physics and reality - einstein

8/3/2019 Physics and Reality - Einstein

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P H Y S I C S A N D R E AL IT Y .BY

ALBERT EINSTEIN.(Translation by Jean Piccard.)

I. GENERAL CONSIDERATION CONCERNING THE METHOD OF SCmNCE.I t h a s o f t e n b e e n s a i d , a n d c e r t a i n l y n o t w i t h o u t j u s t i -f ic a ti o n, t h a t t h e m a n o f s c ie n c e is a p o o r p h i l o s o p h e r . W h yt h e n s h o u l d i t n o t b e t h e r i g h t t h i n g f o r t h e p h y s i c i s t t o l e tt h e p h i lo s o p h e r d o t h e p h i lo s o p h i z i n g ? S u c h m i g h t i n d e e db e t h e r i g h t t h i n g a t a t i m e w h e n t h e p h y s i c i s t b e l i ev e s h e

h a s a t h is d is p o s a l a r ig i d s y s t e m o f f u n d a m e n t a l c o n c e p t sa n d f u n d a m e n t a l l aw s w h i c h a r e s o w e ll e s ta b l is h e d t h a tw a v e s o f d o u b t c a n n o t r e a ch t h e m ; b u t , i t c a n n o t b e r ig h ta t a t i m e w h e n t h e v e r y f o u n d a t i o n s o f p h y s i c s it se l f h a v eb e c o m e p r o b l e m a t i c a s t h e y a r e n o w . A t a t i m e lik e t h ep r e s e n t , w h e n e x p e r i e n c e f o rc e s u s t o se e k a n e w e r a n d m o r es ol id f o u n d a t i o n , t h e p h y s i c i s t c a n n o t s i m p l y s u r r e n d e r t o t h ep h i l o s o p h e r t h e c r i ti ca l c o n t e m p l a t i o n o f t h e t h e o r e t ic a lf o u n d a t i o n s ; fo r, h e h i m s e l f k n o w s b e s t, a n d f ee ls m o r e s u r e l yw h e r e t h e s h o e p i n c h e s . I n l o o k i n g f o r a n e w f o u n d a t i o n , h em u s t t r y t o m a k e c le a r in h is o w n m i n d j u s t h o w f a r th ec o n c e p t s w h i c h h e u s e s a r e j u s t i f i e d , a n d a r e n e c e s s i t i e s .T h e w h o l e o f s c ie n ce is n o t h i n g m o r e t h a n a r e f i n e m e n t o fe v e r y d a y t h i n k i n g . I t is f o r t h is re a s o n t h a t t h e c ri ti ca lt h i n k i n g o f th e p h y s i c i s t c a n n o t p o s s ib l y b e r e s t r ic t e d t o t h ee x a m i n a t i o n o f t h e c o n c e p t s o f h i s o w n sp e c if ic f ie ld . H ec a n n o t p r o c e e d w i t h o u t c o n s id e r in g cr i t ic a l l y a m u c h m o r ed i ff ic u l t p r o b l e m , t h e p r o b l e m o f a n a l y z i n g t h e n a t u r e o fe v e r y d a y t h i n k i n g .O n t h e s t a g e o f o u r s u b c o n s c i o u s m i n d a p p e a r in c o lo r fu ls u c c e ss i o n s e n s e e x p e r ie n c e s, m e m o r y p i c t u r e s o f t h e m , r e p re -s e n t a t i o n s a n d fe el in g s. I n c o n t r a s t t o p s y c h o l o g y , p h y s i c st r e a t s d i r e c t l y o n l y o f s e n se e x p e r ie n c e s a n d o f t h e " u n d e r -s t a n d i n g " o f t h e i r c o n n e c t io n . B u t e v e n t h e c o n c e p t o f t h e

