,,! ,,romanes ,,lecture                 
#aibb                                   
,,!                            ,,!ory   
,,( ,,relativity                        
& its                      ,influ5ce on 
,sci5tific ,?\ght                       
,,by                           ,,ar?ur  
,,/anley ,,edd+ton                      
,m4,a41 ,f4,r4,s4               ,plumian
 ,pr(essor ( ,a/ronomy1 ,cambridge      
,presid5t ( ! ,royal ,a/ronomical       
,society                                
,,deliv]$                        ,,9 ,,!
 ,,%eldonian ,,!atre                    
#bd ,,may1 #aibb                        
,,ox=d                          ,,at ,,!
 ,,cl>5don ,,press                      
#aibb          ,has n a deep] m$itation 
taught c]ta9 ( e climate &  age1 t ! :]e
 & ! :5 s my/]i\sly insep>able  f all   
our ?\ghts1 are b sup]ficial t]re/rial  
adhesions to  ?\ght8                    
,,c>lyle1 ,s>tor ,res>tus4              
,ox=d ,univ]sity ,press          ,,!    
,,!ory ,,( ,,relativity      ,9 ! days  

be=e ,cop]nicus ! e>? 01 s x seem$1 an  
immovable  f\ndation on :i* ! :ole      
/ructure ( ! heav5s 0 re>$4 ,man1       
fav\rably situat$ at ! hub ( ! univ]se1 
might well expect t  to him ! s*eme (   
nature w\ld unfold itself 9 its simple/ 
aspect4  ,b ! behavi\r ( ! heav5ly      
bodies 0 n at all simple2 & !  planets  
lit]ally loop$ ! loop 9 fanta/ic curves 
call$ epicycles4  ,! cosmogoni/ _h to   
fill ! skies ) sph]es revolv+ ^u  sph]es
 to be> ! planets 9 _! appo9t$ orbits2 &
 :eels 7  add$ to :eels until ! music ( 
! sph]es seem$ well-nigh dr[n$  9 a     
discord ( :irl+ ma*9]y4 ,!n came "o ( ! 
great  revolutions ( sci5tific ?\ght1   
:i* swept aside ! ,ptolemaic  sy/em (   
sph]es & epicycles1 & reveal$ ! simple  
plan ( !  sol> sy/em :i* has endur$ to  
?is day4    ,! revolution consi/$ 9     
*ang+ ! view-po9t f :i* !  ph5om5a 7    
reg>d$4 ,z pres5t$ to ! e>? ! track ( a 
planet  is an elaborate epicycle2 b     
,cop]nicus bade u transf] ourselves to  
! sun & look aga94 ,in/ead ( a pa? )    

loops & nodes1 !  orbit is n[ se5 to be 
"o ( ! mo/ elem5t>y curves--an ellipse4 
,we h to realize t ! little planet on   
:i* we /& is ( no  great acc\nt 9 !     
g5]al s*eme ( nature2 to unravel t s*eme
 we  mu/ fir/ disemb>rass nature ( !    
di/ortions aris+ f ! local  po9t ( view 
f :i* we obs]ve x4 ,! sun1 n ! e>?1 is !
  real c5tre ( ! s*eme ( ?+s--at lea/ ( 
^? ?+s 9 :i*  a/ronom]s at t "t _h      
int]e/$ !mselves--& by transf]r+  our   
view-po9t to ! sun ! simplicity ( !     
planet>y sy/em becomes  app>5t4 ,! ne$ =
 a cumbr\s ma*9]y ( sph]es & :eels has  
disappe>$4    ,e "o n[ admits t !       
,ptolemaic sy/em1 :i* reg>d$ ! e>?  z ! 
c5tre ( all ?+s1 belongs to ! d>k ages4 
,b to our dismay  we h discov]$ t ! same
 geoc5tric outlook /ill p]meates  mod]n 
physics ?r\gh & ?r\gh1 unsuspect$ until 
rec5tly4 ,x has  be5 left to ,e9/e9 to  
c>ry =w>d ! revolution begun by         
,cop]nicus--to free our conception (    
nature f ! t]re/rial bias  import$ into 
x by ! limitations ( our e>?b\nd        

exp]i5ce4 ,to  a*ieve a m neutral po9t (
 view we h to imag9e a visit to "s  o!r 
heav5ly body4 ,t is a !me :i* has       
attract$ ! popul>  noveli/1 & we (t5    
smile at 8 mi/akes :5 soon] or lat] he  
=gets :]e he is suppos$ to be & end[s 8 
voyag]s ) "s  purely t]re/rial appanage 
impossible on ! /> !y are visit+4  ,b   
sci5tific m51 :o h n ! noveli/'s lic5ce1
 h made !  same blund]4 ,:51 foll[+     
,cop]nicus1 !y /ation !mselves on !     
sun1 !y d n realize t !y mu/ leave beh9d
 a c]ta9 purely  t]re/rial appanage1    
namely1 ! frame ( space & "t 9 :i* m5   
on ?is e>? are accu/om$ to locate !     
ev5ts t happ54 ,x is  true t ! obs]v] on
 ! sun w /ill locate 8 exp]i5ces 9 a    
frame ( space & "t1 if he uses ! same   
faculties ( p]ception &  ! same me?ods (
 sci5tific measurem5t z on ! e>?2 b !   
sol> frame ( space & "t is n precisely !
 same z !  t]re/rial frame1 z we %all   
pres5tly see4    ,i ?9k y w readily     
und]/& :at is meant by a frame ( space  
& "t4 ,x is ! sy/em ( location to :i* we

 appeal :5 we /ate1  = example1 t "o    
ev5t is #ajj miles di/ant f & #aj h\rs  
lat]  ?an ano!r4 ,! t]ms space & "t h n 
only a vague descriptive  ref]5ce to a  
b\ndless void & an ev]-roll+ /ream1 b   
d5ote an  exact quantitative sy/em (    
reckon+ di/ances & "t-int]vals4         
,e9/e9's fir/ great discov]y 0 t !re are
 _m su* sy/ems (  reckon+--_m possible  
frames ( space & "t--exactly on all f\rs
  ) "o ano!r4 ,no "o ( ^! c be di/+ui%$ 
z m  fundam5tal ?an ! re/2 no "o frame r
 ?an ano!r c be  id5tifi$ z ! scaffold+ 
us$ 9 ! con/ruction ( ! _w4 ,&  yet "o (
 !m does pres5t itself to u z be+ !     
actual space &  "t ( our exp]i5ce2 & we 
recoil f ! o!r equival5t frames  :i*    
seem to u artificial sy/ems 9 :i*       
di/ance & duration are  mix$ up 9 an    
extraord9>y way4 ,:at is ! cause ( ?is  
invidi\s  selection8 ,x is n det]m9$ by 
any?+ di/9ctive 9 ! frame2 x  is det]m9$
 by some?+ di/9ctive 9 u--by ! fact t   
our  exi/5ce is b\nd to a p>ticul>      
planet & our motion is ! motion  ( t    

planet4 ,nature (f]s an inf9ite *oice ( 
frames2 we select  ! "o 9 :i* we & our  
petty t]re/rial conc]ns take ! mo/      
di/+ui%$ position4 ,our mis*iev\s       
geoc5tric outlook has cropp$  out aga9  
unsuspect$1 p]suad+ u to insi/ on ?is   
t]re/rial  space-"t frame :i* 9 ! g5]al 
s*eme ( nature is 9 no way  sup]ior to  
o!r frames4    ,! m closely we exam9e ! 
processes by :i* ev5ts are assign$  to  
_! positions 9 space & "t1 ! m cle>ly d 
we see t  our local circum/ances play a 
consid]able "p 9 x4 ,we h no m  "r to   
expect t ! space-"t frame on ! sun w be 
id5tical  ) our frame on ! e>? ?an to   
expect t ! =ce ( gravity  w be ! same   
!re z "h4 ,if !re 7 no exp]im5tal       
evid5ce  9 support ( ,e9/e9's !ory1 x   
w\ld nev]!less h made a  notable advance
 by expos+ a fallacy und]ly+ ! old] mode
 (  ?\ght--! fallacy ( attribut+        
unque/ion+ly a m ?an local  significance
 to our t]re/rial reckon+ ( space & "t4 
,b !re  is abundant exp]im5tal evid5ce =
 detect+ & det]m9+ !  diff]5ce betwe5 ! 

