Anti_causal_arguments_10 1     No  Place  for  Causes?   Causal  Skepticism  in  Physics   Mathias  Frisch     Abstract   According  to  a  widespread  view,  which  can  be  traced  back  to  Russell’s  famous  attack  on  the  notion   of  cause,  causal  notions  have  no  legitimate  role  to  play  in  how  mature  physical  theories  represent   the  world.    In  this  paper  I  critically  examine  a  number  of  arguments  for  this  view  that  center  on  the   asymmetry  of  the  causal  relation  and  argue  that  none  of  them  succeed.    More  positively,  I  argue  that   embedding  the  dynamical  models  of  a  theory  into  richer  causal  structures  can  allow  us  to  decide   between  models  in  cases  where  our  observational  data  severely  underdetermine  our  choice  of   dynamical  models.     1.  Introduction   Is  there  a  place  for  the  concept  of  cause  in  physics?    There  is  a  venerable  tradition,  dating  back  at   least  to  Bertrand  Russell’s  famous  “On  the  Notion  of  Cause”  (1918),  arguing  that  causal  notions  can   play  no  legitimate  role  in  how  physics  represents  the  world.    Russell  himself,  of  course,  argued  not   only  that  causal  notions  have  no  place  in  modern  physics,  but  also  that  this  implies  that  the  notion   of  cause  ought  to  be  expunged  entirely  from  our  conception  of  the  world.    By  contrast,  recent   defenders  of  broadly  neo-­‐Russellian  arguments  concede  that  some  concept  of  cause  may  play  a   useful  role  in  our  folk  understanding  of  the  world  or  even  in  the  special  sciences—causal  concepts,   they  argue,  are  an  important  and  perhaps  ineliminable  component  of  our  conception  of  the  world   from  our  perspective  as  intentional  agents  embedded  into  that  world—but  they  maintain,  in   agreement  with  Russell,  that  such  concepts  have  no  place  in  the  conception  of  the  world  presented   to  us  by  our  well-­‐established  theories  of  physics.     The  list  of  philosophers  who  have  expressed  skepticism  about  causation  in  physics  is  both   extensive  and  distinguished,  including  Patrick  Suppes  (1970),  Richard  Healey  (1983),  Bas  van   Fraassen  (1992),  Hartry  Field  (2003),  Huw  Price  (2007),  John  Norton  (2003,  2007,  2009),  and  John   Earman  (2011).    Others,  including  Jim  Woodward  (2007)  and  Chris  Hitchcock  (2007)  have  argued   that  at  least  certain  aspects  of  our  common  sense  causal  notion  become  increasingly  strained  when   applied  to  physics.    The  general  argumentative  strategy  consists  in  pointing  to  one  or  several   supposed  contrasts  between  causal  relations  and  the  kind  of  structures  presented  to  us  by  the   2   theories  of  physics  and  to  argue  that  the  existence  of  these  contrasts  undermines  the  applicability   of  causal  reasoning  to  physics.    Perhaps  the  most  telling  contrast  is  supposed  to  be  that  between  the   asymmetry  of  the  causal  relation  and  the  putative  time-­‐reversal  invariance  of  the  dynamical  laws  of   our  mature  physical  theories.    In  this  paper  I  want  to  examine  whether  this  particular  contrast  can   be  forged  into  a  successful  argument  to  show  that  there  is  no  place  for  causal  representations  in   physics  and  will  argue  that  anti-­‐causal  arguments  appealing  to  the  asymmetry  of  causation  fail.   Even  though  I  will  defend  the  thesis  that  causal  notions  can  play  a  role  in  physics,  I  am  not   interested  in  arguing  for  a  range  of  views  that  Norton  has  grouped  together  as  “causal   fundamentalism”  or  “causal  foundationalism”:    I  am  not  defending  the  view  that  causal  notions  play   a  role  in  all  our  well-­‐established  theories  of  physics,  or  that  our  most  fundamental  theories  of   physics  provide  us  with  a  conception  of  the  world  as  causal,  or  that  it  is  the  job  of  all  theories  of   physics  to  describe  causal  relations  in  their  domain  of  investigation.    Rather  I  am  here  interested  in   the  much  more  modest  thesis  that  asymmetric  causal  notions  play  an  important  role  in  the  way  in   which  at  least  some  of  our  well-­‐established  physical  theories  represent  the  world.    That  is,  I  am  not   advocating  what  Huw  Price  and  Brad  Weslake  have  called  a  “hyperrealism”  about  causation  and   which  holds  that  causation  is  “something  ‘over  and  above’  physics.”    According  to  Price  and   Weslake’s  hyperrealist,  “physics  itself  may  be  time-­‐symmetric  [yet]  there  is  a  further,  causal,  aspect   of  reality  which  is  asymmetric.”    (Price  and  Weslake  2009)    By  contrast,  I  wish  to  argue  that  causal   representations  are  themselves  an  integral  part  of  physics.    While  the  dynamical  equations  of  many   of  our  mature  theories  of  physics  are  time-­‐reversal  invariant,  this  does  not  imply  that  the  physical   theories  as  a  whole  are  time-­‐symmetric.   Yet  I  do  not  here  wish  to  defend  a  causal  metaphysics.    I  want  to  maintain  that  causal   relations  are  more  fully  engrained  in  how  physical  theories  represent  the  world  than  Russellian  and   neo-­‐Russellian  arguments  seem  to  allow.    But  my  thesis  that  asymmetric  causal  structures  play  a   role  in  physics  only  aims  to  put  causal  relations  on  a  par  with  other  physical  properties  and   relations  that  are  represented  in  our  physical  theories  and  models.    As  such  the  thesis  is   metaphysically  neutral  and,  in  particular,  does  not  entail  a  commitment  to  a  ‘weighty’  non-­‐Humean   causal  metaphysics.   My  overall  defense  of  my  thesis  consists  of  two  prongs:  a  negative  project  aimed  at  showing   that  arguments  intended  to  establish  that  asymmetric  causal  relations  cannot  be  an  integral  part  of   theorizing  in  physics  fail—this  will  be  the  focus  of  sections  2  and  3  of  this  paper—and  a  second,   positive,  part  arguing  that  there  are  certain  domains  of  physics  in  which  time-­‐asymmetric  causal   notions  do  in  fact  play  a  genuinely  explanatory  role.    In  section  4  I  will  discuss  one  specific  example   3   of  such  causal  reasoning,  concerning  our  inference  to  the  existence  of  a  field  source  based  on  local   observations  of  disturbances  in  the  radiation  field.   The  arguments  I  examine  in  this  paper  are  broad  in  scope  and  appeal  to  what  are  supposed   to  be  generic  features  of  physical  representations.    Their  aim  is  to  establish  that  there  is  no  room   for  causal  notions  in  any  of  what  one  may  call  “our  mature  theories  of  physics”.    Mature  theories  are   not  merely  our  most  fundamental  theories,  such  as  general  relativity,  quantum  field  theory  or  a   putative  ‘final  theory’  of  quantum  gravity.    Rather,  a  mature  theory  of  physics  is  any  theory  that  is   taught  to  physics  students  today  and  that  present-­‐day  physicists  use  to  represent  physical   phenomena—that  is,  a  mature  theory  is  any  theory  currently  ‘on  the  books,’  including  classical   theories  such  as  Newtonian  mechanics  or  classical  electrodynamics.   In  the  next  section  I  discuss  the  suggestion  that  the  fact  that  physical  theories  centrally   involve  abstract  mathematical  structures  shows  that  these  theories  do  not,  or  perhaps  even  cannot,   also  involve  causal  relations.    Section  3  criticizes  arguments  that  aim  to  show  that  asymmetric   causal  relations  are  incompatible  with  the  time-­‐symmetric  laws  of  physical  theories.    While  the   discussion  in  these  two  sections  is  at  a  general  level  without  making  reference  to  any  specific   scientific  theory,  the  argument  I  will  consider  in  section  4—an  argument  for  the  claim  that  causal   principles  can  play  no  explanatory  role  in  physics—is  best  addressed  in  a  concrete  setting.    In  a   previous  paper  (Frisch  2010)  I  argued  that  causal  representations  play  an  important  role  in   accounting  for  our  experimental  interventions  into  physical  systems.    In  the  present  paper  I  want  to   focus  on  a  purely  observational  case—that  of  stellar  observations.    Against  recent  claims  by  John   Norton  (2009)  and  John  Earman  (2011)  that  causal  notions  are  both  vague  and  dispensible,  I  will   that  causal  representations  play  an  essential  inferential  and  explanatory  role  in  radiation  theory.     2.  Formulas  and  State-­‐Space  Models   I  want  to  begin  my  discussion  with  an  argument  by  Russell  (Russell  1918),  in  which  he  argues  that   imprecise  common  sense  causal  regularities  are  replaced  in  physics  by  precise  laws  that  have  the   form  of  functional  dependencies.    His  argument  appears  to  be  this.    Putatively  causal  claims  need  to   be  underwritten  by  universal  causal  regularities  of  the  form  “All  events  of  type  A  are  followed  by   events  of  type  B.”    But  in  trying  to  find  such  regularities,  we  are  faced  with  the  following  dilemma.     Either  the  events  in  question  are  specified  only  vaguely  and  imprecisely.    In  this  case  the  resulting   regularities  might  be  multiply  instantiated,  but  they  are  formulated  too  imprecisely  to  be  properly   scientific.    Or  the  events  in  question  are  specified  precisely,  but  then  the  resulting  regularities  are   instantiated  at  most  once.    Physics  avoids  this  dilemma  by  providing  us  with  precise  functional   4   dependencies  between  variables  representing  properties  of  event  types.    Russell  claims  that  such   functional  dependencies  have  replaced  putatively  causal  regularities  in  physics,  but  it  does  not   follow  from  the  fact  that  physical  theories  present  us  with  functional  dependencies  that  these   dependencies  themselves  cannot  be  interpreted  causally.    How,  then,  might  we  try  to  establish  the   claim  that  there  is  no  legitimate  place  for  an  asymmetric  notion  of  cause  in  mature  theories  of   physics?   During  his  discussion  of  Newton’s  law  of  gravity  Russell  says  that  “in  the  motion  of  mutually   gravitating  bodies,  there  is  nothing  that  can  be  called  a  cause  and  nothing  that  can  be  called  an   effect;  there  is  merely  a  formula.”  (141,  my  emphasis)    This  claim  is  echoed  decades  later  by  Bas  van   Fraassen,  who  answers  Nancy  Cartwright’s  question  (Cartwright  1993)  “why  not  allow  causings  in   the  models?”  as  follows:   To  me  the  question  is  moot.    