Again about causality for tachyons in macrophysics

L]~]~RV. ~L ~UOVO C~MEN~O

VOL. 18, ~ . 5

29 G e n n a i o

1977

Again about Causality for Tachyons in Macrophysics (*). M. P A V ~ (**) and E. R ~ C A ~ (***) Istituto di Fisica Teorica dell' Universit~t - Catat~ia (ricevuto il 9 N o v e m b r e 1976)

This is a second auswer to the c o m m e n t s by BASAN0, i.e. a brief c o m m e n t on rcf. 0). A l t h o u g h (~e x t e n d e d reh~tivity ~)(2,3) allows us to solve a~y causM p a r a d o x b o t h w i t h usual particles and w i t h tachyons (4), nevertheless a n u m b e r of p a r a d o x e s are often proposed. In particular, as au answer to ref. (5), we a l r e a d y show,~d (a) t h a t t a c h y o n s do not i m p l y any causal viohttion e~ett ia macro-physics. H o w e v e r , in ref. (1) t h a t a u t h o r claims t h a t our procedure (a) le~tds to new, different p a r a d o x e s : wc are going to show h o w those p r e s u m e d difficulti~s do not exist. ~Vc agree about Basano's discussion in Sects. l and 2 of ref. 0), where dcf. (3) j u s t represents our view. Let us merely observe tha~: i) if an observer A ' p r o g r a m s ~ (~~achyon cxch,~nger ~>P to opcr~te (~in a certain w a y )>, nothing w i t h i u r c l a t i v i t y requires t h a t this (( certain w a y ~) is Lorentz i n v a r i a n t , i.e. ~mothcr observer A will see P to operate a priori in ~ di//ere,~t w:~y (with t a e h y o n s ) ; ii) our recent works (3) are not in c o n t r a s t w i t h wh:~t t h e classical theory o/ tachyous (~-) (~ha,'.~ bcen m a i n t a i n i n g for years )~ (i), since we still m a i n t a i n t h a t the na, mcs (( source )), c2 ,

so that they cannot b(~ absorbed by A', then tachyons T will proceed beyond A" u n t i l whe,n absorbed (2) by another j a r detector B , (see fig. 1), whose speed w will of course satisfy the condition (1 bis)

wV
c2/V and w < c2/V) that it must be w < u. Let us stress once again t h a t - - i n developing tachyons' t h e o r y - - i t is always necessary to take due account of the proper sources a n d detectors, for the reasons (***) reported, e.g., in r(;f. (2,a). Let us now pass to choose A ' as our reference frame. Then B and tachyons T will appear with the transformed velocities

(3)

w

w. . . .

u

1 - - uw/cO-

< o,

and (4)

}. . . .

< 0, 1 - - u V / c ~"

(*) F o r s i m p l i c i t y , wr use t h e s a m e s i m b o l s for m a c r o - o b j e c t s a n d t h e i r a t - r e s t o b s e r v e r s . (**) I n a n y case, let us r e p e a t t h a t n o s t a n d a r d (, causal ptu'adoxes ~ (2) w o u l d a r i s e since t h e y were c o m p l e t e l y solved e l s e w h e r e (4). W c a r e here d e a l i n g w i t h p a r a d o x e s of d i H e r e n t n a t u r e : cf. rcf. (3). R e m e m b e r , m o r e o v e r , t h a t t h e e m i t t e r is t h e r e f e r e n c e f r a m e h e r e (we mearL t r i~l its own f r a m e ) . (***) I . e . , for t h e f a c t t i l e r - - i f A sends t ~ c h y o u s to B - - a l w a y s fv~mes e x i s t a c c o r d i n g to w h i c h it is B t h a t sends t a c h y o n s to A ; a~ld i n p a r t i c u l a r , (,critlcal ,~ f r a m e s ~ l w a y s e x i s t o b s e r v i n g A, B as oonnected t h r o u g h a n i n s t a n t a n e o u s , s y m m e t r i c a l e x c h a n g e (~-,~).

136

M. PAV,~ff; and ~. RECA~II U

w