LIFETIMES OF CATOM DECAYS The phenomenon of the entry of cmatter into the material sector or the analogous entry of matter into the cosmic sector, involving the passage from spacetime domain to timespace domain, may be called “scalar inversion” to emphasize the nature of the alteration of the reference frame. Scalar inversion involves two things: firstly, a transformation of motion in time (or space) to motion in space (or time), through the unit speed boundary, in all the three dimensions. Secondly, the emergence of a catom, for example, into the material sector can take place only from inside a single unit, since the three dimensions of time have nothing in common with the three dimensions of space—both having not more than a point contact, as it were (p. 154, Nothing But Motion—hereinafter NBM). Therefore, in following up the calculation of various quantities across the boundary in scalar inversion, from the cosmic sector to the material sector, for example, consideration must be given to: (i) the loss of dimensional “information” during the alteration of the viewpoint from the temporal reference frame to the spatial reference frame and (ii) the space equivalent of time occurring within a single unit. As a result of the first point above, it is known that the full influence of spatial (or temporal) effects does not get transmitted across the boundary except when it involves only one dimension. On the other hand, only a fraction 1/c in the case of twodimensional effects, and a fraction 1/c² in the case of threedimensional effects gets transmitted. (See p. 185, New Light on Space and Time—hereinafter NLST). I will refer to this as criterion No. II in the sequel. Regarding the second point above, namely, concerning the relation between quanttties within the outside single unit, “...The time region speed, and all quantities derived therefrom, which means all of the physical phenomena of the inside region...are . . second power expressions of the corresponding quantities of the outside region.” (p. 155, NBM) I will refer to this as criterion No. IV. In order to find the lifetimes of the cosmic atoms in the material environment it is necessary to apply both the above criteria. The first step in deriving the lifetimes is to recognize that, in view of the scalar inversion, the spatiat extension of the catom, being the analog of the lifetime in material sector, bears a relationship to the latter. As such we start with the consideration of the spatial extension of the incoming catom. Now, scalar inversion is not possible with anything more than one unit in each dimension. Depending on the number of dimensions of the motion eventually acquired during the inversion process, the amount of space involve~ in the one, two and threedimensional cases is respectively s, s² and s³ (where s is the unit space expressed in the c.g.s. system). Let us refer to this as criterion No. I. The remaining criterion, No. III, necessary for our calcula tion is the recognition of the fact that the temporal equivalent of a spatial extension s across the inversion boundary is s/c (where c, the unit speed, is expressed in the c.g.s. system). The result of apptying the above four criteria to the one, two and threedimensional situations is given in the following table.
The same result could have been obtained more simply though showing less details of the underlying process by directly noting that the clocktime involved in the one, two and threedimensional cases of the decay is t, t² and t³ respectively (where t_{0} is the unit time expressed in the c.g.s. system). The measured values of the lifetimes could then be obtained by applying the criterion No. IV, as t^{½}, (t²)^{½} and (t³)^{½} respectively. Further, in the calculations above if the extension space involved is taken as p/4s² and p/6s³ respectively in the two and threedimensional cases, based on symmetrical probability, instead of s² and s³ , we have the computed values of the lifetimes in the respective situations as 1.348 × 10^{16} and 1.357 × 10^{24} secs. The acquisition of gravitational charges by the incoming catoms has an effect on the above lifetimes which can be evaluated in the following manner. In view of the scalar inversion, it must be noted that the gravitational charge of the material sector, being a twodimensional rotational vibratory time displacement, is foreign to the spacetime character of the basic rotational displacement of the catom. In the analogous case of a material atom, for example, a gravitational charge of the cosmic sector is tantamount to a magnetic charge in the material environment. Consequently the calculation of the influence of a rotational vibration of spacetime direction opposite to that of the basic rotation, on various quantities requires the consideration of the appropriate interregional ratio. For exampte, “...the motion that costitutes the charge is on the far side of another regional boundary—another unit level—and is subject to ... interregional transmission factors.” (p. 163, NBM). Further, “... interregional ratio ... accounts for the small ‘size’ of atoms. According to the theory ..., there can be no physical distance less than one natural unit ... but ... the measured interatomic distance is reduced by the interregional ratio, and this measured value is therefore in the neighborhood of 10^{8} cm” (p. 1545, NBM). In exactly the same manner, the acquisition of a gravitational charge by the catom, in view of the interregional ratio, has the effect of shortening the measured lifetime by a factor of 1/156.44. (While it is clear that the interregional ratio operates here, I am not certain that its vaiue is 156.44 in this case.) An atom is a double rotating system. The rotational vibration that is a gravitational charge establishes a coupling with one of these two rotational systems. In the case of an acquisition af one more gravitational charge, the second rotational vibratory displacement acquired acts on the second rotational system of the catom rather than adding to the previous system already modified by the first gravitational charge. As such, the computation of the lifetime in this case involves the application of the interregional ratio once more. Thus the measured lifetime in the case of two gravitational charges acquired is shortened by a factor of 1/(156.44)² The lifetimes, with or without the gravitational charges, in the one, two and threedimensional situations are, therefore, as follows:
