l y , t akes a s i t s cen t ra l p rob l em the p rob l em o f how the

con t i nuous f i e l d can i n t e rac t w i th d i s c re t e ma t t e r . Tha t t h i s cons t i t u t es a

f u n d a m e n t a l p r o b l e m f o r t h e w h o l e f r a m e w o r k o f c la s s i c a l p h y s i c s s e e m s t o

hav e be en rea l i zed by E ins t e in soon a f t e r P l anc k ' s t r a i l b l az ing w ork . ~28)

Viewed as a sus t a ined a t t empt t o e s t ab l i sh , c l a r i fy and sha rpen t he con f l i c t

be tween f i e ld and pa r t i c l e , e l ec t rom agn e t i sm an d a m ech an i cs o f pa r t i c le s ,

E i n s t e i n 's o t h e r w i s e a p p a r e n t l y d iv e r s e w o r k p u b l i sh e d i n 1 90 5 o n B r o w n i a n

mot ion (des igned t o e s t ab l i sh t he ex i s t ence o f a t oms) , spec i a l r e l a t i v i t y and

t h e p h o t o n h y p o t h e s i s , t a k e s o n a s t r i k in g u n i t y o f p u r p o s e . T h e r e a r e

g r o u n d s , t h e n , f o r h o l d i n g t h a t f r o m t h e o u t s e t , q u a n t u m t h e o r y a r o s e o u t o f

c o n c e r n w i th t h e f i e ld / p a r t i c le p r o b l e m . S u b s e q u e n t d e v e l o p m e n t s - - s u c h a s

C o m p t o n ' s w o r k o n p h o t o n - - e l e c t r o n s c a t t e r i n g , d e B r o g l i e ' s t h e o r y o f

m a t t e r w a v e s , a n d i t s e x p e r i m e n t a l c o r r o b o r a t i o n , H e i s e n b e r g ' s m a t r i x

m e c h a n i c s a n d S c h r 6 d i n g e r ' s w a v e m e c h a n i c s , s e r v ed o n l y t o d e e p e n th e

c o n f l i c t . I t i s t h e f a i l u r e o f Q M t o s o l v e t h i s f u n d a m e n t a l , c o n c e p t u a l

p r o b l e m - - t h e c l a s s i c a l f i e l d / p a r t i c l e p r o b l e m o r t h e q u a n t u m m e c h a n i c a l

w a v e / p a r t i c l e p r o b l e m - - w h i c h m a k e s i t n e c e s s a r y t o i n t e r p r e t Q M a s a

t h e o r y a b o u t o b s e r v a b l e s , a b o u t t h e o u t c o m e o f p e r fo r m i n g m e a s u r e m e n t s .

A s l o n g a s n o c o n s i s t e n t m i c r o r e a l i st ic o n t o l o g y f o r t h e q u a n t u m d o m a i n i s

fo r t hcoming , i t i s imposs ib l e t o i n t e rp re t QM as a t heo ry t ha t i s , i n t he f i r s t

i n s t a n c e , e x c l u s i v e l y a b o u t m i c r o s y s t e m s , a b o u t h o w t h e y i n t e r a c t a n d

evo lve i n space - t ime . I t i s t hus under s t andab l e why E ins t e in , s eek ing a mic ro

rea l i s ti c r e so lu t i on o f t he f i e l d /pa r t i c l e p rob l em, sh ou ld j udg e the H e i sen -

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6 2 Maxwell

b e r g - B o h r i n t e r p re t a ti o n o f Q M t o b e a " t r a n q u i li z i n g p h i l o s o p h y - - o r

r e l i g i o n - - . . , s o d e l i c a t e l y c o n t r i v e d t h a t , f o r t h e t i m e b e i n g , i t p r o v i d e s a

g e n t l e p i l l o w f o r t h e t r u e b e l i e v e r f r o m w h i c h h e c a n n o t v e r y e a s i l y b e

a ro us ed " , (21) an evasion r a t h e r t h a n a s o l u t i o n o f t h e p r o b l e m . A s E i n s t e in

w r o t e t o h i s f r ie n d M . B e s s o t o w a r d s t h e e n d o f h is l i fe : " A l l t h e s e f i f ty y e a r s

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

q u e s ti o n ' W h a t a re l ig h t q u a n t a ? ' N o w a d a y s e v e r y T o m , D i c k a n d H a r r y

th inks he k now s i t , bu t h e i s mi s t a k e n . '( 29 )

T h e s o l u t i o n o f f e r e d h e r e t o t h e c l a s s i c a l f i e l d / p o i n t p a r t i c l e p r o b l e m ,

a n d t o t h e q u a n t u m m e c h a n i c a l w a v e / p a r t i c le p r o b l e m ( to E i n st e in ' s p r o b l e m

c o n c e r n i n g t h e p h o t o n ) i s t h a t t h e u n i v e r s e is m a d e u p o f s m e a r o n s . T h e

c r u c i a l s t e p o f t h i s p r o p o s e d s o l u t i o n i s t o a d o p t a p r o b a b i l i s t i c

g e n e r a l i z a t i o n o f t h e c l a s s i c a l ( d e t e r m i n i s t i c ) n o t i o n o f p h y s i c a l p r o p e r t y .

W i t h i n c l a s s i c a l p h y s i c s , p h y s i c a l p r o p e r t i e s o f f u n d a m e n t a l p h y s i c a l

e n t i t i e s - - w h e t h e r c h a r g e a n d m a s s o f p a r t i c le s , o r fi e ld i n t e n s i ty o f

f i e l d s - ~ d e t e r m i n e h o w p h y s i c a l e n t i ti e s i n t e r a c t a n d e v o l v e i n s p a c e a n d t i m e

deterministieally I f n o w w e w i s h t o r e t a i n t h e c l a s s i c a l i d e a t h a t t h e a c t u a l

p h y s i c a l s t a t e s o f i n d i v id u a l m i c r o s y s t e m s d e t e r m i n e th e i r s u b s e q u e n t

e v o l u t i o n , a n d a t t h e s a m e t i m e w e w i s h t o h o l d t h a t N a t u r e i s f u n d a m e n t a l l y

p r o b a b i l i s t i c r a t h e r t h a n d e t e r m i n i s t ic , t h e n w e a r e o b l i g e d to g e n e r a l i z e t h e

c l a s s ic a l ( d e t e r m i n i s t ic ) n o t i o n o f p h y s i c a l p r o p e r t y t o f o r m t h e n o t i o n o f a

p r o b a b i l i s t i c a l l y d e t e r m i n i n g p h y s i c a l p r o p e r t y o r p r o p e n s i t y ( a p o i n t

d i sc us se d in m or e de t a i l e ls ewhere (Z4)) . Th e o u t c o m e o f t h i s de c i s ive s t e p is

t o a b a n d o n a l t o g e t h e r t h e c l a s s i c al f ie l d a n d p a r t i c le , a n d i n s t e a d a d o p t th e

n e w k i n d o f e n t i ty , th e s m e a r o n . A c c o r d i n g t o t h is v i e w p o i n t , th e

m y s t e ri o u s n e s s o f t h e q u a n t u m d o m a i n i s t o b e u n d e r s t o o d a s a ri si n g o u t o f

o u r u n f a m i l i a r i t y w i t h o b j e c t s t h a t h a v e p r o p e n s i t i e s a s b a s i c p r o p e r t i e s

