Is matter infinitely divisible or not ?

I know that what was once thought of as indivisible, like an proton, is now regarded as divisible into quarks.

I find it hard to imagine that subatomic particles, even if they can be broken down further, can be infinitely divisible. In fact, i wonder if quantum uncertainty would play a role: would we ever know for sure that the particle had divided? ( I have only an informal acquaintance with quantum mechanics, so what I just said might be nonsense!)

But if they could be infinitely divided, that would actually be pretty wild!

Then there is another possibility, that a physicist friend likes to remind me of. Namely, all of particle physics might be nothing more than an elegant mathematical model that explains observed phenomena very well, but it might not be literal reality at all. In face, he would say that about physics in general. He is prone to utter things like, "When you ask what 'really' happens, I have no idea what you mean!" Needless to say, he is a [i]theoretical[/i] physicist!

(My background: I am Christian, but I don't see the relevance of that to this discussion.)