Dr. N.L. Kachhara
It is clear from above that the known universe matches only the middle loka, which is flat. It appears that scientific observations are limited to middle loka only that contains all stars and galaxies. The upper loka and lower loka do not contain stars and so do not produce the common radiations, which can be detected by normal instruments. The solution of general relativity equation of Einstein, however, considers matter and radiations of all kinds and should be applicable to whole loka. As a first approximation the assumptions made above for the solution of general relativity equations are satisfied in the case of loka. Loka contains energy and momentum in the form of vargana (primarily eight- touch) and aggregates. It also contains vacuum energy in the form of vargana (primarily four- touch) and paramanus. The space is simply connected and so space and time in space-time can be assumed separate. The space can also be considered isotropic and homogeneous in the middle loka and also in upper and lower loka as first approximation. The symmetrical structure of islands and oceans in the middle loka is similar to the universe. In the upper and lower loka the centrally located mobile zone is denser than the surrounding region but this difference can be neglected in the first instance. The upper loka and lower loka being different from the middle loka the curvature of space in the three loka is expected to be different. With this difference in mind we compare different solutions obtained for different curvatures with Jain loka of fig 6.3. We find the upper loka is like an extended sphere, the lower loka is like a hyperboloid and the small region of middle loka can be regarded as flat. Thus we see that solutions of simplified general relativity equations for different curvature of space can be jointly compared to the three parts of loka. The agreement can be improved by considering the specific structures of upper and lower loka and the presence of vacuum energy by including the cosmological constant in the equations.
We must recognize the limitation of the mathematical equations of general relativity in describing the partial aspects of reality. For example they do not tell us whether the space-time described by them is a part of bigger reality. According to Jain philosophy loka, the space-time, containing all matter, energy, jivas etc. is a finite part of infinite akasa. The space-time relationship established in the presence of matter and energy is described by these equations but akasa being devoid of pudgala etc. does not enter the relationship.
It is pertinent to consider the significance of the assumed values of Ω for upper and lower loka. It was mentioned earlier that the upper loka contains lands of heavens where the souls having merit are reborn. The karma bodies of souls having merit is composed of lighter negative karman varganas. The lands of heaven provide attraction to these meritorious souls and so must have a positive character. This means that heavens must be made up of positive varganas, which are heavier. The celestial beings living in heavens have protean bodies, may be like plasma. The lands required for such bodies should also be of similar kind, called vimana (aircraft) meaning that these lands may be floating freely in their regions. Their constituent positive varganas make them heavier and attractive only to meritorious souls, souls having demerit cannot enter these lands. Similarly, the lands in lower loka should be made of negative varganas attracting souls with demerit and karma bodies made of heavier positive karman varganas. Such souls cannot enter the heavens made of positive varganas. So we have justification for mobile zone in upper loka being comparatively dense for which Ω >1 and the mobile zone in lower loka to be comparatively light giving Ω< 1. These considerations apply only to the mobile zone. The region outside this zone contains only small nano organisms and therefore must contain energy in subtle rarefied form giving Ω<<1. The first outer layer is supposed to be dense like water, middle layer like air and the last layer like rarefied air. As an approximation the layers may be represented by Ω = 1.
An interesting aspect of this model is that the positive upper loka and negative lower loka may provide an electromagnetic system on galactic scale pervading the whole loka. In fact, the mobile zone may work as a permanent magnet having positive pole in the upper loka and negative pole in the lower loka. If this is so, then electromagnetic force also becomes important in deciding the space-time geometry in addition to the gravitational force considered in general relativity equations. The structure of finite loka having gravitational and electromagnetic forces must be stable. The steady state theory of Jain philosophy is then proved beyond doubt.
The Bhagawati canon provides some basis for the shape of loka. First, the dharma and adharma are responsible for division between loka and aloka that is existence of a finite loka in infinite akasa. It was stated earlier in chapter 2 that but for the existence of dharma and adharma the matter in the loka would either spread out and vanish in infinite akasa or contract into a big Crunch; the loka loosing its identity and existence in both cases. Second, it is stated in Bhagawati canon that the particular shape obtained in upper, middle, and lower loka are also due to dharma and adharma. The dharma and adharma are in expanded state in some regions and in contracted state in other regions. They are in expanded state in the upper loka providing a drum (mridanga) like shape. They exist in contracted state in the middle loka giving a compact shape. Dharma and adharma are again in expanded state in the lower loka providing a flare out as observed.
Presuming that dharma, adharma, and akasa bear a one-to one relationship, that is one predasa of dharma and adharma coincide with one pradesa of akasa, the akasa (or space) also experiences expansion and contraction similar to dharma and adharma. We can see a direct correlation between space density of matter and expansion and contraction of dharma and adharma and hence that of the space. The space is seen to contract and expand according to distribution of matter. However, the primary reason for the shape of loka appears to be expansion and contraction of dharma and adharma, the agents of motion and rest of matter, energy, and soul, the space abound by dharma and adharma follows them and assumes an appropriate shape.
The above scenario may have implication for mathematical investigation of shape of loka. Can dharma and adharma be considered mathematical fields? If so, then their consideration in the evaluation of shape of loka along with matter and energy may prove important and significant in deciding the geometry. A steady state finite loka does not seem to be a mathematical impossibility.
