Relative Abundance of the Elements
Prof. K.V.K. Nehru, Ph.D.

A general physical theory, like the Reciprocal System, should satisfy two types of criteria in order to
establish its truth. Firstly, it should be able to explain completely those physical phenomena that
remained recalcitrant without explanation in the previous theories. More desirably, it should lead to
predictions which are definitely in conflict with those of the preceding theories but can be validated by
observation or experimentation. The second type of requirement to be satisfied by the general theory is
that it is not inconsistent with any of the definitely established physical facts. This may be called the
negative criterion, whereas the previous one may be called the positive criterion.

It can be seen that the positive criterion, being more powerful in establishing the new theory, demands
greater attention (and challenge) from the point of view of its proponents. The negative criterion, on the
other hand, is a rather weak condition for positively establishing the new theory. Further, in view of the
extremely vast number of genuine physical facts that were recognized, it is neither possible nor
worthwhile to bestow more than a limited amount of consideration—especially in the early stages of
the development of the new theory—to showing that the theory is not inconsistent with any of these
facts. However, the negative criterion, though a weak one in establishing the new theory, is all-
powerful in invalidating it if a single instance of inconsistency is found. For this reason the adherents of
the conventional theory not infrequently, tend to invoke the negative criterion, having already armed
themselves with some sort of explanations for some of these facts. They often ask how the new theory
accounts for some of such recognized facts. In such instances—especially when information of a
quantitative nature is involved—it is incumbent on the proponents of the new theory to pay more
consideration and work out the details to demonstrate that the negative criterion is well satisfied.

I wish to bring to your attention two such questions which lectures on the astronomical aspects of the
Reciprocal System invariably seem to elicit. The first one of these is about the genesis of the elements
and their relative cosmic abundance. The second concerns the background microwave radiation and the
value of its temperature. These, therefore, seem to warrant greater consideration in working out the
details in the context of the Reciprocal System. The detailed study of the cosmic abundance problem is
also important from the point of view of stellar evolution and energy generation processes.

In the following I attempt a cursory analysis of the cosmic abundance problem, giving nothing more
than a general outline of the argument.

According to the Reciprocal System (i) the element building process starts with the formation of
hydrogen from the decay products of cosmic matter—namely, the massless neutrons and their
equivalents—ejected into the material sector;' (ii) the assembling of the elements with higher atomic
numbers then continues by the successive additions of the positive rotational displacement units
(PDU).’ Let:

Na = the total number of PDU in the material sector of the universe, locked up in the material
atoms
N, = the total number of atoms in the material sector

1 Larson, Dewey B., Nothing But Motion, (Portland, OR, North Pacific Publishers, 1979), p. 215.
2 Larson, Dewey B., The Structure, of the Physical Universe, (Portland, OR, North Pacific Publishers, 1959), pp. 105-108.

Reciprocity 13 Ne 3 page 28 Copyright ©1985 by ISUS, Inc. All rights reserved. Rev. 16

2 Relative Abundance of the Elements

N. = the number of rotational displacement units ejected into the cosmic sector from the material
sector

= the number of rotational displacement units ejected into the material sector from the cosmic
sector (under steady state conditions)

N, = the number of free PDU in the material universe involved in transmuting the elements
N, = the number of atoms of the element with atomic number Z
a, = the relative cosmic abundance of the element Z = N,/N;

We will consider the element with atomic number Z. We find that its population, N,, is being increased
by the atoms that get transmuted to element Z from lower Z values. At the same time N, is being
decreased by those atoms that get transmuted to atomic numbers higher than Z. In addition, some
atoms of element Z are lost through Type II explosions. Since the universe as a whole is under steady
state, the number N, can be taken as constant. This means that the inflow must be equal to the outflow.

1 Total PDU

The total number of the positive rotational displacement units contained in all the atoms in the material
sector is given by

N,=),,2N,=N,), Za, (1)

2 Transmutation, Outgoing

O,, the number of atoms of element Z that are outgoing by getting transmuted to element(s) of higher
atomic number by combining with the free PDU can be arrived at as follows:

Let D, be the number of PDU captured by the atoms of element Z, out of Nn, the total number of PDU
available for transmutation. Then, the ratio D,/N; must be equal to the ratio of the PDU locked up in all
the atoms of element Z to the total number of PDU in the material sector. That is,

D, ZN, D.=Z(N.a.) N, 7
=——,, or = a

N,, Na Z L Z Nu ( )
Now, the major portion of the outgoing atoms from element Z end up as atoms of element Z+1. This
involves the capture of a single PDU by each atom. Let this number of atoms be \O,. In addition, it is
also probable that a small fraction of the atoms capture simultaneously two PDU, resulting in
transmutation to element Z+2. Let this number be »O,. Thus O, is made up of two parts, ;O, and 2O,,
such that

,0O,=kO, and ,0,=(1-k)O, (3)
where & is a distribution fraction.

Of the number of D,, we take that the number of PDU involved in the single capture event is ,D, and
the number involved in the double capture event is »D,. Then ,D, = \O,, whereas 2D, = 2 x .O,. Using
Equation (3) we have

D,=,D,+,D,=,0,+ 2X,0,=[k+ 2(1-k)]O,=(2-k)O,

Relative Abundance of the Elements 3

Substituting for D, from Equation (2),

Za, (4)

3 Transmutation, Incoming

From what has been said above, it can be seen that the number of atoms, I, coming in by getting
transmuted to element Z from elements of lower atomic number comprises two separate streams: 1,.1,
the number that is coming in from element Z-l due to single capture, and I,.2, the number coming in
from element Z-2 due to double capture (see Figure 1).