Copyr ight , 1936 , by Albert Einste in.349


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3 5 A L B E R T E I N S T E I N . [J . F . I ." re a l e x t e r n a l w o r l d " o f e v e r y d a y t h i n k i n g r e st s e x c l u s i v e l yo n s e n s e i m p r e s s i o n s .N o w w e m u s t f ir st r e m a r k t h a t t h e d i f fe r e n ti a ti o n b e t w e e ns e n s e i m p r e s s i o n s a n d r e p r e s e n t a t i o n s i s n o t p o s s ib l e ; o r, a tl e as t i t is n o t p o ss ib l e w i t h a b s o l u t e c e r t a i n t y . W i t h t h ed i s c u s s io n o f t h i s p r o b l e m , w h i c h a f f e c ts a ls o t h e n o t i o n o fr e a l i t y , w e w i l l n o t c o n c e r n o u r s e l v e s b u t w e s h a l l t a k e t h ee x i s te n c e o f s e n s e e x p e r i e n c e s a s g i v e n , t h a t is to s a y a s p s y c h i ce x p e r i e n c e s o f s p e c ia l k i n d .I b e l ie v e t h a t t h e f ir s t s t e p i n t h e s e t t i n g o f a " r e ale x t e r n a l w o r l d " is t h e f o r m a t i o n o f t h e c o n c e p t o f b o d i l yo b j e c t s a n d o f b o d i l y o b j e c t s o f v a r i o u s k in d s . O u t o f t h em u l t i t u d e o f o u r s en s e e x p e r i en c e s w e t a k e , m e n t a l l y a n da r b i tr a r i l y , c e r t a i n r e p e a t e d l y o c c u r r i n g c o m p l e x e s o f s e n sei m p r e s s i o n ( p a r t l y i n c o n j u n c t i o n w i t h s e n se i m p r e s s i o n sw h i c h a r e i n t e r p r e t e d a s s ig n s f o r s e n s e e x p e r i e n c e s o f o t h e r s ) ,a n d w e a t t r i b u t e t o t h e m a m e a n i n g - - t h e m e a n i n g o f t h eb o d i l y o b j e c t . C o n s i d e r e d l o g ic a l ly t h i s c o n c e p t is n o t i d e n -t ic a l w i t h t h e t o t a l i t y o f s e n se i m p r e s s i o n s re f e rr e d t o ; b u t i tis a n a r b i t r a r y c re a t io n of t h e h u m a n ( or a n i m a l ) : m l n d . O nt h e o t h e r h a n d , t h e c o n c e p t o w e s i ts m e a n i n g a n d i ts ju s -t i f i c a t i o n e x c l u s i v e l y t o t h e t o t a l i t y o f t h e s e n s e i m p r e s s i o n sw h i c h w e a s s o c i a te w i t h i t .T h e s e c o n d s t e p is t o b e f o u n d i n t h e f a c t t h a t , in o u rt h i n k i n g ( w h ic h d e t e r m i n e s o u r e x p e c t a t io n ) , w e a t t r i b u t e t ot h i s c o n c e p t o f t h e b o d i l y o b j e c t a s i g n i f i c a n c e , w h i c h i s t o ah i g h d e g r e e i n d e p e n d e n t o f t h e s e n se i m p r e s s i o n w h i c h o r i g-i n a l l y g i v e s r is e t o i t. T h i s is w h a t w e m e a n w h e n w e a t t r i b -u t e t o t h e b o d i l y o b j e c t " a r e al e x i s t e n c e . " T h e ju s t i f i c a t i o no f s u c h a s e t t i n g r e s t s e x cl u s i v e ly o n t h a t f a c t t h a t , b y m e a n so f s u c h c o n c e p t s a n d m e n t a l r e l a t io n s b e t w e e n t h e m , w e a rea b l e t o o r i e n t o u r s e l v e s in t h e l a b y r i n t h o f s e n s e i m p r e s s i o n s .T h e s e n o t i o n s a n d r e la t i on s , a l t h o u g h f re e s t a t e m e n t s o f o u rt h o u g h t s , a p p e a r t o u s a s s t r o n g e r ' a n d m o r e u n a l t e r a b l e t h a nt h e i n d i v i d u a l s e n s e e x p e r i e n c e it se lf , t h e c h a r a c t e r o f w h i c ha s a n y t h i n g o t h e r t h a n t h e r e s u l t o f a n i ll us io n o r h a l l u c i n a t i o nis n e v e r c o m p l e t e l y g u a r a n t e e d . O n t h e o t h e r h a n d , t h e s ec o n c e p t s a n d r e la t io n s , a n d i n d e e d t h e s e t t i n g o f r ea l o b j e c t sa n d , g e n e r a l l y s p e a k i n g , t h e e x i s t e n c e o f " t h e r e a l w o r l d , "h a v e j u s t i f ic a t io n o n l y in s o fa r a s t h e y a r e c o n n e c t e d w i t h