frames ( diff]5tly circum/anc$ obs]v]s4 
,mu* ( ! evid5ce is too te*nical to be  
discuss$ "h1 & ,i c  only ref] to !     
,mi*elson-,morley exp]im5t4 ,i fe> t "s 
( y  mu/ be gett+ r tir$ ( !            
,mi*elson-,morley exp]im5t2 b  ^? :o g  
to a p]=mance ( ,hamlet h to put up ) ! 
,pr9ce  ( ,d5m>k4    ,?is fam\s exp]im5t
 is a simple te/ :e!r light travels at !
  same spe$ 9 two diff]5t directions4 ,=
 ?is purpose an app>atus is  con/ruct$ )
 two equal arms at "r angles1 provid+   
two equal  tracks = ! light4 ,a beam (  
light is divid$ into two p>ts s t  "o "p
 travels along "o arm & back1 & ! o!r   
along ! o!r  arm & back4 ,! two rays !n 
re-unite1 & by delicate int]f]5ce  te/s 
x is possible to tell if "o has be5     
delay$ m ?an !  o!r2 a delay ( less ?an 
a ?\s&-billion? ( a second c\ld be      
detect$4 ,! exp]im5t is simply a race   
betwe5 two light-rays )  equal tracks1 b
 po9t+ 9 diff]5t directions2 ! result   
turns out  to be a dead-heat4 ,at fir/  
sight ?is is j :at w\ld be expect$2  &  

"o almo/ wond]s :y x %\ld h be5 ?\ght   
wor? :ile to  try ! exp]im5t4 ,b        
,mi*elson1 l a good ,cop]nican1 _h      
/ation$  himself on ! sun to wat* !     
race2 accord+ly he realiz$ t !  app>atus
 0 be+ borne along by ! e>?'s orbital   
motion ) a  spe$ ( #bj miles a second4  
,consequ5tly ! light does n travel      
exactly ! d\ble l5g? ( ! arm2 />t+ at "o
 end x has to g  to ! turn+-m>k at ! o!r
 end :i* has mov$ on a little 9 !       
meantime2 !n x returns to ! place :i* ! 
/>t+-m>k has  travell$ to :il/ ! race is
 9 progress4 ,t does n add up to        
exactly ! d\ble-l5g? ( ! arm4 ,mak+ !   
calculations we easily  f9d t1 al?\gh ! 
two arms are equal1 ! two light-j\rneys 
are  unequal2 ! competitor ^: track lies
 9 ! l9e ( ! e>?'s  motion has ! long]  
j\rney1 & is at a disadvantage4 ,& yet  
accord+ to ! exp]im5t he does n suff] ! 
expect$ delay4 ,f  our /&po9t on ! sun1 
! exp]im5t seems to h gone wrong2       
,cop]nicus has met ) a rebuff1 &        
,ptolemy is triumphant4    ,b t is      

because we h n admitt$ ! full           
consequ5ces (  transf]r+ our /&po9t to !
 sun4 ,we h all ! :ile be5  keep+ "o    
foot on e>?4 ,( c\rse1 ! :ole exp]im5t  
turns on !  two arms hav+ be5 fir/      
adju/$ to p]fect equality4 ,?is c\ld    
only  be asc]ta9$ by exp]im5t2 & ! te/  
appli$ 0 to rotate !  app>atus ?r\gh a  
"r angle1 s t if1 = example1 ! j\rney 9 
! l9e ( ! e>?'s motion _h _h ! advantage
 ( ! %ort] arm  on "o occasion1 !       
transv]se j\rney w\ld h _h x on !       
repetition4 ,t is a p]fectly            
satisfactory te/ = a t]re/rial  obs]v]2 
to turn a rod f "o direction to ano!r is
 ! simple &  direct way ( m>k+ out equal
 l5g?s4 ,b ! te/ is n  satisfactory to  
an obs]v] on ! sun2 he w\ld n ?9k (     
attempt+  to p>tition equal l5g?s (     
space by means ( rods travell+ at #bj   
miles a second4 ,8 frame ( space--!     
space n only ( ref9$  measurem5t1 b also
 ( ! crud] measurem5ts made ) !         
s5se-organs ( 8 body :i* det]m9e 8      
p]ception ( space--is  p>tition$ by     

appliances at re/ relatively to him1    
e4g4 8 own eyes  & limbs4 ,l5g?s (      
objects c>ri$ on ! e>? mu/ be judg$ by  
him  accord+ to ! room !y occupy 9 8 own
 frame4 ,9 ! space ( !  t]re/rial obs]v]
 ! two arms ( ! app>atus 7 adju/$ to    
equal l5g?2 b 9 ! re-p>tition$ space ( !
 sol> obs]v] !y  may q well occupy      
unequal l5g?s1 & :5 we take ! view-po9t 
( an obs]v] on ! sun we mu/ n ov]look   
?is inequality4 ,?is  inequality is n s 
mu* an hypo!sis propos$ to acc\nt =     
,mi*elson's result z a direct d$uction f
 x4 ,! two light-j\rneys  7 f\nd to     
occupy equal times2 ?is cle>ly %[s t !  
arm 9 !  less fav\r$ direction is %ort] 
?an ! o!r s z to  c\nt]balance ! h&icap 
to :i* ,i h ref]r$4#a    ,:5 ! app>atus 
is turn$ ?r\gh a "r angle1 ! exp]im5t   
/ill  gives ! same result4 ,x does n    
matt] :i* ( ! two arms we place  9 ! l9e
 ( ! e>?'s motion2 t arm mu/ be %ort]   
?an !  o!r4 ,9 o!r words ea* arm mu/    
automatically contract :5 x is  turn$ f 
! transv]se to ! longitud9al position ) 

respect to  its l9e ( motion4 ,?is is ! 
fam\s ,fitz,gerald contraction ( a  mov+
 rod4 ,x is ( ! same am\nt :atev] !     
mat]ial ( ! rod1  & dep5ds only on !    
spe$ ( its motion4 ,= ! e>?'s orbital   
motion ! contraction am\nts to "o "p 9  
#bjj million2 9 fact !  e>?'s diamet] 9 
! direction ( its motion is always      
%ort5$ by  #b in*es1 ! transv]se diamet]
 be+ unaffect$4    ,?is contraction ( a 
mov+ mat]ial object 0 fir/ reveal$ to u 
by  ! ,mi*elson-,morley exp]im5t2 b x is
 n at all disagreeable to  !oretical    
anticipations4 ,we h to rememb] t a rod 
consi/s ( a  l>ge numb] ( molecules kept
 9 position by _! mutual =ces4 ,!  *ief 
=ce is ! =ce ( cohesion1 & !re is little
 d\bt t  ?is is ( electrical nature4 ,b 
:5 ! rod is set 9 motion1 !  electrical 
=ces inside x mu/ *ange4 ,= example1 ea*
 electric  *>ge :5 put 9 motion becomes 
an electric curr5t2 & !  curr5ts w ex]t 
magnetic attractions on ea* o!r :i* did 
n  occur 9 ! sy/em at re/4 ,"u ! new    
sy/em ( =ces !  molecules w h to f9d new

 positions ( equilibrium2 !y become     
diff]5tly spac$2 & x is !re=e n surpris+
 t ! =m (  ! rod *anges4 ,)\t go+ beyond
 ! classical laws ( ,maxwell we  c      
anticipate !oretically :at w be ! new   
equilibrium /ate (  ! rod1 & x turns out
 to be contract$ to ! exact am\nt       
requir$  by ! ,mi*elson-,morley result4 
,! contraction ( ! mov+ rod ought n to  
surprise u2 x w\ld be  mu* m surpris+ if
 ! rod 7 to ma9ta9 ! same =m 9 spite  ( 
! alt]ation ( ! electrical =ces :i*     
det]m9e ! spac+  ( ! molecules4 ,b !    
rem>kable ?+ is t ! contraction is  only
 app>5t accord+ to ! outlook ( ! sol>   
obs]v]2 & we on  ! e>?1 :o travel ) !   
rod1 _c appreciate x4 ,! fact t  !      
contraction happ5s to be v small is     
irrelevant4 ,= conv5i5ce  suppose t !   
e>?'s velocity is #h1jjj times fa/]1 s t
 !  contraction am\nts to some?+ l a    
half ! orig9al1 l5g?4 ,we  %\ld /ill    
fail to notice x 9 ev]yday life4 ,let u 
say t !  direction ( ! e>?'s motion is  
v]tically upw>ds4    ,i turn my arm f   

horizontal to v]tical & x contracts to  
half its  l5g?4 ,no1 y _c conv9ce me ,i 
am wrong2 ,i am n afraid ( a            
y>d-measure4 ,br+ "o & measure my arm2  
fir/ horizontally1 !  result is #cj     
in*es2 n[ v]tically1 ! result is        
#cj--;half-in*es6  ,because y mu/       
rememb] t y h turn$ ! scale into ! l9e  
( ! e>?'s motion s t ea* in*-division   
contracts to half an  in*4 ',b we c see 
t y\r arm does n contract4 ,are we n to 
tru/ our eyes8' ,c]ta9ly n1 unless y    
fir/ correct y\r visual  impressions = !
 contraction ( ! ret9a 9 ! v]tical      
direction1  & = ! effect ( our rapid    
motion on ! app>5t direction (          
propagation ( ! waves ( light4 ,y w f9d1
 :5 y calculate  ^! corrections1 t !y j 
conceal ! contraction4 ',b if !         
contraction takes place1 ought "o n to  
feel x happ5+ to ! arm8'  ,n necess>ily2
 ,i am an obs]v] on ! e>?1 & my feel+s l
  o!r s5se-impressions belong to !      
geoc5tric outlook on nature1  :i*       
,cop]nicus has p]suad$ u to ab&on4      

