Schmidt Collapse of the State Vector

8/12/2019 Schmidt Collapse of the State Vector

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Found a t ions o f Phys ic s . Vo l . 12 , No . 6 , 198 2

ol lapse of the S ta te Vec torand Psychok ine t i c Effec t

H e l m u t S c h m i d t 1

Rece ived Oc tobe r 5 , 1981

Euge ne Wign er an d o the r s have specu la t ed tha t the co l l apse o f t he s t a t evec to r du r ing an obse rva t ion migh t be a phys i ea l ly r ea l p rocess so tha t somemodi f i ca tion o f cu rren t quan tum theory wou ld be r equ i r ed to descr ibe thein terac t ion wi th a conscious observer appropr ia te ly.

Expe r imen ta l r epor t s on the psychok ine t i c e ff ec t a s a men ta l i n fluence ont h e o u t c o m e o f q u a n t u m j u m p s s u g g e s t t h a t p e rh a p s t h is e f f ec t m i g h t b e v i t a l f o ran unde r s t and ing o f t he obse rve r 's ro le i n quan tum mechan ics.

Com bin ing these two specu la t ions we in t roduce a r educ tion p r inc ip l e tha tp rov ides fo r t he g radua l r educ t ion o f a m acroscop iea i ly ambiguous s t a t e anda l lows s imul t aneous ly fo r t he occur rence o f som e psychok ine t i c e ff ec t in thep rocess o f obse rva tion .

The r e su l ti ng mod e l l eads to man y o f the pa rad ox ica l , bu t l og ica l lycons i s ten t , f ea tu r e s o f t he psychok ine t i c e ffec t t ha t have been r epor ted , andma kes fu r the r t e s tab le p red ic t ions .

The mod e l does no t t ouch on the more p ro jbu nd ques t ions o f consc iousness .Bu l t he mod e l imp l ie s t ha t t he r e su l t o f a consc ious obse rva t ion , t he co l l apse o fthe s ta te vector, becomes access ib le to the exper im enter, wi th the psych okine t ice ffec t a s p robe : W he the r S chrdd inge r ' s ea t has no t o r has co l lapsed the s ta t evec to r de t e rmines whe the r o r no t t he l a t e r hum an obse rve r can s t i ll exe r t apsychokinet ic inf luence on the resul t .

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

C o n s i d e r t h e c a s e o f a b i n a r y q u a n t u m d e c i s i o n t h a t l e a d s t o t w o p o s s i b l em a c r o s c o p i c a l l y d i ff e re n t o u tc o m e s . Ta k e a s a t y p i c a l e x a m p l e a n i n d et e r-

m i n i s t i c b i n a r y r a n d o m e v e n t g e n e r a t o r ~1 t h a t , a f t er t r i g g e r i n g , s e l e c tsr a n d o m l y a r e d o r a g r e e n l a m p t o b e l i t .

J M ind Science Found ation , 102 W. Rector, Suite 21 5, San A ntonio, Texas 78216.

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0015 9018 /82/060 0-056 5503 .00/0 1982 Plenum PuNishing Corpora t ion


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I f , b e f o r e t h e t r i g g e r i n g , t h e s y s t e m c a n b e d e s c r i b e d b y a s t a t e v e c t o r,then a f t e r the t r igger ing th i s s t a te vec to r

~ ) = a ~ l ) + b ~ 2 ) w ith ( 1 ~ ) = ( ~ , [ ~ , ) = ( ~ 2 1 ~ 2 ) = 1 (1 )

a p p e a r s a s th e s u p e r p o s i t io n o f t h e t w o m a c r o s c o p i c a l l y d i f fe r en t st a te s ~ )and ~2) where the red o r g reen l amp i s l i t , r e spec t ive ly. We say tha t the s t a tev e c t o r ~ ) i s m a c r o s c o p i c a l l y a m b i g u o u s .

T h e o c c u r r e n c e o f m a c r o s c o p i c a l l y a m b i g u o u s s t at e s h a s le d t o m u c hc o n t r o v e r s e y b e c a u s e w e s e e m t o o b s e r v e s u b j e c t i v e l y o n l y m a c r o s c o p i c a l t ys h a r p s ta t es a n d n e v e r t h e s u p e r p o s i t i o n o f t w o o r m o r e m a c r o s c o p i c a l l y

d i ffe ren t s t ates . In sp i t e o f th i s s ti ll ong o ing d i scuss io n ab ou t the p ro peri n t e r p r e t a t i o n o f q u a n t u m t h e o r y , ~2'3) t h e r e i s l a rg e l y a g r e e m e n t o n t h e p r a c -t i c a l a s p e c t s o f th e m a t t e r :

W e c a n u s e S c h r 6 d i n g e r 's e q u a t i o n a s lo n g a s n o o b s e r v a t i o n i s m a d e ,a n d c a l c u la t e a s i f t h e o b s e r v a t i o n w o u l d i n d u c e a r a n d o m j u m p o f t h es t a t e v e c t o r ~ ) i n t o t h e m a c r o s c o p i c a l l y s h a r p v e c t o r s G ) o r 4 2 ) w i t h t h ep r o b a b i l i t i e sa a * a n d b b * , r e s p e ct iv e l y. T h i s c o r r e s p o n d s t o a r e d u c t i o n o ft h e d e n s i t y m a t r i x f r o m

p = ~ ) (~ = a a * ~ i ) ( ~ + a b* ~ l ) (~ 2 +b a * ~ 2 ) ( ~ l + b b * ~ 2 ) ( ~ 2 ( 2 )

t o t h e r e d u c e d m a t r i x

p = a a * ~ l ) ( ~ ~ + b b * ~ z ) ( ~ z (3 )

I t m a y a p p e a r r e a s o n a b l e t o s e e t h is r e d u c t i o n a s a t r a n s i t io n f r o m a nu n d e c i d e d s i t u a t i o n i n t o a p h y s i c a l l y r e a l s t a t e w h e r e n a t u r e h a s m a d e u p h e rm i n d f o r o n e o r t h e o t h e r o u t c o m e . B u t , s u r p r i s i n g l y, t h e f o r m a l i s m o fq u a n t u m t h e o r y d o e s n o t a c c o u n t f o r t h is t r a n s i t io n , b u t r a t h e r r e fe r s t o a

s o m e w h a t e l u s i v e e x t e r n a l o b s e r v e r t o d e f i n e p h y s i c a l r e a l i t y. C e r t a i n l yq u a n t u m t h e o r y i s l o g i c a l ly s e l f c o n s i s t e n t. A n d t h e i n a b il i ty o f t h ef o r m a l i s m t o d e fi n e a n a b s o l u t e r e a l i ty m a y c o n v e y to u s s o m e p r o f o u n dt r u t h a b o u t n a t u r e a n d i t s o b s e r v e r s .