( s u c h f a m i l i a r m a c r o p r o p e n s i t i e s a s t h e u n b i a s e d n e s s o f a di e, f o r e x a m p l e ,

b e i n g e x p l i c a b le i n t e rm s o f c l a s s ic a l d e t e r m i n i s t i c p h y s i c a l p r o p e r t i e s , a n d

r a n d o m l y v a r y i n g i n i t i a l c o n d i t i o n s w i t h e a c h t o s s ) .

T h u s t h e s m e a r o n v e r s i o n o f Q M i n p r i n c i p l e p r o v i d e s a n a c c e p t a b l e

m i c r o r e a l i s ti c s o l u t i o n t o t w o p r o b l e m s t h a t l ie a t t h e h e a r t o f c l a s s ic a l a n d

q u a n t u m p h y s i c s - - t h e c l a s s i c a l f i e l d / p a r t i c l e p r o b l e m a n d t h e q u a n t u m

w a v e / p a r t i c l e p r o b l e m - - w h e r e a s o r t h o d o x Q M f a i l s t o r e s o l v e s a t i s f a c t o r i l y

b o t h p r o b l e m s .

4 . A s a r e s u lt o f p r o v i d i n g a m i c r o r e al i s ti c s o l u ti o n t o t h e w a v e / p a r -

t i c l e p r o b l e m , s m e a r o n Q M c a n i m m e d i a t e l y c l a i m a f u r t h e r i m p o r t a n t

a d v a n t a g e o v e r o r t h o d o x Q M . I t is n o t j u s t t h a t t h e s m e a r o n v e r s i o n o f Q M

e n t i r e l y a v o i d s t h e e n d l e s s ly d is c u s s e d a n d u n r e s o l v e d p r o b l e m o f

m e a s u r e m e n t t h a t p l a g u e s o r t h o d o x Q M . M u c h m o r e i m p o r t a n t , s m e a r o n

Q M , h a v i n g i ts o w n d i s t in c t i v e p h y s i c a l o n t o l o g y , e n a b l e s u s i n p r i n c i p l e t o

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expla in and unders tand complex macro objec ts and phenomena as be ing

sole ly the outcom e of in terac t ions between micro sys tems, namely smearons .

This cannot be achieved by or thodox QM, s ince or thodox QM must

presuppose the existence of comp lex mac ro objects (measuring instrum ents)

in any actual physical application. Smearon QM thus has greater

explanatory power than or thodox QM. Or, put t ing th is poin t s l ight ly

differently, smearon QM can in principle fully explain the empirical success

of classical physics, n ot needing in any w ay itself to presuppose som e part o f

c lass ica l physics . Orthodo x Q M canno t do th is , jus t because some par t of

c lass ica l physics must be presupposed by the theory for a t rea tment of

measurement. In other words, orthodox QM is a severely

ad hoe

theory in

that i t consists of two conceptual ly inharm onious par ts , ( i) quantum

postulates and (i i) classical or quasiclassical postulates for a description of

prepara t ion and measurement . Smearon QM is not ad hoe in this way,

having no essential need for

ad hoc

classical or quasiclassical postulates:

thus i t has grea ter explanatory power (accept ing tha t explanatory power is

related to non

ad hoeness .

Although smearon QM makes no appeal to measurement or c lass ica l

physics, nevertheless the theory is st i l l experimentally testable. We can

(conjecturally) identify photographic plates, bubble chambers etc. , with

complex sys tems of smearons: smearon QM wil l then make predic t ions

about enduring smearon s ta tes which we can ident i fy with observable t racks

in photographic plates and bubble chambers. Any appeal to classical physics

is , as i t were, a matter of practical convenience rather than conceptual

necessity.

5. The long standing failure of the physics com mu nity to accept, or

even to consider , the sm earon vers ion of QM can be unders tood as be ing due

to the accidents of intellectual history. During the decade 1925-35, when the

problem of how to interpret QM was an alive issue for the physics

community , the debate was polar ized in to two opposing camps. On the one

hand the Bohr-Heisenberg camp advocated the abandonment of c lass ica l

determinism and micro rea l ism, and on the o ther hand the Einste in-

Schr6dinger camp advocated re ta in ing determinism and microreal ism. Both

camps seem to have taken for granted tha t the aban donm ent of de terminism

involved the aband onm ent of micro rea l i sm --per haps in par t because of the

general accep tance, at the time, o f subjectivist ~conceptions o f pro bab ility,

which implied tha t a fundam enta l ly probabi l is t ic physics could not be

microrealistic . As a result , the best possibili ty seems to have been overlooked

entirely, namely to retain classical micro realism but to abandon classical

determinism--by hold ing tha t micro rea l is t ic proper t ies de termine the

physica l evolu t ion of indiv idual micro sys tems probabitistiealty.

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6 4 Maxwell

The c losest approach to th is sm ear on viewpoint was de Brogl ie ' s

1927 theo ry o f the do ubl e solution . ~17) De Brogtie 's theor y entirely fails ,

however, to adopt a probabilist ic generalization of the classical deterministic

notion of physical property. On the contrary, de Broglie 's theory charac-

terizes micro systems in terms of classical physical properties, the statist ical

aspects of QM being in troduced somew hat analogou sly to the way in which

statistics is introduced in classical statist ical mechanics. Thus, from the

smearo n standpoint, de B roglie 's appro ach fails to go to the heart of the

problem.

Subsequently, some writers have introduced notions closer to the

propens ity notion emp loyed here. Thu s Heisenb erg 's ~3~potenti view, and

M ar ge na u's ~31) l tency view, can both be understood to be attr ibuting

propensities to microsystems determining (probabilist ically) the values of

observables on mea surem ent; and Popper 's ~1) prope nsity view explicit ly

atributes propensities to experimental set ups. However, these views all

appeal, implicit ly or explicit ly, to measurement: they thus fail to constitute

exclusively micro rea l is t ic propensi ty vers ions of QM -- th e crucia l feature of

the smearon view proposed here.