,take a pair ( compasses & twiddle !m on
 a %eet ( pap]4 ,is !  result+ curve a  
circle or an ellipse8 ,cop]nicus f 8    
/&po9t  on ! sun decl>es t ow+ to !     
,fitz,gerald contraction ! two  po9ts   
drew ne>] toge!r :5 turn$ 9 ! direction 
( ! e>?'s  orbital motion2 h5ce ! curve 
is flatt5$ into an ellipse4 ,b "h ,i    
?9k ,ptolemy has a "r to be he>d2 he    
po9ts out t f !  beg9n+ ( geometry      
circles h always be5 drawn ) compasses 9
  ?is way1 & t :5 ! ^w 'circle' is      
m5tion$ e intellig5t  p]son und]/&s t   
?is is ! curve meant4 ,! same p5cil l9e 
is  9 fact a circle 9 ! space ( !       
t]re/rial obs]v] & an ellipse  9 ! space
 ( a sol> obs]v]4 ,x is at ! same "t a  
mov+  ellipse & a /ation>y circle4 ,i   
?9k t illu/rates z well z  possible :at 
we mean by ! relativity ( space4    ,x  
is sometimes compla9$ t ,e9/e9's        
conclusion t ! frame (  space & "t is   
diff]5t = obs]v]s ) diff]5t motions t5ds
  to make a my/]y ( a ph5om5on :i* is n 
aft] all intr9sically  /range4 ,we h se5

 t x dep5ds on a contraction ( mov+     
objects  :i* turns out to be q 9        
accordance ) ,maxwell's classical  !ory4
 ,b ev5 if we h succe$$ 9 expla9+ x to  
ourselves  intelligibly1 t does n make !
 /atem5t any ! less true6 ,a new  result
 may (t5 be express$ 9 v>i\s ways2 "o   
mode ( /atem5t may  s\nd less my/]i\s2 b
 ano!r mode may %[ m cle>ly :at w  be ! 
consequ5ces 9 am5d+ & ext5d+ our k4 ,x  
is =  ! latt] reason t we emphasize !   
relativity ( space--t  l5g?s & di/ances 
diff] accord+ to ! obs]v] impli$4       
,di/ance  & duration are ! mo/          
fundam5tal t]ms 9 physics2 velocity1    
accel]ation1 =ce1 en]gy1 & s on1 all    
dep5d on !m2 & we c  sc>cely make any   
/atem5t 9 physics )\t direct or indirect
  ref]5ce to !m4 ,surely !n we c be/    
indicate ! revolution>y  consequ5ces (  
:at we h le>nt by ! /atem5t t di/ance & 
duration1 & all ! physical quantities   
d]iv$ f !m1 d n z  hi!rto suppos$ ref]  
to any?+ absolute 9 ! ext]nal _w1 b  are
 relative quantities :i* alt] :5 we pass

 f "o obs]v] to  ano!r ) diff]5t motion4
 ,! consequ5ce 9 physics ( !  discov]y t
 a y>d is n an absolute *unk ( space1 & 
t :at  is a y>d = "o obs]v] may be      
eighte5 in*es = ano!r obs]v]1  may be   
comp>$ ) ! consequ5ces 9 economics ( !  
discov]y t  a p\nd /]l+ is n an absolute
 quantity ( weal?1 & 9 c]ta9            
circum/ances may 'really' be sev5 &     
sixp5ce4 ,! !ori/ may  compla9 t ?is la/
 /atem5t t5ds to make a my/]y ( ph5om5a 
( curr5cy :i* h really an intelligible  
explanation2 b x is a  /atem5t :i*      
comm5ds itself to ! man :o has an eye to
 !  practical applications ( curr5cy4   
,ptolemy on ! e>? & ,cop]nicus on ! sun 
are bo? contemplat+  ! same ext]nal     
univ]se4 ,b _! exp]i5ces are diff]5t1 & 
x  is 9 ! process ( exp]i5c+ ev5ts t !y 
become fitt$ into  ! frame ( space &    
"t--! frame be+ diff]5t accord+ to !    
local circum/ances ( ! obs]v] :o is     
exp]i5c+ !m4 ,t1 ,i  take x1 is ,kant's 
doctr9e1 ',space & "t are =ms (         
exp]i5ce4'  ,! frame !n is n 9 ! _w2 x  

is suppli$ by ! obs]v] &  dep5ds on him4
 ,& ^? relations ( simplicity1 :i* we   
seek :5 we  try to obta9 a compreh5sion 
( h[ ! univ]se functions1 mu/ lie 9  !  
ev5ts !mselves be=e !y h be5 arbitr>ily 
fitt$ into !  frame4 ,! mo/ we c hope = 
f any frame is t x w n h  di/ort$ !     
simplicity :i* 0 orig9ally pres5t2 :il/ 
an  ill-*os5 frame may play havoc ) !   
natural simplicity ( ?+s4  ,we h se5 t !
 simplicity ( planet>y motions 0 obscur$
 9  ,ptolemy's frame1 & became app>5t 9 
,cop]nicus's frame4 ,b =  ord9>y        
t]re/rial ph5om5a ! position is rev]s$ &
 ,ptolemy's  frame all[s _! natural     
simplicity to become app>5t4 ,9         
,cop]nicus's frame ! mo/ simple ph5om5a 
are br\ght ab\t by highly  complicat$   
processes :i* mutually cancel "o ano!r4 
,ord9>y  objects contract & exp& z !y   
are mov$ ab\t1 & ! *anges are  conceal$ 
by an elaborate conspiracy 9 :i* all !  
quantities (  nature--electrical1       
optical1 me*anical1 gravitational--h    
jo9$4 ,9  ,cop]nicus's frame we h a     

great complication ( description :i* has
  no c\nt]p>t 9 any?+ occurr+ 9 !       
ext]nal _w2 because !  t]ms ( our       
description ref] to ! irrelevant process
 ( fitt+ into  ! select$ frame ( space &
 "t4 ,?is elaborate ,cop]nican s*eme  r 
rem9ds "o ( ! s*emes ( ! ,:ite ,knight--
          ,b ,i 0 ?9k+ ( a plan         
,to dye "o's :isk]s gre51      ,& always
 use s l>ge a fan        ,t !y c\ld n be
 se54      ,we d n d5y ! subtlety & !   
rem>kable effici5cy ( ! plan2  b we may 
be all[$ to "q :e!r x is ! simple/      
int]pretation ( ! drab monotony ( ! face
 ( nature pres5t$ to  u4 ,! simple fact 
is t a t]re/rial or ,ptolemaic frame    
fits  naturally ! t]re/rial ph5om5a1 & a
 sol> or ,cop]nican frame  fits !       
ph5om5a ( ! sol> sy/em2 b we _c make "o 
frame  s]ve = bo? )\t introduc+         
irrelevant1 complications4    ,we g     
beyond ,cop]nicus n[adays1 & are n      
cont5t ) a visit to  ! sun4 ,:y *oose ! 
sun r ?an "s o!r /> 9 ord] to  obta9 an 
undi/ort$ view ( ?+s8 ,! a/ronom] n[    

places himself  s z to travel ) ! c5tre 
( gravity ( ! /ell> univ]se1 &  is n ev5
 !n q satisfi$4 ,! physici/ dreams ( a  
l& (  ,weissni*two1 :i* %all be truly at
 re/ 9 ! e!r4 ,we realize !  di/ortion  
import$ into ! _w ( nature by ! p>o*ial 
/&po9t  f :i* we obs]ve x1 & we try to  
place ourselves s z to  elim9ate ?is    
di/ortion--s z to obs]ve t :i* actually 
is4 ,b  x is a va9 pursuit4 ,:]ev] we   
pit* our cam]a1 ! photograph is         
necess>ily a two-dim5sional picture     
di/ort$ accord+ to ! laws (  p]spective2
 x is nev] a true semblance ( ! build+  
itself4    ,we mu/ try ano!r plan4 ,i d 
n ?9k we c ev] elim9ate  altoge!r !     
human elem5t 9 our conception ( nature2 
b we c  elim9ate a p>ticul> human       
elem5t1 namely1 ?is framework ( space  &
 "t4 ,if our ?\ght mu/ be an?ropoc5tric1
 x ne$ n be  geoc5tric4 ,nor are we     
p]man5tly bett] (f if we m]ely sub/itute
  ! space-"t frame ( "s o!r /> or /&>d (
 motion4 ,we mu/  leave ! frame entirely
 indet]m9ate4 ,:5 we d t1 we f9d t  ! _w