The  reason  is  that,  as  far  as  I  can  seen,  the  models   which  scientists  offer  us  contain  no  structure  which  we  can  describe  as  putatively   representing  causings,  or  as  distinguishing  causings  and  similar  events  which  are   not  causings.    […]  Some  models  of  group  theory  contain  parts  representing  shovings   of  kid  brothers  by  big  sisters,  but  group  theory  does  not  provide  the  wherewithal  to   distinguish  those  from  shovings  of  big  sisters  by  kid  brothers.    The  distinction  is   made  outside  the  theory.  (van  Fraassen,  1993,  437-­‐8)1   While  Russell’s  remark  suggests  that  a  theory  ought  to  be  strictly  identified  with  a  set  of  formulas,   van  Fraassen  argues  that  a  theory  consists  of  a  set  of  state-­‐space  models.    But  even  though  the  two   disagree  on  whether  theories  ought  to  be  understood  syntactically  or  semantically,  they  agree  that   there  is  no  place  for  causal  notions  in  physics.    According  to  van  Fraassen’s  view  of  scientific   representation  more  generally,  a  scientific  theory  presents  us  with  a  class  of  abstract  mathematical   structures  that  we  use  to  represent  the  phenomena.    These  structures,  van  Fraassen  suggests,   cannot  be  used  to  represent  causal  relations  or  do  not  contain  a  distinction  between  causal  and   non-­‐causal  relations.    Russell’s  and  van  Fraassen’s  general  idea  seems  to  be  that  it  is  the  abstract   mathematical  nature  of  physical  theories  that  is  inhospitable  to  causal  notions.     As  a  first  attempt,  we  might  try  to  reconstruct  Russell’s  and  van  Fraassen’s  suggestions  in   terms  of  the  following  explicit  argument:   1 This  remark  occurs  within  the  context  of  a  discussion  that  also  involves  modal  aspects  of  the   causal  relation.    It  is  important,  however,  to  keep  the  two  aspects—the  putative  modality  and  the   asymmetry  of  the  causal  relation—distinct.    In  the  present  quote  van  Fraassen  unambiguously  is   concerned  with  the  asymmetry:  the  question  he  asks  is  the  mathematical  formalism  of  the  theory   allows  us  to  distinguish  asymmetric  shovings  of  brothers  by  sisters  from  their  inverse,  and  not   whether  the  shovings  in  some  sense  are  necessitated.   5   2.1 The  content  of  a  physical  theory  is  exhausted  by  a  set  of  formulas  or  state-­‐space  models.   2.2 Causal  relations  are  not  part  of  the  formulas  or  state-­‐space  models  of  a  theory.   2.3 Therefore,  causal  relations  are  not  part  of  the  content  of  physical  theories.   One  might  think  that  (2.2)  is  false  (or  at  least  not  obviously  true)  and  that  causal  relations  can  be   part  of  a  model.    After  all,  in  many  disciplines  scientists  speak  of  ‘causal  models’  or  ‘causal   equations’.2    But  according  to  van  Fraassen’s  view,  the  models  presented  by  a  scientific  theory  are,   in  the  first  instance,  uninterpreted  abstract  mathematical  structures—structures,  which  only   acquire  a  representational  role  when  they  are  used  or  taken  by  us  as  representing  certain   phenomena.    A  causal  model  or  causal  equation,  on  this  view,  could  only  be  causal  insofar  as  the   model  or  equation  is  used  to  represent  what  are  taken  to  be  causal  relations.3    The  point  might  be   obscured  by  van  Fraassen’s  use  of  the  term  ‘model’,  which  has  several  different  meanings  in  the   philosophy  of  science,  but  (2.2)  is  simply  a  consequence  of  the  claim  that  the  core  of  a  physical   theory  consists  of  abstract  mathematical  structures,  which  on  their  own  are  uninterpreted  and  do   not  represent  anything.    Put  in  terms  of  Russell’s  syntactic  framework,  at  the  core  of  the  theory   there  is  ‘merely  a  formula’.       If  understood  as  referring  to  uninterpreted  formulas  or  mathematical  structures,  (2.2)   appears  to  be  true,  but  under  this  disambiguation  (2.1)  is  obviously  false.    No  theory  of  physics  can   be  strictly  identified  with  a  set  of  formulas  or  uninterpreted  state-­‐space  models,  since  in  order  to   make  any  claims  about  the  world,  the  theory  has  to  contain  an  interpretation  which  tells  us  which   bits  of  the  formalism  are  hooked  up  with  which  bits  of  the  world.    Minimally,  a  theory’s   interpretation  has  to  specify  the  theory’s  ontology—it  has  to  specify  which  parts  of  the  world  the   different  components  of  the  mathematical  structures  are  intended  to  represent.4    But  once  we  see   that  the  austere  view  of  theories  as  consisting  solely  of  a  mathematical  formalism  or  set  of  abstract   mathematical  structures  is  untenable  and  that  an  interpretive  framework  needs  to  be  part  of  a   theory  the  question  arises  why  this  framework  could  not  be  rich  enough  to  include  causal   assumptions  as  well.    For  example,  an  interpretive  framework  for  Newton’s  laws  might  not  merely   2 This  point  was  raised  by  an  anonymous  referee. 3 Just  as  models  of  F=ma  are  not  intrinsically  models  of  Newtonian  systems  but  only  if  we  use  F,  m,   and  a  to  represent  force,  mass,  and  acceleration,  respectively. 4 As  Richard  Healey  has  reminded  me  in  conversation,  one  might  think  that  on  van  Fraassen’s  view   (or  at  least  according  to  the  view  van  Fraassen  appears  to  have  defended  in  The  Scientific  Image   (van  Fraassen  1980))  a  theory  does  not  require  an  interpretational  framework.    On  that  view  a   theory  is  true,  if  it  has  models  that  are  isomorphic  to  the  phenomena.    The  problem  with  that  view,   however,  is  that  there  may  be  too  many  isomorphisms  and  hence  that  almost  all  theories  come  out   as  (almost)  trivially  true. 6   specify  that  m  represents  mass,  F  force,  and  a  acceleration  but  might  include  the  causal  assumption   that  forces  are  causes  of  accelerations.    That  is,  we  cannot  conclude  from  the  fact  that  an   uninterpreted  formula  F=ma  does  not  on  its  own  mark  F  as  cause  and  a  as  effect,  that  the  causal   “distinction  is  made  outside  the  theory.”   Thus,  our  first  attempt  at  distilling  a  successful  argument  out  of  Russell’s  and  van  Fraassen’s   remarks  failed.    A  second  suggestion  is  that  there  might  be  constraints  on  what  can  be  part  of  the   formalism’s  interpretation  that  exclude  causal  notions.    Thus,  John  Earman  has  proposed  that  a   theory’s  content  is  exhausted  by  a  formalism  together  with  what  he  calls  a  “minimal  interpretation”   (Earman  2011).    Thus,  we  should  replace  (2.1)  with  the  following  claim:   2.1’    the  content  of  a  physical  theory  is  exhausted  by  a  set  of  state-­‐space  models  or  a  set  of   formulas  together  with  a  minimal  interpretation.   But  instead  of  answering  the  question  as  to  what  is  allowed  to  be  part  of  the  theory’s  interpretive   framework,  this  proposal  merely  postpones  the  question.    What  can  properly  be  part  of  the  minimal   interpretation  and  on  what  grounds  can  causal  interpretations  of  certain  mathematical  relations  be   excluded?    Earman’s  suggestion,  echoing  Russell’s  view,  is  that  a  minimal  interpretation  is  one  that   is  free  from  “philosophy-­‐speak”  and,  thus,  cannot  involve  the  notion  of  cause.    But  this  still  does  not   provide  an  argument  in  support  of  the  causal  skeptic,  for  what  is  lacking  is  an  account  of  what   distinguishes  ‘philosophy-­‐speak’  from  legitimate  ‘physics-­‐speak’.    The  criterion  cannot  be  to   exclude  notions  that  are  employed  by  philosophers  but  not  by  physicists,  since  the  physics   literature  is  replete  with  appeals  to  causality—for  example,  as  “physically  well-­‐founded   assumption”  (Jackson  1975,  312),  as  “fundamental  assumption”  (Nussenzveig  1972,  4)  or  as   “general  physical  property”  (Nussenzveig  1972,  7),  or  even  as  the  “most  sacred  tenet  in  all  of   physics”  (Griffiths  1989,  399).   Van  Fraassen’s  remarks  quoted  above  suggest  an  alternative  way  of  spelling  out  the  idea  of   a  minimal  interpretation:  only  those  terms  are  a  legitimate  part  of  the  interpretive  framework  that   correspond  to  a  part  of  the  formalism:  for  each  physical  correlate  of  the  mathematical  models   posited  in  the  interpretation  we  have  to  be  able  to  identify  the  structure  in  the  models  that   represents  that  part  of  the  world.    The  anti-­‐causal  claim  then  is  that  there  are  no  substructures  in   the  mathematical  models  presented  to  us  in  physics  that  can  be  described  as  representing  causings.     For  example,  one  might  ask  where  in  the  state  space  models  defined  by  Newton’s  laws  we  find   anything  that  could  be  taken  to  represent  causal  relations.    What  is  more,  van  Fraassen  even   appears  to  suggest  that  causal  relations  cannot  be  represented  structurally  in  a  mathematical   model,  for  he  says  that  “group  theory  does  not  provide  the  wherewithal  to  distinguish”  asymmetric   7   causal  relations  from  their  inverses  or,  in  his  example,  shovings  of  kid  brothers  by  big  sisters  from   shovings  of  big  sisters  by  kid  brothers.    Asymmetric  causal  distinctions,  therefore,  would  have  to  be   drawn  outside  a  theory.   To  take  this  last  worry  first,  causal  assumptions  can  be  represented  structurally.     Interpreting  a  theory  causally  may  be  thought  of  as  embedding  the  theory’s  state  space  models  into   larger  model-­‐theoretic  structures  that  contain  asymmetric  relations  between  state  space  variables.     The  state  of  a  system  S(t)  is  given  by  the  values  of  a  set  of  variables  s1(t),  s2(t),  …,  sn(t),  …,  which  may   be  finite  or  infinite.    The  dynamical  laws  of  a  theory  define  a  class  of  dynamical  models  specifying   dynamically  possible  sequences  of  states,  which  can  be  represented  in  terms  of  state  space  models.     We  can  then  define  an  asymmetric  and  transitive  relation  C=  over  the  set  of  states  S,   which  defines  a  partial  ordering  over  the  set  of  states  in  a  model.    C  can  be  interpreted  as  the  causal   relation:  S(t2)  bears  C  to  S(t1)  exactly  if  S(t1)  is  a  cause  of  S(t2).    If  two  states  do  not  stand  in  relation   C  then  they  are  not  causally  related.    