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PSICONS, IMAGINARY TACHYONS: AN  INTRODUCTION – 1988

 G .S. Sarti

Two basic types of three space dimensions tachyons may be distinguished: Feinberg (1967) and Goldoni (1972).

Both os them have real mass when in movement. In the case of tachyon-psi or psicons, here described by Sarti – 1988, proposed, the situation is the opposite: the protomass is real and bradyonic, and the mass in superluminal movement is imaginary:

m =     im_o / (v² – 1)^1/2

 The total energy of the psicons is also imaginary:

E² = P² + m² < 0 : (v² / v² – 1 > 1)

                                       ⁰

For that reason the psicon is connected to other no real forms of mind energy well related to semantic informacional and neguentropic processes.

WAVE FUNCIONS TACHYONS – PSI OR PSICONS

The wave  functions associated with psicons shall not form a packet because its group velocity would be subluminal. The function  τΨ, a plane wave obtained as a solution of the Schroedinger’s equations without interaction potentials, is associated with the psicons:

 τψ = exp i(κx - ωt)

 Since the  τψ  functions d’ont form packets, by manipulating the de Broglie expressions we obtain:

v_phase = λμ = E/P = (1 + m² /p²)^1/2 > 1

                                                                       ⁰                

Moreover, taking into account that the wave number k and the angular frequency w are constants, we conclude that the linear momentum p and the to tal energy E of the particle are determinated.

Considering the uncertainty principle and the Born’s postulate, the spacial and temporal indeteminations of the psicons are infinite:

Δx = ∞

Δt = ∞

∫ (τψ)^*(τψ)dV = ∞

                                                    space-time                           

As a result, the psiconic particles have maximum probability, 1, throughout every point of space and time. We have an ocean of psicons which covers all space-time.

APPLICATION TO COSMOGENESIS OF BRADIONS

Bearing in mind that different functions  τψ do not maintain linear relation λμ = c and that phase constants (κx - ωt)_n are differents then the wave functions τψ are dispersively propagated and their superposition must form a subluminal packet more or less localized.

The packet frmed in that manner represents a real particle. If the wave number κ lies in a narrow interval  Δκ , the superpositins of Fourier plane waves will be:

ψ = ∫  _Δκ  a (κ) (τψ) d κ

By using Taylor expansion with a fixed value  κ₀ and not considering terms greater then one degree, we obtain:

ω( κ ) = ω₀ + (dω/dκ)κ₀ (κ - κ₀₎

The result is a real group – particle with definite probabilities of space-time occupation in the interval (0,1):

ψ =  (τψ)_{0   ●}   integral modulation with group velocity

This demonstration represents a first try on the use of the psicons. Such proceeding may be of help to understand parapsycological and  other PSI-phenomena related to the origin of matter.