 common to all obs]v]s--9 :i* ea* obs]v]
 traces a  diff]5t space-"t frame       
accord+ to 8 own outlook--is a _w (  f\r
 dim5sions4 ,:5 we look at any object1  
say a *air1 ! impression  on our eyes is
 a two-dim5sional picture dep5d+ on !   
position f  :i* we are look+2 b we h no 
difficulty 9 conceiv+ ( !  *air z a     
solid object1 n to be id5tifi$ ) any "o 
( our  two-dim5sional pictures ( x1 b   
giv+ rise !m all z ! position  ( !      
obs]v] is v>i$4 ,we mu/ n[ realize t ?is
 solid *air 9  ?ree dim5sions is itself 
only an appe>ance1 :i* *anges accord+   
to ! motion ( ! obs]v]1 & t !re is a    
sup]-object 9  f\r-dim5sions1 n to be   
id5tifi$ ) ! ?ree-dim5sional *air  9    
,ptolemy's s*eme1 or ! same *air 9      
,cop]nicus's s*eme1 b  giv+ rise to bo? 
^! appe>ances4 ,! syn!sis ( a           
?ree-dim5sional *air f a numb] ( flat   
pictures is easy to u  because we are   
accu/om$ to assume diff]5t positions 9  
rapid  succession2 inde$ our two eyes   
give u slightly diff]5t po9ts (  view   

simultane\sly4 ,by %e] necessity our    
bra9s h be5 =c$ to  con/ruct !          
conception ( ! solid *air to comb9e ^!  
*ang+  appe>ances4 ,b we d n v>y our    
motion to any appreciable ext5t &  our  
bra9s h n hi!rto be5 call$ ^u to comb9e 
! appe>ances  = diff]5t motions2 ?us !  
ef=t :i* we n[ ask ! bra9 to  make is a 
novel "o4 ,t expla9s :y ! result seems  
to transc5d our  ord9>y mode ( ?\ght4   
,! discov]y1 or "o %\ld r say !         
r$iscov]y1 ( ! _w (  f\r dim5sions is   
due to ,m9k[ski4 ,e9/e9 _h work$ out    
fully !  relations betwe5 ! frames (    
space & "t = obs]v]s )  diff]5t motions4
 ,to ! g5ius ( ,m9k[ski we owe !        
realization  t ^! frames are m]ely      
sy/ems ( p>titions arbitr>ily drawn     
across a f\r-dim5sional _w :i* is common
 to all obs]v]s4    ,!re is a /range    
delusion t ! f\r? dim5sion mu/ be some?+
  :olly beyond ! conception ( ! ord9>y  
man1 & t only !  ma!matician c be       
initiat$ into its my/]ies4 ,x is true t 
!  ma!matician has ! advantage ( und]/&+

 ! te*nical ma*9]y  = solv+ ! problems  
:i* may arise 9 /udy+ ! _w ( f\r        
dim5sions2 b z reg>ds ! conception ( !  
f\r dim5sions ( !  _w 8 po9t ( view is !
 same z t ( anybody else4 ,is x  suppos$
 t by int5se ?\ght he ?r[s himself into 
"s /ate (  trance 9 :i* he p]ceives "s  
hi!rto unsuspect$ direction  /ret*+ away
 at "r angles to l5g?1 bread?1 &        
?ickness8 ,t  w\ld n be mu* use4 ,! _w (
 f\r dim5sions1 ( :i* we are n[  speak+1
 is p]fectly famili> to ev]ybody4 ,x is 
obvi\s to e  "o--ev5 to ! ma!matician--t
 ! _w ( solid & p]man5t  objects has    
?ree dim5sions & no m2 t objects are    
arrang$ 9  a ?reefold ord]1 :i* = any   
p>ticul> individual may be analys$  into
 "r-&-left1 backw>ds-&-=w>ds1 up-&-d[n4 
,b x is no  less obvi\s to e "o t ! _w (
 ev5ts is ( f\r  dim5sions2 t ev5ts are 
arrang$ 9 a f\rfold ord]1 :i* 9 !       
exp]i5ce ( any p>ticul> individual w be 
analys$ into  "r-&-left1                
backw>ds-&-=w>ds1 up-&-d[n1             
soon]-&-lat]4  ,! subject ( our /udy is 

ext]nal nature1 :i* is a _w ( ev5ts1    
common to all obs]v]s b repres5t$ by !m 
diff]5tly 9 _!  p>o*ial frames ( space &
 "t2 x is obvi\s to ! mo/  commonplace  
exp]i5ce t ?is absolute _w conta9s a    
f\rfold  ord]4#b    ,! news t ! ev5ts   
ar\nd u =m a _w ( f\r dim5sions is z    
/ale z ! news t ,que5 ,anne is dead4 ,! 
reason :y ! relativi/  resurrects ?is   
anci5t truism is because x is only 9 ?is
 undissect$  comb9ation ( f\r dim5sions 
t ! exp]i5ces ( all obs]v]s  meet4 ,9   
our own exp]i5ce "o dim5sion is %>ply   
sep>at$ f !  o!r ?ree & is di/+ui%$ z   
"t2 b our exp]i5ce is solely  t]re/rial1
 & if we insi/ on build+ ! s*eme (      
nature on purely  t]re/rial exp]i5ce we 
are limit+ ourselves to ! m$iaeval      
geoc5tric sy/em ( ! _w4    ,we h be5    
accu/om$ to reg>d ! endur+ _w z compos$ 
( a  cont9u\s succession ( in/antane\s  
/ates1 z ?\gh ! _w (  ev5ts 7 /ratifi$4 
,ea* ev5t is suppos$ to lie 9 a def9ite 
in/ant or /ratum1 & ! ord]ly succession 
( ^! /rata makes up  ! :ole ( reality4  

,! in/ant 'n[' repres5ts "o su* /ratum  
runn+ ?r\gh\t ! univ]se4 ,inde$ we are  
accu/om$ to ext5d x  beyond ! univ]se1 &
 we ev5 use ! ^w 'n[' ) ref]5ce to  !   
exi/5ce ( ^? :o h pass$ away f ! mat]ial
 _w4 ,!  inve/igations ( ! relativity   
!ory %[ incontrov]tibly t ?is  suppos$  
/ratification is an illusion2 !re is n !
 slighte/  evid5ce = su* a view (       
_w-/ructure4 ,! in/antane\s /ate1  :i*  
we h hi!rto tak5 to be a natural /ratum 
9 !  f\r-dim5sional _w ( ev5ts1 is m]ely
 an arbitr>y p>tition  creat$ by        
ourselves to correspond ) our geoc5tric 
outlook4 ,we c  take a diff]5tly incl9$ 
p>tition1#c t is to say1 a section  :i* 
includes on ! "o side ( u ev5ts :i*     
happ5$ a little  :ile ago & on ! o!r    
side ( u ev5ts :i* h n yet  happ5$2 su* 
a f>cical comb9ation is 9 e way         
equival5t to our  s-call$ in/antane\s   
/ate1 & inde$ x is an in/antane\s /ate  
accord+ to ! outlook ( "s non-t]re/rial 
obs]v] ) suitably  assign$ motion4    ,x
 is s contr>y to our natural prejudices 

to recognize t !  _w-wide in/ant n[ is  
creat$ by ourselves & has no exi/5ce    
ap>t f our geoc5tric outlook1 t ,i w    
sp5d a few mom5ts  try+ to %[ its       
artificiality4 ,:5 ,i say t ,i am       
consci\s ( an  in/ant n[1 ,i am only    
consci\s ( x 9 s f> z x is ,,"h--inside 
me4 ,:at !n has l$ me to imag9e t !re   
exi/s a cont9uation (  x outside me8 ,x 
is because ,i look out on ! _w & see    
v>i\s  ev5ts happ5+ 'n['1 s t ,i jump to
 ! conclusion t ?is  in/ant ( :i* ,i am 
consci\s has to be ext5d$ to include    
!m4 ,b t idea is ano!r inh]itance f !   
d>k ages1  ov]?r[n by ,rm] 9 #afge4 ,x  
is n ! ev5ts !mselves b !               
s5se-impressions to :i* !y give rise :i*
 are happ5+ 9 !  in/ant n[4 ,s my       
ju/ification = plac+ ! ev5ts outside me 
9  ! in/ants ( :i* ,i am consci\s has   
entirely disappe>$4  ,un=tunately1      
h[ev]1 ! crude outlook 0 n aboli%$1 b   
pat*$  up2 x 0 f\nd t ! imm$iate        
difficulties c\ld be met by  locat+ !   
ext]nal ev5ts n 9 ! in/ant ( our visual 

