﻿1 
  Prindj)Ie 
  of 
  Relativity 
  and 
  Xon-Xewtoniaii 
  Mechanics. 
  517 
  

  

  although, 
  as 
  we 
  shall 
  show, 
  this 
  is 
  equally 
  true 
  of 
  other 
  uni- 
  

   versally 
  accepted 
  physical 
  conceptions. 
  We 
  are 
  only 
  

   justiiied 
  in 
  speaking 
  of 
  a 
  body 
  in 
  motion 
  when 
  we 
  have 
  in 
  

   mind 
  some 
  definite, 
  though 
  arbitrarily 
  chosen, 
  point 
  as 
  a 
  

   point 
  o£ 
  rest. 
  The 
  distortion 
  of 
  a 
  moving 
  body 
  is 
  not 
  a 
  

   physical 
  change 
  in 
  the 
  body 
  itself, 
  but 
  is 
  a 
  scientific 
  fiction. 
  

  

  When 
  Lorentz 
  first 
  advanced 
  the 
  idea 
  that 
  an 
  electron 
  or 
  

   in 
  fact 
  any 
  moving 
  body 
  is 
  shortened 
  in 
  the 
  line 
  of 
  its 
  motion, 
  

   he 
  pictured 
  a 
  real 
  distortion 
  of 
  the 
  body 
  in 
  consequence 
  of 
  a 
  

   real 
  motion 
  through 
  a 
  stationary 
  ?ether, 
  aud 
  his 
  theory 
  has 
  

   aroused 
  considerable 
  discussion 
  as 
  to 
  the 
  nature 
  of 
  the 
  forces 
  

   which 
  would 
  be 
  necessary 
  to 
  produce 
  such 
  a 
  deformation. 
  

   The 
  point 
  of 
  view 
  first 
  advanced 
  by 
  Einstein, 
  which 
  we 
  have 
  

   here 
  adopted, 
  is 
  radically 
  different. 
  Absolute 
  motion 
  has 
  no 
  

   significance. 
  Imagine 
  an 
  electron 
  and 
  a 
  number 
  of 
  observers 
  

   moving 
  in 
  different 
  directions 
  with 
  respect 
  to 
  it. 
  To 
  each 
  

   observer, 
  naively 
  considering 
  himself 
  to 
  be 
  at 
  rest, 
  the 
  electron 
  

   will 
  appear 
  shortened 
  in 
  a 
  different 
  direction 
  and 
  by 
  a 
  

   different 
  amount 
  ; 
  but 
  the 
  physical 
  condition 
  of 
  the 
  electron 
  

   obviously 
  does 
  not 
  depend 
  upon 
  the 
  state 
  of 
  mind 
  of 
  the 
  

   observers. 
  

  

  Although 
  these 
  changes 
  in 
  the 
  units 
  of 
  space 
  and 
  time 
  

   appear 
  in 
  a 
  certain 
  sense 
  psychological, 
  we 
  adopt 
  them 
  rather 
  

   than 
  abandon 
  completely 
  the 
  fundamental 
  conceptions 
  of 
  

   space, 
  time, 
  and 
  velocity, 
  upon 
  which 
  the 
  science 
  of 
  physics 
  

   now 
  rests. 
  At 
  present 
  there 
  appears 
  no 
  other 
  alternative. 
  

  

  JSon-Xeictonian 
  Mechanics. 
  

  

  Having 
  obtained 
  these 
  relations 
  for 
  the 
  units 
  of 
  space 
  and 
  

   time, 
  we 
  may 
  turn 
  to 
  some 
  of 
  the 
  other 
  important 
  quantities 
  

   used 
  in 
  mechanics. 
  

  

  Let 
  us 
  again 
  consider 
  two 
  systems, 
  a 
  and 
  5, 
  in 
  relative 
  

   motion 
  with 
  the 
  velocity 
  v. 
  An 
  experimenter 
  A 
  on 
  the 
  first 
  

   system 
  constructs 
  a 
  ball 
  of 
  some 
  rigid 
  elastic 
  material, 
  with 
  

   a 
  volume 
  of 
  one 
  cubic 
  centimetre, 
  and 
  sets 
  it 
  in 
  motion, 
  with 
  

   a 
  velocity 
  of 
  one 
  centimetre 
  per 
  second, 
  towards 
  the 
  system 
  h 
  

   (in 
  a 
  direction 
  perpendicular 
  to 
  the 
  line 
  of 
  relative 
  motion 
  of 
  

   the 
  two 
  systems). 
  On 
  the 
  other 
  system, 
  an 
  experimenter 
  h 
  

   constructs 
  of 
  the 
  same 
  material 
  a 
  similar 
  ball 
  with 
  a 
  volume 
  

   of 
  one 
  cubic 
  centimetre 
  in 
  his 
  units, 
  and 
  imparts 
  to 
  it, 
  also 
  in 
  

   his 
  units, 
  a 
  velocity 
  of 
  one 
  centimetre 
  per 
  second 
  towards 
  a. 
  

   The 
  experiment 
  is 
  so 
  planned 
  that 
  the 
  balls 
  will 
  collide 
  and 
  

   rebound 
  over 
  their 
  original 
  paths. 
  Since 
  the 
  two 
  systems 
  

   are 
  entirely 
  symmetrical, 
  it 
  is 
  evident 
  by 
  the 
  principle 
  of 
  

   relativity, 
  that 
  the 
  (algebraic) 
  change 
  in 
  velocity 
  of 
  the 
  first 
  

  

  