6. Ele me ntary QM is not amenable to a micro realistic (smearon )

interpretation. This is because elementary QM treats forces, for example the

electromagnetic force, in a thoroughly classical way, in terms of a potential

funct ion for example . Only wave packet col l is ion theory or quantum f ie ld

theory, capable of characterizing forces in terms of interactions between

microsystems (as the exchange of virtual particles for example), can be

amenable to microrealistic (smearon) interpretation. The task that l ies before

us is thus to develop a fu l ly f ledged quantum smearon theory to replace

or thodox wave packet col l is ion theory , and u l t imate ly or thodox quantum

field th eory.

We have here a further explanation for the failure of the physics

com mun ity to take up the smearon idea . In i t ia lly QM was not amenable to

such an interpretation. Later, when the smearon idea became viable with the

development of wave packet col l is ion theory , and quantum f ie ld theory , the

Copenhagen doctr ine had hardened in to a dogma.

In view of points 1, 2, 5, and 6, I conclude that the smearon inter-

pretation of QM is a viable interpretation, at least as acceptable as the

orthodo x an d all other no nor thod ox interpretations. In view of points 3 and

4, I conclude that the smearon interpretation is actually superior to the

or thodox in terpre ta t ion , and to most o ther nonorthodox in terpre ta t ions .

The matter might be summed up like this. I t is a long standing and

fundamenta l a im of theore t ica l physics , of na tura l phi losophy, to a t tempt to

explain and un ders tand diverse , complex ma cro ph enom ena ent i rely in te rms

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o f i n t e r a c t i o n s b e t w e e n a v e r y f e w d i ff e r e n t s o r t s o f f u n d a m e n t a l p h y s i c a l

e n t i t i e s - - w h e t h e r a t o m s , p o i n t p a r t i c l e s , f i e l d s o r w h a t e v e r . I n d e e d , a s I h a v e

a r gue d e l s e whe r e , 32-34) we c a n sc a r c e ly un de r s t a nd the o r e t i c a l ph ys i c s a s a

r a t i o n a l e n t e r p r i s e u n l e ss w e s e e it as p r e s u p p o s i n g t h a t s o m e k i n d o f u n i fi e d

p a t t e r n o r s t r u c t u r e e x i s t s i n h e r e n t i n a l l n a t u r a l p h e n o m e n a - - a p a t t e r n o r

s t r u c t u r e t o b e c h a r a c t e r i z e d i n t e r m s o f s o m e a s y e t t o b e d i s c o v e r e d

u n i fi e d , f u n d a m e n t a l p h y s i c a l t h e o r y w h i c h s p e c if ie s h o w t h e v e r y fe w

d i f fe r e n t s o rt s o f f u n d a m e n t a l p h y s i c a l e n t it i es t h a t e x i s t e v o l v e a n d i n t e r a c t .

T h e r e f o r e , i t i s o n l y w i t h e x t re m e r e l u c t a n c e t h a t w e s h o u l d a b a n d o n w h a t

m a y b e c a l l e d t h e p o s t u l a t e o r r e q u i r e m e n t o f m i c r o r e a l i s m :

i ) D i v e r s e , c o m p l e x m a c r o p h e n o m e n a c a n i n p r i n c i p l e b e e x p l a i n e d a n d

u n d e r s t o o d i n t e r m s o f i n t e r a c t io n s b e t w e e n a v e r y fe w d i f f e re n t so r t s o f

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

c h a r a c t e r i z i n g t h e p r o p e r t i e s o f t h e s e f u n d a m e n t a l e n t i ti e s. A f u n d a m e n t a l

p h y s i c a l t h e o r y , i n o r d e r t o b e f u l l y a c c e p t a b l e , m u s t b e r e a l i s t i c i n t h i s

sense .

G r a n t e d t h a t w e a c c e p t i ), i t i s n a t u r a l t h a t w e sh o u l d a c c e p t :

i i) T h e e v o l u t i o n o f a n y i s o l a t e d p h y s i c a l s y s t e m i s d e t e r m i n e d d e t er -

m i n i s t i c a l l y o r p r o b a b i l i s t i c a l l y ) b y t h e a c t u a l p h y s i c a l c h a r a c t e r i s t i c s , t h e

phy s i c a l s t a t e , o f t he i nd iv idua l sy s t e m in que s t ion , a t som e in s t a n t .

I f, i n a dd i t i on to i ) a nd i i) , we a lso a c c e p t t ha t :

i i) N a t u r e is f u n d a m e n t a l l y p r o b a b i l i s t ic , a n d n o t d e t e r m i n i s t i c ;

t h e n o u r h a n d s a r e t i e d ; w e a r e o b l i g e d t o h o l d t h a t :

i v ) O n l y t h e o r i e s t h a t a r e m i c r o r e a l i s t i c a n d a t t r i b u t e p r o p e n s i t i e s t o

f u n d a m e n t a l p h y s i c a l e n t i t i e s c a n b e f u l l y a c c e p t a b l e .

S m e a r o n Q M f u l l y a c c o r d s w i t h t h i s b a s i c , h i g h l y p l a u s i b l e r e q u i r e m e n t

iv ), wh e r e a s a l l o the r ve r s ions a n d in t e r p r e t a t i on s o f QM f a il t o s a t i s f y t h i s

r e q u i r e m e n t . T h i s i s t h e g r e a t a d v a n t a g e o f s m e a r o n Q M o v e r a l l o t h e r i n te r -

p r e t a t i ons .

2 . T H E U N I F I E D D E T E R M I N I S T I C P R O B A B I L I S T I C P R I N C I P L E

I n t h i s s e c t i o n I i n d i c a t e a n a d d i t i o n a l r e a s o n f o r a t t e m p t i n g t o d e v e l o p

a m i c r o r e al is t ic s m e a r o n v e r s i o n o f q u a n t u m t h e o r y .

O n e o b v i o u s f e a t u re o f o r t h o d o x q u a n t u m t h e o r y i s t h a t i t p o s t u la t e s

b o t h d e t e r m i n i s t i c a n d p r o b a b i l i s t i c l a w s o f e v o l u t i o n f o r s y s t e m s . T h e

q u a n t u m s t a te s o f s y s t e m s e v o l v e d e t e r m i n i s t i c a l l y if n o m e a s u r e m e n t is

m a d e , p r o b a b i l i s t i c a ll y , i n g e n e r a l, i f a n d o n l y i f a m e a s u r e m e n t i s m a d e .