B u t s t i l l , w e m i g h t w a n t t o l o o k f o r o t h e r l e s s e x t r e m e f o r m u l a t i o n s o fq u a n t u m t h e o r y, m o r e i n a c c o r d a n c e w i t h o u r i n d i v i d u a l l y c o l o r e d f e e l i n g so f p la u s ib i li ty. T h e r e w e m a y a i m in o n e o f t w o d i r e c ti o n s : W e m a y e it h ert r y t o r e f o r m u l a t e t h e t h e o r y s u c h t h a t n o m a c r o s c o p i c a l l y a m b i g u o u s s t a t e sd o a r is e a n d t h e h u m a n o b s e r v e r p l a y s n o m o r e c r u c i a l a r o l e t h a n o t h er

r e c o r d in g e q u i p m e n t , o r w e m a y a c c e p t t h e s i n g u la r r o l e o f t h e h u m a no b s e r v e r.

T h e f ee li ng t h a t t h e h u m a n o b s e r v e r o r h u m a n c o n s c i o u s n e s s p l a y s as in g u l a r r o le i n q u a n t u m t h e o r y h a s a l r e a d y b e e n e x p r e s s e d b y th e e a r l ypi on ee rs in th e f ield. (4)


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Collapse of the State Vector and sycho kinetic Effect 67

M ost specifically, W igner (5) ch am pio ned the idea that i t is hu ma nconsciousness that causes the col lapse of the s ta te vector, whereas in theabsence o f observers conv ent ional quan tum theory, even with itsmacroscopically ambiguous states, is valid. In the following we will pursuethis idea.

The use of the te rm consc iousn ess in th is con tex t ma y be somewhatpretentious. There are certainly no claims that our studies should shed l ighton the profound problems of consciousness as ra ised by Buddhis t m edi ta torsor other thinkers.

The hypothesis that i t i s the act of observat ion that col lapses the s ta te

vector seems not accessible to ver i f icat ion because the two densi ty matr icesof (2) and (3) lead in quantum theory to the same expectat ion values for a l lpossible exper iments . But i f the val idi ty of quantum theory were suspendedin the act of observat ion, Wigne r argues , th is might have observableimplications.

Experim ental indicat ions that hum an consciousness might do even mo rethan col lapse s ta te vectors comes from rather extensive laboratory work inparapsychology. Let me ment ion here in par t icular the exper iments on the'psychokinet ic effect (PK) . T he f i rst reports on this effect cam e from

Lo uisa and J. B. Rhine, (6,v) base d on ex perim ents in which hum an subjectst r ied to affect the o utcom e of dice fa lls. These ear ly exper iments have been,r ight ly or wrongly, much cr i t ic ized. The basic f inding, however, that thehuman wil l can under ce r ta in condi t ions a ffec t the ou tcom e of randomprocesses was apparent ly confi rmed by many la ter researchers workingunder mo re sophis t icated tes t condi t ions . After Jo hn Beloff 8) had pointedout that the ideal targets for the mental ef fort in a PK expe rime nt should beindeterminis t ic qua ntum jump s, Cha uvin and Ge ntho n ~91 reported posi t iveresul ts f rom experiments where highly motivated teenagers t r ied to s low

down or speed up the count ing ra te of a Geiger counter exposed to a weakradioact ive source. Subsequent ly I reported a large number ofexperiments~J0.11) in wh ich hu m an subje cts w ere app are ntly a ble to affec t thedec is ions made by quantum mechanica l ( inde te rmin is t i c ) random numbergenerators . These exper iments emphasised, apar t f rom the exis tence of a PKeffect, the ind epend ence of the effect of space, t ime, com plexity and similarfactors that would l imit the effectiveness of the conv ent ional physicalforc es . Th e m ost recent , s ta t is t ical ly a s t ronom ical ly s ignificant confi r-

mat ion o f PK act ion on an indeter inis t ic rand om num ber generator was

repo rted by R. G. J ahn and B. Dunne. (12)Unfortunately even the most successful workers in this f ie ld have to

agree that the exper iments are s t i l l ra ther tedious and t ime consuming: Firs t ,the effects are small so that many trials are needed for statist icalsignificance. Second, only some selected subjects perform reasonably well ,


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568 Schmid|

b u t e v e n t h e re t h e e x p e r i m e n t e r s h a v e t o w o r k v e r y h a r d t o k e e p t h e s u b j e c t 'si n te r e s t a n d m o t i v a t i o n a l i v e f o r th e o f t e n s t r e n u o u s o r e v e n p a i n f u l m e n t a le f f o r t r e q u i r e d f o r s u c c e s s. T h i s s i t u a t i o n m a y c h a n g e w i t h m o r e s k il le de x p e r i m e n t e r s g e t t i n g i n v o l v e d , b u t , i n t h e m e a n t i m e , i t m a y e x p l a i n w h yo n l y f e w o f t h e c h a l l e n g in g q u e s t i o n s r a i s e d in t h e f o ll o w i n g h a v e s o f a r b e e ns t u d i e d e x p e r i m e n t a l l y.

T h e r e a d e r m a y w o n d e r w h e t h e r i t i s r e a s o n a b l e a t t h i s s t a g e t o t h e o r i z em u c h a b o u t t h e P K m e c h a n i s m b e fo r e e x p e r im e n t e r s h a v e m a n a g e d t o g e tt h e e f fe c t u n d e r b e t t e r c o n t r o l . B u t w i t h a n e f f e c t s o p a r a d o x , s o c o n t r a r y t oe v e r y d a y i n t u i ti o n , i t i s v i t a l t o h a v e s o m e s e l f c o n s i s t e n t m o d e l t h e o r i e s i no r d e r t o d e s i g n s y s t e m a t i c e x p e r i m e n t s .

C o n s i d e r i n g t h e r e p o r t e d n o n l o c a l o r in s o m e s e n se e v e n n o n c a u s a lf e a t u r e s ~13) o f t h e P K e f f e ct o n e m i g h t b a s e a P K m o d e l o n s o m e e x p l i c it l yn o n c a u s a l m e c h a n i s m , q u i te i n d e p e n d e n t o f t h e q u a n t u m m e c h a n i c s . O n es u c h m o d e l h a s b e e n r e p o r t e d p r e v i o u s l y. (~ 4) B u t t h is p a r t i c u l a r m o d e ls e e m e d l i m i te d i n i ts u se f u l n e ss b y th e o c c u r e n c e o f s o m e d i v e rg e n c ep r o b l e m .

T h e f i r s t a t t e m p t t o l i n k t h e P K p r o b l e m e x p l i c i t l y w i t h b a s i c q u e s t i o n so f q u a n t u m t h e o r y w a s m a d e b y W a l k e r ~5~ w h o b a s e d h is d i s cu s s io n o n

h i d d e n v a r i a b l e t h e o r ie s . L a t e r s o m e o f t h e s e i d ea s w e r e c l a ri f ie d a n de x t e n d e d b y M a t t u c k , (16~ u s i n g t h e B o h m - B u b h i d d e n v a r i a b l e t h e o r y . I n t h i sm o d e l t h e m i n d c a n a f f e c t t h e h i d d e n v a r i a b l e s w h i c h i n t u r n d e t e r m i n e t h eo u t c o m e o f th e r a n d o m p r o c e s s e s o f q u a n t u m t h e o ry. T h i s i d ea s e e m sa t t r a c t i v e i n s o f a r a s t h e h id d e n v a r i a b l e s h a v e a l r e a d y s o m e n o n l o c a lf e a t u r e s s o t h a t , n a i v e l y s p e a k i n g , t h e m i n d g r a b b i n g a n d c h a n g i n g a h i d d e nv a r i a b l e c o u l d p r o d u c e o b s e r v a b l e e f f e c t s a t s o m e d i s t a n t l o c a t i o n .