I

a Oe ee

I
z-2 E

Figure 1: Population Flow to and from Element Z
From Equation (3) we note that
I, ,=,0,_,= ( 1 = k) 035 and
Lp jO neh O ne

Thus, the total number of incoming atoms adding to the population of element Z is, (substituting Z+2
and Z+ respectively, for Z in Equation (4))

I=1,_,+1

z-l

-|n. 2(2-#)](1-#(2~2) k(Z—1)a..] ©)

4 Ejection

We will assume that the relative abundance in the matter that is ejected to the c-sector by the Type II
explosions is the same as that in the material sector of the universe in general. If is the number of atoms
of element Z that are ejected, we have the total number of PDU that are leaving the material sector by
way of ejection as

N=). ZE, (6)

If the matter is uniformly distributed, we have E, proportional to N,; that is, E = g x N,, where g is a
fraction less than 1.0. Then

4 Relative Abundance of the Elements

E,=gN,a, (7)
Therefore, from Equation (6) above,
N= Z(gN,a)=gN,d, Za,
Hence, from Equation (1), N. = g x Na, or g = N./Nag. Finally, from Equation (7),

N,
N

E.=|Niy*]4.
=v Foe) 2,

Zz

(8)

5 Equilibrium

By steady state we mean, in the material sector, uniformity with respect to time. Under steady state
conditions, therefore, the relative abundance does not vary. That is, N,, the number of atoms of the
element Z is constant. (That is, N,, the number of atoms of the element Z, is constant.) In other words, I
= O,+ E, (see Fig. 2). Thus, from Equations (4), (5) and (8),

N

Mise (2) [(1-#)(Z-2)a,_,+ k(Z—-1)a,_,]
alg Na (2-k)
-|v,8(2-8 Za,+ nea, (9)
a Caran
a 7, ia
where
o=w CoH) (10)
6 Hydrogen

Since with Z = 1, hydrogen is the first element, the case of inflow from elements of lower atomic
number does not arise. On the other hand, the displacement units ejected from the c-sector form the
incoming flow. Since, of the N, displacement units entering the material sector, N, PDU are used up for
the purpose of transmutation, the number of PDU that eventually transform to hydrogen atoms is N, -
N,. Therefore, from Equations (4) and (8), balancing the inflow and the outflow,

NoN/N = af a,t [va

d

n

or,

Relative Abundance of the Elements 5

ye gs. (11)

Since a, is a function of a;, a; cancels out from both sides of the Equation (11). The equation, therefore,
serves as the compatibility criterion between values of o and k.

Further, since N, = x N,,

2a (12)

Equation (12) is the normalizing condition which fixes the value of a;, and hence of all a,, for given
values of o and k.

7 Comparison with Empirical Data

The values of the two parameters o and k in the above equations are to be arrived at by logical
processes from the postulates of the Reciprocal System. This still remains to be done. Meanwhile, a
good agreement with the empirical values of the relative cosmic abundance’ can be demonstrated by
appropriate choice of o and k. The theoretical curve is plotted in Figure 2, with o = 9.5 and k= 0.9.

Arca # Ni Theoretical Curve
s

*e,

Z, Atomic number

Figure 2: Relative Abundance

It must be noted that, in the figure, the abundance values are plotted on a logarithmic scale and hence
the discrepancy between the theoretical and the observational values wherever it occurs should not be
underestimated. However, it is clear that, as far as it goes, the trend of the theoretical curve conforms
well to the actual.

3. American Institute of Physics Handbook, 1963.

6 Relative Abundance of the Elements

Further refinement is in order in considering the possibility of transmutation by triple or multiple
capture of PDU, which have a nonzero probability at the higher Z values. In fact, the comparatively
higher abundance of the Even-Z elements over those of the Odd ones can be explained on the basis of
the corresponding distribution in the values of & for the single, double, or higher multiple capture
events. Remembering that the atomic number is the net total electric displacement units, and Even-Z
can be seen to correspond to an Odd speed 1/(1+Z). As Larson explains,* Odd speeds (like 1/3 or 1/5)
are the direct result of scalar directional reversals, whereas Even speeds (like 1/4 or 1/6) are obtained
only by way of compounding two Odd speeds. As such, the probability of an Odd speed (Even-Z) is
comparatively higher than that of an Even speed (Odd-Z).

Among the assumptions made, the first is that the relative abundance is uniform in the universe. The
second one is that the magnetic ionization level is zero. This may be true only in the case of interstellar
and intergalactic matter, most of which lies undetected. Consequently, the contribution of this matter to
the cosmic abundance is not reflected adequately in the observational values. The zero ionization level
assumption, therefore, is likely to give rise to a large error in the predicted values, especially at the
higher atomic numbers. Evaluation based on the consideration of the atomic weight rather than the
atomic number will be more appropriate to the situation as it takes care of the rotational displacement
present as the gravitational charge as well.

Another important factor that has not been taken into account in this preliminary analysis is the
disintegration of matter that occurs on attaining the destructive thermal limit (as in the stellar energy
generation process). Also to be considered is the effect of supernova explosions on the abundance of
the Fe group of elements, and the possibility that the relative abundance in the matter ejected out of the
material sector in Type II explosions is considerably different from that applicable at large.

4 Larson, Nothing But Motion, op. cit., p. 98.