8/13/2019 Action at a Distance in Classical Physics - Mary B Hesse

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Action at a Distance Classica Physics

y y Hess *

T HEl tic a m that "ma e ca n ac where it is is e e ve y genera me ap y a pri cipIes f und i s e e f e e eve -h ce tu y wh b e he re ev ce f cie c e ry eve w e he

me apby i e ee dis ded. G e 5 c pri cipIes ave tu the eve m hysics: f exam e, he c se va o m otO y a d L i z w ic w ge e iz a d g ve preci e n n tee e tu y as ct e e c se a i D e er ; a d e

pri cip e ha oa w ks y e sh r t r w ic was hai e y Mat s as a metap i p i pIe s s thy f sup eme Be g a dw e d t y va ia i a metb d i ics a d dy amics

We may ega these me aphys c s a eme s as ge e a za i s f mm ex e e ce r m a f m ar s ck eas a ie a aJ gic y e ame s ruc re a re. is ey a ike scie c y-

p hes , t ey ac the si f a g y e and are a e C

va us i er e a s de e i g n he y e e y i whi h th y a e u dy are f he ative y ke hyp theses u are ur si f scie ce nt w ch he fac are ma e may

i es ske ch ar he h s ca a gr u d e th se pri cipIes,ame y, e ege m ss i ity a a a dista ce a d try t nter-re e f e c ve s es ha have ari e r u d i , t m f riva

th ries u i t rms f e c ice f s ta e m e s r a guef r he d crip hysi a h me a

t has cha ac e s c hys cs ha s y a i s w c pr -

u e r te p d e m a are c i ere c da es r a-me ex a i s Acti s nv vi g cha ge f e tie such s um a em ra e, are ex a e te ms m i a e ve tb r w ds mec a ics r 1 y vi e c categ rie hysics. T e ty s f ac i e a mi te mecha cs were f be e-s ed at the eg i g the m e cie c p i he ec s x p a the c ge m ti d y y c mmun ca i r m si e

y a y i ate wer s vi g w h es thems ves gwcr its Kep er with he m me s s pr si g ha i rea i g

hysics the w r a ima s u e y e w r : the w r sha e c c pti vi a e er pr u g qu ta ive ha ges sh u e e- p a y at f m c ica e . duci g ua ti tive c a ges

of L di England. TI I (O o d, '95) p . e .

337

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MARY 8. HESSE

wo ld sh w n e iably t at a phys ca ag n y ist d in he ur 1e e of force." h

( ) The ac n of gravity is e nd upon t e m ss 01 b t reac ng par esan t ei stanc apart ty s i t s of aUra in; a g t

hv n eJ 1 ny h si by " c t p of t ic i5c 0 btwe o em, b a pur c t r a at a sace, and oe eefoe p t t e "h c y e J ke nba lt.

Sec w t egard to adia on:( ) Lines rad atio are a e by t e prop s 01 he nt ve ng medium

both n c r a tu e and in tra sverse r enta on a ou thei a s ( ty)( ) The re re time f r he r p opa atio

( ) h y are n t depe ent upon a s d a on arti eHe e we btai t e high st p f t a th g no h ng ponde a e , yett e ne of o ce have a hys ca ex s ence d pe ent, in a m e f t eb y r at g o of h e b y receiv ng e rays " 2{

d w t egar l e ect ic i d ct o( nes f e ect c n ct n are a ted by he a er a e m, t s

ot cert n w e her, n a vac m, the w be straig ike ho orav ty o cu e N c it on 01 o ar ty s been obs ved

() No t me has n s o l b re ire o he r prop gatio( ii A co d eact g rti e s r q r d

Fou w t reg r to e ect ic c rrent( ) Cu ent i a ecte y the me m as r ga ds r t o a q ant ty a d

s nt a y re ated t a mteial med um( i Time s req r f r prop atio even n goo co d cto s

( i e nes of fo are e t e m ted s i a isch ge, o e e s a con-t n o In t ca es he cu rent epe s w e tremit es as fo

nsta ce tw ch rge co cto s, r t e p at s o a vo a c c !e e are t s t ee y s o fo ces erte over a d stance