I n t h e f o l l o w i n g w e w i l l n o t u s e h i d d e n v a r i a b l e s b u t r a t h e r s t u d y h o wt h e S c h r 6 d i n g e r e q u a t i o n m i g h t b e m o d i f ie d i n t h e m o s t s i m p l e m a n n e r s u c h

a s t o a l lo w f o r a P K e f f ec t a n d a n a u t o m a t i c r e d u c t i o n o f t h e s ta t e v e c t o ru n d e r a n o b s e r v a t i o n .

T h e n e x t t w o s e c t i o n s s e r v e a s p r e p a r a t i o n f o r s e c . 4 w h e r e w e i n t r o d u c et h e r e d u c t i o n e q u a t i o n t h a t p r o v i d e s f o r a s m o o t h r e d u c t i o n o f t h e s ta t ev e c t o r i n t h e p r o c e s s o f o b s e r v a t i o n . T h e r e d u c t i o n p r i n c i p l e w il l l e a v e r o o mf o r a p s y c h o k i n e t i c e f f e c t s o t h a t , f o r e x a m p l e , t h e s t a t e o f ( 2 ) m a y g e tr e d u c e d i n t o a m i x t u r e

P = P ~,)(~ , +q ~2)(~2 ( 3 ' )

w h e r e t h e c o e ff i c ie n t s p ' a n d q ' m a y b e d if f e re n t f r o maa* a n d bb* in (3).


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2. B I N A R Y O B S E RVAT I O N A N D A S S O C I AT E D M A C R O S C O P I CP R O J E C T I O N O P E R AT O R

C o n s i d e r f i r s t a b i n a r y o b s e r v a t i o n w h e r e t h e o b s e r v e r c a n d i s t i n g u i s ho n l y t w o p o s s i b l e o u t c o m e s , l i k e t h e l i g h t i n g o f a r e d o r a g r e e n l a m p . A f t e ro n e o f th e l a m p s h a s b e e n l it , b u t b e f o r e th e o b s e r v e r h a s b e c o m ec o n s c i o u s l y a w a r e o f t h e r e su l t, w e c a n w r i t e th e s t a t e v e c t o r ( 1 ) a s

w i t h

4 )

~ = 1 - Q 5 )

Here ~1) , ~ > a r e s ta tes wi th the red o r g reen l amp l i t , r e spec t ive ly, and Q,a r e th e p r o j e c t i o n o p e r a t o r s i n t o t h e s u b s p a c e s o f a ll s ta t e s w i t h re d o r g r e e nl a m p lit. ( W e a r e a s s u m i n g a n a r r a n g e m e n t w h e r e t h e t r ig g e r i n g o f t h eb i n a r y r a n d o m g e n e r a t o r c a u s e s e x a c t l y o n e l a m p t o l i g h t . ) T h e o p e r a t o r sQ, (~ sa t i s fy

Q2=Q=Q , (~2 = Q = Q+ Q (~ - - (~Q = 0 (6 )

M o r e c o m p l e x o b s e r v a t i o n s m a y b e c o n s id e r e d a s a s u p e r p o s i t io n o f m a n yb i n a r y o b s e r v a t i o n s w i t h t h e i r a s s o c i a t e d p r o j e c t i o n o p e r a t o r s .

3. S TAT E M I X T U R E S

I f a s y s t e m c a n b e d e s c r i b e d b y a s i n g l e n o r m a l i z e d s t a te v e c t o r ~ ) w i t ht h e c o r r e s p o n d i n g d e n s i t y m a t r i x

7 )

t h e n

( ~ t ~ ) = T r ( q ) = l , q2 = q ( 8)

W e w i ll c a ll a n y m a t r i x t o f t h is f o r m a p u r e s t a te d e n s i ty m a t r i x o rp u r e s t a t e p r o j e c t i o n o p e r a t o r.

C o n s i d e r n e x t a n e n s e m b l e o f p o s s i b l e s ta t e v e c t o r s ~ i) , ' < v ) w h e r e ~ i)

o c c u r s w i t h t h e p r o b a b i l i t y P 1 -W e w il t w r i t e t h i s e n s e m b l e a s a w e i g h t e d m i x t u r e o f p u r e s ta t e

p r o j e c t i o n o p e r a t o r sN

2 = P , t /, @ P2 qz @ ' + PN r/N = M ixPi ~ ( 9 )


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5 7 0 S c h m i d t

with

~/i = ~,)(~ i, TrQ Ii) = 1 (1 0)

We c a l l t h e m i x t u r e n o r m a l i z e d i f

N

N o r m ( u ) = ~ P i = 1 (1 1)i = 1

Th e @ sym bo l i n (9 ) i nd i ca t e s t he i nc lu s ion o f t he fo l lowing s t a te w i thi t s s ta t i s t i ca l weigh t in to the mix ture ; i t does no t ind ica te an a lgebra icadd i t i on o f t he m a t r ice s . T he l a s t exp re s s ion i n (9 ) is s imp ly a sho r thandno ta t i on fo r t he p r eceed ing exp re s s ion .

An a lgeb ra i c add i t i on o f t he t e rm s i n (9 ) l e ads t o t he dens i t y m a t r i x

N

p = Z 12)i = 1

In conven t iona l quan tum theo ry t he dens i t y ma t r i x a lone t e l l s u s a l l t he r e i st o kno wn abou t t he sy s t em , i. e., we m ay fo rge t t he ind iv idua l s t a te s f romwhich t he m ix tu re o r ig ina t ed . I n t he fo l l owing fo rma l i sm , how eve r, t h is i s no t

q u i t e t r u e : s o m e t i m e s w e h a v e t o r e m e m b e r m o r e a b o u t t h e m i x t u r e t h a n t h es u m o f ( 1 2 ).

W e c a n d e f in e t h e s u m o f t w o m i x t u r e s

/a+ = / l j @/a 2 (13)

b y m e rg in g t h e t w o e n s e m b l e s w h e re , h o w e v e r, m e m b e r s c o r r e s p o n d i n g t othe same s ta te can be combined , i . e . ,

A ~ , ) ( ~ @ B { ~ ) ( ~ = (14 + B ) { , ) ( { , ( 1 4 )

A d i f f e r e n c e b e t w e e n t w o m i x t u r e s

~ _ = v l & (1 5)

m ay be de f ined i f a ll m em ber s o f~ t 2 a r e con t a in ed i n t 1 w i th sma l l e r o r equa lweights .

In t he fo l l owing we wi ll o f t en wan t t o l e ave t he num ber o f e l emen t s i n amix tu re open . Then i t i s conven i en t t o wr i t e t he mix tu re i n (9 ) i n t he fo rm

u = Mix P q)q 16)t

where t he mix tu re i s ex t ended ove r a l l r ep re sen t ed pu re s t a t e dens i t ymatr ic ies r / .


