Lifetime of C-Argon, the Muon
Prof. K.V-K. Nehru, Ph.D.

Larson states that the apparent lifetime of c-argon is the sum of its own proper lifetime and the time
required for the conversion of the c-krypton rotations to massless neutrons.’ This conversion of the
cosmic type rotation, namely (3)-(3)-0 of c-Kr, to the material type rotation, M 2-2-0 of massless
neutron, involves two distinct steps: firstly, there is the “scalar inversion” resulting in the change of
scalar direction, from the standpoint of the temporal zero (the initial level of negative rotation) to that
of the spatial zero (the initial level of positive rotation), converting the (3)-(3)-0 rotations to the 1-1-0
rotation (along with the concomitant conversion of the rotational base). Secondly, there is a “splitting”
phenomenon which results in two single rotating systems of the massless neutrons, M 2-’4-0, from the
double rotating system of the above 1-1-0 rotation. Thus, the apparent lifetime of c-Ar comprises of the
three components: (i) the proper decay time of the c-Ar, (ii) the inversion time and (111) the splitting
time.

1 The Decay Time

The proper lifetime of the c-Ar, ty, in the material environment is the one-dimensional lifetime, tip,
which has been evaluated’ at 1.23314810° sec, Thus

Tj=l psec. (1)

tip is also the unit of time that is relevant in the computation of the inversion and the splitting times.

2 The Inversion Time

It must be recalled that the two sectors of the physical universe—the material and the cosmic—are
distinguished by the nature of the reference frames to which each belongs. The time-space region of our
sector is reckoned from the standpoint of the stationary spatial frame of reference, while the space-time
region of the cosmic sector is reckoned from the standpoint of the stationary temporal reference frame.
The one-dimensional lifetime, tip, was evaluated from a consideration of the kinetics of the entry from
the space-time region to the time-space region.

However, in the inversion of the rotational units of the cosmic type to those of the material type there is
an additional factor to be taken into consideration. This is because, while the evanescent manifestation
of a decaying c-atom in the material sector is analogous to the temporary sojourn of an alien visitor on
tourist visa, the scalar inversion amounts to nothing less than a complete nationalization. The c-atom
exists inside one natural unit of time, the “space region” of the space-time sector, whereas the material
atom (or particle) exists inside one natural unit of space, the “time region” of the time-space sector.
Consequently, the inversion of the c-atom involves the crossing of the unit time boundary as well as the
unit space boundary. But since our observations and measurements are carried out in the time-space
region, outside the unit space (time region), the additional factor we need to consider is that arising out
of the crossing of the unit time boundary only.

1 Larson, Dewey B., Nothing But Motion, North Pacific Publishers, Oregon, 1979, pp. 195-196.
2 K.V.K. Nehru, “Lifetimes of C-Atom Decays,” Reciprocity XI(1), 1981, p. 34.

Reciprocity 11 Ne 3 page 29 Copyright ©1982 by ISUS, Inc. All rights reserved. Rev. 7

2 Lifetime of C-Argon, the Muon

Tho total number of possible directions—the quantization of orientation, we may say—in the time
region that the scalar effect of the rotation can take is calculated by Larson’ to be 156.44. Therefore, in
the absence of any preferential direction, the probability p, that the scalar inversion takes place in a unit
of time (i.e., tip) would be 1/156.44.

But this number, 156.44, is specifically applicable to the time region motion only in relation to our
spatial zero point of view, or the analogous case of the space region motion in relation to the temporal
zero point of view. As already mentioned, the inversion of the negative rotations (3)-(3)-0 to the
positive rotations 1-1-0 is tantamount to switching the viewpoint from the negative zero to the positive
zero. Although this entails no change from the natural standpoint, it amounts to a shifting of 8
displacement units from the standpoint of our stationary reference system.* In view of this 8 unit
separation between the positive and negative zero points, the total number of possible orientations in
the space region, namely 156.44 as reckoned from the negative zero standpoint, becomes 8 x 156.44,
when reckoned from the positive zero standpoint. Consequently, the probability of inversion, p,
becomes 1/(8 x 156.44).

Over and above these, there is a numerical amplification arising out of the fact that x units measured
from zero speed in time are equivalent to 8-x units measured from zero speed in space. Thus, one unit
of motion in time “... the smallest amount that can exist, is equivalent to seven units measured from the
spatial zero...”.° Remembering that, whereas the previous factor 8 applies on the other side of the unit
time boundary and therefore increases the total possibilities (i.e., reduces p), the factor 7 magnifies the
motion on this side of the boundary and increases p. Thus we arrive at the value of the probability p, as
7/(8 x 156.44).

Since p is the probability that the inversion takes place in unit time, the mean time required for the
inversion event to complete is 1/p. That is,

8 X 156.4
T.=

F 7 Xtipn Sec. (2)

3 The Splitting Time

The splitting of the double rotating system 1-1-0 (three dimensions) to two of the two-dimensional
rotations M '4-'4-0 (four dimensions in all), involves one unit of time modified by the 4/3 dimensional
factor, that is 4/3 tip. Were, it may be argued that since after the inversion from (3)-(3)-0 to 1-1-0 the
motion has already crossed the unit speed boundary and arrived in the material sector proper, the time
unit relevant is no longer tho one-dimensional lifetime, tip (whioh is applicable during the transition
only), but the natural unit of time, tna. However, why this is not correct will be apparent in a moment.

It must be realized that the 1-1-0 combination is inherently unstable from the probability
considerations,° whereas the massless neutron, M 4-4-0, is a stable structure. Insofar as the scalar
inversion from (3)-(3)-0 leads to the improbable pattern 1-1-0, the splitting time, t, is negative. This is
the same thing as saying, in common parlance, that a more probable condition is realized earlier than a
less probable one. This clarifies the reason why tip, and not tna, is the pertinent time unit in the splitting.
The time computation concerning any event after the 1-1-0 event requires consideration of tna as the

Larson, Dewey B., Nothing But Motion, op. cit., p. 154.

ibid., p. 153.

Larson, Dewey B., Quasars and Pulsars, North Pacific Publishers, Oregon, 1971, p. 97-98.
Larson, Dewey B., Nothing But Motion, op. cit., p. 142.

Nn WwW

Lifetime of C-Argon, the Muon 3

proper time unit since the event 1-1-0 marks the end of the inversion. But the M '4-'4-0 event is before
the 1-1-0 event and thus the relevant time unit is still tip. Thus,

ress SEC. (3)

Finally, from the relations (1), (2) & (3) above, we have the apparent lifetime of c-argon as
T=T,+T,+T,

cs eae 4

8
7 3 X 1.233148 x 10 (4)

=2.2007X10° sec.