Nothing that we can see or feel can be described as a totally
grainless substance. Everything is composed of particles. So why would
I think that space-time would be different ?
Because the new substance needs to fit all of the following criteria:
The substance must have mass and momentum.
The substance must be able to be compressed. The energy required for
this compression must increase as the density increases.
The substance must have a propagation speed. This would be a
consequence of the above mentioned momentum and required energy. If the
mass,
momentum and energy are properly modeled, the propagation speed will be
present within the model.
The substance must be elastic - the energy that is expended in order to compress the substance must be conserved. This means that a high density zone within the substance will expand at a rate that is dependent on the density difference.
When the calculated rate of expansion of a high density zone (within the ambient density substance) would be equal to a speed faster than C (the leading edge of the expanding sphere would be faster than the propagation speed of the ambient substance), the expanding high density zone must bounce off of the ambient substance as it approaches C.
It may be possible for the substance to be composed of particles, but the closest model that we can see is a gas. I have not heard of a stable oscillating particle being observed in any known gas.
I think that what the space-time actually is would be less important than making it easier to model within a computer. The formula that determines how each voxel in the model behaves probably won't be based on tiny particles as much as it will be based on the relationship between mass, energy, and rate of change (E=MC2).