Augusto Garuccio

Erasmo Recami

G. D. Maccarrone

J. P. Vigier

English

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LETTERE AL ~qUOVO CIMENT0 VOL. 27, ~. 2 12 Gcnnaio 1980 On the Physical Nonexistence of Signals Going Backwards in Time, and Quantum Mechanics (*). A .  GARUCCIO Isti tuto di Fisica,  Universit5 di Bari  - Bari ,  I tal ia (**) Ist i tuto Nazio;~ale di Fis ica A~ucleare, Sezione di Bari  - Bari,  I tal ia G. D. ~IACCARRONE Scuola di Spccializzazione in  Fisica, U~irersit5 di Catania - Catania, I tal ia E .  I~ECAMI Istit~to di  Fisica Teorica, UM~'ersit~ di Catania - Catania, I tal ia Istit~tto Nazionale di Fis ica Nucleate, ,~ezio~e di Catania - Catania, I tal ia Centro Sicilia~w di Fisica Nucleare e Struttura della Materia - Catania, I tal ia  J. P. VIGIER Groupe de Pl~ysique Thdorique, It~stitut Henri  Poi~carg - 11 rue P.  et M.  Curie, Paris ,  France (ricevuto il 16 Novembre 1979) A growing number of experiments have been recently performed to test the paradoxical, seemingly nonloeal predictions of quantum mechanics (QM) in Einstein- Podolsky-Rosen's conditions. Recent experiments by CLAUSER and FREEDMAN (1), for instance, confirmed Q3[ and seemed to disagree with Bell inequali ty (which follows from Einstein locality). New experiments, e.g. by ASPECT (2), are moreover going on or being performed (2). In such a situation, careful attention should be paid to the theoretical interpreta- lions put forth to explain the experimental results. In this letter we would like to comment on a recent series of theoretical papers (3), which are essentially characterized (*) W o r k  p a r t i a l l y  s u p p o r t e d  b y  M P I  (ex a r t .  286 T .U. ) ,  b y  C N R ,  a n d  b y  c o l l a b o r a t i o n  b e t w e e n  C N R  ( I t a l y )  a n d  C N R S  ( F r a n c e ) .  (**) T e m p o r a r y  a d d r e s s :  I n s t i t u t  H e n r i  Poincar@, P a r i s ,  F r a n c e .  (i) See e . g . J . F .  CLAUSER: P h y s .  Rev.  Left . ,  36,  1223 (1976);  S. J .  FREEDMAN a n d  J .  F.  CLAUSER; P h y s .  Rev.  Lelt . ,  28,  938 (1972).  (2) See A. ASPECT: P h y s .  Rev.  D ,  14,  1944 (1976);  Prog. Sci .  Culture,  1, 439 (1976);  P h y s .  L e t t . . 4 ,  54,  117 (1975);  a n d  (work  i n  p rog re s s ) .  See a lso  V. RAPISARDA: p r i v a t e  c o m m u n i c a t i o n .  (3) O. COSTA DE BEAUREGARD: N u o v o  Cimento B ,  54, 267 (1979);  42, 41 (1977);  P h y s .  Lett .  A ,  67, 171 (1978);  A n n .  Fond .  de Broglie,  2, 231 (1977).  60 ON THE PHYSICAL NONEXISTENCE OF SIGNALS GOING BACKWARDS IN TIME ETC. ~ l  by the rCle at tr ibuted to the advanced solutions for the sake of explaining (within the orthodox Copenhagen interpretation of QM) the possible noulocM interaction between the measuring apparata, which detect pairs of correlated photons emitted in the singlet state. Namely, in ref. (3) those advanced solutions have been interpreted as actually associated to motion into the past, so that  recourse to an (~ anti-telephone ~) mechanism has been substantially made there (3) (and even over macroscopic distances (3)), in order to render reason of the experience. Let us briefly summarize that  model (3). One utilizes as initial  source an atom 0 which emits at the time t = 0 in a cascade 0-1-0 two correlated photons ~A and ~B that  start to move in opposite directions along the x-axis. One then measures the polariza- t ion of ~ at t ime t~ > 0 (in the direction § x) by the apparatus A, and the polariza- tion of ~ at time t 8 > t~ by the apparatus B (in the direction - -x) .  