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ollapse of the State Vecto r and Psychokinetic E ff e c t 5 7 1

4 R E D U C T I O N P R I N C IP L E

Now we want to formulate a general reduct ion equat ion that cangradual ly reduce the densi ty matr ix of (2) into the form of (3 ' ) . Consider inga binary observat ion with project ion operator Q, the reduct ion process maydepend on the par t icular observer. We wil l use in our model two parameters ,K and e to descr ibe the funct ioning of the observe r in a par t icular binaryobservat ion. T he no nnegat ive p aram eter ~c measures the speed o f thereduct ion process . We wil l cal l K the a ler tness par am ete r in agreementwith the intuit ive feeling that a highly alert observer might produce a faster

col lapse of the s ta te vecto r than a s leepy one. The o ther param eter e , theP K coeff ic ient measu res the s t rength of the associated psychokinet ic effect .This parameter can be posi t ive or negat ive corresponding to an increasedprobabi l i ty for one or the other outco me o f the binary decis ion. We ma yexpect that for a given observer the parameters K and e change with t ime anddepend in a ra ther subt le manner on his momentary mental s ta te .

In the following I will use a Heisenberg representation where the densitymatr ix of the conve nt ional formal ism is constant in time. Then I postulate a

redu ct ion pr inciple that , under the inf luence of an observat ion, ma y break

up a pure s ta te densi ty matr ix into a mixture of other pure s ta te densitymatr ices as fol lows:We wri te the s ta te a t t ime t as a mixture of pure s ta te densi ty matr ices

p( t ) = Mix P t, r/)r/ (17)~7

Here the m atr ix r/ p lays the role of a summ ation param eter and is anormalized pure state density matrix (see Equations 9 and 16), i .e.

t/~ = r/, Tr (r/ ) = 1 (1 8)

Fo r the change of /~(t) under an observ at ion we now p ostulate thereduct ion equat ion

~-7 t(/) = Mix l @ Kr/@ [K + e T r( r/ o) ] o r/Q@K -- g Tr(r/Q )] 0r /0 } P(t , r /) (19)

Note tha t tz t + dr) appears again as a su perposi t ion of pure s ta tedensi ty matr ices and that the reduct ion equat ion conserves the norm of /a( t )(see Equ at ion I 1) so that we m ay assum e that

Norm(/a(t)) = X~P t , r/) = 1 for all t imes (17 a)t

The reduct ion equat ion (19) can be natural ly general ized to the casewhere we have several s imultaneous observat ions with project ion operators

825 12 6 2


8/17

57 Sehmidt

Q, and pa ram e te r s ~c , e s by ex t end ing t he m ix tu re ove r an add i t i ona lpa rame te r s .

~ @ ( t ) = i x I G K q [ K + c Tr ( r / Q x ) ] Q s rl Q I(t , l) ( 1 9 a ), , , [Ks - ~s Tr rlQ ~) ] Q_.srlQs

t n t he absen ce o f a PK e ffec t, whe n e = 0 , t he p r ecedd ing fo rm a l i smcou ld be m uch s imp l if ied . W e co u ld s t ay i n t he f r amew ork o f t he conven -t i o n a l d e n s i t y m a t r i x f o r m a l i s m a n d w o u l d n o t h a v e t o i n t r o d u c e m i x t u r e sl i nked by t he @ op e ra t i on : F o r e = 0 Eq ua t ion (19 ) r eads

- ~ # ( t ) = M i x , ~ c [@ r /@Q q Q @ Q t l Q ] ( 1 9 ' )

In t rod uc t i on t he dens i t y ma t r i x co r r e spo nd ing t o # ( t ) ( see Equ a t ion 12 )

p t ) = ~ P t , t l ) t l (20a )

we can r ewr i t e Equ a t ion (19 ~) a s an equa t i on fo r t he dens i t y ma t r i x

t ) = - - i r p t ) + K [ Q p t ) Q +Qp( t )Q] (20b )

T h i s e q u a t i o n d e sc r ib e s t h e e x p o n e n t i a l d e c a y o f t h e m i x e d e l em e n t s( e l emen t s l i nk ing t he two mac roscop ica t l y d i f f e r en t s t a t e s ) i n t he dens i t yma t r i x unde r an obse rva t i on .

I f there i s a P K effec t , e 4= 0 , then we can no longer redu ce (19) in to ane q u a t i o n o f m o t i o n f o r t h e d e n s i t y m a t r i x a l o n e b e c a u s e t h e n ( 1 9 ) c o n t a i n se l emen t s qu ad ra t i c i n r/. Th en w e have t o u se t he more de t a i l ed fo rma l i sm

wi th mix tures .T o g ive an ex amp le , le t u s in t eg ra t e (19 ) fo r the ca se o f a b ina ry obse r-

va t ion wi th the in i t i a l ly pure s ta te

# (0 ) = q = ~ ) { ~ (21 )

where ~) i s the s ta te vec tor f rom (1) .Le t u s wr i t e aga in

(22) > = = l

T h e n w e h a v e

Tr ( r /Q) = a a * , Tr ( r /Q) = b b * (23 )


9/17

Collapse of the S ta te Vector and sychokine t ic Effect 57

N o w ( 1 9 ) c a n b e s o l v e d b y t h ea n s a t z

/. t t) = C t)~ ) ~ @ A t)a a * ~ l ) ~ l @B t ) bb * ~2) ~2

= C t ) q A t ) OrlO @ B t ) o~ la( 2 4 )

i . e . , du r ing the measu remen t t he in i t i a l pu re s t a t e b reaks up in to a mix tu rewi th o nly th ree co nt r ib u t in g pro jec t ion op era to rs , r/0 = ~) (~ , ~]1= ~ 1 ) ~ 1 a n d~ 2 = ~2) ~.

F r o m ( 1 9 ) a n d ( 2 4 ) w e o b t a i n

o r i n t eg ra t ed

d t ) = - ~ c t )

A t ) = K + ebb *) C t)

B t ) = x - e a a * ) C t )

c ( t ) = e - ~

( 2 5 )

e ) -~ t ) (26)A ( t ) = l + - - b b * ( 1 - eK

B ( t ) = ( 1 e a a * ) 1 - - e - ~ t )

T h e n t h e f in a l s ta t e ( i f t h e o b s e r v a t i o n i s c o m p l e t e d w i t h u n c h a n g e dva lues o f x an d e ) i s g iven by

/ z m ) = l + - ~ b b* )a a * ~ ,) ~ , @ 1 - - ~ a a * ) b b *{2 ) {2( 2 7 )

T h e r e d u c t i o n e q u a t i o n g u a r a n t e e s t h a t t h e f in a l m i x t u r e is n o r m a l i z e d . B u tt h e r e i s t h e f u r t h e r r e q u i r e m e n t w e h a v e n o t y e t c o n s i d e r e d t h a t t h e c o e f -f ic ien ts A ( t ) a ndB t )i n ( 2 6 ) m u s t a l w a y s b e n o n n e g a t i v e , f o r a ll a d m i s s i b l ev a l u e s o f a a * a n d b b* a a * + b b * = 1 , 0 < ~ a a * ~1) . Th i s imposes theres t r ic t ion

tel ~< x (2 8)

N o t e t h a t t h e f in a l m i x t u r e ~ ( m ) i n (2 7 ) r e m a i n s u n c h a n g e d i f s u b s e -q u e n t l y t h e s a m e o b s e r v a t i o n ( Q ) i s r e p e a t e d b y a n o t h e r o b s e r v e r ( w i t hpa ram e te r s ~c , e ) . Th i s i s ea s i ly ve r i f ied by app ly ing (19 ) t o t he m ix tu re o f(27) .


