As noted above, in the standard model of particle physics, particles are modeled as idealized point like objects without size.
My theory is that if a unit has space, it can still be divided in half.
This could possibly be true if space is really continuous as assumed in relativity...however such an assumption leads to infinites, divergences (inconsistences) between relativity and quantum mechanics...so we know something is not quite right with this idea as currently formulated.
You can read about Planck scale physics: you will find that below some minimum length/area/or volume, such as about 10
-33 cm length, things cannot be further divided because quantum froth (uncertainty) may take hold...everything becomes jumbled in energetic undulations... time/space/matter as we know it becomes quantum foam...and these distinct entities as we know them on large scales become energetic uncertainties...akin, perhaps, to Heisenberg uncertainty...
An analogy to this minimum size at Planck scale in string theory is called "T duality" where, as a string radius is decreased in one model, it is the same as increasing the radius in another string model...so again there appears to be some minimums which nature may dictate.
But there is no absolute incontavertible experimental proof to any of the above explanations.