L e t u s c o n j e c t u r e t h a t i n t h i s r e s p e c t q u a n t u m t h e o r y r e f l e c t s a r e a l ,

o b j e c t i v e f e a t u r e o f t h e p h y s i c a l u n i v e r s e it se l f. In N a t u r e , p h y s i c a l s y s t e m s

r e a l ly d o e v o l v e s o m e o f t h e t i m e i n a c c o r d a n c e w i t h d e t e r m i n i s t i c l a w s ,

825/12/6 5

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6t6 Maxwell

s o m e o f th e t i m e i n a c c o r d a n c e w i t h p r o b a b i l is t ic l a w s . L e t u s c a ll th e i d e a

tha t t he phys i ca l un ive r se r ea l l y i s l i ke t h i s t he unified deterministic-

probabilistic thesis--the

U D P t h e s i s .

I f t h e U D P t h e si s is tr u e , th e n a n y u n i f i e d f u n d a m e n t a l p h y s i c a l t h e o r y

w i ll h a v e t o d o j u s t ic e t o t h i s a s p e c t o f N a t u r e : t h e t h e o r y w i ll h a v e t o

p o s t u l a te b o t h d e t e r m i n i s ti c a n d p r o b a b i l is t ic l a w s o f e v o l u t io n , a n d s h o w

p r e c i s e l y h o w t h e s e c o h e r e n t l y i n t e r m e s h . L e t u s c a l l t h i s t h e U D P

r e q u i re m e n t . I t c a n b e r e g a r d e d a s a m e t h o d o l o g i c a l r u le : in o r d e r to b e

a c c e p t a b le , a u n i f ie d f u n d a m e n t a l p h y s i c a l t h e o r y m u s t a t l e a s t s a t i s fy t h e

U D P r e q u i r e m e n t .

T h e U D P t h e s i s a n d m e t h o d o l o g i c a l r u l e t o g e t h e r c a n b e r e g a r d e d a s

be ing a

physical principle

a n a l a g o u s t o s u c h p h y s i c a l p r i n c ip l e s a s M a c h s

p r i nc ip l e , t he spec i a l p r i nc ip l e o f r e l a t i v i t y , t he p r i nc ip l e o f Loren t z

invar i ance , E ins t e in s p r i nc ip l e o f equ iva l ence , t he p r i nc ip les o f conse rv a t i on

o f en e r g y , m o m e n t u m a n d a n g u l a r m o m e n t u m , th e p r in c ip l e o f c o n s e rv a t io n

o f c h a r g e , t h e p r in c i p l e o f C P T s y m m e t r y , g a u g e i n v a r i a n c e . I n e a c h c a s e ( s o

w e m a y h o l d ) w e h a v e a p r i n c i p l e w h i c h a t t r i b u t e s a r a t h e r g e n e r a l c h a r a c -

t e r is t ic t o Na tu re , and t hen r equ i res accep t ab l e t heo r i es to co n fo r m to ce r t a i n

f o rmal

r equ i rem en t s i n o rde r t o do j u s t i ce t o t he pos tu l a t ed charac t e r i s t ic .

M a n y v a l u a b l e p h y s i c a l t h e o r i e s h a v e b e e n d e v e l o p e d t h r o u g h t h e

p o s t u l a t i o n o f s u c h p r i n ci p le s , a n d t h e e n d e a v o u r t o m o d i f y e x i st in g t h e o ri e s

s o a s t o r e n d e r t h e ( n e w , m o d i f i e d ) t h e o r y c o m p a t i b l e w i t h th e p o s t u l a t e d

p r inc ip l es . Th i s was how E ins t e in deve loped spec i a l and genera l r e l a t i v i t y .

S i n c e E i n s t e i n s w o r k s y m m e t r y a n d i n v a r i a n c e p r in c i p le s h a v e c o m e t o p l a y

a n e v e r i n c r e a s i n g l y i m p o r t a n t r o l e i n t h e o r e t i c a l p h y s i c s , b o t h f o r t h e

d e v e l o p m e n t a n d f o r th e a p p r a i s a l o f t h e o r ie s .

In s ec . 1 above I p u t fo rw ard j u s t such a p r i nc ip le : i t m ay be ca l l ed t he

p r inc ip l e o f

m icro realism.

Thi s p r i nc ip l e a s se r t s : t he un ive r se i s made up o f

a f ew d i f f e ren t so r t s o f fundamen ta l phys i ca l en t i t i e s i n t e rac t i ng i n acco r -

d a n c e w i th a c o h e r e n t s y s t e m o f p h y s i c a l la w s ( a ll m a c r o p h e n o m e n a b e in g

t h e o u t c o m e o f c o m p l e x i n t e r a c t i o n s b e t w e e n m a n y s u c h e n t i t i e s ) . A c c o r d i n g

t o t h i s p r i n c i p l e a f u n d a m e n t a l p h y s i c a l t h e o r y , i n o r d e r t o b e u l t i m a t e l y

accep t ab l e , m us t be capa b l e o f be ing i n t e rp re t ed as spec i fy ing exc lus ive ly

l aws o f i n t e rac t i on b e tween a f ew d i f f e ren t so r t s o f bas i c phy s i ca l en t it i e s

(pa r t i c l e s , f i e l d s , o r wha t ever ) . Above (and e l s ewhere ) I have a rgued i n

e f fe c t, t h a t w e o u g h t t o r e q u i re o f a n y a c c e p t a b l e f u n d a m e n t a l p h y s i c a l

t heo ry t ha t i t s a t i s f i e s t h i s p r i nc ip l e o f mic ro r ea l i sm s ince i t i s on ly i n t h i s

c a s e t h a t a t h e o r y c a n b e f u l l y u n i f ie d , c o n c e p t u a l l y c o h e r e n t , n o n - a d

hoe

or ,

i n o th e r w o r d s , f u l l y e x p l a n a t o r y . O r t h o d o x Q M f a i ls t o s a t i s fy t h e p r i n c ip l e

o f mic ro r ea l i sm , i n t ha t i t f a i l s t o r e so lve t he wave /pa r t i c l e (o r f i e l d /pa r -

t i c l e ) d i l emma in a mic ro r ea l i s t i c f a sh ion . As a r e su l t , o r t hodox QM mus t be

i n t e r p r e t e d a s s p e c i f y i n g ( i n p a r t ) h o w m i c r o s y s t e m s i n t e r a c t w i t h m a c r o

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(classical) measuring instruments. Just for this reason, orthodox QM is

seriously

d hoe

( in a usual ly unnot iced way) in tha t the theory is made up

of two conceptual ly incoherent par ts , quantum postu la tes p lus some par t of

classical physics for a treatment of measurement. A precise smearon version

of quantum theory would however be fully micro realistic and, as a result ,

would be free of this

d hoe

dependence on classical physics.