10/17

57 Sehmidt

5. T H E P S Y C H O K I N E T I C E F F E C T ( P K )

Cons ide r aga in t he b ina ry r andom gene ra to r w i th t he r ed and g reenl a m p . A c c o r d i n g t o c o n v e n t i o n a l q u a n t u m m e c h a n i c s , t h e p r o b a b i l i t i e s f o rthe red or g reen lam p to l igh t a re ( (2 ) o r (27 ) wi th e = 0)

p = a a , q = bb (29)

Un de r t he i n f luence o f a PK e ff ect t he se p robab i l i t i e s a r e changed (27 ) t o

p ' = l + - ~ - q p , = 1 - - - - p q (3 0)

In t he ca se o f a sym m et r i c r and om gene ra to r, p = q = , we ge t

1 1 e 1 1 ep ' = - - - - , q ' - ( 3 1)

-2 -+ 4 t# 2 4 K

Here t he r e s t r i c t i on f rom (28 ) l im i t s t he max ima l ave rage succes s r a t e t o

P~ax = 3 = 75 o~ (32 )

The ac tua l l y r epo r t ed s co r ing r a t e s a r e l ower ; t yp i ca l l y, a f ew pe rcen t abovet h e 5 0 % c h a n c e s c o r i n g r a t e .

N o t e t h a t t h e p r o b a b il it i es p ' , q ' i n ( 3 0 ) d e p e n d o n l y o n t h e o b s e r v e rpa ram e te r s ~c, ~ and on t he p r im ary p rob ab i l i t y v a lues p , q. A pa r t f r om tha t ,t he succes s r a t e o f a sub j ec t in a P K expe r im en t is in ou r mod e l i ndependen to f t h e i n t e rn a l s t r u c t u re a n d t h e c o m p l e x i t y o f t h e i n d e te r m i n i s ti c r a n d o mgene ra to r. Th i s f ea tu r e , t he com plex i ty i ndepe nden ce , s eems in ag reem en twith the ex pe r im en tal evide nce. (~ ~)

6 . A M A C R O S C O P I C E P R E X P E R I M E N T

In d i s cus s ing t he E ins t e in -Podo l sky -Rosen expe r imen t , one u sua l l ycons ide r s tw o m ic rosco p ic sy s t ems A and B tha t a r e spa t i a ll y s epa ra t ed bu tq u a n t u m m e c h a n i c a l l y c o rr e la t e d . I n t h e fr a m e w o r k o f c o n v e n t i o n a lq u a n t u m t h e o r y s u c h a n a r r a n g e m e n t c a n n o t b e u se d f o r t r an s m i t t in g i n f o r -m a t i o n f r o m A t o B .

T h e P K m e c h a n i s m i m p l ie d b y th e r e d u c t io n e q u a t i o n ( 1 9 ) c o u l d

change t h i s, how eve r. Tak e , f o r example , t he ca se whe re t he sy s t em s A and Ba re two pho tons i n a co r r e l a t ed s t a t e

1 { A + ) ( B + ) + A - ) B - - ) } ( 3 3 )


11/17

o l l a p s e o f t he S t a t e Vec t o r and Psy chok ine t i c E ff ec t 7

w h e r e A + ) , A - - ) , a n d B + ) , B - - ) a r e tw o p o l a r i s a ti o n s t a te s fo r p h o t o n A o rB , r e spec t i ve ly.

T h e n i m m e d i a t e ly a f t e r a n i d e al m e a s u r e m e n t o f th e p o l a r i s a ti o n o fp h o t o n A , t h e s t a te o f t h e t o t a l sy s t e m p h o t o n s p l u s m e a s u r i n g d e v i c e ) c a nbe wr i t t en

~) = ~ {~+ ) + ~--)} 34 )X 2

with

~ + = A + B + S + , ~ - - = A - - B - - S - - 35)

w h e r e S + ) a n d S - ) a r e st a te s o f t h e m e a s u r i n g d e v i ce t h a t h a sm a c r o s c o p i c a l l y r e c o r d e d an A + ) o r A - ) p o l a r i s at i o n s ta te o f t h e p h o t o n ,respec t ive ly.

W h e n t h e h u m a n o b s e r v e r b e c o m e s a w a r e o f t h e in s t r u m e n t r e a d in g , t hes t at e s ~+) and ~ - - ) a re e igens ta t e s o f t he co r r e spo nd ing p ro j ec t i on ope ra to rQ , so t ha t t he f ina l m ix tu re becom es [Eq . 27 ) w i thaa* = bb* = 1/2]

11 oo )= 1 t ~ 1 e

+ - ~ - ~ 7 ) ~ + ) ~ + @ ~ 4 x ) ~ - ) ~ - 3 6)

To t r ansm i t a s i gnal f rom A to B we wou ld need a su ff i ci en t num ber o fco r r e l a t ed ph o ton pa i r s and an obse rve r a t A wi th t he PK ab i l it y t o bi a s t her a te o f o b s e r v e d A + e v e nt s. T h e n t h is c o u l d b e i m m e d i a t el y a f t e rw a r d sobse rved a t B a s a co r r e sp ond ing b i a s i n t he r a t e o f obse rv ed B + even ts , sot h a t w e w o u l d h a v e a n u n c o n v e n t i o n a l m e a n s f o r i n f o r m a t i o ntransmission.~17)

Bu t i f ou r m ode l i s r i gh t, then t h i s i n fo rm a t ion t r ansmis s ion shou ld

w o r k a s w e ll w h e n A a n d B a r e m a c r o s c o p i c s y s t em s . T a k e a s e x a m p l e t h isa r r angem en t : F i r s t a b ina ry r an dom gene ra to r is a c t i va t ed t o l igh t a red o r ag reen l amp . N ex t a po l a ro id co lo r c am era t akes two iden t i ca l p i c tu r e s o f t hel i t l amp . Then t he deve loped p i c tu r e s a r e i n se r t ed i n to two opaque enve lopes ,A and B , and t he enve lopes a r e t aken t o d i f f e r en t l oca t i ons . Th i s p rocedu reshou ld be con duc t ed so t ha t a t t h i s s tage no hu m an obse rv e r i s aw are o f t hegene ra t ed co lo r. Then na tu re ha s no t ye t dec ided fo r r ed o r g r een ; we have amac roscop icaUy ambiguous s t a t e , w i th t he p i c tu r e s i n t he two enve lopesq u a n t u m m e c h a n i c a l l y c o r r e l a t e d : T h e y a r e e i t h e r b o t h r e d o r b o t h g r e e n . I f

now a succes s fu l PK sub j ec t opens t he enve lopeA, t r y ing t o en fo rce t heappe a rance o f t he co lo r r ed , t h is e f fo r t wou ld be im m ed ia t e ly a f t e rwardsobse rvab l e a s an i nc r ea sed p robab i l i t y fo r t he co lo r r ed i n t he enve lope B .Aga in we wou ld need a su ffi c ien t num ber o f co r r e l a t ed p i c tu r e pa i r s t o havean e f f i c ien t com m unica t i ons l ink .