G avity whe e p opaga f the f rce y phys c i e th ough t e nte -med at sp ce s ot supp sed to e ist RadiatjQn w ere he p op at on do s ist an where the pro a ng neor ay , nc p u has ste ce i depen ent eit e t s rc e r erminatio an,

Ectry, wh re t e p p gat ng p ce h nte ne ate s ence e aray u at he s ame time de en s up n h e t em es of he ne o fo 25I ma etic act n e a y the e? Have t e ines of mag e c o ce a

phys c e st n an f so, s i sta c e 1ect ic in uct n o y amic eI ., p. 40. D Ibid., p. 411.

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AC ON AT A DISTA CE 347 a elect c cur e t? F y a sw s h s thr q es ons in c of mag etic ines o orc as fo ows:

( ) T ey ave ot show o a ct a y way by any medium o hert a ron. On t e o he d t he erna ines mus bec rve he of a ectangula bar et n vacuum, si ce y eg at one le an en at he o h r, and a a ay "can o o c ve cu v l nes of fo ce w t o cond t ons o a p s a ex stence ha ermed ate s e f tbey st it not by a s e sion o cl s, s thec e of st c r ct o , b t by he cond t on o s a f f om5uch ma er al ar c es 2

ii No m as ee s ow o be ed o o t o o mag c act o( h l s a e e nde o opp s ole at th trem t es Mag ic

ines of force ave ma y o ies c mo w th os of elect ic duction a d rent, d can obably be sa d o be "rea t e s me5ense he e ev e e o Fa aday takes t be t c vat re, an e ac b t cu rent uce in a cu t by mere motion in a magnet eld He ema ns agn c to he e state o ma te o ae he wh c accou ts or em, w ther a c e t o a st ess o any o e m dicat o o t e med m

Whe Ke vin s owed t e m t at c va e ce of va o s way o ese t g mag e ic a o an ma ema ca ana w en eat ow cur

e t ow a e ct and mag e c of force, Fa aday ec e h mselfs reng hened in s v ew t at e es of orce e es nt 0me h g hysica y ea ; o er wor s he was epa ta e mat ematica ana o w ho he hy ca ess as evidence fo p y a eality is nte es ng onote, o, ha he re are o s ea o p ys r y n conn ct o w th ao i o o space f e f om mat a art cles I s ite o t e in

eas ng mec an za on o ys s, he ot o 0 "r y was se om whol yr tr ed matte - -mot on

Begi n g w h t e wo o a ay a s ma hemat ca s cc rs onem s d st guis ea ly b tween wo way of o e ing act o at a sta ce, way wh h may be c es ect vely t e m anica ob em and ma hema ca p em

he me an cal ob em s inher t from t e phy o he seve n hce t y and o ns t e u s io w ave en conside e abo e abo he u t ma e nature o mat e an ae her an of he r man e of p pagating act o AH he m orta t at em t to 8we h s ue ion we e t ms 0 a o s bst ce aving mechan a ro e ies ext s o , a on motionm orce In t e ine centu y m an ca mo e s 0 heo ies are stg t, b s c ear t at t ms o no e t e m c o

l o ac on s possible T e r o fo s m a models a p 4 -

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MARY B. H SSE

no lo ge t ought 1 iteraJ desc iptions e ities e st g ture b to Jy te p ta o s, s o m chan dev ces o p en en t a a edes r ed mat ema ic 1y b t wh ul ima e n t e ca Dot e ega ded ascrudely m caJ.

Take o e ple Maxwell's mec a icaJ m e o the elec o g e ic thHe a o n s o he p o p ion o elect e ic e s by a q asi-ma e ialelas c me m in wh ch tubes 1 mag e ic fo ce a e vo lamen s ca si gension the ed um Jong he en h and p e s e a a ly he vo ex

mo o s m de si e y "id e pa es etw o e vo and ano be he ux o these p t cles iD a co duc or rep ese ts electr c current d theird splac ment a sula g med um p ces d ele c e ec s Th s m eapp es to so-cal ed r e sp o a e as w as to e t rio 1 mata d Ma w sh e a h s a ions 1 he e ec Det c e d c e d