The  result  is  a  class  of  what  one  might  call  potential  causal   models  of  a  theory.    Depending  on  the  theory  in  question,  we  can  also  introduce  more  fine-­‐grained   causal  relations    defined  over  individual  state  variables  si.   Applying  this  to  van  Fraassen’s  toy  example,  we  can  see  that  group  theory  does  provide  the   wherewithal  to  distinguish  shovings  of  sisters  by  brothers  from  shovings  of  brothers  by  sisters:    we   can  define  an  asymmetric  relation  R  over  the  domain  of  objects  consisting  of  all  sisters  and   brothers,  which  we  interpret  as  the  ‘a  shoves  b’  relation,  and  there  will  be  models  in  which  some  a   that  are  sisters  stand  in  relation  R  to  some  b  that  are  brothers,  but  in  which  no  brothers  stand  in   relation  R  to  any  sisters.    In  these  models  it  will  be  true  that  some  sisters  shove  their  brothers  but  it   will  not  be  true  that  any  brothers  shove  their  sisters.   One  might  reply  that  all  that  group  theory  allows  us  to  do  is  to  define  an  asymmetric   relation,  but  the  formalism  itself  does  not  allow  us  to  distinguish  between  the  relation  ‘x  is  a  cause   of  y’  and  the  relation  ‘x  is  an  effect  of  y’:  the  formalism  alone  does  not  distinguish  between  the   ‘shoves’  and  ‘is  shoved  by’  relation—and  perhaps  this  is  van  Fraassen’s  point.    But  just  as  the   formalism  on  its  own  cannot  determine  which  objects  its  different  variables  represent  and   represents  certain  objects  only  in  virtue  of  it  being  used  to  represent  these  objects,  our  use  can   equally  determine  that  a  given  asymmetric  relation  represents  the  ‘cause’  rather  than  the  ‘effect’   relation.           What  remains  is  van  Fraassen’s  first  worry,  for  while  there  might  be  structures  which  we   “can  putatively  describe  as  representing  causings,”  van  Fraassen  could  maintain  that  these   structures  are  not  part  of  the  models  scientists  do,  as  a  matter  of  fact,  use.    To  present  a  theory,  he   8   would  insist,  is  simply  to  present  a  class  of  (suitably  interpreted)  state  space  models,  defined  by  a   theory’s  basic  equations.    But  it  is  not  obvious  to  me  that  this  last  claim  is  correct.    As  the  above   quotes  suggest,  physicists  often  do  invoke  causal  assumptions.    And  such  informal  appeals  to  causal   principles  could  be  understood  as  implicitly  defining  a  causal  structure  into  which  models  of  the   dynamical  equations  are  thought  to  be  embedded.    Since  the  causal  structures  in  question  often  are   very  simple  there  may  be  little  or  nothing  gained  from  adding  a  formal  representation  of  this   structure  to  the  theory’s  equations.    Nevertheless,  if  we  want  to  offer  a  formal  reconstruction  of  a   theory,  say,  along  the  lines  of  van  Fraassen’s  semantic  view,  we  would  have  to  include  a   representation  of  any  causal  assumptions,  even  if  physicists  themselves  never  represent  these   assumptions  formally  in  terms  of  a  partial  ordering  relation.    Of  course,  to  establish  whether   physicists’  explicit  appeal  to  causal  assumptions  in  any  particular  theory  ought  to  be  indeed   understood  as  a  commitment  to  a  causal  structure  would  require  a  more  detailed  case-­‐by-­‐case   investigation.    My  present  point  is  merely  that  we  cannot  conclude  simply  from  the  fact  that  the   models  of  a  set  of  equations  do  not  contain  structures  representing  asymmetric  causal  relations  that   scientific  theories  contain  no  asymmetric  causal  assumptions  and  that  any  causal  “distinction  is   made  outside  the  theory.”   If  we  want  to  establish  that  causal  relations  cannot  be  part  of  how  physics  represents  the   world,  we  need  a  more  substantive  argument  than  merely  an  appeal  to  the  formal  character  of   functional  dependencies  or  state-­‐space  models.    What  is  it  exactly  about  the  mathematical   machinery  of  physical  theories  that  may  appear  to  render  it  incompatible,  or  at  least  make  it  sit  ill,   with  causal  notions?    The  suggestion  I  want  to  examine  now  is  that  the  time-­‐reversal  invariance  of   the  dynamical  equations  is  incompatible  with  asymmetric  causal  relations.     3.  Time-­‐reversal  invariance   The  contrast  between  the  time-­‐reversal  invariance  of  the  dynamical  laws  and  the  time-­‐asymmetry   of  the  causal  relation  can  be  fashioned  into  an  explicit  anti-­‐causal  argument  as  follows:   3.1  Causal  relations  are  temporally  asymmetric.   3.2  The  physical  laws  of  our  well-­‐established  theories  have  the  same  character  in   both  the  forward  and  backward  temporal  directions.   3.3    Therefore,  there  is  no  place  for  time-­‐asymmetric  causal  relations  in  a  theory   with  time-­‐symmetric  laws.   3.4.    Therefore,  there  is  no  place  for  the  causal  relations  in  our  well-­‐established   theories  of  physics.   9   Both  premises  (3.1)  and  (3.2)  would  deserve  further  comment:    (3.1)  appears  to  deny  the   possibility  of  instantaneous  causation,  while  (3.2)  might  strike  one  as  obviously  false:    there  are   many  well-­‐established  but  non-­‐fundamental  theories  that  are  not  time-­‐symmetric,  and  there  are   even  arguably  fundamental  theories  that  are  not  time-­‐reversal  invariant.    But  we  can  restrict  our   attention  to  well-­‐established  theories  that  are  not  explicitly  phenomenological,  like   thermodynamics  is,  and  follow  the  perhaps  unjustified  practice  of  ignoring  failures  of  time-­‐reversal   invariance  in  more  fundamental  physics.    Thus,  here  I  want  to  focus  on  the  inference  from  premises   (3.1)  and  (3.2)  to  (3.3).   One  might  read  this  inference  as  simply  relying  on  the  same  assumptions  about  the  content   of  a  physical  theory  as  the  argument  in  the  preceding  section—the  assumption  that  the  content  of  a   theory  is  exhausted  by  a  set  of  state  space  models  with  a  minimal  interpretation  that  associates  the   “mathematical  squiggles”  of  an  equation  with  physical  quantities.    This  is  how  Alyssa  Ney   apparently  reads  her  reconstruction  of  what  seems  to  be  essentially  the  same  argument  (Ney  2009,   748).    Alternatively,  the  appeal  to  the  time-­‐reversal  invariance  of  the  laws  might  be  taken  to  add   something  to  the  argument  above.    The  claim  then  is  that  while  in  principle  causal  notions  could  be   part  of  the  interpretive  framework  of  a  theory,  the  fact  that  a  theory  has  time-­‐reversal  invariant   laws  prohibits  that  it  be  interpreted  causally.    But  it  is  unclear  why  we  should  accept  this  claim.   Assume,  for  instance,  that  the  theory  in  question  is  deterministic  (or  near-­‐deterministic).     What  the  argument  denies,  then,  is  that  if  the  full  set  of  causes  of  an  event  determine  the  occurrence   of  an  effect—that  is,  if  the  theory  is  causally  forward  deterministic,  a  complete  set  of  effects  cannot   similarly  determine  the  occurrence  of  their  joint  cause,  and  this  premise  does  not  appear  to  be   defensible.    Mackie’s  INUS  condition  account,  for  example,  has  the  consequence  that  under  some   very  weak  additional  assumptions,  causes  are  not  just  INUS  conditions  of  their  effects,  but  effects   are  also  INUS  conditions  of  their  causes.    But  it  does  not  follow  from  this  fact,  that  it  is  impossible  to   supplement  Mackie’s  account  with  some  condition  that  allows  us  asymmetrically  do  distinguish   causes  from  effects.5    More  generally,  it  is  hard  to  see  why  the  notion  of  an  event  asymmetrically   causing  certain  effects  should  be  incompatible  with  the  effects  determining  the  occurrence  of  their   causes.    The  claim  that  causes  in  some  sense  bring  about  their  effects  does  not  seem  to  preclude  the   possibility  that  the  occurrence  of  certain  events  can  be  used  to  infer  the  occurrences  of  their  causes.   Usually  the  claim  that  time-­‐reversal  invariant  laws  are  incompatible  with  time-­‐asymmetric   causal  relations  is  made  without  offering  any  further  argument.    For  example,  Erhard  Scheibe   5 See  (Newton-­‐Smith  1983)  for  a  proposal  of  how  one  might  introduce  the  asymmetry  of  the  causal   relations  into  a  Mackie-­‐style  account  of  causation. 10   maintains,  after  pointing  to  the  contrast  between  time-­‐symmetric  laws  and  time-­‐asymmetric  causal   relations,  that  “this  suffices  to  seal  the  fate  of  event-­‐causality.”  (Scheibe  2006,  213)6    One  of  the  few   exceptions  to  this  rule  is  an  argument  by  Norton  (in  his  reply  to  my  (2009)  discussion  of  the  role  of   causal  assumptions  in  the  derivation  of  dispersion  relations)  that  aims  to  show  that  one  can  derive   a  contradiction  from  the  conjunction  of  time-­‐symmetric  dynamical  laws  with  a  time-­‐asymmetric   asymmetric  causal  assumption.    I  want  to  quote  Norton’s  argument  in  full:   Now  imagine  a  universe  completely  empty  excepting  two  processes  that  we  will  call  ‘A’  and   ‘B’.  Process  A  has  an  incident  wave,  a  dielectric,  and  a  scattered  wave.  Process  B  is  the  time   reverse  of  A.    The  two  processes  are  completely  isomorphic  in  all  properties.  Any  property   of  one  will  have  its  isomorphic  correlate  in  the  other.  Any  fact  about  one  will  have  a   correlate  fact  obtaining  for  the  other.  One  might  be  tempted  to  imagine  that  one  of  the  two   processes  is  ‘really’  the  ordinary  one,  progressing  normally  in  time;  while  the  other  is  a   theoretician’s  fantasy,  a  possibility  in  principle,  but  in  practice  unrealizable.  The  essential   point  of  the  example  is  that  no  property  of  the  A  and  B  systems  distinguish  which  is  which.     Every  property  of  one  has  a  perfect  correlate  in  the  other.    Let  us  assume  that  Frisch’s   principle  of  causality  applies  to  one  of  these  processes,  the  A  process,  for  example.  That  will   be  expressed  as  a  condition  that   the  present  state  of  the  process  depends  only  on  its  past  states.  Exactly  what  ‘depends’  may   amount  to  is  to  be  decided  by  the  principle.    All  that  matters  for  our  purposes  is  that  an   exactly  isomorphic  condition  of  dependence  will  be  obtained  in  the  B  process,  except  that  it   will  be  time  reversed.    