12/17

5 7 6 S c h m i d t

F o r a p r a c t ic a l l y m o r e c o n v e n i e n t s t u d y o f t h is m a c r o s c o p i c q u a n t u mc o r r e l a t i o n e f f e c t , o n e c o u l d a c t i v a t e a b i n a r y r a n d o m g e n e r a t o ra u t o m a t i c a l l y m a n y t i m e s a n d r e c o r d t h e b i n a r y s i g n a l s a s c l i c k s i n t h e r i g h to r l e f t c h a n n e l , r e s p e c t i v e l y, o f a c a s s e t t e t a p e r e c o r d e r. N e x t o n e w o u l dc o p y t h e ta p e a n d t h e n s e n d o n e t a p e ( s y s t e m A ) t o a P K s u b je c t a n d k e e pt h e o t h e r t a p e ( s y s t e m B ) i n th e l a b o r a t o r y . T h e s u b j e c t w o u l d l is te n t h r o u g hs t er e o h e a d - p h o n e s t o t h e t a p e A t r y i n g t o r e c e i v e m o r e c l i c k s in , s a y, t h er i g h t c h a n n e l . T h e n a r e c o u n t i n g o f t h e c li c k s o n ta p e B i n t h e l a b o r a t o r yshou ld f ind an ex cess o f s igna l s in the r igh t chann e l .

S e v e r a l s i m i l a r e x p e r i m e n t s w i t h s l ig h t l y d if f e re n t f o r m s o f d a t a s t o r a g eand d i sp lay hav e sugg es ted the ex i s tence o f the cor re la t io n e ffec t, ~13) ina g r e e m e n t w i t h o u r m o d e l .

7. S U P E R P O S I T I O N O F T W O O B S E RVA T I O N S

A . B i n a r y e v e n t s e en b y t w o o b s e r v e r s s im u l t a n e o u s l y

I f tw o o b s e r v e r s w i t h p a r a m e t e r s x l , e I an d ~ 2 ,~ 2 l o o k a t th e s a m eb i n a r y e v e n t Q= Q ~ Q2 t h e n t h e s e o b s e r v e r s , a c c o r d i n g t o ( 1 9 a ) , a c t l i k eo n e o b s e r v e r w i t h t h e p a r a m e t e r s

K = K 1 K 2 , G ~ - 6 1 e 2 (37)

a n d t h e s e a r e t h e p a r a m e t e r s t o b e u s e d i n E q u a t i o n ( 3 0 ) f o r t h e c a l c u l a t i o no f t h e to t a l c o m b i n e d P K e f fe c t. N o t e t h a t ( f o r o u r n o n e g a t i v e I< v a l u e s )

2 2 e l ~ 2 C e l< i m pl ie s - - < - - < - - ( 38 )

K 2 K 1 K 2 K K 1

s o th a t t h e c o m b i n e d P K e f fe c t f r o m t h e t w o o b s e r v e r s c a n n o t b e s t r o n g e rt h a n t h e e f f e c t f r o m t h e b e t t e r P K s u b j e c t a l o n e .E x p e r i m e n t e r s h a d i n it ia l ly a s s u m e d n a i v e ly t h a t t h e c o m b i n e d e f f o r t o f

t w o p o s i t i v e P K s c o r e r s s h o u l d l e a d t o a n e n h a n c e d e f f e c t . B u t n o s u c h e f f e c th a s b e e n r e p o r t e d .

To u n d e r s t a n d o u r r e s u l t i n t u i ti v e ly, n o t e t h a t t h e P K e f f e ct o c c u r s o n l y int h e p r o c e s s o f r e d u c t io n f r o m t h e m a c r o s c o p i c a l l y a m b i g u o u s s ta t e in t o t h ec o l l a p s e d s t at e , a n d t h a t e a c h o b s e r v e r c a n a p p l y h is P K e f f o r t o n l y to t h a tf r a c t i o n o f t h e i n it ia l s t a t e t h a t i s n o t c o l l a p s e d b y t h e o t h e r o b s e r v e r.

B . S u b s e q u e n t O b s e r v a t io n s o f t h e s a m e B i n a r y E v e n t

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


13/17

Collapse of the State Vector and sychokinetic Effect 577

reduct ion, wi th a mixture given by (27) , so that a subsequent observat ion ofthe lamps would change nothing.

But i f the f i rs t observ at ion were interrupted at some t ime t o so th at theobserver had only a subl iminal impression of the color, then only a cer ta infrac tion ~ of the init ial state were reduc ed, leaving us with a mixture of theform [see (24) and (26) with 0 = 1 - e - ~t]

/ ~ : ( 1 - 0 ) ) ( @ v ~ ( l + e ~ b b * ] a a * l ) ( ,

@ 0 ( 1 - ~ - L a a * t bb*~2)(~ zt~

(39)

Assuming subsequent ly a complete observat ion by the second observer,the f inal mixture becomes

p (o o) = (1 + 2bb*) aa*~)(~ @ (1 -- J,aa*) bb*~z)(~2 (40)

with

= o + 1 - o) 42 )K 1 K 2

An incomplete reduct ion, s imilar to (39) might a lso resul t i f the hum anobserver is half as leep or inat tent ive so that he forgets immediately what hehas seen, or perhaps even i f a cat or a cock roac h has observ ed the lamps.

T o tes t exper imen tal ly whether and to what extent a cat s ob servat ionmight have re duc ed the initial state, let the ca t s ob serv ation be followed by acomp lete hum an observat ion by an observer with know n P K effect , e /K > 0.

Assu ming that the cat reduce s the fraction 0 of the init ial state, anddisregarding for simplicity a possible cat PK effect, the final mix turebeco me s [(40) and (41) w ith e I = O,e2 R7 2 = ~ ~]

t (oo)= [t + (l + ~)--~ bb* ]aa*~l)(~l

@[ 1 1 0) e ]- -- -- aa * bb*~2)(~ 2K

(42)

Provided that we had an ob server with suff ic ient ly s table PK perfor-mance, we could measure his success ra te with and without previous obser-vat ion of the lamps by the cat . (The observ er should not know whether ornot there was a cat observing, so that he approaches both s i tuat ions in thesame mental state.)


14/17

5 7 8 S e h m i d t

Eq uat io n 42) g ives for the success ra tes in the two s i tua t ions

bw t o u t a t ]a a *

p w ith cat) = [1 + 1 - v~)bb *]aa*

f rom w hich the va lue o f ~ can be de r ived .