As is well known, some doubts may be cast on the fact that the quantum-mechanical correlations between the results of these two measurements can actually be interpreted within the concept of locality, i.e. in terms of ordinary signals travelling from one ap- paratus (A) to the other (B). In  order to overcome this problem within the usual Copenhagen interpretation of QM, they assumed in ref. (3) that  at the time t~ of the measurement performed by A on ~ a signal--corresponding to an advanced po ten t ia l~s ta r t s  from the apparatus A and travels backwards in time along the light-cone, and thus supposedly carries information (about the result of that  measurement) back to 0 at t -~ 0. A second signal, then, carries information forward in time to B at t = tB: therefore arriving at the appa- ratus B simultaneously with the photon VB- Before criticizing that  possible mechanism, we want to premise that  there is nothing formally wrong from the mathematical point  of view with that  proposal. I t  is evidently compatible with the Copenhagen interpretation expressed in the relativistic S-matrix formalism. I t  is also formally compatible with the time-reversible formalism of quantum theory. Indeed, if ~(t, x) is a wave solution of the Laplace-Beltrami equa- tion, also ~0(--t, x) is a solution as well: a point that  we shall touch upon again at the end of this letter. The troubles apparently lie with its physical consequences; what is at stake in such an use of the advanced potentials is the existence of causality in real phenomena. Let us recall that  such an approach (contrary to the usual practice in electrodynamics (4) which mix advanced and retarded potential solutions) implies the use of isolated ad- vanced solutions in (~ isolated )> space-time regions. Then, following ref. (3), one could utilize those advanced solutions for an <( anti-telephone >) mechanism (i.e. for commu- nicating with one's past[), even over macroscopic distauces ... Evidently, that pos- sibility would raise new theoretical problems since--following Einste in--one usually, implicitly assumes that :  i) positive energy can be associated only with particles moving forward in t ime; it) actual signals and/or information can only be carried by positive- energy objects (an assumption which appears to be consistent with information theory). Indeed, in the present understanding of physical reality, negative-energy objects (travelling forward in time) cannot exist for many known reasons. For  istance, did they exist, a << bubble ~) of vacuum could then suitably decay into a couple of particles (e.g. nucleons), one bearing negative energy and the other positive energy (5). Such spontaneous vacuum instabilities would have the tendency to possess divergent probabilities (unless the vacuum decays into zero-energy tachyons, which is not the (4) See e .g .F .  R/~In~LICH: Classical Charged Particles ( R e a d i n g ,  Mass . ,  1965).  (s) R .  ~r a n d  E.  RECAMI" Phys. Left. B, 65, 148 (1976).  ~2 A. GARUCCIO, G. D. MACCA-RRON:E, :E. I~ECAMI and 5. P. VIGIER case here  considered (5)), leading i m m e d i a t e l y  to u ~ p h y s i c a l  si tuat ions.  E v e n  if one supposed the  nega t ive-energy  par t ic les  to be devoided  of any in terac t ions  except  the  g rav i t a t iona l  one, never theless  a d iagram of the  type  depic ted  in fig. 1 (where two vacuum-bubb les  become unstable  under  the  mu tua l  exchange of a gravi ton)  would  y i e l d - - f o r  any kind of ord inary  par t ic les  a, b - - a  (( cosmic ~) flux as b ig  as the  one ac- tua l ly  observed on ly  lor  neutr inos.  This  shows tha t  nega t ive  energies (for objects  mov ing  forward in t ime)  do not  seem to be ac tua l ly  allowable.  Fig. 1. - A diagram helping to show that negative-energy particles cannot exist in relativistic physics Symbols a, a, b, b represent positive-energy (negative-energy) particles. See the text. Our a im is to stress once more tha t  the  advanced  potent ia ls  are ac tual ly  to be asso- c ia ted to (orthodox) mot ions  of sui table pos i t ive-energy ant i -objec ts  forward in t ime.  To show this,  let  us notice tha t  advanced  solutions are got  f rom the  re ta rded  ones by  the  s imple (and only) appl icat ion of a nonor thochronous  Loren tz  t rans format ion  L~ e ~ i  (*). The  Lorentz  t ransformat ions  L ~, which change (among the  others) the  sign of t ime ,  have  the  obvious p roper ty  of changing also the sign of energy  and of all  the  four th  components  of all four-vectors  associated to the  same observed object.  