Indeed,  using  the  time  order  natural  to  process  A,  we  would  have  to   say  that  the  principle  of   causality  requires  the  present  states  of  process  B  to  depend  upon  its  future  states.  In  short,   if  the  principle  applies  to  process  A,  it  fails  for  process  B;  and  conversely.    This  is  a  reductio   ad  absurdum  of  the  applicability  of  Frisch’s  principle  of  causality  to  scattering  in  classical   electrodynamics.  (Norton  2009,  481-­‐2)     The  argument  appears  to  be  this.    Let  us  begin  by  postulating  time-­‐symmetric  dynamical  laws  that   allow  a  certain  process  A  to  occur,  which  is  itself  time-­‐asymmetric.    Since  the  laws  are  time-­‐ symmetric  they  also  allow  the  time-­‐reverse  of  A,  the  process  B,  to  occur.    If  we  then  posit  in  addition   a  general  causal  principle,  according  to  which  future  states  causally  depend  on  past  states  (but  not   6 “Schon  [mit  diesem  Kontrast]  scheint  mir  das  Schicksal  der  Ereigniskausalität  als  fundamentaler   Gesetzlichkeit  besiegelt  zu  sein.”  (the  translation  into  English  is  my  own) 11   past  states  on  future  states)  and  which  we  assume  that  A  satisfies,  we  can  derive  a  contradiction:  on   the  one  hand,  since    A  satisfies  the  causal  principle  but  the  dynamical  laws  are  time-­‐symmetric,  B,  in   virtue  of  being  the  time  reverse  of  A,  will  satisfy  an  inverse  causal  principle  according  to  which  a   past  state  of  the  process  B  causally  depends  on  its  future  states  (but  not  vice  versa).    But  on  the   other  hand,  since  the  causal  principle  is  assumed  to  be  general,  B  will  also  satisfy  the  original   principle  and  future  states  of  the  process  should  depend  on  the  past  state  (but  not  vice  versa).    This   concludes  the  reductio  ad  absurdum.   Schematically,  the  argument  may  be  presented  as  follows:   3.5   There  is  a  time-­‐asymmetric  dynamical  process  A  governed  by  time-­‐symmetric   dynamical  laws.   3.6   B,  the  temporal  inverse  of  A,  is  dynamically  possible.  (5)   3.7   A  and  its  temporal  inverse  B  have  exactly  the  same  physical  properties.  (5,  6)   3.8   For  all  processes,  future  states  causally  depend  on  past  states  (but  not  vice  versa).   (Causal  Principle)   3.9   Future  states  of  A  causally  depend  on  its  past  states.  (8)   3.10   Past  states  of  B  causally  depend  on  its  future  states  (but  not  vice  versa).  (7,  9)   3.11     Future  states  of  B  causally  depend  on  its  past  states  (but  not  vice  versa).  (8)   That  is,  the  conjunction  of  time-­‐symmetric  dynamical  laws  with  a  time-­‐asymmetric  causal  principle   results  in  a  contradiction.   Premise  (3.5)  cannot  be  assailed,  since  even  though  we  assume  the  laws  to  be  time-­‐ symmetric,  many—and  in  some  intuitive  sense,  most—models  of  the  laws  will  be  time-­‐asymmetric.     But  a  defender  of  a  causal  principle  should  resist  the  steps  of  the  argument  leading  to  (3.10),  and  in   particular  the  inference  from  (3.5)  to  (3.7)  and  (3.10):    It  does  not  follow  from  the  assumptions  that   B  is  the  dynamical  time-­‐reversal  of  process  A  and  that  A  satisfies  a  time-­‐asymmetric  causal   principles,  that  B  will  satisfy  an  inverse  causal  principle.    Since  Norton’s  inference  might  strike  one   as  initially  plausible  I  want  to  be  belabor  this  point  a  bit.    Let  us  assume  that  purely  dynamical   models  of  A  and  B  can  be  represented  by  non-­‐directed  graphs:     (A)   and   (B)     According  to  the  causal  principle,  both  models  can  be  embedded  into  richer  structures  that  include   an  asymmetric  relation,  which  can  be  represented  by  adding  a  direction  to  the  graphs:     12     (Acausal)     (Bcausal)         Norton  points  out  that  there  is  nothing  in  the  purely  dynamical  models  (that  is  the  mathematical   structures  satisfying  the  dynamical  laws)  that  tells  us  which  model  is  which—there  is  no  intrinsic   difference  between  the  two  dynamical  models—but  the  symmetry  is  broken  in  the  directed  causal   models.    And  since  the  principle  of  causality  is  a  general  principle,  once  we  ‘add  the  arrowheads’  to   one  graph,  as  it  were,  this  fixes  the  direction  of  the  arrows  in  the  other  graphs.    Whatever  models   are  used  to  model  two  physical  processes  A  and  B,  respectively,  we  know  that  their  orientations  are   opposite  to  each  another.     According  to  Norton  “the  principle  of  causality  requires”  also  that  we  represent  the   putatively  causal  process  B  by  the  inverse  graph:     (Banti-­‐causal)     Norton’s  reason  is  that  it  follows  from  the  fact  that  the  two  processes  A  and  B  are  time-­‐reverses  of   each  other  that  there  is  no  property  that  distinguishes  them.    Since  there  is  no  physical  difference   between  the  two  processes  A  and  B,  whatever  reasons  we  might  have  for  adding  arrows  to  the   graph  representing  A  from  the  vertex  of  degree  two—that  is,  the  vertex  with  two  edges  at  the   bottom  of  the  graph  above—to  the  two  vertices  of  degree  one,  the  very  same  reasons  would  imply   that  we  have  to  draw  arrows  in  the  graph  representing  B  from  the  vertex  with  degree  two  at  the  top   of  the  graph  to  the  two  arrows  with  degree  one  at  the  bottom.   But  this  step  of  the  argument  begs  the  question  against  a  defender  of  a  causal  principle,  who   maintains  that  it  is  precisely  the  causal  properties  of  the  two  processes  that  distinguish  them:    In   the  causal  process  A  the  event  represented  by  the  vertex  of  degree  two  causes  the  events   represented  by  the  two  vertices  of  degree  one,  whereas  in  the  causal  process  B  the  events   represented  by  the  two  vertices  of  degree  one  cause  the  event  represented  by  the  vertex  of  degree   two.    That  is,  (3.7)  does  not  follow  from  (3.5)  alone,  but  requires  as  additional  assumption  the  claim   that  the  physical  properties  of  a  physical  system  are  exhausted  by  those  captured  in  the  dynamical   equations  governing  the  system  and  this  is  precisely  the  assumption  that  a  defender  of  a  principle   of  causality  wishes  to  deny,  who  would  want  to  insist  that  the  arrows  in  the  causal  model  also   represent  physical  properties  of  the  system—properties  that  cannot  be  derived  from  the  dynamical   13   equations  alone.7    While  there  is  no  difference  between  the  two  purely  dynamical  models   represented  by  the  two  non-­‐directed  graphs—indeed  they  arguably  are  one  and  the  same—there  is   a  difference  between  the  two  physical  processes  represented  and  that  difference  consists  in  the   difference  in  causal  structure  represented  in  the  two  directed  graphs  Acausal  and  Bcausal.          Of  course  the  causalist’s  assumption  that  there  are  properties  that  distinguish  the  two   processes  but  are  not  represented  in  the  dynamical  equations  is  open  to  challenge  and  one  can  try   to  argue  that  any  appeal  to  asymmetric  causal  structures  in  addition  to  a  theory’s  purely  dynamical   models  is  unfounded  or  scientifically  unjustified.    Indeed,  immediately  after  presenting  his  reductio   argument,  Norton  suggests  considerations  to  this  effect  and  I  will  discuss  these  considerations   below.    Yet  once  we  add  as  additional  premise  the  claim  that  positing  causal  structures  is   unjustified,  it  becomes  unclear  what  the  overall  structure  of  Norton’s  argument  is  meant  to  be.    The   additional  premise  would  itself  have  to  be  supported  by  an  argument,  but  such  an  additional   argument  would,  if  it  could  be  made  successfully,  render  the  reductio  proposed  by  Norton   superfluous.    If  one  were  able  to  show  that  there  are  no  legitimate  reasons  for  positing  a  physical   difference  between  processes  A  and  B,  the  causalist  would  be  defeated  and  there  would  be  no  work   left  to  be  done  for  the  reductio  argument.    Thus,  without  an  additional  argument  for  the  implicit   premise  in  the  argument  from  2.5  to  2.7  the  reductio  begs  the  question  against  the  causalist,  but  if   we  had  such  an  additional  argument,  that  alone  would  suffice  to  make  the  case  against  the  causalist.     4.  Broadcast  waves  and  starlight   Up  until  now  I  have  considered  appeals  to  time-­‐reversal  invariance  as  aiming  to  show  that  it  is   impossible  to  interpret  a  theory  with  time-­‐reversal  invariant  laws  time-­‐asymmetrically  causally.8     But  I  have  just  suggested  that  there  may  be  another  (and  I  take  it  arguably  more  plausible)  position   according  to  which  it  would  be  a  mistake  to  accept  a  causal  principle  not  because  it  is  strictly   incompatible  with  time-­‐symmetric  laws  but  because  there  are  no  good  reasons  for  positing  causal   properties  and  relations  in  addition  to  the  non-­‐causal  properties  represented  in  the  dynamical   laws.    The  basic  equations  of  a  theory  that  is  future-­‐  as  well  as  past-­‐deterministic  define  both  an   7  Even  though  I  am  following  Norton  here  in  expressing  the  argument  in  terms  of  real  physical   properties  of  a  process,  the  point  I  wish  to  make  here  is  independent  of  the  debate  about  scientific   realism.    A  defender  of  a  principle  of  causality  can  also  be  an  instrumentalist  and  argue  that  the   causal  relations  in  our  models  no  more  represent  real  properties  than  other  properties  or  relations   in  our  models.    My  claim  here  is  that  there  is  no  principled  reason  for  treating  causal  properties   differently  from  other  kinds  properties  and  relations  of  our  models  (and  of  the  real  world  systems   we  are  modeling). 8 This  is  also  what  (Field  2003)  appears  to  argue. 14   initial  and  a  final  value  problem.    If  we  begin  with  the  system’s  initial  state,  then  the  dynamical   equations  determine  the  system’s  subsequent  evolution;  if  we  take  the  system’s  final  state  to  be   given,  then  the  dynamical  equations  determine  the  system’s  earlier  evolution.    Thus,  one  might  be   tempted  to  agree  with  Fritz  Rohrlich,  who  once  maintained  that  the  “identification  of  causality  with   prediction  rather  than  retrodiction  in  a  time-­‐symmetric  system  of  equations  is  completely   arbitrary.”  (Rohrlich  1990,  51  italics  in  original)9    Thus,  while  there  may  be  no  good  arguments  that   strictly  disallow  interpreting  a  theory  causally,  it  might  nevertheless  be  the  case  that  there  could  be   no  scientifically  legitimate  reasons  for  supporting  an  asymmetric  causal  interpretation  of  a  theory.   My  discussion  has  been  rather  general  so  far,  but  the  question  whether  positing  causal   relations  is  justified  can  only  be  addressed  in  a  concrete  setting  and  by  examining  specific  examples   of  physical  theories  in  which  causal  notions  might  be  thought  to  be  play  a  role.    The  example  Norton   himself  discusses  is  the  putatively  causal  asymmetry  characterizing  radiation  fields  associated  with   an  oscillating  source  and  I  want  to  focus  on  that  asymmetry  here  as  well.10    Consider  an  antenna   that  broadcasts  into  empty  space.11    The  radiation  emitted  by  the  antenna  is  a  coherently  diverging   field  traveling  to  spatial  infinity.    Call  this  ‘process  A’  in  accordance  with  the  terminology  introduced   above.    The  temporal  inverse  of  this  process—one  that  is  also  allowed  by  the  wave  equation  in  the   presence  of  wave-­‐sources—is  a  field  that  is  coherently  collapsing  into  the  antenna  and  is  absorbed.     Call  this  ‘process  B’.    Norton  in  effect  argues  that  since  both  processes  are  physically  possible,  there   can  be  no  scientifically  legitimate  reason  for  representing  A  and  B  in  terms  of  the  causal  structures   Acausal  and  Bcausal,  respectively.    Appealing  to  a  causal  principle  would  be  justified,  Norton  suggests,   only  if  the  principle  allowed  us  correctly  to  exclude  certain  dynamically  possible  processes  as   causally,  and  hence  physically,  impossible.    But  in  the  case  at  issue  both  processes—the  diverging   9 Despite  what  Rohrlich  says  here,  he  seems  to  believe  now  that  there  can  be  good  reasons  for   interpreting  a  theory  with  time-­‐reversal  invariant  laws  causally  asymmetrically.    (See  Rohrlich   2006) 10 Norton’s  paper  is  a  response  to  my  (2009a),  where  I  argue  that  dispersion  theory  invokes  causal   assumptions.    Norton  apparently  assumes  in  his  reply  that  the  relevant  asymmetry  in  this  case  just   is  an  instance  of  the  electrodynamic  wave-­‐asymmetry  that  he  discusses.    I  am  less  sure  than  he  is,   however,  that  the  two  cases  are  as  closely  related  as  he  suggests.    I  have  two  concerns:  first,   dispersion  theory  is  just  one  particular  application  of  the  general  framework  of  linear  response   theory,  which  also  has  many  applications  outside  of  electrodynamics;  and,  second,  there  appears  to   be  a  formal  disanalogy  between  the  Green’s  functions  used  in  the  two  cases:    while  the  Green’s   function  for  the  wave  equation  has  a  temporal  inverse,  the  inverse  Green  function  in  the  case  of   linear  response  theory  is  not  mathematically  well-­‐defined.    That  is,  while  one  can  solve  the  wave-­‐ equation  both  as  an  initial  value  problem  and  a  final  value  problem,  one  cannot,  it  seems,  represent   a  linear  response  system  through  a  final  value  problem.   11 In  order  to  bring  out  the  asymmetry  as  simply  and  clearly  as  possible  I  am  adjusting  Norton’s   specific  example  slightly.    The  example  of  the  antenna  is  discussed  in  (Earman  2011). 15   and  the  converging  radiation  fields—are  physically  possible.    To  be  sure,  we  generally  do  not   observe  radiation  coherently  converging  on  a  source,  but  it  is  in  principle  possible  to  set  up  such   processes,  for  example  with  the  help  of  perfect  mirrors  or  the  carefully  correlated  action  of  multiple   sources  of  radiation.    Hence  adding  a  causal  principle  does  no  real  work  in  the  present  case—it   amounts  to  adding  a  distinction  that  makes  no  difference—and  therefore  is  not  scientifically   justified.   Yet,  as  I  want  to  argue  now,  causal  notions  play  a  scientifically  legitimate  role  in  radiation   theory,  even  though  they  do  not  provide  an  additional  constraint  on  what  is  dynamically  possible.     Understanding  the  relation  between  sources  and  fields  causally  plays  both  an  important  inferential   and  an  important  explanatory  role  in  the  theory.   I  want  to  preface  my  argument  with  a  clarification  of  the  argument’s  target.    There  is  a   sizeable  literature  defending  the  thesis  that  the  asymmetry  between  diverging  and  converging   waves  ultimately  is  of  thermodynamic  origin.    This  literature  suggests  one  possible  kind  of  anti-­‐ causal  argument—an  argument  that  can  concede  that  a  causal  account  could  in  principle  provide  an   explanation  of  the  asymmetry,  but  argues  that  the  thermodynamic  account  offers  a  superior   explanation.    That  is,  the  argument  compares  two  prima  facie  scientifically  legitimate  explanations   and  argues  that  one  of  them  is  superior  to  the  other  or,  perhaps,  that  one  of  them  is  more   fundamental  than  the  other.   Now,  it  is  not  prima  facie  obvious  how  a  thermodynamic  explanation  of  the  absence  of   converging  radiation  would  proceed  in  the  case  of  an  antenna  broadcasting  into  empty  space.    For   in  this  case  we  are  not  dealing  with  a  closed  system  and  the  asymmetry  between  coherently   diverging  and  coherently  converging  radiation  seems  to  be  entirely  an  asymmetry  in  initial   conditions:  coherent  radiation  coming  in  from  spatial  infinity  in  one  case  and  the  absence  of  any   coherent  incoming  radiation  in  the  other.    Yet  since  there  is  not  enough  room  to  more  fully  assess   this  argumentative  strategy  here,12  my  present  aim  is  more  modest:  Instead  of  showing  that  causal   representations  are  an  irreducible  part  of  radiation  theory,  I  merely  want  to  show  that  introducing   causal  relations  can  play  both  an  explanatory  and  an  inferential  role.    Thus,  my  target  here  is  the   stronger  thesis  that  a  causal  principle  fails  dramatically  even  when  considered  on  its  own  and  not   only  by  comparison  to  some  other  putative  explanation  of  the  asymmetry  of  radiation  phenomena.   Imagine  you  are  looking  up  at  the  night  sky  and  observing  the  light  emitted  by  a  particular   star.    What  licenses  your  inference  that  the  observed  radiation  was  indeed  emitted  by  a  star  as  its   12 But  see  (Frisch  2005;  2006;  forthcoming)  for  criticisms  of  a  version  of  the  thermodynamic   argument.   16   source  rather  than  it  being  source-­‐free  radiation  coming  in  from  spatial  infinity?    It  appears  to  be   almost  religious  dogma  among  certain  philosophers  of  physics  that  the  content  of  a  physical  theory   is  exhausted  by  the  models  of  its  dynamical  equations  and,  hence,  that  the  only  way  to  use  a  theory   to  make  empirical  predictions  is  to  solve  an  appropriate  initial  (or  final)  value  problem.    In  our  case   the  initial  value  problem  requires  a  specification  of  the  state  of  the  field  and  of  all  sources  on  a   Cauchy  surface—a  spacelike  cross  section  of  a  lightcone  centered  on  the  putative  source—that  is   then  fed  into  the  Maxwell-­‐Lorentz  equations.    But  in  fact  the  only  data  we  have  at  our  disposal  for   inferring  the  existence  of  the  star  are  our  highly  localized  observations  of  the  radiation  fields.     Neither  do  we  know  the  fields  on  anything  close  to  a  complete  initial  value  surface  nor  do  we  have   independent  access  to  the  trajectories  of  the  source—the  star  emitting  the  radiation.    Thus,  if  the   only  tools  at  our  disposal  for  making  inferences  about  the  putative  sources  of  stellar  radiation  were   the  dynamical  laws  applied  to  an  initial  value-­‐problem,  it  would  be  a  complete  mystery  as  to  how   we  can  ever  come  to  know  of  the  existence  of  a  star.   But  we  do  seem  to  be  able  to  make  justified  inferences  about  the  state  of  the  cosmos  at   earlier  times.    What  then  is  the  structure  of  these  inferences?    The  answer  is  that  our  inference  to   the  existence  of  a  star  as  the  source  of  the  observed  radiation  is  a  paradigmatically  causal  inference:   the  radiation  fields  observed  at  different  spacetime  points  are  highly  correlated  with  one  another   and  we  infer  from  these  correlations  to  the  existence  of  a  common  cause.  In  fact,  the  locally   observed  fields  are  correlated  in  several  different  ways.    What  we  observe  are  relatively  strong   disturbances  in  a  very  weak  background  field.    There  is  an  (almost)  perfect  coincidence  in  the   luminosities  and  spectral  distributions  of  the  radiation  observed  at  different  locations.    And  even   more  strikingly,  the  shapes  of  the  field  disturbances  received  at  different  spatial  locations  match  so   closely,  that  they  can  be  made  to  interfere  with  one  another—a  fact  that  is  exploited  in  stellar   interferometry.    The  degree  of  partial  coherence  in  this  last  sense  can  be  expressed  in  terms  of  so-­‐ called  ‘coherence  functions’  associated  with  the  waves  (see,  e.g.,  Born  and  Wolf,  1999,  ch.  10).   Since  the  directions  from  which  the  correlated  field  disturbances  at  different  times  are   observed—their  celestial  latitudes  and  longitudes—are  such  that  the  fields  can  be  associated  with   the  trajectory  of  a  single  localized  source  in  relative  motion  to  us,  we  infer  the  existence  of  a  star  as   common  cause  of  our  observations  as  providing  the  best  explanation  for  the  observed  correlations.   Thus,  the  inference  to  the  existence  of  a  single  star  as  source  of  the  radiation  is  a  standard   example  of  an  inference  to  a  common  cause—an  inference  pattern  is  widely  used,  both  in  the   sciences  and  in  common  sense  reasoning.    Indeed,  in  discussions  of  correlation  functions  in  the   physics  literature  it  seems  to  be  simply  presupposed,  without  need  for  a  justification,  that  strong   17   correlations  among  field  disturbances  generally  allow  us  to  infer  to  a  common  source  and,   conversely,  that  the  absence  of  a  common  source  would  result  in  uncorrelated  fields.    