A generalized Lorentz transformation and its implications for observability of tachyons

Abstract

I t is now genera l ly be l i eved t h a t t h e poss ib i l i ty of ex is tence of par t ic les t r ave l l i ng fa s t e r t h a n l i gh t ( t achyons) is n o t exc lud ing b y t h e special t h e o r y of r e l a t iv i ty . T h o u g h t h e poss ib i l i ty of these pa r t i c les ha s b e e n u n d e r cons idera t ion for some t i m e (1-6), cons iderab le t heo re t i ca l i n t e r e s t ha s b e e n g e n e r a t e d in t h e l a s t decade b y t h e d iscuss ion of these pa r t i c les b y B~LA~UIX et al. (s) in 1962. Discuss ion of t a c h y o n s in r e l a t iv i s t i c q u a n t u m m e c h a n i c a l t e r m s h a v e been g iven b y FEINBERG (7), ECKER (s), ARONS a n d SUDARSttAN (9), SUDARSttAN (10) a n d SCH~O]~ (n). E x p e r i m e n t a l m e t h o d s of sea rch ing for t a c h y o n s h a v e b e e n s u m m a r i s e d r ecen t l y b y SUDARSHAN (10). Some of t h e p rope r t i e s of t he se pa r t i c les r e l e v a n t for t h e i r e x p e r i m e n t a l de t ec t i on are : t h e y possess i m a g i n a r y r e s t mass , b u t rea l pos i t ive ene rgy a n d m o m e n t u m , t r a v e l a lways w i t h ve loc i ty u g r e a t e r t h a n t h e ve loc i ty of l i gh t c in all i ne r t i a l f l a m e s a n d lose ene rgy (E) as t h e i r ve loc i ty increases ( u : 0% E = 0). T a e h y o n s i f c h a r g e d c o u l d also, u n d e r c e r t a i n a s sumpt ions , e m i t Cc rcnkov r a d i a t i o n in v a c u u m . E x p e r i m e n t a l a t t e m p t s to d e t e c t t a c h y o n s (~ 16) h a v e been m a d e w i t h n e g a t i v e resu l t s so far . W h i l e t a c h y o n s arc c o m p a t i b l e w i t h t h e t h e o r y of r e l a t iv i ty , t h e y h a v e f a r r each ing impl ica t ions for t h e concep t of causa l i ty . T he f u n d a m e n t a l diff iculty ar ises as follows.