In  fact ,  any advanced  solut ion (e.g. in the  e lec t romagnet ic  case) refers also to nega t ive  energy,  whenever  it  refers to nega t ive  t ime ;  this  can be verif ied by  direct  inspect ion of the  re levan t  propagators  (6) (t > 0; h = 1): ( la)  Grit(r ,  t) = - -  i (2~)-3fexp [ i p .  r - -  iE t ]  d3p , (lb) G~d,(r, t) = i (2z ) -a fexp  [ ip .  r - -  iE t ]  dap  , and agrees wi th  the  general  fact  that ,  when  connect ing the  two dua l  (four-posit ion and four -momentum)  spaces th rough  Four ie r - type  t ransformat ions  (h = 1): (2a) f ( p ,  E )  : (2z) 2 f F ( r ,  t) exp [ i p .  r - -  i E t ] d 4 x  , a change of the  t-sign in the  first space implies  a change of the  E-s ign in the  second, dual  space (2b) ] (p ,  - -  E )  ~ (2~)-2~F(r,  - -  t) exp [ ip .  r - -  iE t ]  d4x . d (*) For simplicity, let us confine ourselves to the proper, homogeneous Lorentz groups: .Sz~ (ortho- chronous) and o,~ (nonorthochronous). (6) See e . g . R .  FInscuI (Editor): Elementi introduttivi di ]isica dello stato solido (Torino, 1968). ON THE PHYSICAL NONEXISTENCE OF SIGNALS GOING BACKWARDS IN TIME ]~TC. ~ The previous considerations allow us to conclude t h a t - - i n  relativistic physics--  if an object moves backwards in time, then it is endowed also with negative energy; and, vice versa, negative-energy objects can exist only when travelling backwards in time. At this point, as is well known (7), it is enough to apply the celebrate Sttiekelberg- Feynman (~ reinterpretation principle ,)(~) in order to obtain that  a (~ negative-energy particle travelling backwards in time )~ will show up as an (orthodox) antiparticle trav- elling forward in t ime and bearing positive energy. As shown in ref. (~.8), the reinter- pretation principle (RIP) not only can but  must be applied in  such cases. I t  is essentially based on the following two points (7,s) : i) any observer, being a maeroscopieaI system, does move forward in t ime;  ii) any emission (absorption) of a negative quant i ty  is equiv- alent to absorption (emission) of the corresponding positive quanti ty,  since (--). (--) = = ( -k ) ' (+ ) .  For details, let us again quote ref. (7.s). All what precedes finds its proper settlement within the (enlarged) theory of special relativity (ESR), founded on the group . ~  u ~f~ instead that  on the group s176162 The ESR formulation of special relativity thus includes into a unique scheme both par- ticles and antiparticles (~,s) (where the latter can be defined and introduced in rurely relativistic terms !). The ESR, as is now intuitive,  is based on the two ordinary postu- lates of special relativity and on a (~ third postulate ~) (~.s) which implements, briefly speaking, the (~ RIP  ~. This (~ third postulate ,> enforces the validity of the principle of (retarded) causality, and simultaneously allows the (( prediction ~)(*)--for each par- ticle or object considered--of existence and correct properties of its antiparticle or antiobjeet. Mathematically, we thus conclude (s) that  the advanced solutions (**) (e.g., in A at time tA) describe entering anti-objects (in the case of photons, entering photons) endowed with positive energy and motion forward in time, rather that  outgoing objects endowed with an (~ unphysical ~> motion backwards in time. We have also seen, on the contrary, that  if they were by hypothesis to be associated to actual motion backwards in time, then the (~ objects ~) supposedly described by those advanced solutions could find no room within the realm of present-time relativistic physics (even if such solutions could go on maintaining their rSle in the mathematical elaborations) (***). (~) See e.g.E.  RECAMI: Found. Phys., 8, 329 (1978); F.  CALDIROT.A a n d  E. RECAMI* in  Italian Slfldies in the Philosophy o] Science, edi ted  b y  M. I)ALBA CHIARA (Boston,  Mass. ,  1980); E.  R E C ~ I :  i n  Albert Einstein 1879-1979: Relativity, Quanta, and Cosmology in the Development o/ the Scienti/ic Thought o] A. Einstein, ed i t ed  b y  F. DE FINIS, Chap.  16 (New York ,  N, Y., 1979); i n  Centena~'io di Einstein: astroIisica e cosmologia, gravi~azione, q u a n t i e  relativit~ negti svituppi del pensiero scienti]ico di A.  