Thus,  Born   and  Wolf  elucidate  the  idea  of  measuring  correlations  between  locally  received  disturbances  in   terms  of  possible  interferences  by  contrasting  the  case  of  strong  correlations,  when  light  comes   from  a  single  “very  small  source  of  a  narrow  spectral  range,”  with  the  case  of  zero  correlations,   when  the  two  observation  points  “each  receive  light  from  a  different  physical  source”  (Born  1999,   555).     Here  is  an  example  of  the  same  kind  of  inference  from  outside  physics:  in  a  string  of  bank   robberies  the  police  discover  similar  kinds  of  little  plastic  toys  left  behind  at  each  crime  scene—a   fact  that  is  not  made  public  by  the  investigators.    The  police  infer  from  these  discoveries  that  the   robberies  were  committed  by  one  and  the  same  gang  rather  than  by  different  groups  that  operate   in  complete  independence  from  one  another.     There  is  a  large  literature  on  how  properly  to  reconstruct  such  inferences  to  a  common   cause.    One  formulation  of  a  principle  of  the  common  cause  (PCC)  underwriting  such  inferences   states  that  if  two  quantities  X    and  Y  are  correlated  and  X  and  Y  are  not  related  as  cause  and  effect,   then  X  and  Y  are  the  joint  effects  of  a  common  cause  Z.    In  Reichenbach’s  original  formulation  the   principle  also  contains  a  screening-­‐off  condition  according  to  which  the  common  cause  Z  screens  off   any  probabilistic  dependence  between  X  and  Y.    As  has  been  much  discussed  in  the  literature,   however,  there  are  several  counterexamples  to  the  principle  of  the  common  cause  (see  Arntzenius   2010  for  a  survey).    These  counterexamples  can  be  avoided,  if  we  think  of  the  principle  as  a   defeasible  epistemological  guide  rather  than  as  a  metaphysical  principle  and  if,  following  Eliot   Sober  (Sober  1984;  2001),  we  construe  common  cause  inferences  comparatively  as  involving  a   comparison  of  the  likelihood  conferred  on  the  evidence  by  a  common  cause  explanation  with  the   likelihoods  of  competing  separate  cause  explanations.    Thus,  as  I  want  understand  it,  the  principle   of  the  common  cause  asserts  that  it  is  reasonable  to  posit  the  existence  of  a  localized  common  cause   to  explain  distant  correlations,  unless  there  is  a  separate  cause  explanation  that  (i)  confers  a  higher   likelihood  on  the  explanandum  and  (ii)  does  not  merely  engage  in  “explanatory  buck  passing”   (Sober  1984,  221)  by  proposing  to  explain  distant  correlations  at  one  time  by  even  earlier  distant   correlations.     How  should  we  cash  out  the  claim  that  the  disturbances  in  the  radition  field  are  correlated?     One  option  would  be  to  try  to  express  the  degree  of  correlation  non-­‐probabilistically  entirely  in   terms  of  the  correlation  function.    The  problem  with  this  suggestion  is  that  the  correlation  function   depends  on  properties  of  the  source  that  seem  not  to  track  very  well  the  degree  of  confidence  with   18   which  we  are  willing  to  infer  the  existence  of  a  common  source.    For  example,  the  absolute  value  of   the  correlation  function  is  much  smaller  for  sunlight  than  for  starlight  (since  the  distant  stars   appear  almost  as  point  sources),  nevertheless  we  just  as  readily  infer  the  existence  of  the  sun  from   the  direct  sunlight  we  observe  as  we  infer  the  existence  of  a  star  from  the  observed  stellar   radiation.       Alternatively,  we  could  try  to  express  the  idea  of  correlation  in  terms  of  perfect   coincidences:    Within  a  generally  very  weak  background  field,  the  luminosities  and  spectral   decompositions  of  stronger  field  disturbances  at  different  observation  points  match  (almost)   perfectly  and  (due  to  the  spatio-­‐temporal  distribution  of  the  disturbances)  can  therefore  be   associated  with  the  trajectory  of  a  single  source.     But  one  could  also  express  the  correlations  probabilistically:    There  is  a  certain  small  but   non-­‐zero  probability  of  observing  a  relatively  strong  non-­‐zero  field  disturbance  coming  in  from  an   arbitrary  direction  in  the  sky.    But  the  conditional  probability  of  detecting  radiation  from  one   direction,  given  that  we  detected  radiation  from  the  same  (or  rather  appropriately  related)   direction  earlier  is  muc  higher.    That  is,  we  are  allowed  to  infer  the  existence  of  a  star  as  common   cause  form  the  fact  that  the  field  disturbances  at  two  different  locations  are  strongly  correlated,   since  the  correlations  are  far  more  probable,  given  the  hypothesis  that  the  disturbances  were   produced  by  one  and  the  same  source,  than  if  we  assume  separate  causes,  be  it  different  sources   acting  independently  of  each  other  or  source-­‐free  fields  coming  in  from  spatial  infinity.    We  can   express  this  more  formally,  where  the  relata  of  the  causal  relation  are  taken  to  be  the  values  of   variables:     Pr(F(t1,x1)  &  F(t2,x2)/  S(tret1,  xret1)  &  S(tret2,  xret2))  >>  Pr(F(t1,x1)  &  F(t2,x2)/  S(tret1,  xret1)  &  S*(tret2,  xret2))           (1)   Here  F(t1,x1)  and  F(t2,x2)  are  the  values  of  the  electromagnetic  fields  at  the  observation  points  (t1,x1)   and  (t2,x2),  respectively,  and  S(tret1,  xret1)  represents  the  state  of  the  source  s  at  what  is  known  as  the   “retarded”  point—the  point  on  the  backward  lightcone  of  (t1,x1)  at  which  the  source  s  would  have  to   have  been  located  to  give  rise  to  the  field  F(t1,x1).    S*  represents  a  separate  source  s*,  while  the  state   of  the  source  s  at  (tret2,  xret2),  S(tret2,  xret2),  follows  (quasi-­‐)  deterministically  from  its  earlier  state   S(tret1,  xret1).    That  is,  S(tret1,  xret1)  acts  as  a  common  cause  of  both  field  observations  F(t1,x1)  and   F(t2,x2).   The  overall  process  is,  of  course,  deterministic  (at  least  as  long  as  we  treat  it  purely  within   classical  electrodynamics):  initial  fields  in  the  remote  past  together  with  the  field  associated  with   the  stars  as  sources  nomologically  determine  what  the  observed  fields  will  be.    This,  one  might   19   think,  leads  to  two  problems  for  my  account:    First,  demanding  that  the  common  cause  screen  off  its   effects  from  one  another  might  seem  problematic.    Not  only  is  it  trivially  true  that  there  will  be  a   screening-­‐off  event  in  the  case  of  deterministic  theories,  but  there  also  will  be  screening-­‐off  events   in  the  future  of  the  distant  correlations  to  be  explained.    What,  then,  licenses  our  inference  to  the   existence  of  a  past  common  cause?    The  deterministic  setting,  however,  does  not  guarantee  that  the   events  in  question  will  be  localized.    That  is,  a  principle  positing  the  existence  of  a  localized  common   cause  is  not  trivial.    Future  screening-­‐off  events,  in  the  case  of  our  example,  will  generally  be  highly   non-­‐local:  disturbances  in  the  radiation  field  diverge  from  their  common  source  and  will  be  more   and  more  dispersed  in  the  future.   A  second  worry  is  that  all  the  probabilities  in  question,  and  in  particular  the  likelihoods,  will   be  either  zero  or  one,  since  the  process  is  deterministic,  and  that,  hence,  will  not  be  able  to  apply   likelihood  reasoning.    Yet,  since  we  have  direct  observational  access  neither  to  the  free  fields  prior   to  the  putative  emission  events  nor  to  the  present  fields  on  a  complete  initial  value  surface,  we   cannot  set  up  a  full-­‐fledged  initial-­‐  or  final-­‐value  problem.    Rather  we  somehow  have  to  infer,  based   on  our  localized  observations,  what  both  initial  fields  and  the  fields  associated  with  any  sources   might  have  been.    That  is,  our  problem  is  somehow  to  carve  up  the  total  locally  observed  field  into  a   component  associated  with  past  sources  and  a  source-­‐free  incoming  field.    Without  any  additional   assumptions  this  would  be  impossible:  our  localized  observations  simply  do  not  provide  us  with   enough  information  to  infer  both  the  state  of  any  sources  and  the  initial  field  and  are  compatible   with  multiple  different  combinations  of  initial  fields  and  radiation  fields.   What  we  observe  are  relatively  focused  packets  of  radiation  (which  we  interpret  as  light   emitted  by  stars)  within  a  background  field  that  is  approximately  equal  to  zero,  or  at  least  is  very   weak.    We  infer  from  this  that  the  field  disturbances  coming  from  a  single  direction  are  due  to  a  star   as  their  common  cause.    But  it  is  also  consistent  with  our  evidence  that  there  existed  strong   correlations  among  source-­‐free  initial  fields  in  spatially  distant  regions  at  some  remote  time  in  the   past  that  resulted  in  macroscopic  fields  converging  onto  the  putative  trajectory  of  the  star,  passing   over  it,  and  then  rediverging—mimicking  (for  later  observers)  the  presence  of  a  star.    The  further   back  in  time  we  followed  such  source  free  fields,  the  weaker  these  fields  would  be  as  they  become   more  and  more  dispersed  toward  the  past,  originating  in  what  ultimately  would  have  been   extremely  delicately  coordinated  microscopic  correlations  among  very  distant  field  regions.   If  such  fields  are  equally  as  compatible  with  our  observational  evidence,  why  do  we  infer   the  existence  of  localized  common  cause  rather  than  the  existence  of  delicately  set  up  correlations   among  source-­‐free  incoming  fields?    The  latter  hypothesis  violates  our  prohibition  against   20   explanatory  buck  passing,  since  it  accounts  for  the  spatially  distant  correlations  in  terms  of  even   more  spatially  dispersed  correlations  in  the  remote  past.    We  can  exclude  this  explanation  by   positing  that  the  initial  fields  are  effectively  random—or  rather  as  random  as  possible,  given  our   observational  evidence.13  Making  this  assumption  explicit  we  get:   Pr(F(t1,x1)  &  F(t2,x2)/  S(tret1,  xret1)  &  random  initial  fields)  >>  Pr(F(t1,x1)  &  F(t2,x2)/  random  initial   fields)   (2)   The  initial  randomness  assumption  can  itself  be  motivated  by  a  causal  representation  of  the   phenomena  at  issue.    