An y s ignificant physica l pr inc ip le however app arent ly p lausib le , m ay of

course be fa lse (as the downfal l of par i ty invar iance so dramatica l ly

il lustrated). Here let us conjecture that the UDP principle is true. The UDP

character of or thodox QM , so obvious a fea ture of the theory a t a superf icia l

level at least, is, we are to supp ose (in view of the grea t emp irical succ ess of

QM) a deep objective feature of the physical universe i tself . Any ultimately

acceptable fundamental physical theory must specify precisely how deter-

ministic and probabilist ic laws of evolution intermesh in a consistent,

conceptual ly coherent fashion .

Superficially, orthodox QM suggests the UDP principle: does orthodox

QM precisely satisfy this principle? Does orthodox QM specify precisely

how deterministic and probabilist ic laws interconnect?

The answ er to this question must be: No It is jus t this crucial issue of

how determinis t ic and probabi l is t ic laws in terconnect tha t or thodox QM

fudges. (And to make matters worse, in the l i terature inadequate physics is

covered up, " justif ied" even, with bad, positivistic philosophy.)

One indica t ion of the fa i lure of QM to sa t is fy prec ise ly the UDP pr in-

ciple is the range of interpretations of QM that various thinkers have been

able to develop, which differ radically on just the crucial point of how deter-

minism and probabilism are interrelated.

At one extreme there is the view that everything is in a sense

cont inuously probabi lis t ic , so tha t even when the quan tum s ta te of a physica l

sys tem evolves "determinis t ica l ly" , in accordance with Schr6dinger ' s t ime

dependent equation let us say, in reali ty, at a deeper ontological level, the

system is physically evolving in a continuously probabilist ic fashion, from

instant to instant. De Broglie, Vigier, Popper, Land~, and others have put

forward various probabilist ic versions or interpretations of QM which in

effect postulate physical probabilism during the deterministic evolution of the

quantum s ta te of any sys tem. Some have even explored the poss ib i l i ty tha t

space an d time have a discrete character, this discreteness of space-time

being responsible for the probabitist ic character of all physical interactions

occurr ing in an only approximate ly cont inuous space- t ime manifo ld . This

kind of view makes i t quite impossible to interpret Schr6dinger 's t ime

dependent equat ion--or i ts re la t iv is t ic modif ica t ion--as specify ing physica l ,

onto logica l de terminism. Schr6dinger ' s equat ion can only have approximate

"m ac ro" val id ity , in tha t i t is based (according to th is k ind of view) on the

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6 8 Maxwell

f a l s e , o n l y a p p r o x i m a t e l y v a l i d , a s s u m p t i o n t h a t s p a c e a n d t i m e a r e c o n -

t i n u o u s .

O n t h e o t h e r h a n d , a t t h e o t h e r e x t r e m e , t h e r e i s t h e v i e w t h a t N a t u r e i s

u l t i m a t e l y d e t e r m i n i s t i c , s o t h a t o r t h o d o x Q M , b e i n g p r o b a b i l i s t i c , s u c c e e d s

o n l y i n g i v in g a n e s s e n t ia l l y i n c o m p l e t e s p e c i f i c a ti o n o f t h e p h y s i c a l s t a t e o f

a n y s y s t e m . T h e t y p i c a l ( i n c o m p l e t e ) q u a n t u m s p e c i f ic a t i o n o f t h e s ta t e

a s s o c i a t e d w i t h a p u r e e n s e m b l e o f s i m i l a r l y p r e p a r e d s y s t e m s is s u es i n

p r o b a b i l i s t i c p r e d i c t i o n s b e c a u s e t h e a c t u a l p h y s i c a l c o n d i t i o n s v a r y , f r o m

s y s t e m t o s y s t e m o f t h e e n s e m b l e , in s u c h a w a y a s t o p r o d u c e t h e p r e d i c t e d

p r o b a b i l i s t i c o u t c o m e , e a c h i n d i v i d u a l l y d i s t i n c t i n i t i a l s t a t e e v o l v i n g i n

a c c o r d a n c e w i t h t h e s a m e deterministic l a w s . T h e s t a t i s t i c a l s p r e a d o f

o u t c o m e s i s d e t e r m i n i s t i c a t l y l i n k e d , i n o t h e r w o r d s , t o a s t a t i s t i c a l s p r e a d i n

i n i t i a l c o n d i t i o n s , w h i c h o r t h o d o x Q M , b e i n g i n c o m p l e t e , f a i l s t o c a p t u r e .

O r t h o d o x Q M f a i l s t o m a k e d e t e r m i n i s t i c p r e d i c t i o n s b e c a u s e i t f a i l s t o

de sc r ibe p r e c i se ly e a c h d i s t i nc t i n i ti a l s t a t e , a nd f a i ls t o spe c i f y t he

f u n d a m e n t a l , d e t e r m i n i s t i c la w s o f N a t u r e . T h i s k i n d o f v i ew w a s a d v o c a t e d

b y E i n s t e in . T e n t a t i v e l y , E i n s t ei n h e l d t h a t t h e b a s i c d e t e r m i n i s t i c l aw s c a n

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

I s e v e r y t h i n g c o n t i n u a l l y p r o b a b i l i s t i c ? O r i s n o t h i n g p r o b a b i l i s t i c ? F o r

a ll w e k n o w , e i t h e r o n e o f t h e s e e x t r e m e p o s i t i o n s m a y b e tr u e . H e r e ,

h o w e v e r , w e a r e a d o p t i n g a p o s i t i o n t h a t i s , a s i t w e r e , m i d w a y b e t w e e n t h e

a b o v e tw o e x t r e m e p o s i t i o n s , a c c o r d i n g t o w h i c h p h y s i c a l s y s t e m s e v o l v e a t

t i m e s d e t e r m i n i s t i c a l l y , a t t i m e s p r o b a b i l i s t i c a l l y , r o u g h l y a s o r t h o d o x Q M

p o s t u l a t e s. A c c o r d i n g t o t h i s o r t h o d o x i n t e r p r e t a t i o n o f Q M , a ll s y s te m s

e v o l v e d e t e r m i n i s t i c a l l y w h e n n o m e a s u r e m e n t s a r e m a d e : p r o b a b i l i s t i c

e v e n t s o c c u r o n l y w h e n m e a s u r e m e n t s a r e p e r f o r m e d . T h i s i s r e a l l y t h e h e a r t

o f t h e C o p e n h a g e n i n t e rp r e t a ti o n o f Q M , t h e c o m m o n a s s u m p t i o n i n t h e

o t h e r w i se s o m e w h a t d i v e rs e v i ew s o f B o h r , H e i s en b e r g , B o r n , D i r a c - - a n d o f

m o s t c o n t e m p o r a r y p h y s i c i s t s .

