# How could spacetime become discretised at the Planck scale?

What do you mean by the dynamics ? The interaction between particles of matter ? What is vacuum and what is gravitational field ? Is it the same or completely differrent things ?
Quickly, because I have to go. By dynamics I mean the gravitational theory and the theory defining particle interactions. The vacuum state is uniquely defined by the dynamics and there is no ambiguity at this level.

Thank you careful for exciting discussion.

There is a somewhat simpler and slightly different answer to most of the ones given here (though maybe a little 'heretical').

We need to start with a few definitions for time -Lets be clear time isn't simple, classical Newtonian time is a discontinuity with two dimensional regions and a point in the middle. Each region is unique and totally different to the others and classical observation says that only the present or 'point time' actually exists. The future is a collapsing superposition of probabilities of the point time, and the past is the cumulative information state of the point time, neither actually exist separately.
You can roughly extrapolate point time (instantaneous time) down to the quantum limit or below, maybe down to Plank time itself. Now look at and add point time and space time together, within point time no region of space time can be much bigger than about an atom across (very roughly). Put very simply within this tiny region time actually can behave like a physical dimension, outside it time as observed behaves like a point.

Everything else beyond this is guess work but we can begin with a simple observation. Empty space can be empty (to Relativity) but distance is tied to energy by gravity and kinetic energy, this can be used to describe space time and ties it to three spatial dimensions. Now space time as defined is four dimensional and each dimension adds a power to the total energy density, in short physical space time can't stay stable over large regions which is why it breaks up into discontinuities. The region that breaks down as far as we can guess is time which is why we experience reality as we do.
Now the breakdown region is at the speed of light (where space and time actually unify) which excludes normal matter and is only accessible to objects of zero or 'imaginary' mass. This means that it forms an impenetrable barrier between us and what is outside, the big question is about what is beyond that barrier. Is there a greater physical space time or is space time just an abstract concept? don't expect relativity to give a definitive answer on this because the basic equations still work either way. The problem is that for point time the whole universe is basically in the FTL region. General Relativity solves this by saying that the universe does not exist in the present but only the past and future. (I won't comment on my opinion of that, but all of these ideas can be extended much much further.)