Slower-than-Light Spin-1/2 Particles Endowed with Negative Mass Squared

Abstract

Extending in a straightforward way the standard Dirac theory, we study a quantum mechanical wave-equation describing free spinning particles --which we propose to call &#34;Pseudotachyons&#34; (PT&#39;s)-- which behave like tachyons in the momentum space, but like subluminal particles (v<c) in the ordinary space. This is allowed since, as it happens in every quantum theory for spin-1/2 particles, the momentum operator (that is conserved) and the velocity operator (that is not) are independent operators, which refer to independent quantities. As a consequence, at variance with ordinary Dirac particles, for PT&#39;s the average velocity is not equal to the classical velocity, but actually to the velocity &#34;dual&#34; of the classical velocity. The speed of PT&#39;s is therefore smaller than the speed of light. Since a lot of experimental data seems to involve a negative mass squared for neutrinos, we suggest that these particles might be PT&#39;s, travelling, because of their very small mass, at subluminal speeds very close to c. The present theory is shown to be separately invariant under the C, P, T transformations; the covariance under Lorentz transformations is also proved. Furthermore, we derive the kinematical constraints linking 4-impulse, 4-velocity and 4-polarization of free PT&#39;s