ived rom it g vi g the p tion o lect omag et c d t b nc w h evel y o I gh is model we e ended as a d sc ip io 1 the u ima e p t c1es 1

u e it wo d e di c t to say whe he i nvolve ion at a d sta c oTbe eq ations o he m e a e hose 1 a co n ous e c u d med um

b the ques ion o whe he th s m i m is u imately co nuous o is e ie u d ded b i de s o mo e det led nowledge o h moco s tu o 1 ma te a d ae he ma er d ethe l ma ely consis 1d sc e e s mp e a oms e cha s a e tha so e tio at a sta ce ove

a omic d s ance a le wiI have t be pos a d; otherw se it ecomes imposs le to co o the c hes on o s But M xwe is co ce e o yo e p ain a o e w D ista t d es wi h u s mi g e e ste oo ce ca b e 1 g direc y at sensi e di c s f On the ques ion owhe e the is disc ete o co nuous M e11 em ks:

It is e me e t m m s e sti mp i e p f m i t co ti o t om se p te p t

i id ut e e o h n c se e n pp g e t r omp s J t b p e e

e l i t i t e m i i i ise t e m i m e y s A med m, e e umo e s $ i ! d si , m e deed e y t m i Si W 's e i tex-m e e i a t iqe e e . . i p l mo a st i s 8

Th s II s a e he so 1 d cu y h t ises w e one at mp s t takmec a ical mode s s i e desc ip ons 1 a u nd ng om t em

a swe to e qu s on wheth ac ioD a a d s an c s n a e o notOne ge erally b omes involv n a i te eg e s ioD wee b d es aDite is a s is p ain co inuous s ess the inte ve ing me mth s st ess s e pla ed the mo a co s itu o o e med um wh ch mi se invo ve ion at a d s n e a d so o The e e o he e amp 1 he

"A dynam tory of e e q e O L 1 $> . . 7 4

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AC ON A A S ANC 349sa e sor : Helm o tz in r u < term en i g v sc s ty n o a-t ons 01ae mo ion, b t K lv po nted o 2' cosi y p d es he na o o of pa t c s t e se ves a d p s m ly i ou orc e weeae pa e wo d t ea s to be tak te a y nvol h rma

mot o of a t cl w thin th p ticl . A in Lo e t s eo y o e c e fo e o a mac osc c c a t c s r la y or es o ito s itu t lect s a d o es o cha ges ! ar spok no "

S ch l s eg ate t s mer y a way s g a o tbe ao te a ema ica eq a ions u no sol o problem ac o at

a d s ce s fou d by g s echan a e l erally Maxw lim el is ca e t x la t e s at o h mo a rt mo

[ r e ow e i e ' c p f a mec n i of v ew o ete e wh t te io s mot o s 1 e b e of du ! me a h me o 1T e e tio r e g t m t o n w h t f y e n n m y wh t wkw rd ot r g t forwar

m e o n n i ing .A a la e er

ave me em t d i e rti i o motia par lar of $t i r t men Ine t r vo y ypot o j d i s ng s

t d e el t ty e e e k ow e w sh me e y d c m d f the e o m w ch w J s st m i de s d n the sch rase p e o s de e Utr ve o

In ng o e E e of ! e , eve I e stl te y

On he o e ha th a h matica a of he ro em o ac o a as nce a e i c eas ngly or n as t e t e of mechan al els

b e s d The ma hemat caI roble may e aid ha ee that o re e p e g ac o at a stan e an action y o tac s tha co cep s a ned ele a o a phy s wh e f n amen s we e

co g mo and mo e a s ra t a d ess e ha ca a who e s ctU e was mo e eas y u derstood terms o ma hema cs of m ha ic d Is

Ke vin a s rie of a ema ca a rs eg n ng n 8 2 thatsame a h cal fo malism co d e s r he laws of u

ow o h ow o e ec c an agne ic ph ome a a o astici y usa so rc o u o o hea s he ana ogue o a lec c c a ge m t c e

so c of el c c rr ; o ow a a ogu o of fo c

B (C m )91

L t T c (L19), p. 13 14

u 01 lo" S