43)

C T w o Different Binary Observations

Cons ide r two p ro j ec t ions ope ra to r s Q~ and Q2 co r re spond ing tod i f f e ren t b ina ry m acrosc op ic obse rva t ions . The n we m ay a s sum e ~18) t ha tthese mac roscop ic ope ra to r s Q1 and Q2 commute . Wi th an in i t i a l s t a t er / = ~ ) ~ c o n v e n t i o n a l q u a n t u m m e c h a n i c s g i v e s f o r t h e p r o b a b il it ie sa s soc i a t ed wi th the obse rva t ions o f one o r bo th va r i ab le s

P Q, = 1) = Tr r/Q1), P Qz= 1) = Tr r/Q2 )

P Qj = 1, Q2 = 1 ) = Tr r /Ql Q2)

Sam e wi th Q~ or Q2 rep laced by Q1, Q2

44)

I f t he expec ta t ion va lue fo r Qz is i ndepende n t o f the ou tcom e o f a p rev iousQ~ measu remen t , t hen

P Q, = 1, Q 2 = 1 ) = P Q , = 1 ) P Q 2 = 1) 45)

o r

Tr r /Q1 Q2) = Tr r /Q 0 T r qQ z)

Sam e wi th Q1 or Qz rep laced b y Q1, Q246)

Re tu rn ing to ou r mode l , l e t u s a s sume tha t f i r s t a comple t e obse rva t ionof Q~ wi th ~c1 , e~) i s mad e and subseq uent ly a com ple te ob serva t ion of Q2wi th Kz, e2) . By app ly ing 27) twice we c an eas i ly ca lcu la te the f ina l

mix tu re and the p robab i li t ie s fo r t he fou r poss ib l e ou tcom es o f t he two obse r-va t ions . Le t me l i s t here expl ic i t ly only the resu l t ing average va lue for theobse rvable Q2 :

Tr Q,G)]K2 ] X r ,IQ Q2)

+ ez Tr01Q,,Qz)] Tr r/ ~i Q:)x2 Tr r/Q1)

47)


15/17

o l la p s e o f t h e S ta t e Ve c t o r a n d P s y c h o k i n e t i cEffect 579

In the spec ia l case tha t the observa01es QI and Q2 a re independent inthe s ense o f conven t ion a l qua n tum theo ry, ( 47 ) r educes w i th (46 ) t o

P Q 2 = I ) = [ I + ~ Tr t lQ 2)] Tr ~IQ2) (48 )

i.e ., i n t h i s c a se t he ou t com e o f t he s e cond o bse rva t i on i s i ndepend en t o f anyreduc t i on o r P K e ff ec t exe r t ed by t he f i r s t obse rve r.

Le t m e m en t ion i n t h is c on t ex t an ac tua l expe r im en t (I9 ) pe r fo rm ed inthe fo l lowing s teps :

1, W i th t he he lp o f r ad ioac t i ve decay s as sou rce s o f t r ue r ando m ness a s ixd i g i t ( d e c i m a l ) r a n d o m n u m b e r i s g e n e r a t e d a n d r e c o r d e d .

2 . Th i s num ber i s obse rved ca r e fu l ly by t he expe r imen te r.

3 . Th e num ber i s f ed a s s eednum ber i n to a de t e rmin i s t i c com pu te rr a n d o m n e s s p r o g r a m s u c h a s t o p r o d u c e a b i n a r y q u a s i r a n d o m s e q u e n c e.

4 . Th e b ina ry s equence is d i sp l aye d to a PK sub j ec t a s a s equence o f r edand g reen s igna l s ( o r i n some o the r way ) wh i l e t he sub j ec t t r i e s t o en fo rcet h e a p p e a r a n c e o f m a n y r e d s ig n al s.

I n pa r t o f t he expe r im en t the obse rva t i on i n s tep 2 was om i t ted . I n th i s c a set h e P K s u b j ec t e n c o u n t e r s a n o n c o l l a p s e d e n s e m b l e o f m a n y d i ff e re n tpos s ib l e co lo r s equences co r r e spo nd ing t o t he d i f f e ren t pos s ib l e s eednum ber sso t ha t t he con d i t i ons fo r a P K e ff ec t we re ce r t a in ly g iven .

Bu t t he ou t c om e o f t he expe r im en t showed a PK e ff ect a l so i n t he pa r twhe re t he expe r imen te r had l ooked a t t he s eednumber s . Thus t he r e appea redto be no s ign i fi c an t co l lapse , even t houg h the expe r im en te r had eno ugh in fo r-ma t ion t o de r ive f rom the s eed -number i n p r inc ip l e ( a f t e r some hou r s o f

penc i l and pape r ca l cu l a t i on ) t he f i na l l y d i sp l ayed b ina ry s equence .Th i s r e su l t m ay he lp u s to a be t t e r unde r s t and ing o f wh a t con s t i t u t es acon sc iou s obse rva t i on t ha t co l l apse s the st a t e vec to r. N o te t ha t t he

seednum ber s d id no t conv ey m ean ing fu l i n fo rm a t ion t o t he obse rve r, o ri n f o r m a t i o n h e c o u l d r e m e m b e r ( th e l arg e n u m b e r o f s e e d n u m b e r s u se d i nthe who le expe r imen t we re i n spec t ed i n one s i t t i ng ) . I t i s t r ue t ha t t hee x p e r im e n t e r m i g h t h a v e r e m e m b e r e d s o m e f e a t u r es o f t h e s e e d n u m b e r s . F o rexam ple , he migh t have c oun ted t he re l a t i ve f r equenc i e s o f even and oddseednumber s and t ha t m igh t have i nduced some pa r t i a l co l l apse . Bu t t h i s

cou n t is i ndepende n t o f the f r equenc i e s o f g r een and r ed s i gna l s i n t he b ina rysequence so t ha t a cco rd ing t o ou r p r ev ious ca l cu l a t i on (48 ) t h i s pa r t i a lr educ t i on does no t a f f ec t t he succes s o f t he P K e ffo r t .


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7. C O N C L U S I O N

O u r m a i n c o n c e r n i n t h i s p a p e r w a s t h e s e a r c h f o r s o m e s e lf c o n s i s t e n tf o r m a l i s m t h a t m i g h t d e s c r i b e t h e r e p o r t e d p s y c h o k i n e t i c e f f e c t s . Wi t he x p e r i m e n t a t i o n i n t h i s f i e l d s l o w a n d t e d i o u s , a n d w i t h t h e r e p o r t e d e f f e c t sf a r o u t s id e t h e r a n g e o f o u r e v e r y d a y i n t u i ti o n , t h e r e i s a n e e d f o r th e o r e t i c a lm o d e l s , n o m a t t e r h o w t e n t a t i v e a n d p r e l i m i n a r y, t o h e l p i n t h e p l a n n i n g o fs y s t e m a t i c e x p e r i m e n t s.

U s i n g t h e a v a i l a b le f r a m e o f q u a n t u m t h e o r y t o f o r m u l a t e s u ch a f ir stm o d e l s ee m s e c o n o m i c a l : M a n y e a r li e r a t t e m p t s a t c h a n g i n g q u a n t u mm e c h a n i c s h a v e s h o w n th a t ev e n s m a l l m o d i f i c at io n s o f t he f o r m a l i s m c a nl e a d t o a p p a r e n t l y u n r e a s o n a b l e e f f e c t s . A n d b y p o s t u l a t i n g a p a r t i c u l a rr e d u c t i o n m e c h a n i s m t o a c c o m p a n y a n o b s e r v a t i o n , w e a r e l ed t o a

l o g ic a l ly s e lf c o n s i s te n t m o d e l t h a t c a n a c c o m o d a t e p s y c h o k i n e t i c e f fe c ts a n dm a k e s q u a n t i t i v e p r e d i c t i o n s f o r f u t u r e P K e x p e r i m e n t s .