p]ception  ( !m b 9 an in/ant :i* we _h 
exp]i5c$ a little "t  back--all[+1 z we 
say1 = ! "t ( propagation ( light4 ,?us 
our in/ants 7 /ill made to ext5d ?r\gh  
space2 b !y 7  c>ri$ l p>titions among !
 ev5ts by an artificial process (       
computation1 & no long] by imm$iate     
intuition4 ,! relativity !ory           
recognizes ^! worldwide in/ants = :at !y
 are--artificial  p>titions con/ruct$ = 
purposes ( calculation4 ,i may add t x 9
  no way tamp]s ) ! local in/ants :i* =m
 ! /ream ( our  consci\sness2 x fully   
recognizes t ! *a9 ( ev5ts 9 su* a      
"t-succession is a s]ies ( an entirely  
di/9ctive "* f  ! succession ( po9ts    
along a l9e 9 space4 ,^? :o suspect t   
,e9/e9's !ory is play+ unju/ifiable     
tricks ) "t %\ld  realize t x leaves    
entirely unt\*$ t "t-succession ( :i*   
we h intuitive k1 & conf9es itself to   
ov]haul+ !  artificial s*eme ( "t :i*   
,rm] fir/ introduc$ into physics4    ,! 
/udy ( ! f\r-dim5sional _w ( ev5ts gives
 u a new insight  into ! processes (    

nature because x removes ! irrelevant   
/ratification 9 a p>ticul> direction--! 
in/antane\s  /ates--:i* we h s          
unnecess>ily introduc$ 9 our cu/om>y    
outlook4 ,:5 ?is /ratification is ignor$
 we are enabl$ to see !  processes 9 _! 
simple/ aspect1 ?\gh n1 ( c\rse1 9 _!   
mo/  famili> aspect4 ,we mu/ di/+ui%    
betwe5 simplicity & famili>ity2  a pig  
may be mo/ famili> to u 9 ! =m ( ra%]s1 
b !  un/ratifi$ pig is a simpl] object (
 /udy to ! biologi/ :o  wi%es to und]/& 
h[ ! animal functions4    ,i w conclude 
?is "p ( ! argum5t ) an exp]im5tal      
application :i* illu/rates ! p[] (      
,e9/e9's me?od4 ,mu* /udy  has ( late   
be5 giv5 to electrons mov+ ) v high     
spe$s2 =  example1 !  p>ticles %ot (f f 
radioactive sub/ances are  negative     
electrons :i* sometimes atta9 spe$s (   
#ajj1jjj miles a  second4 ,x is f\nd by 
exp]im5t t ! rapid motion produces an   
increase ( mass ( ^! p>ticles4 ,i want  
to %[ t ! !ory (  relativity gives a v  
simple explanation ( j h[ ?is increase (

  mass occurs4 ,b ,i mu/ fir/ rem>k t an
 explanation _h be5  previ\sly giv5 :i* 
_h g5]ally be5 accept$ z satisfactory4  
,!  ph5om5on 0 actually pr$ict$ by ,j4  
,j4 ,?omson be=e relativity 0  ?\ght (2 
because1 assum+ t ! mass ( a p>ticle is 
(  electrical orig91 an application (   
,maxwell's equations %[s t x  ought to  
increase ) velocity4 ,b ! precise law ( 
increase _c  be pr$ict$ on ?is basis1   
s9ce v>i\s plausible assumptions lead to
  slightly diff]5t results4 ,moreov]1   
,maxwell's equations are aft] all  only 
empirical laws1 ) a my/]y ( _! own2 x 0 
a notable  advance to connect ! *ange ( 
mass at high spe$s ) o!r  ph5om5a ^:    
/rang5ess has disappe>$ by long         
famili>ity1 b  !re is /ill scope = a m  
f>-rea*+ explanation4 ,e9/e9 takes  u   
/raight to ! root ( ! my/]y1 & he cle>s 
up "o po9t :i*  0 mislead+1 if n        
actually wrong1 9 ! old] explanation4 ,!
  *ange ( mass does n 9 any way dep5d on
 :e!r ! mass is (  electrical orig9 or  
n2 x arises simply f ! fact t mass is a 

relative quantity1 dep5d+ by its        
def9ition on ! relative  quantities l5g?
 & "t4 ,let u look at !  p>ticle f its  
own  po9t ( view2 x is j an ord9>y      
electron 9 no way diff]5t f  any o!r4   
',b x is travell+ unusually rapidly8'   
',t'1 says !  electron1 'is a matt] (   
op9ion4 ,s f> z ,i am aw>e ,i am at re/1
 if  ! ^w re/ has any mean+4 ,9 fact ,i 
0 j contemplat+ )  amazem5t y\r         
extraord9>y spe$ ( #ajj1jjj miles a     
second )  :i* y are %oot+ pa/ me4' ,(   
c\rse our motion is ( no  p>ticul>      
conc]n to ! electron1 & x w n modify its
  con/itution on our acc\nt2 s x keeps  
its mass1 radius1 electric  field1 c41  
equal to ! /&>d con/ants apply+ to      
electrons 9  g5]al4 ,^! t]ms are        
relative1 & ref] !re=e to "s  p>ticul>  
frame ( space & "t--cle>ly ! frame      
appropriate to an  electron 9           
self-contemplation1 viz4 ! "o )1 respect
 to :i* x  is at re/4 ,b ?is frame is n 
! usual geoc5tric frame to :i*  we ref] 
quantities su* z l5g?1 "t1 & mass2 !re  

is a  diff]5ce ( #ajj1jjj miles a second
 betwe5 our /ation ( obs]vation  & t ( !
  p>ticle 9 self-contemplation4 ,x is a 
m]e matt]  ( geometry to discov] :at !  
p>ticle's l5g?s & times become  :5      
ref]r$ to ! p>titions :i* we h drawn    
across ! _w4  ,b :5 we calculate !      
consequ5tial *ange ( mass result+ f  !  
*anges ( l5g? & "t1 we f9d t x %\ld be  
increas$ 9  precisely ! proportion      
indicat$ by ! mo/ ref9$ exp]im5ts4    ,!
 po9t is t e electron1 at re/ or 9      
motion1 is a p]fectly  con/ant /ructure2
 b we di/ort x by fitt+ x into !        
space-"t  frame appropriate to our own  
motion ) :i* ! electron has no  conc]n4 
,! great] our motion ) respect to !     
electron1 !  great] w be ! di/ortion4 ,!
 di/ortion is n produc$ by any  physical
 ag5cy at "w 9 ! electron2 x is a purely
 subjective  di/ortion dep5d+ on our    
trans=mation ( ! ref]5ce frame (  space 
& "t4 ,?is di/ortion involves a *ange 9 
our physical  description ( ! electron 9
 t]ms ( mass1 %ape1 size2 & 9  p>ticul> 

! *ange ( mass agrees precisely ) t f\nd
  exp]im5tally4    ,y see t x is n      
altoge!r idle discuss+ ! natural        
space-"t  frames = obs]v]s mov+ ) huge  
velocities4 ,we "k ( no animate  obs]v]s
 ) ^! spe$s2 b we d "k ( inanimate      
mat]ial  objects4 ,_! common resemblance
 is obscur$ :5 we ref] !m               
indiscrim9ately to our irrelevant       
geoc5tric frame2 we ?9k !y h  alt]$ _!  
prop]ties1 v>i$ 9 mass1 & s on2 b !     
resemblance  is re/or$ :5 we ref] ea*   
individual to ! frame appropriate to  x1
 & s describe !m all 9 comp>able t]ms4  
,our measurem5ts ( di/ance 9 space are  
f\nd to be subject to c]ta9  laws--!    
laws ( geometry4 ,b x has n[ become     
impossible to reg>d  ! subject (        
space-geometry z complete 9 itself4     
,consid] a triangle  =m$ by ?ree po9ts  
7or ev5ts7 9 ! f\r-dim5sional _w2 if we 
happ5 to h drawn our in/antane\s /rata s
 t ! ?ree po9ts  lie 9 "o /ratum1 !n !  
triangle is a space-triangle & its      
prop]ties fall )9 ! scope ( our         

classical geometry4 ,b ano!r  obs]v] w  
draw 8 /rata 9 a diff]5t direction1 & = 
him !  triangle w\ld be p>tly 9 space & 
p>tly 9 "t1 s t x w\ld  n be a fit      
subject = space-geometry4 ,! subject (  
geometry is 9 a  desp]ate condition1    
because ,cop]nicus & ,ptolemy n m]ely   
disagree  z to ! geometry ( a           
configuration2 !y ev5 disagree z to :e!r
  a giv5 configuration is "o to :i*     
space-geometry is applicable4 ,x  is    
cle> t to save x we mu/ ext5d our       
geometry s z to include  "t z well z    
space4 ,let me give an illu/ration ( ?is
 ext5sion4  ,! t]re/rial obs]v] c h a   
space-triangle 7=m$ by ?ree  po9ts or   
ev5ts at ! same in/ant7 ^: sides he c   
measure )  scales2 he c also h a        
'"t-triangle'1 =m$ by ?ree ev5ts on     
diff]5t dates1 ^: sides he mu/ measure )
 clocks4#d ,y all  "k ! law ( !         
space-triangle--t if y measure ) a scale
  f ,a to ,b & f ,b to ,c ! sum ( !     
read+s is always  great] ?an ! measure f
 ,a to ,c4 ,x is n s well kn[n t  !re is