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March, 1936.] PHYSICS AND REALITY. 35Isense impressions between which they form a mental con-nection.The ver y fact th at the total ity of our sense experiences issuch tha t by means of think ing (operations with concepts, andthe creation and use of definite functional relations betweenthem, and the co6rdination of sense experiences to these con-cepts) it can be put in order, this fact is one which leaves usin awe, but which we shall never unde rsta nd. One ma y say" the eternal m ys te ry of the world is its comprehens ibility."It is one of the great realisations of Immanuel Kant that thesetting up of a real external world would be senseless withoutthis comprehensibility.In speaking here concerning " comprehensibility, " theexpression is used in its most modes t sense. It implies: theproduction of some sort of order among sense impressions, thisorder being produced by the creation of general concepts, rela-tions between these concepts, and by relations between theconcepts and sense experience, these relations being deter-mined in an y possible manner . It is in this sense th a t theworld of our sense experiences is comprehensible. The factthat it is comprehensible is a miracle.In my opinion, nothing can be said concerning the m annerin which the concepts are to be made and connected, and howwe are to co6rdinate them to the experiences. In guiding usin the creation of such an order of sense experiences, successin t h e result is alone the dete rmin ing factor. All th at isnecessary is the statement of a set of rules, since without suchrules the acquisition of knowledge in the desired sense wouldbe impossible. One may compare these rules with the rulesof a game in which, while the rules themselves are arbitrary,it is their rigidity alone which makes the game possible.However, the fixation will never be final. It will have validityonly for a special field of application (i.e. there are no finalcategories in the sense of Kant).

The connection of the elem enta ry concepts of every da ythinking with complexes of sense experiences can only be com-prehended intuit ively and it is unadap tabl e to scientificallylogical fixation. The totali ty of these connec tion s,- -noneof which is expressible in notional terms,--is the only thingwhich differentiates the g reat building which is science from a


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3 5 2 A L B E R T E I N S T E I N . [J. F. I.

lo g ic al b u t e m p t y s c h e m e o f c o n c e p ts . B y m e a n s o f t h e sec o n n e c t i o n s , t h e p u r e l y n o t i o n a l t h e o r e m s o f s c ie n c e b e c o m es t a t e m e n t s a b o u t c o m p l e x e s o f s e n se e x p e ri e n ce s .W e s h al l c a l l " p r i m a r y c o n c e p t s " s u c h c o n c e p t s a s a red i r e c t ly a n d i n t u i t iv e l y c o n n e c t e d w i t h t y p i c a l c o m p l e x e s o fs e n se e x p e r i en c e s . A l l o t h e r n o t i o n s a r e - - f r o m t h e p h y s i c a lp o i n t o f v i e w - - p o s s e s s e d o f m e a n i n g , o n l y in s o fa r a s t h e ya r e c o n n e c t e d , b y t h e o r e m s , w i t h t h e p r i m a r y n o t i o n s .T h e s e t h e o r e m s a re p a r t i a l l y d e f i n i t io n s o f t h e c o n c e p t s ( a n do f t h e s t a t e m e n t s d e r i v e d l o g ic a ll y f r o m t h e m ) a n d p a r t i a l l yt h e o r e m s n o t d e r i v a b l e f r o m t h e d e f i n i t i o n s , w h i c h e x p r e s s a tl e a s t i n d i r e c t r e l a t i o n s b e t w e e n t h e " p r i m a r y c o n c e p t s , " a n din th i s w a y b e t w e e n s e n se e x p e ri en c e s . T h e o r e m s o f t h el a t t e r k i n d a r e " s t a t e m e n t s a b o u t r e a l i ty " o r la w s o f n a t u r e ,i .e . t h e o r e m s w h i c h h a v e t o s h o w t h e i r u se f u l n e s s w h e n a p p l i e dt o s e n s e e x p e r i e n c e s c o m p r e h e n d e d b y p r i m a r y c o n c e p t s .T h e q u e s t i o n a s to w h i c h o f t h e t h e o r e m s sh a ll b e c o n s i d e r e da s d e fi n i t io n s a n d w h i c h a s n a t u r a l l aw s w il l d e p e n d l a rg e l yu p o n t h e c h o s e n r e p r e s e n t a t i o n . I t r e a ll y b e c o m e s a b s o l u t e l yn e c e s s a r y t o m a k e t h is d i f f e re n t i a t i o n o n l y w h e n o n e e x a m i n e st h e d e g re e t o w h i c h t h e w h o l e s y s t e m o f c o n c e p t s c o n s i d er e dis n o t e m p t y f r o m t h e p h y s ic a l p o i n t o f v ie w .