O n t h e m o r e s p e c u l a t i v e s i d e o n e m i g h t w o n d e r w h e t h e r t h e c o n n e c t i o nb e t w e e n q u a n t u m t h e o r y a n d p s y c h o k i n e s i s is p e r h a p s o f a m o r e p r o f o u n dn a t u r e . C o u l d t h e s i n g u l a r r o le o f t h e h u m a n s u b j e c t a s s o u r c e o f t h e P Ke ff e c t b e r e l a te d t o t h e c o n t r o v e r s i a l r o l e o f t h e o b s e r v e r i n q u a n t u m t h e o r y,

a n d d o e s t h e r e p o r te d P K e f fe c t o n q u a n t u m j u m p s i n d ic a t e s o m e i n c o m -p l e t e n e s s i n t h e c u r r e n t q u a n t u m f o r m a l i s m ?Ta k i n g t h is c o n n e c t i o n s e r i o u s ly, o u r m o d e l d e s c r i b e s th e r e d u c t i o n o f a

m a c r o s c o p i c a l l y a m b i g u o u s s t a te i n t h e p r o c e s s o f o b s e r v a t i o n a s ap h y s i c a l l y r e a l p r o c e s s. A n d t h e P K e f fe c t a p p e a r s a s a n e w t o o l f o r t h e

p h y s i c i st t o d i s ti n g u is h b e t w e e n c o l l a p s e d a n d n o n c o l l a p s e d s ta te s .T h e m o d e l d o e s n o t a t t e m p t t o e x p la i n th e n a t u r e o f c o n s c i o u s n e s s a n d

i ts r e l a t i o n s h i p t o b a s i c q u a n t u m t h e o r y. I t t r e a t s t h e h u m a n o b s e r v e r a n d it si n t e r a c t i o n w i t h t h e r e st o f t h e w o r l d in a p u r e l y p h e n o m e n o l o g i c a l m a n n e r.

N e v e r t h e l e s s , th e m o d e l m a y b e r e le v a n t w i th r e g a r d t o v e r y b a s i c q u e s t i o n sb e c a u s e i t su g g e s t s t h a t o n e a s p e c t to c o n s c i o u s n e s s , i ts a c t i o n o n t h e s ta t ev e c t o r c o l l a p s e , c a n b e a p p r o a c h e d e x p e r i m e n t a l l y.

I n t h e p r e s e n t e d , n o n r e l a t i v i s t ic f o r m a t i o n o f o u r m o d e l , w e c o u l du p h o l d c a u s a l i t y i n a c e r ta i n s e n s e : C o n s i d e r, f o r e x a m p l e , t h e c a s e w h e r e ad e c i s i o n b y a b i n a r y r a n d o m g e n e r a t o r i s a u t o m a t i c a l l y r e c o r d e d a n d o n eh o u r l a t e r i n s p e c t e d b y a n o b s e r v e r w h o e x e r t s a p s y c h o k i n e t i c e f f ec t . T h i sm i g h t s u g g e s t t h a t t h e l a t e r e f f o r t o f th e o b s e r v e r h a d a f f e c t e d t h e e a r li e rr a n d o m d e c is io n i n a n o n c a u s a l m a n n e r. B u t i f w e a b a n d o n t h e r e q u i r e m e n t

o f a n a b s o l u t e m a c r o s c o p i c r e a l i t y a n d a d m i t m a c r o s c o p i c a l l y a m b i g u o u ss t a te s , t h e n a t t h e t i m e o f o b s e r v a t i o n th e p h y s i c a l r e a l i t y c o n s i s t s o f t h et w o o p t i o n s a n d t h e o b s e r v e r ' s e f f o r t s d o n o t h a v e t o r e a c h i n t o t h e p a s t i norder to se lec t one o f the two offe red poss ib i l i t ie s .

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


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v e c t o r m i g h t a p p e a r a s a t i m e s y m m e t r i c c o l l a p s e a n d a n t i c o l l a p s e ' ' (2 ) a n d

n o n c a u s a l i t y w o u l d b e u n a v o i d a b l e . B u t w h e t h e r s u c h a n in t e r e s t i n gg e n e r a l i z a t i o n is p o s s i b l e r e m a i n s t o b e s e en ,

R E F E R E N C E S

1. H. Schmidt,J. AppL Physics 4 1 , 4 6 2 ( t 9 7 0 ) .2 . B. S . Dewit t and R. N. Graham,Am. J. Phys. 39, 724 (1971).3. B. d 'Espagnat,Conceptual Foundations of Quantum Mechanics (W. A. Benjamin, Inc.,

Reading, MA, 1976).

4 . J . yon Neumann,Mathematische Grundlagen der Quantenmechanik (Springer, Berlin,1932); English translation:Mathematical Foundations of Quantum Mechanics (Pr incetonU. Press, Princeton, 1955); F. London and E. Bauer, La Th+orie de l 'Observation enM~chanique Quant ique (H ermann , Par is , 1939).

5. E. P. W igner, Remarks on the Mind Body Proble m . inThe Scientist Speculates (BasicBooks, Inc. , New York 1962), pp. 284-302.

6. L. E. Rhine and J. B. Rhine, J .Parapsychology 7, 20 (1943).7. L. E. Rhine,Mind Over Matter (Macmil lan, N.Y, , t970) .8. J , Belo ff and L . Evans,J. Soe. Psychical Res. 41, 41 (1961).9 . R. Chauvin and J . Genthon,Z. f Parapsychologie und Grenzgebiete der Psychologic 8,

140 (1965).

10. H. Schmidt,New Scientist and Science Journal 24 757 (June 197I)o1I . H. Schmidt , Evide nce for Dire ct Interact ion between the Hu m an M ind and External

Quantum Processes . in1977 Proceedings of the International Conference on Cyberneticsand Society. IEEE Inc., New York.

12. B. Dunne, R. Jahn, and R. Nelson, A n R EG Exper iment wi th Large Data BaseCapabi l i ty. inResearch in Parapsychology (Scarecrow Press, Metuchen,N . J . 1981); R.G. Jahn, Proc. IEEE Vol. 70, No. 2, 136 (1982).

13. H. Schmidt,J. Am. Soc. Psychical Res. 70, 267 (1967).14. H. Schmidt,Found. Phys. 8, 463 (1978).15. E. H. Walker, Fou ndat io ns of Paraphysical and Parapsychologicat Phenom ena. in

Quantum Physics and Parapsychology (Parapsychology Foundat ion, Inc . , New York,1974).

16. R. D. M at tuck and E. H. Walker, The A ct ion of Consciousness on Mat ter, a QuantumMech anical Theory of Psychokinesis . inThe Iceland Papers (Essentia ResearchAssociates. Amherst , wk 1979). pp. 11t-159.

t 7. O. C os ta de B eauregard,Psychoenergetics 4, 11 ( 198 i) .I8. G. Ludwig,Die Grundtagen der Quantenmechanik (Springer Verlag, Berlin, 1954).19. H. Schmidt,J. Parapsychology 45, 87 (1981).20. O. Costa de BeauregardFound. Phys. 6, 539 (1976); O. Costa de Beauregard,Found.

Phys. 10, 514 (1980).

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