It's comparatively easy (cum grano salis) to grasp the following concepts:
- Euclidean space-time (continous space and continuous time)
- classical mechanics (discretely distributed matter in continous space and continuous time)
- Minkowskian space (continously intermingled space and time)
- special relativistic mechanics (discretely distributed matter in continously intermingled space and time)
- classical electrodynamics
- classical quantum mechanics (discrete energies, continuously distributed matter in continous space and continuous time)
- quantum electrodynamics
- general relativity (continously intermingled space-time and matter)
Accordingly, there are lots of introductory texts and text-books.
It's also easy to grasp
- numerical simulations (on artificially - and mostly unphysically - discretized spaces, times, and space-times)
- cellular automata (on unphysical regular spatial grids)
It's definitely hard to grasp (for somehow graspable reasons)
- quantum gravity
I do not know whether there are empirical evidences for a discrete space-time or only theoretical desiderata, anyhow I cannot figure a discrete space and/or time out.
Why is it so hard to introduce and explain the concept of a physical discrete space-time?
Why are there no easy to understand introductory texts or text-books on definitions, concepts, models, pros and cons of discrete space, time, and - finally - space-time?
Respectively: Where are they?
Are the reasons for this maybe related to the reasons why quantum gravity is so hard to grasp?
Answer
I think you're looking for something like Regge Calculus (there are plenty of extra refs in this link, and many more in this one).
You can also check this article, Quantum Gravity and Regge Calculus.
Furthermore, this guy has a whole research area in this topic (discrete spaces, etc)!
So, there's plenty of stuff out there... you just have to look. ;-)
(Edited) PS: In fact, here's the name of the game: Discrete Differential Geometry. Google away...
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