St ra t i fi ca t io n o f t he Sc i en t i f ic Sy s t e m ,T h e a i m o f s c ie n c e is , o n t h e o n e h a n d , a c o m p r e h e n s i o n ,a s complete a s p o s si bl e, o f t h e c o n n e c t i o n b e t w e e n t h e s e n s e

e x p e r ie n c e s in t h e i r t o t a l i ty , a n d , o n t h e o t h e r h a n d , t h ea c c o m p l i s h m e n t o f t h is a i m by the use of a minimum of primaryconcepts and relations. ( S e e k i n g , a s f a r a s p o s s i b l e , l o g i c a lu n i t y i n t h e w o r l d p i c t u r e , i . e . p a u c i t y i n l o g i c a l e l e m e n t s . )S cie nc e. c o n c e r n s t h e t o t a l i t y o f t h e p r i m a r y c o n c e p t s , i .e .c o n c e p t s d i re c t l y c o n n e c t e d w i t h s e n se e x p er ie n c e s , a n dt h e o r e m s c o n n e c t i n g t h e m . I n i ts f ir st s t a g e o f d e v e l o p m e n t ,s c ie n c e d o e s n o t c o n t a i n a n y t h i n g e lse . O u r e v e r y d a yt h i n k i n g is s a ti sf ie d o n t h e w h o l e w i t h t h i s le v e l. S u c h as t a t e o f a ff a ir s c a n n o t , h o w e v e r , s a t i s f y a s p i r i t w h i c h isr e a ll y s c i e n ti f i c al ly m i n d e d ; b e c a u se , t h e t o t a l i t y o f c o n c e p t sa n d r e la t io n s o b t a i n e d in t h is m a n n e r is u t t e r l y l a c k i n g inlo g ic a l u n i t y . I n o r d e r t o s u p p l e m e n t t h i s d e f ic ie n c y , o n ei n v e n t s a s y s t e m p o o r e r in c o n c e p t s a n d r e la t io n s , a s y s t e m


