...in case of space and time not being continuous particles would be teleporting themselves all the time..
The causality requires, the particles cannot propagate at distance through "nothing". Instead of this, they're undulating through space like less or more dense clusters of Aether foam - pretty like the flocks of foam along water surface.
This model requires, every bubble of foam remains filled by smaller bubbles, recursively. While the nested level has no apparent limitations, from distant perspective the interior of foam bubbles is formed by remote generation of another bubbles.
...we can apprehend space with mathematics in a way that we cannot apprehend with direct experimentation..
Question is, what the "direct experimentation" is. Most of physical experiments are indirect, i.e. by interpretation based. We never saw the electron, photon, atom nuclei - they're all the result of indirect observations.