The  principle  of  the  common  cause  states  that  it  is  reasonable  to  explain   distant  correlations  among  quantities  by  positing  an  earlier  localized  common  cause.    The   contrapositive  of  that  principle  maintains  that  in  the  absence  of  a  common  cause  it  is  reasonable  to   assume  that  the  quantities  in  question  are  uncorrelated.    Thus,  if  we  do  not  expect  there  to  be  a   localized  common  cause  of  distant  field  values  at  whatever  time  we  choose  as  the  initial  time,  we   expect  the  randomness  assumption  to  be  satisfied.   What  is  the  nature  of  the  probabilities  in  (1)  and  (2)?    I  think  for  our  present  purposes  we   can  be  ecomenical  and  allow  the  probabilities  to  be  whatever  probabilities  one  thinks  are  needed  to   underwrite  explanatory  inferences  in  the  sciences.    If  one  believes  that  epistemic  probabilities  are   sufficient  to  do  this  job,  then  one  can  read  the  randomness  assumption  as  reflecting  our  ignorance   of  the  precise  initial  conditions.    Alternatively,  the  probabilities  may  be  construed  more  objectively,   as  some  form  of  frequencies  or  as  propensities.   I  have  argued  that  common  cause  reasoning  plays  an  important  inferential  role.     Analogously,  the  principle  of  the  common  cause  and  its  converse  (which  states  that  distant   quantities  are  uncorrelated  in  the  absence  of  a  common  cause)  also  play  an  explanatory  role  and,   for  example,  allow  us  to  explain  why  we  observe  diverging  but  not  coherently  converging  waves  in   nature.    Let  us  return  to  the  example  which  we  began  our  discussion  in  this  section.    The  highly   correlated  behavior  of  the  radio  signals  in  processes  A  and  B  above  are  precisely  the  kind  of   phenomena  that  would  call  for  an  explanation  in  terms  of  localized  common  causes.    In  the  case  of   process  A—a  radio  antenna  broadcasting  into  empty  space—such  an  explanation  is  readily   available:  the  action  of  the  antenna  acting  as  common  cause  of  the  field  disturbances  can  explain   the  strong  correlations  among  them.    Contrast  this  with  the  process  B  of  an  anti-­‐broadcast  wave   collapsing  into  the  antenna.    In  this  case  there  is  an  antenna  located  at  the  point  on  which  the  radio   waves  are  centered,  just  as  in  process  A.    Yet  by  hypothesis  the  correlations  in  this  case  possess  no   13 See  (Arntzenius  2010)  for  the  sketch  of  a  general  argument  that  all  inferences  to  a  common  cause   presuppose  an  initial  randomness  assumption. 21   earlier  common  cause.    Thus,  by  the  converse  of  the  principle  of  the  common  cause,  we  would  not   expect  such  a  process  to  occur.   The  field  coherently  converging  onto  the  antenna  presents  a  solution  to  the  dynamical   equations  just  as  much  as  the  diverging  field.    In  fact,  purely  dynamically,  and  considered   ‘atemporally,’  the  two  processes  are  completely  equivalent:    in  both  cases  there  are  coordinated   fields  that  are  correlated  with  the  localized  action  of  an  antenna.    The  symmetry  between  the  two   cases  is  broken,  however,  once  we  embed  purely  dynamical  models  of  the  two  processes  into   richer,  causal  structures.    Process  A    then  appears  to  be  normal  and  entirely  to  be  expected,  since   the  correlations  among  the  disturbances  can  be  explained  by  their  common  cause.    Process  B,  by   contrast,  seems  ‘contrived’,  ‘mysterious’  or  ‘improbable’,  since  the  correlations  do  not  have  a   common  cause.   Note  that  the  preceding  discussion  does  not  depend  on  the  fact  that  an  antenna  or  a  star  is  a   macroscopic  object.    The  inferential  and  explanatory  structure  would  be  exactly  the  same  in  the   case  of  a  microscopic  charge,  such  as  a  single  oscillating  electron,  at  least  as  long  as  we  model  the   charge  classically.    The  only  difference  is  that  the  disturbances  in  the  radiation  field  diverging  from   the  electron  as  their  source  would  be  less  easy  to  detect  empirically.       In  invoking  a  causal  explanation  of  why  we  normally  do  not  find  coherently  converging   waves  I  am  not  denying  the  possibility  of  carefully  setting  up  such  waves.    The  way  to  do  this  is  to   arrange  a  large  number  of  radiating  objects  and  set  them  into  coherent  motion  such  that  the  waves   diverging  from  each  individual  source  combine  to  an  overall  converging  wave.    But  notice  that  in   this  case  the  coordinated  behavior  of  the  wave  can  once  again  be  explained  by  appealing  to  a  local   common  cause  in  its  past,  namely  the  mechanism  we  used  to  set  the  collection  of  distant  sources   into  coherent  motion.    Thus    the  explanatory  role  of  the  causal  principle  in  the  present  case  is  not  to   prohibit  certain  dynamically  permissible  processes;  rather  the  principle  explains  why  certain   dynamically  allowed  processes  are  radically  improbable,  while  their  temporal  inverses  are  utterly   familiar  to  us.   Our  local  observations  of  packets  of  stellar  radiation  severely  underdetermine  which   dynamical  model  of  the  wave  equations  correctly  represents  the  phenomena,  but,  as  I  have  argued,   embedding  the  dynamical  models  into  richer  causal  structures  allows  us  to  decide  between   possible  models  by  inferring  the  existence  of  a  localized  common  cause  of  observed  correlations.     That  is,  we  infer  that  the  locally  observed  radiation  was  emitted  by  a  star  not  merely  by  an  appeal   to  the  dynamical  laws  governing  electromagnetic  radiation  but  rather  by  using  a  combination  of   dynamical  and  causal  reasoning.    Moreover,  while  I  have  only  discussed  one  type  of  example  here,  it   22   is  easy  to  see  that  the  discussion  generalizes  to  a  wide  class  of  observations  in  physics,  since  only   very  rarely—if  ever—are  we  in  a  position  to  know  the  state  of  a  system  on  a  full  initial  (or  final)   value  surface.   But  have  I  really  shown  that  the  notion  of  cause  plays  an  important  role  in  reasoning  in   physics?    Someone  might  argue  that  even  if  one  were  to  grant  that  our  inference  to  the  existence  of   a  star  are  justified  by  the  kind  of  reasoning  I  have  described,  this  still  does  not  show  that  this   reasoning  needs  to  invoke  the  notion  of  cause.    It  would  be  enough,  one  might  claim,  simply  to   postulate  the  initial  randomness  assumption  and  then  use  the  likelihood  principle  or  Reichenbach’s   principle  to  infer  the  existence  of  the  star  without  ever  using  the  term  ‘cause’.    The  explanatory   work  is  done  by  the  randomness  assumption  and  the  probabilistic  principles.    Calling  the  reasoning   ‘causal’  seems  to  be  no  more  than  add  an  empty  honorific,  or  so  one  might  argue.    I  want  to  make   the  following  four  points  in  reply  to  this  objection.   First,  as  I  have  argued,  the  initial  randomness  assumption  can  itself  be  motivated  by  a   causal  picture  of  the  world  and  fits  well  with  our  explanatory  enterprise  of  aiming  to  explain  distant   correlations  in  terms  of  earlier  common  causes.    Let  us  assume  a  set  of  variables  F  that  has  no   determinants  outside  of  F.    That  is,  for  each  variable  it  is  the  case  that  it  has  a  complete  set  of  causes   in  F  and  conditional  on  that  set  what  value  the  variable  takes  is  independent  of  the  values  of  any   variables  outside  of  F.    Then  it  follows  from  the  converse  of  the  principle  of  the  common  cause  that   it  is  very  likely  that  the  values  of  any  variables  that  are  not  related  as  cause  and  effect  and  do  not   have  a  common  cause  will  be  uncorrelated.   Second,  recall  that  my  aim  here  is  not  to  defend  a  causal  metaphysics  but  merely  to  argue   that  certain  causal  representations  play  an  important  role  in  physics.    I  want  to  leave  it  open  what   metaphysical  conclusions,  if  any,  one  might  want  to  draw  from  this  fact.    The  explanatory  and   inferential  patterns  that  I  identified  are  commonly  taken  to  be  an  instance  of  paradigmatically   causal  reasoning.    That  strikes  as  a  good  enough  reason  to  conclude  that  there  is  a  place  for  causal   reasoning  in  physics.    Yet  ultimately  it  is  not  crucial  what  label  we  attach  to  this  kind  of  reasoning.     What  is  important  is  that  it  is  a  time-­‐asymmetric  reasoning  that  goes  beyond  what  is  implied  by  the   time-­‐reversal  invariant  dynamical  laws  and  our  local  observations  but  nevertheless  plays  an   important  explanatory  and  inferential  role  in  physics.   Third,  at  least  some  skeptics  of  causal  reasoning  in  physics  are  willing  to  grant  that  causal   reasoning  plays  a  role  in  common  sense  and  other  sciences.    My  arguments  here  put  pressure  on   this  distinction.    To  the  extent  that  the  use  of  common  cause  reasoning  is  evidence  for  the  role  of   causal  reasoning  elsewhere,  it  also  points  to  a  role  of  causal  reasoning  in  physics.    And  conversely:  if   23   this  kind  of  reasoning  is  not  taken  as  evidence  for  the  presence  of  causal  reasoning  in  physics,  then   neither  can  it  be  evidence  for  causal  reasoning  elsewhere.   Fourth,  postulating  the  initial  randomness  assumption  merely  as  de  facto  constraint  on   initial  conditions  does  not  allow  us  to  make  explanatory  distinctions  of  a  kind  even  causal  skeptics   like  Earman  seems  to  want  to  make.  In  his  discussion  of  the  asymmetry  between  a  diverging   broadcast  wave  and  a  coherently  converging  anti-­‐broadcast  wave—that  is,  between  processes  A   and  B  above—Earman  says  this:   It  would  seem  nearly  miraculous  if  the  time  reverse  of  [the  broadcast  wave]  were   realized  in  the  form  of  anti-­‐broadcast  waves  coming  in  from  spatial  infinity  and   collapsing  on  the  antenna.    The  absence  of  such  near  miracles  might  be  explained  by   an  improbability  in  the  coordinated  behavior  of  incoming  source  free  radiation  from   different  directions  of  space.   Yet  in  what  sense  exactly  is  the  converging  wave  miraculous  or  improbable?    It  follows  from  the   inhomogenous  wave  equation  that  a  source  will  be  associated  with  the  coordinated  behavior   among  distant  disturbances  of  the  field.    