 a precisely analog\s law = !           
"t-triangle--t if y  measure ) a clock f
 ,a to ,b & f ,b to ,c ! sum ( !  read+s
 is always less ?an ! read+ ( a clock   
measur+ directly  f ,a to ,c4 ,9 !      
space-triangle any two sides are toge!r 
great] ?an ! ?ird side2 9 ! "t-triangle 
two sides are  toge!r less ?an ! ?ird   
side4#e ,bo? ^! laws mu/ be comb9$  9   
our g5]al geometry ( f\r dim5sions1 s t 
x w n be q  s simple a geometry z t to  
:i* we are accu/om$4#f    ,b ! po9t to  
:i* ,i w\ld especially direct att5tion  
is ?is4  ,evid5tly ! proposition :i* ,i 
h giv5 y ab\t "t-triangles  _c be       
dissociat$ f ! correspond+ proposition  
ab\t  space-triangles4 ,:5 we give up ! 
m$iaeval geoc5tric /&po9t1 we  mu/      
recognize t !y belong to "o geometry1 ( 
:i* our ord9>y  space-geometry is only a
 "p or projection4 ,b if y exam9e !     
proposition ab\t "t-triangles1 y w see t
 x is a /atem5t  ab\t ! behavi\r (      
clocks :5 !y move ab\t1 a subject :i*   
obvi\sly comes "u ! head+ ( me*anics4   

,:5 we deal ) !  f\r-dim5sional _w we c 
no long] di/+ui% betwe5 geometry &      
me*anics4 ,!y become ! same subject4 ,:5
 we h completely  ma/]$ ! geometry ( !  
_w ( ev5ts1 we %all h inevitably  le>nt 
! me*anics ( x4 ,t is :y ,e9/e91 /udy+ !
 geometry  ( ! _w & discov]+ t x 0      
/rictly non-,euclidean1 f\nd  t he 0 at 
! same "t /udy+ ! me*anical =ce (       
gravitation4 ,& :5 he _h made up 8 m9d  
:i* ( ! possible  v>ieties (            
non-,euclidean geometry 0 obey$1 & s    
settl$ ! laws  ( ! new geometry1 ! same 
decision settl$ ! law ( gravitation--a  
law approximat+ to1 b n id5tical )1 !   
law :i* ,newton _h  giv54    ,"h a wide 
vi/a op5s be=e u4 ,we see t two great   
divisions (  ma!matical physics1 viz4   
geometry & me*anics1 h met 9 !          
f\r-dim5sional _w4 ,x is n m]ely t      
me*anical problems c be  treat$ by      
=mulae orig9ally belong+ to pure        
geometry2 t device  has long be5 9 use4 
,exp]im5tal geometry & me*anics actually
  relate to ! same subject-matt]2 & ! "y

 /ud5t :o discov]s  exp]im5tal laws )   
rul] & compasses & c>dbo>d figures1 &   
lat] goes on to p5dulums &              
spr+-balances1 is develop+ a s+le       
subject :i* _c be divid$ any m ?an !    
subject ( magnetism  c be divid$ f      
electricity4    ,x is ?r\gh ?is         
unification ( geometry & me*anics t ,i  
%\ld  l to approa* ! problem (          
gravitation1 %[+ t a field (  =ce is a  
manife/ation ( ! geometry ( space & "t4 
,b ,i fe>  t t w\ld be too te*nical2 s  
we w approa* x f a  diff]5t angle4      
,we h %[n t ! contemplation ( ! _w f !  
/&po9t  ( a s+le obs]v] is liable to    
di/ort its simplicity1 & we h  tri$ to  
obta9 a ju/] idea by tak+ into acc\nt & 
comb9+  o!r po9ts ( view4 ,! m /&po9ts !
 bett]4 ,let u n[  consid] ano!r po9t ( 
view1 :i* we h n previ\sly ?\ght        
ab\t--! po9t ( view ( an obs]v] :o has  
tumbl$ out ( an  a]oplane & is fall+    
headlong4 ,9 _m respects 8 is an ideal  
situation--tempor>ily4 ,un=tunately on  
t]ra firma we are  cont9ually subject$  

to a v di/urb+ influ5ce2 we und]go a    
t]rific bomb>dm5t by ! molecules ( !    
gr\nd1 :i* are hamm]+  on ! soles ( our 
boots ) a total =ce ( "s t5 /one weight 
press+ u upw>ds4 ,n[ our bodies are !   
sci5tific appliances :i*  we use to make
 our common obs]vations ( ! _w4 ,i am   
sure t no  physici/ w\ld p]mit any "o to
 ent] 8 laboratory & hamm] on 8  clocks 
& galvanomet]s :il/ he 0 obs]v+ ) !m2 at
 any rate  he w\ld ?9k x necess>y to    
apply "s corrections = ! effect (  !    
di/urbance4 ,let u !n all[ ourselves to 
fall freely 9 vacuo2  !n we %all be free
 f ?is di/urb+ bomb>dm5t & able to take 
a mu* m natural view ( :at is go+ on    
ar\nd u4    ,:il/ fall+1 we p]=m !      
exp]im5t ( lett+ g an apple held 9  !   
h&4 ,! apple is n[ free1 b x _c fall any
 m ?an x 0  fall+ already2 consequ5tly x
 rema9s pois$ 9 contact ) our  h&4 ,9   
our new outlook--9 our new frame ( space
 & "t--an apple  does n drop4 ,!re is no
 my/]i\s =ce accel]at+ x4 ,&  rememb] t 
?is new frame ( space & "t is ! natural 

frame ( a  free obs]v]2 :]eas ! old     
frame1 9 :i* ! my/]i\s  accel]at+ =ce   
occurr$1 0 ! frame ( a v mu* di/urb$    
obs]v]4 ,x is true t :5 we look d[n at !
 e>? we see trees  & h\ses ru%+ up to   
meet u2 b !re is no my/]y ab\t t4  ,!re 
is an obvi\s cause = x2 pla9ly !y are   
be+ propell$  upw>ds f bel[ by t        
molecul> bomb>dm5t :i* ,i h m5tion$4  ,y
 see t ! apple's view ( ?+s is simpl]   
?an ,newton's4 ,newton  _h to inv5t a   
my/]i\s =ce dragg+ ! apple d[n2 ! apple 
obs]ves only a famili> physical ag5cy   
propell+ ,newton up4    ,x is n my      
purpose to emphasize unduly ! sup]iority
 ( ! apple's  view ov] ,newton's1 b r to
 reg>d bo? on an equal foot+4 ,i  h     
p]haps be5 a little unfair to ,newton4  
,8 position on ! surface  ( ! e>? 0     
un=tunate1 b he w\ld h be5 p]fectly     
cont5t  to be at ! c5tre ( ! e>?1 :]e he
 c\ld h rema9$ )\t  support1 i4e4 )\t   
di/urbance by molecul> bomb>dm5t4 ,f !re
  he w\ld /ill h obs]v$ ! well-kn[n     
accel]ation ( ! apple2  & ! apple w\ld h

 obs]v$ a correspond+ accel]ation (     
,newton  )\t any molecul> bomb>dm5t     
caus+ x4 ,f ei!r po9t ( view  !re is a  
my/]i\s ag5t at "w4 ,h[ %all we picture 
to ourselves  ?is ag5t8 ,%all we picture
 x z a =ce--a tug ( "s k9d8 ,b if  s1 to
 :i* ( !m is ! tug appli$8 ,if we take !
 /&po9t (  ,newton ! tug is appli$ to ! 
apple1 if ! /&po9t ( ! apple  ! tug is  
appli$ to ,newton2 s t 9 our syn!sis (  
all  /&po9ts we _c decide :i* is be+    
tugg$1 & ! picture (  gravitation z a   
tugg+ ag5t becomes impossible4 ,e9/e9   
replaces x  by a diff]5t picture1 :i* we
 %all p]haps bett] und]/& if we  comp>e 
x ) a v simil> revolution ( sci5tific   
?\ght :i*  occurr$ long ago4    ,!      
anci5ts believ$ t ! e>? 0 flat4 ,! small
 portion ( its  surface ) :i* !y 7      
*iefly conc]n$ c\ld be repres5t$  )\t   
s]i\s di/ortion on a flat map4 ,z m     
di/ant c\ntries 7  add$1 x w\ld be      
natural to ?9k t !y also c\ld be includ$
 9  ! flat map4 ,y h all se5 su* maps ( 
! _w1 e4 g4 ,m]cator's  projection1 & y 

