Volume 65B, number 2 PHYSICS LETTERS 8 November 1976 VACUUM INSTABILITY AND TACHYONS: COMMENTS ON A PAPER BY ZELDOVICH ~ R. MIGNANI* and E. RECAMI* International Center for Theoretical Physics, Trieste, Italy Received 20 August 1975 Revised manuscript received 2 August 1976 We show that vacuum instabilities possibly arising because of tachyons do not contradict any experimental evi- dence, and therefore that no objection against tachyon existence can be found even on this ground. In recent times, Zeldovich considered in ref. [1 ] various kinds of possible vacuum instabilities. We are not interested here in his comments about Lee and Wick-type theories or about "negative mass particles" (the latter ones being obviously refused by us [2], in the present understanding of the relativistic theories [2] ). We want, however, to answer him with regard to "hnaginary mass" particles, or better to tachyons (in- cidentally, we showed long ago that tachyons may and must be attributed real rest-masses [3] ). On the basis of special relativity extended to super- lmninal inertial frames and objects [4] we shall invali- date the assertion [1 ] that "the idea of tachyons ... must be forgotten forever". We must emphasize, however, that probably the model of tachyons considered in ref. [1] is not the one suggested by Special Relativity and adopted by us. According to Zeldovich, tachyons seem to be able to assume also negative energy; on the contrary we exclude that possibility (see the following). We there- fore think that the conclusions in ref. [1 ] can apply to any kind of negative-energy particles (tachyons or non-tachyons), but not to the tachyons as they are predicted by (extended) Relativity. We stress again, incidentally, that we too are considering that "nega- tive-energy particles (travelling forward in time)do not exist": this is, incidentally, the assumption of Work supported in part by CNR and INFN. * On leave of absence from Istituto di Fisica, Universitfi di Roma, Roma, and Istituto di Fisica, Universit~ dell'Aquila, L'Aquila, Italy. * On leave of absence from Istituto di Fisica Teorica, Universit~ di Catania, Catania, Italy. 148 ours which automatically leads to the "Reinterpreta- tion Principle" - mentioned in the following. Let us start remembering that the "Extended Relativity" is essentially based on the three postulates [2-4] : (i) Principle of Relativity; (ii) space-time homogeneity and space-isotropy; (iii) the Sttickelberg- Feynman "Reinterpretation Principle". A "duality principle" and a "tachyonization rule" follow [2--5], the latter stating that (classical) laws for tachyons are to be derived by applying a super-luminal "Lorentz transformation" [4] to the corresponding laws for bradyons (= slower-than-light-particles). In particular, the (relativistic) energy of tachyons versus their speed, in the case of motion along x, results as shown, for example, in fig. 13 of ref. [4] : rnoc2 mO~c E = + ~ , px=+x/~2_l, (1) from where one can derive that (free) tachyons with any (real) proper mass m 0 - will possess zero (total energy) only when travelling at infinite speed, that is, only when endowed with a three-momentum magnitude Ipl = mOc (cf. also fig. 12 in ref. [4]). Moreover, all the generalized Lorentz transforma- tions (both sub-luminal and super-luminal) preserve the validity - for the process under transformation - of the (usual) energy, momentunr, angular momentum conservation laws. Since usual particles or antiparticles (bradyons) may bear zero momentum, but they always have posi- tive or null total-energy (E/> m0c2), and tachyons or antitachyons bear either positive of null total-energy (E ~> 0) - and always positive 3-momentum magni- tude Ipl /> mOc - then in our Extended Relativity