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March, 1936.] PH YS ICS AND RE AL ITY . 353retaining the primary concepts and relations of the " firstlayer " as logically derived coneepts and relations. This new" secondary sys tem " pays for its higher logical uni ty byhaving, as its own elementary concepts (concepts of thesecond layer), only those which are no longer directly con-nected with complexes of sense experiences. Fu rt he r strivingfor logical unity brings us to a tertiary system, still poorer inconcepts and relations, for the deduction of the concepts andrelations of the secondary (and so indirectly of the primary)layer. Thus the story goes on un ti l we have arrived at asystem of the greatest concei+able unity, and of the greatestpoverty of concepts of the logical foundations, which arestill compatible with the observation made by our senses.We do not know whether or not this ambition will ever resultin a definite sys tem. If one is asked for his opinion, he isinclined to answer no. While wrestling with the problems,however, one will never give up the hope that this greatest ofall aims can really be attained to a very high degree.An adherent to the theory of abstraction or inductionmight call our layers " degrees of abstraction "; but, I do notconsider it justifiable to veil the logical independence of theconcept from the sense experiences. The relation is notanalogous to that of soup to beef but rather of wardrobenumber to overcoat.The layers are furth ermor e not clearly separated. It isnot even absolutely clear which concepts belong to the primarylayer. As a mat te r of fact, we are dealing with freely formedconcepts, which, with a certainty sufficient for practical use,are i ntuit ively connected with complexes of sense experiencesin such a manner that, in any given case of experience, thereis no uncertainty as to the applicability or non-applicabilityof the sta tement . The essential thing is the aim to representthe multitude of concepts and theorems, close to experience,as theorems, logically deduced and belonging to a basis, asnarrow as possible, of fundamental concepts and fundamentalrelations which themselves can be chosen freely (axioms).The liberty of choice, however, is of a special kind; it is notin any way similar to the liberty of a writer of fiction.Rather, it is similar to that of a man engaged in solving a welldesigned word puzzle. He may, it is true, propose an y word


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354 A L B E R T E I N S T E I N . [ J . F . I .as the solution; but, there is only one word which reallysolves the puzzle in all its forms. It is an ou tcome of faiththat n atu re - - as she is perceptible to ou r five senses - - takesthe cha rac ter of such a well formulated puzzle. The suc-cesses reaped up to now by science do, it is true, give a cer tainencouragement for this faith.The multitude of layers discussed above corresponds tothe several stages of progress which have resulted from thestruggle for un ity in the course of development. As regardsthe final aim, intermediary layers are only of temporarynature. Th ey must eventually disappear as irrelevant. Wehave to deal, however, with the science of today, in whichthese strata represent problematic partial successes whichsupport one another but which also threaten one another,because today's systems of concepts contain deep seated in-congruities which we shall meet later on.It will be the aim of the following lines to demonstratewhat paths the constructive human mind has entered, inorder to arrive at a basis of physics which is logically as uni-form as possible.

2 . M E C H A N I C S A N D T H E A T T E M P T S T O B A S E A LL P H Y S I C S U P O N I T .An impor tan t proper ty of our sense experiences, and, moregenerally , of all of our experience, is its time-like order. Thiskind of order leads to the mental conception of a subjectivetime, an ordinating scheme for our experience. The sub-

jective time leads then through the concept of the bodilyobject and of space, to the concept of objective time, as weshall see later on.Ahead of the notion of objective time there is, however,the concept of space; and, ahead of the latter we find theconcept of the bodily object. The lat ter is direc tly connectedwith complexes of sense experiences. It has been pointedout that one property which is characteristic of the notion" bodily object " is the proper ty which provides tha t weco6rdinate to it an existence, independent of (subjective)time, and independent of the fact that it is perceived by oursenses. We do this in spite of the fact tha t we perceivetemporal alterations in it. Poincarfi has jus tly emphasizedthe fact that we distinguish two kinds of alterations of the


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March, I936.] PH YS IC S AND REAL ITY . 3 5 5

b o d i l y o b j e c t , " c h a n g e s o f s t a t e " a n d " c h a n g e s o f p o s i t i o n . "T h e l a t t e r , h e r e m a r k e d , a r e a l t e r a t i o n s w h i c h w e c a n r e v e r s eb y a r b i t r a r y m o t i o n s o f o u r b o d i e s .