T h i s o r t h o d o x v e r si o n o f Q M m u s t f a il h o w e v e r, to s p e c if y p r e c is e l y

h o w d e t e r m i n i s t ic a n d p r o b a b i l i st i c l a w s i n t e r c o n n e c t d u e t o a n u n a v o i d a b l e

v a g u e n e ss in t h e k e y n o t i o n o f m e a s u r e m e n t . W e m a y s e ek t o s p ec i fy t h e

p r e c i s e n e c e s s a r y a n d s u f f i c i e n t p h y s i c a l c o n d i t i o n s f o r a m e a s u r e m e n t

i n t e r a c t i o n t o o c c u r i n t e r m s o f : ( 1 ) p e r s o n a l o b s e r v a t i o n a n d c o n s c i o u s n e s s ,

( 2 ) t h e o c c u r r e n c e o f a c l a s s i c a l l y d e s c r i b a b l e p r o c e s s , ( 3 ) t h e o c c u r r e n c e o f

a m a c r o p h e n o m e n o n , a n d ( 4 ) t h e o c c u r r e n c e o f a n i rr e v e rs i b le p r o c e ss .

A l l t h e s e s p e c i f i c a t i o n s m u s t i n e v i t a b l y b e s o m e w h a t i m p r e c i s e . I n o r d e r t o

specify

precise

n e c e s s a r y a n d s u f f i c i e n t p h y s i c a l c o n d i t i o n s f o r p r o b a b i l i s t i c

( m e a s u r e m e n t t y p e ) e v e n t s t o o c c u r w i t h in s o m e ( c o m p o s i t e ) p h y s i c a l

s y s t e m w e s h o u l d h a v e t o d o t h i s in t e rm s o f s o m e qu ntum mech nic l

c o n d i t io n o f th e s y s t e m - - s p e c i f i a b l e i n p r e c is e q u a n t u m m e c h a n i c a l t er m s .

B u t i t is j u s t t h is w h i c h t h e o r t h o d o x s t a n d p o i n t d o e s n o t p e r m i t . I n t h e fi r st

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Instead of Particles and Fields A Micro Realist ic Q ua ntu m S m e a r o n T h e o r y 6 1 9

p lace , i f p roba b i l i s t ic eve n t s occu r w hen som e p rec is e

qu ntum mech nic l

p h y s i c a l c o n d i t i o n i s r e a l i z e d w i t h i n a q u a n t u m s y s t e m , p r e s u m a b l y s u c h

p r o b a b i l is t ic e v e n ts w i l l n o t b e c o n f i n e d to m e a s u r e m e n t ; t h e y w i ll o c c u r

e v e n i n t h e a b s e n c e o f m e a s u r e m e n t . T h i s c o n f l i c ts w i th o r t h o d o x Q M .

S e c o n d l y , i f w e a r e t o b e a b l e t o s p e c i fy s o m e physic l c o n d i t i o n f o r

p r o b a b i l i s t i c e v e n t s t o o c c u r w i t h i n c o m p o s i t e m i c r o s y s t e m s , i n p u r e l y

q u a n t u m m e c h a n i c a l t e r m s , t h e n w e m u s t b e a b l e t o i n t e r p r e t q u a n t u m

m e c h a n i c s a s d e s c r ib i n g t h e a c t u a l p h y s i c a l s t a te s o f m i c r o s y s t e m s , i n d e p en -

d e n t l y o f a ll m a c r o ( c la s s ic a l ) p r e p a r a t i o n a n d m e a s u r e m e n t c o n d i ti o n s . W e

mus t , i n o the r words , be ab l e t o g ive a fu l l y mic ro r ea l i s t i c i n t e rp re t a t i on t o

Q M . B u t it is j u s t t h i s w h i c h t h e o r t h o d o x i n t e r p r e t a ti o n o f Q M d o e s n o t

p e r m i t . T h u s , f o r t h e s e t w o r e a s o n s , t h e r e c a n b e n o p r e c i s e , q u a n t u m

m e c h a n i c a l s p e c i f ic a t i o n o f th e p h y s i c a l c o n d i t i o n s f o r p r o b a b i li s ti c e v e n t s t o

o c c u r w i t h in th e f ra m e w o r k o f o r t h o d o x Q M . O r t h o d o x Q M c a n n o t precisely

sa t i s fy t he U D P p r inc ip l e i t so fo rce fu l l y sugges t s.

A p r e c i s e l y f o r m u l a t e d s m e a r o n v e r s i o n o f Q M w o u l d h o w e v e r

p r e c is e ly s a t i s fy t h e U D P p r in c i p le . ( Q u a n t u m s m e a r o n t h e o r y i s in d e e d

d e s ig n e d to d o j u s t th i s. ) F o r a n y a d e q u a t e q u a n t u m s m e a r o n t h e o r y m u s t d o

the fo l l owing :

( 1 ) T h e t h e o r y m u s t s p e c if y t h e m i c r o r e a li s ti c s t a te s o f s m e a r o n s , i n

t e rms o f va lues o f t he de t e rm in i s t i c and p rob ab i l i s t i c phy s i ca l p roper t ie s o f

s m e a r o n s - - t h e q u a s i c l a s si c a l a n d p r o p e n s i t y st a te s o f s m e a r o n s .

