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  1 
  

  

  Principle 
  of 
  Relativity 
  and 
  Kon-Newtonian 
  Mechanics. 
  513 
  

  

  other 
  aAvay 
  from 
  the 
  source 
  o£ 
  liglit, 
  constitutes 
  the 
  really 
  

   remarkable 
  feature 
  of 
  the 
  principle 
  of 
  relativity, 
  and 
  forces 
  

   us 
  to 
  the 
  strange 
  conclusions 
  which 
  we 
  are 
  about 
  to 
  deduce. 
  

  

  Let 
  us 
  consider 
  two 
  systems, 
  moving 
  past 
  one 
  another, 
  with 
  

   a 
  constant 
  relative 
  velocity, 
  provided 
  with 
  plane 
  mirrors 
  aa 
  

   and 
  hh 
  parallel 
  to 
  one 
  another 
  and 
  to 
  the 
  line 
  of 
  motion 
  (fig. 
  1) 
  . 
  

   An 
  observer 
  A 
  on 
  the 
  first 
  system 
  sends 
  a 
  beam 
  of 
  light 
  

   across 
  to 
  the 
  opposite 
  mirror, 
  wdiich 
  is 
  reflected 
  back 
  to 
  

   the 
  starting-point. 
  He 
  measures 
  the 
  time 
  taken 
  by 
  the 
  light 
  

   in 
  transit. 
  

  

  ^ 
  

  

  I 
  

   I 
  

   I 
  

   I 
  

   I 
  

   I 
  

  

  A, 
  assuming 
  that 
  his 
  system 
  is 
  at 
  rest 
  (and 
  the 
  other 
  in 
  

   motion), 
  considers 
  that 
  the 
  light 
  passes 
  over 
  the 
  path 
  oj^o, 
  but 
  

   he 
  believes 
  that 
  if 
  a 
  similar 
  experiment 
  is 
  conducted 
  by 
  an 
  

   observer 
  B 
  in 
  the 
  moving 
  system, 
  the 
  light 
  must 
  pass 
  over 
  

   the 
  longer 
  path 
  mnm', 
  in 
  order 
  to 
  return 
  to 
  the 
  starting-point. 
  

   For 
  the 
  point 
  m 
  moves 
  to 
  the 
  position 
  m^ 
  while 
  the 
  light 
  is 
  

   passing 
  ; 
  he 
  therefore 
  predicts 
  that 
  the 
  time 
  required 
  for 
  the 
  

   return 
  of 
  the 
  reflected 
  beam 
  will 
  be 
  longer 
  than 
  in 
  his 
  own 
  

   experiment. 
  A, 
  however, 
  having 
  established 
  communication 
  

   with 
  B, 
  learns 
  that 
  the 
  time 
  measured 
  is 
  the 
  same 
  as 
  in 
  his 
  

   own 
  experiment 
  *. 
  

  

  The 
  only 
  explanation 
  which 
  A 
  can 
  offer 
  for 
  this 
  surprising 
  

   state 
  of 
  affairs 
  is 
  that 
  the 
  clock 
  used 
  by 
  B 
  for 
  his 
  measure- 
  

   ment 
  does 
  not 
  keep 
  time 
  with 
  his 
  own, 
  but 
  runs 
  at 
  a 
  rate 
  

   which 
  is 
  to 
  the 
  rate 
  of 
  his 
  own 
  clock, 
  as 
  the 
  lengths 
  of 
  the 
  

   paths, 
  opo 
  to 
  mnm'. 
  

  

  B, 
  however, 
  is 
  equally 
  justified 
  in 
  considering 
  his 
  system 
  

   at 
  rest, 
  and 
  A's 
  in 
  motion, 
  and 
  by 
  identical 
  reasoning 
  has 
  

   come 
  to 
  the 
  conclusion 
  that 
  A's 
  clock 
  is 
  not 
  keeping 
  time. 
  

  

  * 
  This 
  is 
  evidently 
  required 
  by 
  the 
  principle 
  of 
  relativity, 
  for 
  contrary 
  

   to 
  A's 
  supposition 
  the 
  two 
  systems 
  are 
  in 
  fact 
  entirely 
  symmetrical. 
  

   Any 
  difference 
  in 
  the 
  observations 
  of 
  A 
  and 
  B 
  would 
  be 
  due 
  to 
  a 
  

   difference 
  in 
  the 
  absolute 
  velocity 
  of 
  the 
  two 
  systems, 
  and 
  would 
  thus 
  

   offer 
  a 
  means 
  of 
  determining 
  absolute 
  velocity. 
  

  

  