w rememb] h[ ,gre5l& appe>s enorm\sly   
exagg]at$ 9 size4 ,n[ ^? :o adh]$ to !  
flat-e>? !ory mu/  hold t ! flat map    
gives ! true size ( ,gre5l&4 ,h[ !n     
w\ld !y expla9 t travell]s 9 t c\ntry   
report$ t !  di/ances 7 mu* %ort]8 ,!y  
w\ld1 ,i suppose1 inv5t a !ory t  a     
demon resid$ 9 t c\ntry :o help$        
travell]s on _! way1  mak+ ! j\rneys    
appe> mu* %ort] ?an !y 'really' 74 ,no  
d\bt ! sci5ti/s w\ld pres]ve _!         
self-respect by us+ "s  ,graeco-,lat9   
polysyllable in/ead ( ! ^w 'demon'1 b t 
mu/ n  disguise f u ! fact t !y 7       
appeal+ to a deus ex  ma*9a4 ,! "n demon
 is r suitable1 h[ev]1 because he has ! 
impi% *>act]i/ic t we _c p9 him d[n to  
any p>ticul>  locality4 ,we might       
equally well />t our flat map ) its     
c5tre 9  ,gre5l&2 !n x w\ld be f\nd t   
j\rneys !re 7 q normal1  & t !          
activities ( ! demon 7 di/urb+ travell]s
 9  ,europe4 ,we n[ recognize t ! true  
explanation is t ! e>?'s  surface is    
curv$2 & ! demoniacal complications     

appe>$ because we  7 =c+ ! e>?'s surface
 into an inappropriate flat frame :i*   
di/orts ! simplicity ( ?+s4    ,:at has 
happ5$ 9 ! case ( ! e>? has happ5$ also 
9 ! case  ( ! _w1 & a simil> revolution 
( ?\ght is ne$$4 ,an  obs]v]1 say at !  
c5tre ( ! e>?1 f9ds t !re is a frame (  
space & "t--a flat or ,euclidean        
frame--9 :i* he c locate ?+s  happ5+ 9 8
 neighb\rhood )\t di/ort+ _! natural    
simplicity4 ,!re is no gravitation1 no  
t5d5cy ( bodies to fall1 s  long z !    
obs]v] conf9es 8 obs]vations to 8       
imm$iate  neighb\rhood4 ,he ext5ds ?is  
frame ( space & "t to great]  di/ances1 
& ultimately to ! e>?'s surface :]e he  
enc\nt]s !  ph5om5on ( fall+ apples4    
,?is new ph5om5on mu/ be acc\nt$ =1  s  
he inv5ts a deus ex ma*9a :i* he calls  
gravitation to ^:  activities !         
di/urbance is attribut$4 ,b we h se5 t  
we may  j z well />t ) ! fall+ apple4 ,x
 has a flat frame ( space  & "t into :i*
 ph5om5a 9 its neighb\rhood fit )\t     
di/ortion2 & f its po9t ( view bodies   

ne> x d n und]go any  accel]ation4 ,b :5
 x ext5ds ?is frame f>!r afield1 !      
simplicity is lo/2 & x too has to       
po/ulate ! demon =ce (  gravitation     
exi/+ 9 di/ant p>ts1 & = example caus+  
undi/urb$ objects at ! c5tre ( ! e>? to 
fall t[>ds x4 ,z we  *ange f "o obs]v]  
to ano!r--f "o flat space-"t frame to   
ano!r--s we h to *ange ! region (       
activity ( ?is demon4 ,is  n ! solution 
n[ app>5t8 ,! demon is simply !         
complication  :i* arises :5 we =ce ! _w 
into a flat ,euclidean space-"t  frame  
into :i* x does n fit )\t di/ortion4 ,x 
does n fit !  frame1 because x is n a   
,euclidean or flat _w4 ,admit a         
curvature  ( ! _w & ! my/]i\s di/urbance
 disappe>s4 ,e9/e9 has  exorciz$ !      
demon4    ,e9/e91 recogniz+ t 9 !       
ph5om5a ( gravitation he 0 n  deal+ ) a 
'tug' b ) a curvature ( ! _w1 _h to     
reconsid] ! law ( gravitation4 ,he c\ld 
n make any possible law (  curvature    
correspond exactly ) ! previ\sly assum$ 
law ( tugg+4  ,?us he 0 l$ to prop\nd a 

new law ( gravitation--a law :i* 9  mo/ 
practical cases diff]s v little f t (   
,newton1 al?\gh  x has an ess5tially    
diff]5t f\ndation4 ,i ne$ n "h dwell on 
!  v rem>kable way 9 :i* ,e9/e9's       
em5dation ( ! law (  gravitation has be5
 confirm$ bo? by ! anomal\s secul> *ange
 9  ! orbit ( ! planet ,m]cury1 & by !  
obs]v$ displacem5t ( !  />s ne> ! sun   
dur+ ! total eclipse ( #aiai4 ,i might1 
h[ev]1  rem9d y t 9 ! latt] obs]vation !
 po9t at issue betwe5  ,newton's &      
,e9/e9's !ory 0 n ! exi/5ce ( a         
deflexion (  light-rays pass+ ne> ! sun 
b ! am\nt ( ! deflexion1  ,e9/e9 pr$ict+
 twice ! deflexion possible on !        
,newtonian  !ory4 ,! l>g] deflexion 0   
quantitatively confirm$ by ! eclipse    
obs]vations4 ,e9/e9's ma9 a*ievem5t is a
 new law1 n a new  explanation1 (       
gravitation4 ,he attributes !           
gravitation ( massive  bodies to a      
curvature ( ! _w 9 ! region surr\nd+ !m 
& s  ?r[s a flood ( light on ! :ole     
problem2 b he is n prim>ily  conc]n$ to 

expla9 h[ mat]ial bodies produce 7or are
 associat$  )7 ?is curvature ( ! _w     
ar\nd !m1 nor h[ ?is curvature is  made 
subject to a law4 ,al?\gh x w\ld be an  
entire misund]/&+  ( ,e9/e9's attitude 9
 prop\nd+ ! g5]al relativity !ory to    
reg>d x z a se>* = an explanation (     
gravitation1 nev]!less ,i  ?9k t ! fur!r
 foll[+ up ( 8 ideas has l$ to a g5u9e  
explanation z complete z c\ld be desir$4
 ,b ,i am n go+ to give  y ! explanation
 9 ?is lecture2 sometimes an explanation
 requires a  great deal ( expla9+4#g    
,i ?9k t we c )\t ma!matics =m a g5]al  
idea ( :y  ,e9/e9 f\nd x necess>y to    
am5d ,newton's law ( gravitation4 ,let u
  return to ! illu/ration ( ! pig1 &    
imag9e t we wi% to  discov] ! law gov]n+
 ! di/ribution ( fat & lean 9 !  animal4
 ,f ! breakfa/-table /&po9t a plausible 
type ( law  w\ld be t half ( ea* ra%] is
 fat & ! o!r half lean2 & if  ?is turn$ 
out to be confirm$ v approximately by   
obs]vation we  might well imag9e t we _h
 discov]$ ! exact law ( porc9e          

/ructure4 ,b ! case is alt]$ if we give 
up ! breakfa/-table  /&po9t &           
contemplate ! animal 9 a m g5]al way1   
rememb]+  t he has n be5 design$ ) any  
p>ticul> ref]5ce to !  s]ies ( ra%]s    
into :i* our groc] has *os5 to slice    
him4 ,we mu/  n[ look = a diff]5t type (
 law altoge!r4 ,two possibilities may   
arise4 ,we may f9d t our propos$ law1   
al?\gh express$ 9  breakfa/-table       
p>lance1 is nev]!less equival5t to a    
possible  biological law2 x may be      
imm$iately capable ( translation into a 
m  g5]al /atem5t :i* makes no ref]5ce to
 a p>ticul>  /ratification4 ,b on ! o!r 
h&1 x may happ5 t ! sugge/$  law _c be  
fre$ f ?is ref]5ce to a p>ticul> sy/em (
  slic+4 ,9 t case we c only reg>d x z  
approximate1 p]haps  hold+ fairly well =
 ! slices ( :i* we h mo/ exp]i5ce b     
becom+ less & less accurate 9 ! m       
tortu\s p>ts ( !  animal4 ,bo? ^! cases 
are illu/rat$ 9 ,e9/e9's modifications (
  classical !ory4 ,newton's law (       
gravitation explicitly ref]s to a       

space-"t frame & !re=e to a _w /ratifi$ 
into in/antane\s  /ates4 ,x proves to be
 impossible to free x f ?is ref]5ce to a
  p>ticul> /ratification )\t modify+ x4 
,9 fact if ! crucial  a/ronomical       
obs]vations _h %[n t ,newton's law & n  
,e9/e9's  0 ! exact law ( gravitation1  
?is w\ld h be5 evid5ce ( a  real        
/ratification ( ! /ructure ( ! _w--a    
/ratification  reveal$ by no o!r        
ph5om5a4 ,e9/e9's law is ! simpl] law   
because x is consi/5t ) :at we n[ "k ( !
 g5]al plan (  _w-/ructure2 ,newton's   
law c\ld only be made possible by       
introduc+  a novel & specializ$         
feature--a /ratifi$ arrangem5t (        
/ructure--:i* is n reveal$ 9 any o!r    
ph5om5a4    ,maxwell's laws (           
electromagnetism af=d an example ( ! o!r
 type4  ,^!1 x is true1 are /at$ z      
relat+ to ! p>ticul> slices (  ! _w (   
ev5ts1 :i* are s]v$ up to u l ra%]s     
in/ant by  in/ant4 ,b !y c be re/at$1   
)\t alt]ation ( effect1 9 a  =m mak+ no 
ref]5ce to slices4 ,?is is a v rem>kable