T h a t t h e r e a r e b o d i l y o b j e c t s t o w h i c h w e h a v e t o a s c r ib e ,w i t h i n a c e r t a i n s p h e r e o f p e r c e p t i o n , n o a l t e r a t i o n o f s t a t e ,b u t o n l y a l t e r a t i o n s o f p o s i t io n , is a f a c t o f f u n d a m e n t a l i m -p o r t a n c e f o r t h e f o r m a t i o n o f t h e c o n c e p t o f s p a c e ( in a c e r t a i nd e g r e e e v e n f o r t h e j u s t i f i c a t i o n o f t h e n o t i o n o f t h e b o d i l yo b j e c t i t s e lf ) . L e t u s c a ll s u c h a n o b j e c t " p r a c t i c a l l y r i g i d . "

I f, a s t h e o b j e c t o f o u r p e r c e p t i o n , w e c o n s i d e r s i m u l -t a n e o u s l y ( i .e . a s a s i n g le u n i t ) t w o p r a c t i c a l l y r ig i d b o d i e s ,t h e n t h e r e e x i s t fo r t h is e n s e m b l e s u c h a l t e r a t i o n s a s c a n notp o s s i b ly b e c o n s i d e r e d a s c h a n g e s o f p o s i t i o n o f t h e w h o l e ,n o t w i t h s t a n d i n g t h e f a c t t h a t t h i s is t h e c a se f o r e a c h o n e o ft h e t w o c o n s t i t u e n t s . T h i s l e a d s t o t h e n o t i o n o f " c h a n g eo f r e l a t i v e p o s i t i o n " o f t h e t w o o b j e c t s ; a n d , i n t h i s w a y a l s ot o t h e n o t i o n o f " r e l a t i v e p o s i t i o n " o f t h e t w o o b j e c t s . I t isf o u n d m o r e o v e r t h a t a m o n g t h e r e l a t i v e p o s i t i on s , t h e r e iso n e o f a s p ec i f ic k i n d w h i c h w e d e s i g n a t e a s " C o n t a c t . " 1P e r m a n e n t c o n t a c t o f t w o b o d i e s i n t h r e e o r m o r e " p o i n t s "m e a n s t h a t t h e y a r e u n i t e d a s a q u a s i r ig id c o m p o u n d b o d y .I t is p e r m i s s ib l e t o s a y t h a t t h e s e c o n d b o d y f o r m s t h e n a( q u as i r ig id ) c o n t i n u a t i o n o n t h e f ir s t b o d y a n d m a y , i n i tst u r n , b e c o n t i n u e d q u a s i r i g i d ly . T h e p o s s i b i l i ty o f t h e q u a s ir ig id c o n t i n u a t i o n o f a b o d y is u n l i m i t e d . T h e r e a l e s s e n c eo f t h e c o n c e i v a b l e q u a s i r ig i d c o n t i n u a t i o n o f a b o d y B 0 i s t h ei n f in i t e " s p a c e " d e t e r m i n e d b y i t .

I n m y o p in i o n , t h e f a c t t h a t e v e r y b o d i l y o b j e c t s i t u a t e din a n y a r b i t r a r y m a n n e r c a n b e p u t i n to c o n t a c t w i t h t h eq u a s i r ig id c o n t i n u a t i o n o f a p r e d e t e r m i n e d a n d c h o s e n b o d yB 0 ( b o d y o f r e l a t i o n ) , t h i s f a c t is t h e e m p i r i c a l b a s is o f o u rc o n c e p t i o n o f s p a c e . I n p r e - s c i e n t i f i c t h i n k i n g , t h e s o li de a r t h ' s c r u s t p l a y s t h e r Sl e o f B 0 a n d i ts c o n t i n u a t i o n . T h ev e r y n a m e g e o m e t r y i n d i c a t e s t h a t t h e c o n c e p t o f s p a c e isp s y c h o l o g i c a l l y c o n n e c t e d w i t h t h e e a r t h as a n a s s ig n e d b o d y .T h e b o l d n o t i o n o f " s p a c e " w h i c h p r e c e d e d a l l s c i e n ti f ic

i It is in the nature of things that we are able to talk about these objectsonly by means of concept s of our own creation, con cepts which themselves arenot subj ect to definition. It is essential, however, th at we make use only of suchconcep ts concerning whose cogrdination to our experience we feel no d oubt.


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