Okay, the first useful result.

Planck kinda proved this already, in a way, but I'm deriving it from basic principles. Just math. Even a 1 hz photon can be partitioned.

The proof uses the same logic as Tsirelson's bound, and it's remarkably easy.

I will illustrate by example.

Consider a double slit experiment. Some of the photons go this way, some go that way, they interfere on the other side. The experiment requires a coherent light source, which means spins are correlated on the way in.

Here's the important observation: they're also correlated on the way out. The interference pattern doesn't happen if detectors are placed at the slits.

What does this tell us?

It tells us, that information is neither created nor destroyed, when the photons traverse the slits. It's being conserved.

Two possibilities obtain: slit traversal is either a stochastic process, or it's not. If it's not, the lack of information is unsurprising, however we have proven that photons can be subdivided. Why? Because the experiment works with a single photon (no interference pattern, obviously, but you can show passage through both slits).

If it is (stochastic), nonsqtr's law says the generator has to be symmetric, in a particular kind of way, to get the information invariance.

In the non-stochastic case the phase is shifted by the slit, so if the correlation remains the phases must be shifted by equal amounts. In the stochastic case this need not be so, however the outcomes must symmetrize with the phase shifts (to retain coherence).

We can calculate the required symmetries quite easily, at least for pairwise correlations. (Entanglement beyond pairs is out of scope for this discussion).

To see this we build the transition matrices the same way Tsirelson does (btw it turns out these are the vertices of a graph, which is very convenient), with the constraint that the change in total information must be 0 (which is basically a "null measurement").

Under these conditions, using the Khalfin identity on the correlated pair, we find that

A0 B0 + A0 B1 + A1 B0 = A1 B1

This is the required symmetry when the observable is null. This tells us that A has anti-parity with B, which is only possible if there is a conditional expectation (essentially the same situation as having a non-zero expectation in the vacuum state). Which is not possible, in this scenario, unless there is a change in correlation. Which by definition there can't be because the correlations remain. Which in turn tells us we can't have a non-zero expectation which means we MUST have subunits ("partitions" - the parities of which must be complementary).

This kind of thinking suggests the photon can be further divided into "dust particles", which at this point are undescribed and unnamed but the math says they must exist.

Warning: stochastic parity is something different from geometric parity.