Purely  dynamically  coherently  converging  waves  are  no   more  improbable  than  diverging  waves.    All  that  the  dynamics  tells  us  is  that  there  will  be  distant   correlations  in  the  field  somewhere—be  it  in  the  past  of  the  action  of  the  source  in  the  form  of  a   converging  wave,  or  in  the  future  of  the  source  as  diverging  wave,  or  perhaps  as  a  linear   combination  of  the  two.   Moreover,  dynamically  there  is  nothing  especially  odd  about  coordinated  behavior  of   incoming  source-­‐free  radiation.    Dynamically,  both  diverging  and  converging  waves  can  be   represented  both  in  terms  of  an  initial  value  problem  and  a  final  value  problem.    An  initial  value   problem  represents  the  total  wave  F  as  a  sum  of  a  source-­‐free  incoming  field  and  a  diverging  field   associated  with  the  antenna:  F=Fin+Fdiv.    A  final  value  problem  represents  the  total  wave  as  a  sum  of   a  source-­‐free  outgoing  field  and  a  converging  field:  F=Fout+Fcon.    Both  representations  are   representations  of  one  and  the  same  field.    Now,  if  we  represent  a  converging  wave  in  terms  of  an   initial  value  problem,  the  wave  will  appear  as  incoming  source-­‐free  radiation.    But  if  we  represent   the  same  wave  in  terms  of  a  final  value  problem,  the  converging  wave  appears  as  being  associated   with  the  source.    By  the  same  token,  a  diverging  wave  can  be  represented  either  as  outgoing  source-­‐ free  radiation  (in  a  final  value  problem)  or  as  associated  with  the  source  (in  an  initial  value   problem).     Positing  the  initial  randomness  assumption  breaks  the  symmetry  between  the  different   representations.    And  it  may  be  that  when  Earman  says  that  the  absence  of  converging  waves  might   24   be  explained  by  an  improbability  of  coordinated  behavior  in  the  incoming  radiation  he  is  appealing   to  nothing  more  than  the  inintial  randomness  as  de  facto  constraint.    But  the  quote  above  suggests   otherwise.    Earman  seems  to  suggest  that  there  is  something  apparently  ‘near-­‐miraculous’  about   one  class  of  solutions  to  the  dynamical  equations  and  that  there  is  a  need  to  explain  the  absence  of   such  ‘near-­‐miracles’.    But  it  is  unclear  what,  from  a  strictly  non-­‐causal  perspective,  this   miraculousness  might  consist  in.    Coherently  converging  anti-­‐broadcast  waves  represent   dynamically  perfectly  possible  situation,  which  happen  to  be  rendered  unlikely  by  the  de  facto   initial  conditions.   Consider  the  following  analogy:    a  ball  is  released  at  the  top  of  a  wedge-­‐  or  roof-­‐shaped   inclined  plane  and  rolls  down  on  the  wedge’s  left  hand  side.    As  an  explanation  for  the  ball’s   trajectory  we  appeal  to  the  ball’s  initial  conditions  according  to  which  the  ball  was  released  slightly   to  the  left  of  the  peak  of  the  wedge.    It  also  is  dynamically  possible  for  the  ball  to  roll  down  the  ride   hand  side.    Even  though  the  ball  does  not  follow  this  second  trajectory,  since  it  is  incompatible  with   the  ball’s  initial  conditions,  there  is  nothing  ‘near-­‐miraculous’  about  this  second  dynamically   possible  solution.    Similarly,  absent  additional  causal  considerations,  there  is  nothing  miraculous  or   ‘contrived’  about  the  non-­‐actual  solutions  to  the  inhomogenous  wave-­‐equation.   Moreover,  it  is  natural  to  assume  that  it  converging  radiation  is  improbable  precisely   because  it  would  require  coordinated  behavior  in  the  “incoming  source  free  radiation  from   different  directions  of  space,”  as  Earman  says.    But  again  a  strictly  non-­‐causal  construal  of  radiation   phenomena  cannot  support  this  intuition.    On  a  strictly  non-­‐causal  picture,  there  is  no  more  reason   to  expect  that  incoming  radiation  from  different  directions  should  be  uncoordinated  as  there  is  to   expect  that  source  free  outgoing  radiation  will  be  uncoordinated.     4.  Conclusion   I  have  argued  that  a  widely  held  view—the  view  that  asymmetric  causal  relations  cannot  play  a   legitimate  role  in  physical  theories—is  not  underwritten  by  convincing  arguments.    Neither  the  fact   that  physical  theories  present  us  with  classes  of  abstract  mathematical  structures  nor  the  fact  that   (at  least  many  of)  the  dynamical  laws  of  our  mature  physical  theories  are  time-­‐symmetric  provides   a  compelling  argument  against  the  possibility  of  causal  notions  playing  a  role  in  physics.    Finally  I   have  argued,  by  examining  the  asymmetry  of  wave  and  radition  phenomena,  and  in  particular  the   case  of  stellar  observations  as  a  concrete  example  where  this  asymmetry  manifests  itself,  that   causal  assumptions  can  play  an  important  inferential  and  explanatory  role  in  physics.     25   References   Arntzenius,  Frank,  "Reichenbach's  Common  Cause  Principle",  The  Stanford  Encyclopedia  of   Philosophy  (Fall  2010  Edition),  Edward  N.  Zalta  (ed.),  URL  =     Born,  Max  and  Emil  Wolf.  1999.  Principles  of  Optics,  seventh  edition.  Cambridge:    Cambridge   University  Press.   Callender,  Craig.  2000.  Is  Time  'Handed'  in  a  Quantum  World?  Proceedings  of  the  Aristotelian   Society,  June,  247-­‐269.   Cartwright,  Nancy.  1993.  Defence  of  `This  Worldly'  Causality:  Comments  on  van  Fraassen's  Laws   and  Symmetry.  Philosophy  and  Phenomenological  Research  53  (2):  423-­‐429.   Earman,  John.  2011.  “Sharpening  the  Electromagnetic  Arrow(s)  of  Time”.  in  The  Oxford  Handbook   on  Time.  Edited  by  Craig  Callender.  Oxford:  Oxford  University  Press.   Field,  Hartry.  2003.  "Causation  in  a  Physical  World".  In  The  Oxford  Handbook  of  Metaphysics,  edited   by  M.  Loux  and  D.  Zimmerman.  Oxford:  Oxford  University  Press.   Fraassen,  Bas  van.  1980.  The  Scientific  Image.  Oxford:  Oxford  University  Press.   Fraassen,  Bas  van.  1993.    Armstrong,  Cartwright,  and  Earman  on  Laws  and  Symmetry.  Philosophy   and  Phenomenological  Research  53  (2):  431-­‐444.   Frisch,  Mathias.  2005.  Inconsistency,  Asymmetry,  and  Non-­‐Locality:    A  Philosophical  Investigation  of   Classical  Electrodynamics,  Oxford  University  Press.   ______________.  2006.    “A  Tale  of  Two  Arrows,”  Studies  in  the  History  and  Philosophy  of  Modern  Physics   37,  542-­‐558.   ______________.  2009a.  “‘The  most  Sacred  Tenet’?  Causal  Reasoning  in  Physics,”  British  Journal  for  the   Philosophy  of  Science  60  (September  2009)  459-­‐474.   ______________.  2009b.  “Philosophical  Issues  in  Electromagnetism,”  Philosophy  Compass  4/1:  255–270.   ______________.  2010.  “Causal  Models  and  the  Asymmetry  of  State  Preparation”  in  EPSA  Philosophical   Issues  in  the  Sciences.  Launch  of  the  European  Philosophy  of  Science  Association,  eds.  M.   Suárez,  M.  Dorato  and  M.  Rédei.  Springer  Verlag.   ______________.  forthcoming.  “Statistical  mechanics  and  the  asymmetry  of  causal  influence,”  in  David   Albert’s  Time  and  Chance,  eds.  Barry  Loewer,  Eric  Winsberg,  and  Brad  Weslake,  Harvard   University  Press.   Griffiths,  David.  1989  Introduction  to  Electrodynamics.  2nd  ed.  Prentice-­‐Hall.   Healey,  Richard.  1983.  Temporal  and  Causal  Asymmetry.  In  Space,  Time,  and  Causality,  edited  by   Richard  Swinburne.  Dordrecht:  D.  Reidel  Publishing  Co.   26   Hitchcock,  Cristopher.  2007.  What  Russell  Got  Right.  In  Causality,  Physics,  and  the  Constitution  of   Reality:  Russell's  Republic  Revisited,  edited  by  H.  Price  and  R.  Corry.  Oxford:  Oxford   University  Press.   Jackson,  John  David.  1975.  Classical  Electrodynamics.  2nd  ed.  New  York:  John  Wiley  &  Sons.   Newton-­‐Smith,  W.  H.  1983.  Temporal  and  Causal  Asymmetry.  In  Space,  Time,  and  Causality,  edited   by  Richard  Swinburne.  Dordrecht:  D.  Reidel  Publishing  Co.   Ney,  Alyssa.  2009.  "Physical  Causation  and  Difference  Making."  British  Journal  for  the  Philosophy  of   Science  60  (4):737-­‐764.   Norton,  John  D.  2003.  Causation  as  Folk  Science.  Philosophers'  Imprint  3  (4),   http://www.philosophersimprint.org/003004/;  reprinted  as  pp.  11-­‐44  in  H.  Price  and  R.   Corry,  Causation  and  the  Constitution  of  Reality:  Russell’s  Republic  Revisited.  Oxford:   Clarendon  Press.   Norton,  John  D.  2007.  Do  the  Causal  Principles  of  Modern  Physics  Contradict  Causal  Anti-­‐ Fundamentalism?  In  Thinking  about  Causes:  From  Greek  Philosophy  to  Modern  Physics,   edited  by  P.  K.  Machamer  and  G.  Wolters.    Pittsburgh:  University  of  Pittsburgh  Press.   Norton,  John  D.  2009.  "Is  There  an  Independent  Principle  of  Causality  in  Physics?"  British  Journal  for   the  Philosophy  of  Science.  pp.  475-­‐86.   Nussenzveig,  H.  M.  1972.  Causality  and  Dispersion  Relations.  New  York:    Academic  Press.   Price,  Huw.  2007.  Causal  Perspectivalism.  In  Causality,  Physics,  and  the  Constitution  of  Reality:   Russell's  Republic  Revisited,  edited  by  H.  Price  and  R.  Corry.  Oxford:  Oxford  University  Press.   Price,  Huw  &  Weslake,  Brad  (2009).  The  time-­‐asymmetry  of  causation.  In  Helen  Beebee,  Peter   Menzies  &  Christopher  Hitchcock  (eds.),  The  Oxford  Handbook  of  Causation.  Oxford   University  Press.   Rohrlich,  Fritz.  1990.  Classical  Charged  Particles.  Reading,  MA:  Perseus  Books.   Rohrlich,  Fritz.  2006.  Time  in  Classical  Electrodynamics.  American  Journal  of  Physics  74  (4):  313-­‐ 315.   Russell,  Bertrand.  1918.  On  the  Notion  of  Cause.  In  Mysticism  and  Logic  and  other  Essays.  New  York:   Longmans,  Green  and  Co.   Scheibe,  Erhard.  2006.Die  Philosophie  der  Physiker.  Munich:    Verlag  C.H.  Beck.   Sober,  Eliot.  1984.  "Common  Cause  Explanation"  Philosophy  of  Science  51,  212-­‐241.   Sober,  Eliot.  2001.  "Venetian  Sea  Levels,  British  Bread  Prices  and  the  Principle  of  the  Common   Cause,"  British  Journal  for  the  Philosophy  of  Science  52,  331-­‐346.   Suppes,  Patrick.  1970.  A  Probabilistic  Theory  of  Causality.  Amsterdam:  North-­‐Holland.   27   Woodward,  James.  2003.  Making  Things  Happen:  A  Theory  of  Causal  Explanation.  Oxford:  Oxford   University  Press.   Woodward,  James.  2007.  Causation  with  a  Human  Face.  In  Causality,  Physics,  and  the  Constitution  of   Reality:  Russell's  Republic  Revisited,  edited  by  H.  Price  and  R.  Corry.  Oxford:  Oxford   University  Press.