 prop]ty  ( ,maxwell's equations :i* 0 q
 unkn[n at ! "t !y 7  fir/ put =w>d4 ,x 
0 br\ght to light mu* lat] by ! rese>*es
  ( ,l>mor & ,lor5tz4 ,9 consequ5ce (   
?is ,e9/e9 is able to take  ov] ! :ole  
classical !ory ( electromagnetism       
unalt]$2 he  re/ates x s z to %[ h[ x   
applies g5]ally & is n b\nd up  ) !     
purely t]re/rial po9t ( view1 b he does 
n am5d !  laws4 ,he metes out diff]5t   
treatm5t to ! gravitational laws &      
electromagnetic laws1 because he f9ds ! 
latt] already adapt$ to 8  s*eme4    ,if
 ,i h succe$$ 9 my object1 y w h realiz$
 t !  pres5t revolution ( sci5tific     
?\ght foll[s 9 natural sequ5ce on  !    
great revolutions at e>li] epo*s 9 !    
hi/ory ( sci5ce4  ,e9/e9's special !ory 
( relativity1 :i* expla9s !             
indet]m9at5ess ( ! frame ( space & "t1  
cr[ns ! "w (  ,cop]nicus :o fir/ l$ u to
 give up our insi/5ce on a geoc5tric    
outlook on nature2 ,e9/e9's g5]al !ory (
 relativity1 :i*  reveals ! curvature or
 non-,euclidean geometry ( space & "t1  

c>ries =w>d ! rudim5t>y ?\ght ( ^? e>li]
 a/ronom]s :o  fir/ contemplat$ !       
possibility t _! exi/5ce lay on some?+  
:i* 0 n flat4 ,^! e>li] revolutions are 
/ill a s\rce (  p]plexity 9 *ildhood1   
:i* we soon outgr[2 & a "t w come  :5   
,e9/e9's amaz+ revelations h likewise   
sunk into !  commonplaces ( educat$     
?\ght4    ,to free our ?\ght f ! fett]s 
( space & "t is an aspiration  ( ! poet 
& ! my/ic1 view$ some:at coldly by !    
sci5ti/ :o  has too good reason to fe> !
 confusion ( loose ideas likely to      
ensue4 ,if o!rs h _h a suspicion ( ! end
 to be desir$1 x has  be5 left to ,e9/e9
 to %[ ! way to rid ourselves ( ^!      
't]re/rial adhesions to ?\ght'4 ,& 9    
remov+ our fett]s he  leaves u1 n 7z    
might h be5 fe>$7 vague g5]alities = !  
ec/atic contemplation ( ! my/ic1 b a    
precise s*eme (  _w-/ructure to engage !
 ma!matical physici/4      ,footnote #a3
 ,! only alt]native is t 7relatively to 
a sol>  obs]v]7 ! velocity ( light      
diff]s 9 diff]5t directions1 at  lea/ 9 

! region :]e ! exp]im5t is conduct$4    
,?is w\ld  presumably be due to "s      
influ5ce ( ! mov+ e>? on !  propagation 
( light 7convection ( ! e!r74 ,?is      
explanation 0 at  "o "t fav\r$1 b x c\ld
 n be reconcil$ ) ! obs]v$  ph5om5a ( ! 
ab]ration ( light4    ,footnote #b3 ,!  
relativity !ory does n sugge/ t !re is  
su*  a ?+ 9 nature z a f\r-dim5sional   
space4 ,! :ole object ( !  recognition (
 ! f\r-dim5sional _w is to elim9ate !   
h>ass+  frame ( space4    ,footnote #c3 
,! incl9ation mu/ n exce$ a c]ta9 limit4
 ,?is  limit+ angle may be reg>d$ z a   
fundam5tal con/ant ( !  _w-/ructure1 &  
ow+ to its fundam5tal "* x appe>s 9  _m 
k9ds ( ph5om5a2 = example1 x det]m9es ! 
velocity (  propagation ( light4 ,!     
in/ant on ! sun :i* is simultane\s )  a 
giv5 in/ant on ! e>? is indet]m9ate     
7v>y+ accord+ to !  space & "t frame    
employ$7 b only )9 a range ( #af m9utes4
  ,any ev5t on ! sun happ5+ be=e ?is #af
 m9utes is absolutely 9  ! pa/1 all     
obs]v]s agree+ on ?is po9t2 9 fact x    

w\ld be  possible = u to h already      
receiv$ a wireless message ann\nc+  its 
occurr5ce4 ,ev5ts aft] ! #af m9utes are 
9 ! absolute  future4 ,! neutral zone   
:i* is 7absolutely7 nei!r pa/ nor future
  becomes proportionately wid] z !      
di/ance increases2 at ! ne>e/  fix$ /> x
 ext5ds to #h ye>s1 & at ! mo/ di/ant   
/>s yet  kn[n x rea*es #djj1jjj ye>s4   
,footnote #d3 ,! ?ree ev5ts mu/ n be at 
! same place s9ce t  w\ld give a "t-l9e 
n a triangle4 ,! clock mu/ move s t !   
two ev5ts ^: "t-di/ance is to be det]m9$
 bo? happ5 :]e x  is1 j z ! scale mu/ be
 direct$ s t ! two po9ts fall on  x4 ,y 
are n all[$ to 'b5d' ! clock1 i4 e4     
apply =ce s z to  make x move ) o!r ?an 
uni=m velocity1 any m ?an y are  all[$  
to b5d ! scale by apply+ =ce4           
,footnote #e3 ,( c\rse1 x is n true t   
any two sides are less  ?an ! ?ird side4
 ,a clock1 unlike a scale1 c only       
measure 9 "o  direction1 viz4 f pa/ to  
future1 s t ! sides ,,ab  ,,bc &  ,,ac c
 be *os5 9 only "o way4    ,footnote #f3

 ,?is involves only a comp>atively      
trifl+ g5]alization  ( ,euclidean       
geometry1 n to be confus$ ) !           
'non-,euclidean'  geometry introduc$    
lat] 9 ! lecture4    ,footnote #g3 ,!   
foll[+ brief outl9e w give a h9t ( !    
nature  ( ! explanation4 ,e9/e9's law ( 
gravitation is usually express$  z a set
 ( t5 v l5g?y diff]5tial equations2 ^!  
equations are  exactly equival5t to !   
geometrical /atem5t t '! radius (       
sph]ical curvature ( any #c-;dim5sional 
section ( ! #d-;dim5sional  _w is a     
univ]sal con/ant l5g?1 ! same = all     
po9ts ( !  _w & = all directions ( !    
section'4 ,! law !re=e implies  t ! _w  
has a c]ta9 type ( homog5eity & isotropy
 7n1  h[ev]1 ! complete homog5eity &    
isotropy ( a sph]e74 ,to  expla9 ! law (
 gravitation & ! ph5om5a gov]n$ by x1 we
 h  to expla9 h[ ?is isotropy &         
homog5eity is secur$4 ,our explanation  
is t ! homog5eity & isotropy is n       
initially 9 ! ext]nal  _w1 b 9 !        
measurem5ts :i* we make ( x4 ,x is      

introduc$  9 all our op]ations (        
measurem5t1 because ! appliances :i* we 
use = measurem5t are !mselves "p ( ! _w4
 ,9 ! e>li]  "p ( ?is lecture we saw t !
 contraction ( ! arm turn$ f  horizontal
 to v]tical is n detect$ by measurem5ts 
made ) a  y>d-measure :i* %>es !        
contraction2 9 ! same way any           
anisotropy ( ! _w does n appe> 9        
measurem5ts ( x by  appliances :i*1 be+ 
"p ( ! _w1 %>e ! same anisotropy4  ,!   
law ( gravitation !re=e arises f ! fact 
t a c]ta9  type ( non-homog5eity &      
non-isotropy ( ! _w _c come into        
obs]vational exp]i5ce1 because x is     
necess>ily elim9at$ 9 all  obs]vations &
 measurem5ts made ) mat]ial appliances4 
,! ord]ly  ph5om5a ( gravitation are due
 to ! abs5ce ( c]ta9 conceivable        
effects4 ,we h be5 try+ to f9d a key to 
! my/]y2 b !  secret ( ! lock lies n 9 !
 key b 9 ! w>ds4