( 2 ) T h e t h e o r y m u s t s p e c i fy d e t e r m i n i s t ic l a w s o f e v o l u t i o n f o r

s m e a r o n s g r a n t e d t h a t n o p r o b a b i l is t ic i n t e r a c t i o n s o c c u r. T h e s e t a w s s p e c i fy

t h e d e t e r m i n i s ti c e v o l u t i o n o f th e v a l u e s o f p r o p e n s it ie s i n t h e a b s e n c e o f t h e

p r o b a b i t is t ic a c t u a l i z a t i o n o f t h e s e p r o p e n s it ie s . ( In o r d e r t o u n d e r s t a n d

c l ea r l y wha t i s be ing p roposed he re , cons ide r t he way i n wh ich , w i th in

e l e m e n t a r y Q M , S c h r 6 d i n g e r ' s t i m e d e p e n d e n t e q u a t i o n s p e c i f i e s t h e d e t e r -

m i n i s ti c e v o l u t i o n o f t h e v a l u e o f t h e p o s i t io n p r o b a b i l i t y d e n s i t y o f a n

e l e c tr o n , f o r e x a m p l e . T h e p o s i ti o n p r o b a b i l i ty d e n s i t y c a n b e t h o u g h t o f a s a

p r o p e n s i t y - - t h e p r o p e n s i t y o f t h e e le c t r o n t o i n t e r a c t in a s m a l l r e g io n o f

s p a c e i n a p a r t ic l e l ik e w a y , sh o u l d t h e a p p r o p r i a t e p h y s i c a l c o n d i t io n s t o d o

s o a r i s e ( a p o s i t i o n m e a s u r e m e n t , f o r o r t h o d o x Q M ) . W h e n e v e r t h e e l e c t r o n

s o i n t e r a c ts w e c a n s p e a k o f t h e p r o b a b i l i st i c a c t u a l i z a t i o n o f t h e p o s i ti o n

p robab i l i t y dens i t y . In t he absence o f such a p robab i l i s t i c even t , t he va lue o f

t he po s i t i on p roba b i l i t y dens i t y ( t he va lue o f t h i s p rope ns i t y ) evo lves de te r -

min i s t i ca l l y , a s spec i f i ed by S ch r6d inger ' s equa t i on . )

( 3 ) T h e t h e o r y m u s t s p e c if y p r e c i s e ly t h e p h y s i c a l ( m i c r o r e a li st ic ,

s m e a r o n ) c o n d i t i o n s n e c e s s a r y a n d s u f f ic i e n t f o r p r o p e n si ti e s t o b e c o m e

a c t u a l i z e d - - f o r s o m e t h i n g p r o b a b i l i s t i c t o o c c u r . ( A c c o r d i n g t o s m e a r o n

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62 Maxwell

t heo ry , measu rem en t s a re j u s t a ve ry sm al l subse t o f a ll p robab i l i st i c

ac tu~ i l i za t i ons occu r ing i n Na tu re . )

F rom (1 ) , (2 ) and (3 ) , i t mus t be pos s ib l e , i n p r i nc ip l e , fo r any ac tua l

phy s i ca l sys t em , t o p red i c t p rec i s e ly ( i) t he occ u r ren ce o f p robab i l i s ti c

even t s , ( ii ) t he r an ge o f pos s ib le ou t com es , ( i ii ) t he p rob ab i l i t y o f each

p o s s i b l e o u t c o m e o c c u r r i n g .

A n y sm earo n t he o ry o f th i s t ype (p rec i s e ly spec i fy ing (1 ) , (2 ), and (3 ) )

a u t o m a t i c a l l y s a t i s f i e s t h e U D P p r i n c i p l e . F u r t h e r m o r e , s o i t w o u l d s e e m ,

t h e o n l y w a y i n w h i ch o r t h o d o x Q M c a n b e m a d e t o s a t is f y t he U D P p rin -

c i pl e is t o t r a n s f o r m t h e t h e o r y i n t o a s m e a r o n v e r s io n o f Q M . F o r , a s w e

h a v e s e e n a b o v e , i f Q M is t o s a t i s f y th e U D P p r i n ci p le t h e n ( i) a m i c r o

r e a li s ti c v e r s i o n o f Q M m u s t b e d e v e l o p e d ; ( i i) p re c i se n e c e s s a r y a n d

su f f i c i en t m ic ro cond i t i ons mus t be spec i f i ed fo r p robab i l i s t i c even t s t o

o c c u r - - s o t h a t t h e v a g u e n o t i o n o f m e a s u r e m e n t c a n b e e l im i n a t e d f r o m

t h e b a s ic p o s t u la t e s o f t h e t h e o r y . T h i s w o u l d s e e m t o b e e q u i v a l e n t to

d e v e l o p in g a s m e a r o n v e r s io n o f Q M .

I f, t h e n , w e t a k e t h e s u p e r f ic i a l U D P c h a r a c t e r o f o r t h o d o x Q M

ser ious ly , a s r e f l ec t i ng a deep , ob j ec t ive f ea tu re o f t he p hys i c a l un ive r se i ts e l f,

t h e r e a r e o v e r w h e l m i n g g r o u n d s f o r h o l d i n g t h a t o n l y s o m e s m e a r o n v e r s i o n

o f Q M c a n u l t i m a t e l y p r o v e t o b e s a t is f a c t o r y .

3 M I C R O R E A L I S T I C C O N D I T I O N S F O R P R O B A B IL I ST I C E V E N T S

T h e k e y p r o b l e m t h a t m u s t b e s o l v e d i n o r d e r t o f o r m u l a t e a p r e c i s e

s m e a r o n v e r s i o n o f Q M p h y s i c a l l y a n d e x p e r i m e n t a l l y d i s t in c t f ro m

o r t h o d o x Q M is t o s p e c i fy p re c is e , n e c e s s a r y a n d s u f fi c ie n t , q u a n t u m

t h e o r e t ic a l , p h y s i c a l c o n d i t i o n s f o r p r o b a b i li s ti c e v e n t s t o o c c u r i n c o m p o s i t e

q u a n t u m s y s t e m s , n o s u r r e p t i t i o u s a p p e a l w h a t s o e v e r b e i n g m a d e t o

m e a s u r e m e n t , to i n t e r a c t i o n w i t h m a c r o s y s t e m s , o r t o i rr e v e rs ib l e p r o ce s s e s.

I n t a c k l i n g t h is p r o b l e m I p r e s u p p o se , a s t h e v e r si o n o f o r t h o d o x Q M t o b e

mod i f i ed , non re l a t i v i s t i c wave packe t co l l i s i on t heo ry as s e t ou t , fo r example ,

b y G o l d b e r g e r a n d W a t s o n (35) ( t h o u g h t h e m o d i f i c a t i o n I p r o p o s e c a n - a l s o

be ma de t o q ua n tu m f i e ld t heo ry , a s long as t h i s is i n te rp re t ed ph ys i ca l l y t o

b e a r e f i n e m e n t o f w a v e p a c k e t c o l l i s i o n t h e o r y ) . I n w h a t f o l l o w s , t h e n , t h e

f o r m a l i s m a n d c a l c u l a t i o n s o f w a v e p a c k e t c o l l is i o n t h e o r y a r e t a k e n f o r

g r a n t e d : I s e e k m e r e l y t o m a k e a v e r y sm a l l a d j u s t m e n t t o t h is f o r m a l i s m

w h i c h e n a b l e s u s t o i n t e r p r e t t h e f o r m a l i s m p h y s i c a l l y a s a m i c r o r e a l i s t i c

p r o p e n s i t y t h e o r y , a b o u t t h e e v o l u t i o n a n d p r o b a b i l i s t i c i n t e r a c t i o n s o f

s m e a r o n s , a l l m e a s u r e m e n t s b e i n g n o m o r e t h a n p r o b a b i l i s t i c i n t e r a c t i o n s

b e t w e e n s m e a r o n s w h i c h h a p p e n t o l e a v e o b s e r v a b l e , m a c r o s c o p i c t r a c e s .