Einstein, ed i t ed  b y  1~. PANTALEO, Chapt .  18 (F i renze ,  1979). See also ref. (s). (a) E.  REC&IMI a n d  R.  ~r Riv.  Nuovo Cimento, 4, 209-290, 398 (1974); E.  REOA~I (Ed i to r ) :  Tachyons, Monopoles, and Related Topics ( A m s t e r d a m ,  1978). (*) I n  t he  sense  t h a t  i t  wou ld  h a v e  a l lowed to  p r e d i c t  the  ex i s t ence  of a n t i p a r t i c l e s  e v e n s i n c e  1905 (in pure ly  r e l a t i v i s t i c  t e r m s ) :  cf. ref.  (7,8). (9) R.  MIGNON1 a n d  E. RECA~I: Left. Nuovo Cimento, 18, 5 (1977), (**) A pr ior / ,  to be a s soc ia ted  to * n e g a t i v e - e n e r g y  pa r t i c l e s  t r a v e l l i n g  b a c k w a r d s  in  t i m e  ,. (***) At  l as t ,  le t  us br ief ly  go b a c k  to  t he  * r e ve r s ib i l i t y  *~ p rob lem.  As one knows,  c lass ica l  s tochas t i c  processes  a r e  f u n d a m e n t a l l y  i r r eve r s ib le ,  be ing  assoc ia ted  w i t h  con t inuous ,  i n c r e a s i n g  toss of i n f o r m a -  t i on  on t he  place w he re  the  par t i c le  c a m e  f rom.  Th i s  c a n  be d i r ec t ly  shown,  e.g. b y  a n  a r g u m e n t  of :R. THOM (10), w h i ch  s ta tes  t h a t  a n y  s tochas t i c  set of i n t i t i a l  p a r a m e t e r s ,  inf luenced b y  a n  inf ini te  n u m b e r  of degrees  of f r e e d o m ,  co r re sponds  to a m e a s u r e  of d imen s io n  zero (i.e. to a negligible p robab i l i t y )  i n  t he  space  of t he  inf ini te  m a n y  possible s ta tes ;  so t h a t  t i m e  a l w a y s  flows in  t h e  f o r w a r d  * d i rec t ion .  Now,  as  one  knows,  Nelson s tochas t i c  l aw (~)  r e c o v e r s  r e v e r s i b i l i t y  b y  t a k i n g  a d i f ferent  s ign in  N e w t o n  ( d y n a m i c s )  f u n d a m e n t a l  equa t ion .  Th i s  c an  be a n d  has  been  (1,) in te r -  p r e t e d  b y  m e a n s  of t he  a r g u m e n t  t h a t  q u a n t u m  s tochas t i c  m i x t u r e s  c o n t a i n  bo th  par t i c les  and an t i -  ~ A. GARUCCIO, G. D. MACCARRONE, ]~. I~ECAMI and J.  P. VIGI/~R Two authors (E. R. and J. P. V.) are grateful to J. S. BELL for helpful discussions, and to A. O. BARUT for having forwarded to t heln the opportu~ity to meet together at the 1979 Colloquia on Mathematical Physics at Trabzon and Istanbul. Anothcr author (A. G.) acknowledges a grant of the Italian C.N.R. and the French C.N.R.S. par t ic les .  The  l a t t e r  a lways  m o v e  (so as the  par t ic les )  in  the  f o r w a r d  t i m e - d i r e c t i o n ,  b u t  a re  m a t h e -  m a t i c a l l y  e q u i v a l e n t  to n e g a t i v e - e n e r g y  m o t i o n  b a c k w a r d s  in  t i m e ;  so t h a t  one ge ts  an  apparent ly  revers ib le  process.  (The  word  (, a p p a r e n t l y  ,~ is essent ia l ,  s ince of course  the  a l t e rna t ive ,  s tochas t ic ,  causal  q u a n t u n l - m e c h a n i c a l  mode l  of the  E P R  p a r a d o x  (11) impl ies  only  mo t io n s  in t h e  f o r w a r d  t ime-  direct  ion ). (10) R. THO.~: p r i v a t e  c o m m u n i c a t i o n .  (11) :E. NELSON: Phys .  Rev. ,  450, 1079 (1966). (1~) Cf. also N. CUFARO PETRO,~'I a n d  J. P. VIGIER: Lelt.  Nuovo  Cimento,  26, 149 (1979); J .  P. VIGIER: Lett .  Nuova  Cime~to,  24, 265 (1979). by  Soeietk I t a l i a n a  di Fisica Propr ie tk  l e t t e r a r i a  r i s e r v a t a  Di re t tore  responsabi le :  CARLO C A S T A G N O L I  S t a m p a t o  in  Bologna dalla  Tipograf la  Composi tor i  coi t ipi  della Tipograf la  Monograf  Questo faseicolo b s ta to  ] icenziato da i  torchi  i] 23-I-1980 

On the physical nonexistence of signals going backwards in time, and quantum mechanics

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On the physical nonexistence of signals going backwards in time, and quantum mechanics

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