### A. Superluminal Speed

According to the Jain philosophy, the minimum velocity of a paramāṇu (the ultimate indivisible unit of matter) is one space-unit (ākāśa-pradeśa) per one samaya (the indivisible time-unit), while the maximum velocity is the entire length of the lokākāśa (cosmic space) travelled by a paramāṇu in a single samaya. I have discussed at length both the concepts samaya and lokākāśa in the book. We shall also see that āvalikā which is

^{45}/_{242144}seconds = 1.7 * 10^{-4 }seconds approximately is the practical unit of time which is measurable.One āvalikā covers 'Jaghanya-Yukta

-Asaṃkhyāta'^{[1]}samayas. This number is impossible to be expressed in numerical figures, but it can be shown to have definite measurable value and its lower limit can be calculated. Jain mathematics expresses this number as greater than x wherex = y

^{yyy...........(10134) times}and y = 10^{101043}Again, we shall see that the maximum distance between two extremities of loka is 14 rajjus where a rajju covers asaṃkhyāta yojanas and can be roughly expressed as

R

(rajju)= 10^{10196}light years. Thus the maximum velocity of a

paramāṇuis not less than N light-years per second where N=x^{2}* R and the value of x is as given above.How is this Jain view compatible with the Einsteinian equation of the increase of mass and the inference that nothing can travel faster than the speed of light, the theoretical speed limit of the universe?

Now, we have seen that 'mass' is not an intrinsic quality of

paramāṇu. Mass, according to the Jain view, is one of the four pairs of sparśa which are

- hot-cold

- gluey-dry

- heavy-light

and

- hard-soft.

Paramāṇu(and even material aggregates of some vargaṇās though composed of infinite number of paramāṇus) are catuḥsparśi, i.e., are agurulaghu (literally neither heavy nor light) which means that they have no mass.If we accept the value m

_{0}=0, i.e. aparamāṇuhas no mass, then the equation of the increase in mass with velocity becomes inapplicable, and, therefore, it would be possible that aparamāṇucan travel at a speed higher than that of light.In modern science, some particles such as photon, muon, etc. are postulated as massless. But the word 'massless' here probably does not mean that they are actually possessing no mass.

'A massless particle' is an awkward translation from mathematics to English. Physicists know exactly what they mean by a 'massless' particle. A massless particle is a name they give to an element in mathematical structure. What that element represents in the real world, however, is not easy to describe and in all probabilities does not mean that the particle is completely devoid of mass.

It is well-known that light is affected by gravity and bends when it passes near a massive star. It is also known that light cannot escape back holes and is, therefore, positively affected by gravity which means photons have mass.

In

paramāṇu, we have a different situation altogether - not only, it has zero rest mass but the energy of its motion must be such that it can travel with speed much higher than that of light. This may appear, in some ways, quite contrary to the fundamental inference of relativity theory that nothing can travel faster than light. But relativity itself permits the hypothetical existence of particles called tachyons^{[2]}which came into existence, already travelling faster than light. In the formalisation of the special theory of relativity, tachyons have an imaginary rest mass. Unfortunately, no one knows what an 'imaginary rest mass' means in physical terms, or what the interaction forces could be between tachyons and the ordinary particles or real rest mass.But, there is a fundamental difference between the particles such as tachyons and

paramāṇus. While tachyons transfer energy and momentum through space, in case ofparamāṇus there is no transport of momentum at all but pure energy only. Since momentum is a function of mass, there is no question of transport of momentum in the case of paramāṇu.