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I ns t ea d o f P a r t ic l e s a nd F i e l ds A M i cro R ea l i s t ic Qua ntum

~ ' S m e a r o n T h e o r y 6 2 1

A l l v e r s i o n s o f s m e a r o n Q M i n c l u d e t h e f o l l o w i n g g en e r a l p o s t u l a t e :

( 1 ) G i v e n t w o o r m o r e s y s t e m s , t h e r e is a n a b s o l u t e d i s t i n c t io n

b e t w e en , o n t h e o n e h a n d , q u a n t u m d i s e n t a n g l e d s y s te m s , t h a t h a v e

d i s t i n c t q u a n t u m s t a t e s ( r e p r e s e n t e d b y v e c t o r s i n d i s t i n c t H i l b e r t s p a c e s )

a n d , o n t h e o t h e r h a n d , q u a n t u m e n t a n g l e d ' 6 ~ s y s t e m s , t h a t h a v e o n l y a

j o i n t s t a t e ( r e p r e s e n t e d b y v e c t o r s i n a j o i n t H i l b e r t s p a c e ) , t h e s y s t e m s n o t

h a v i n g d i s ti n c t q u a n t u m s ta te s. S y s t e m s o n l y b e c o m e q u a n t u m e n t a n g le d a s

a r e s u l t o f p h y s i c a l l y i n t e r a c ti n g . S p a t i a l l y d i s t in c t , n o n i n t e r a c t i n g s y s t e m s ,

t h a t h a v e n o t i n t e r a c t e d i n t h e p a s t , h a v e d i s t i n c t q u a n t u m s t a t e s .

T h e p r o b l e m t h a t m u s t b e s o l v e d , i n o r d e r t o f o r m u l a t e a f u l l y f l e d g e d

s m e a r o n v e r s io n o f w a v e p a c k e t Q M , c a p a b l e o f s t a n d in g o n i ts o w n f e e t

i n d e p e n d e n t l y o f c l a s s i c a l p h y s i c s , i s t o s p e c i f y p r e c i s e p h y s i c a l , q u a n t u m

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

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

p r e c i s e , q u a n t u m t h e o r e t i c a l c o n d i t i o n s f o r s m e a r o n s t o i n t e r a c t

p r o b a b i l i s t i c a l l y w i t h o n e a n o t h e r ( e v e n i n t h e a b s e n c e o f m e a s u r e m e n t ) .

W h a t I w i s h t o a d v o c a t e a s a s o l u t i o n t o t h i s p r o b l e m i s t h a t t h e f o l l o w i n g

p o s t u l a te ( 2 ) b e a d d e d t o t h e f o r m a l i s m o f q u a n t u m c o l li s io n t h e o r y .

S u p p o s e a n i n t e r a c t i o n b e c o m e s p o s s i b le ( o n e s y s t em c a n d e c a y , t w o o r

m o r e h i t h e r t o q u a n t u m d i s t i n c t s y s t e m s c a n c o l l i d e ) i n s u c h a w a y t h a t t h e

o u t c o m e o f th e i n t e r a c t i o n t a k e s t h e f o r m o f t w o d i s t i n c t c h a n n e l s , e a c h

c h a n n e l b e i n g c h a r a c t e r i z e d b y i ts d i s ti n c t s t a b l e p a r t i c le s t at e s. L e t t h e s u m

o f t h e r e s t e n e rg i e s o f th e p a r t i c l e s i n c h a n n e l i b e E 1 , t h e s u m o f t h e r e s t

e n e r g ie s o f t h e p a r t i c le s i n c h a n n e l 2 b e E 2 , a n d l e t

A E = I E 1 - E 2 1 .

S u p p o s e

t h e i n t e r a c t i o n p e r s i s t s f o r a p e r i o d 6 t a n d t h e n c e a s e s a t t i m e t ~ , t h e t w o

c h a n n e l s b e c o m i n g o r t h o g o n a l s t a te s [ r e fe r e n c e ( 3 5 ) , p p . 1 1 1 - 9 a n d

A p p e n d i x C ] . I n t h is c a s e :

( 2 ) Af t e r t~ , t he s t a te o f t he sys t e m pe r s i s t s a s a

superpos i t ion

o f t h e

t w o o r t h o g o n a l c h a n n e l s t a t es o n l y f o r a t i m e A t = h / A E ; f o r t ime s g r e a t e r

t h a n

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t h e s t a t e o f t h e s y s t e m i s

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o r

t h e s t a t e o f

c h a n n e l 2 , e v e n t h o u g h n o m e a s u r e m e n t h a s b e e n p e r f o r m e d . ( A l i tt le m o r e

p r e c i se l y , p e r h a p s , w e m a y s u p p o s e t h a t , g i v e n a n e n s e m b l e o f s u c h s y s t e m s ,

e a c h ind iv idua l supe r pos i t i on de c a ys a t a p r e c i se i n s t a n t , s t a t i s t i c a l ly t he

e n s e m b l e o f s u p e r p o s i t i o n s o f a l t e r n a t i v e c h a n n e l s d e c a y i n g e x p o n e n t i a l l y ,

w i th a ha l f l i f e o f

A t .

T h e p r o b a b i l i ty o f t h e s u p e r p o s i t io n d e c a y i n g i n t o

c h a n n e l 1 (o r c h a n n e l 2 ) i s t o b e c a l c u l a t e d i n t h e s t a n d a r d w a y , e m p l o y i n g

t h e fo r m a l is m o f o r th o d o x Q M .

P o s t u l a t e ( 2 ) c a n b e g e n e r a l i z e d t o t a k e i n t o a c c o u n t i n t e r a c t i o n s w h i c h

p r o d u c e N d i s t i n c t i n t e r a c t i o n c h a n n e l s . W e c a n a r r a n g e t h e r e s t e n e r g i e s o f

e a c h c h a n n e l s o t h a t E l