We usually imagine light moving through three-dimensional space as waves or particles spreading outward in all directions. That picture works extraordinarily well for calculations and experiments — but it quietly assumes that space itself is fundamental. Over the last few decades, that assumption has been questioned by several serious lines of theoretical physics.In quantum gravity, holographic ideas suggest that higher-dimensional space can emerge from lower-dimensional structures. In AdS/CFT, for example, a full spacetime is mathematically encoded on a lower-dimensional boundary (Maldacena). Other work links spacetime geometry directly to patterns of quantum entanglement (Van Raamsdonk, Swingle), suggesting that dimensions themselves may arise from deeper informational relationships rather than being basic ingredients of reality.
This paper explores a related but distinct possibility: that light itself propagates fundamentally on a two-dimensional causal interface, and that the three-dimensional space we experience is reconstructed from that deeper process.
Why would nature prefer 2D over 3D?
The motivation isn’t aesthetic or philosophical — it comes from information limits. Any physical process that determines “what happens next” must process information, and information processing has finite capacity. There is a limit to how many independent distinctions can be resolved in a given causal step.
In three dimensions, light spreading outward must influence an ever-growing spherical surface. The number of independent locations grows as the square of distance. If the universe has a finite information budget per causal update, that budget gets spread thinner and thinner. Eventually, there isn’t enough capacity left to commit definite outcomes everywhere on the wavefront.
In two dimensions, this problem disappears. The wavefront grows only linearly with distance, and finite capacity can keep up indefinitely. From this perspective, two dimensions are not chosen — they are forced by consistency. Three-dimensional propagation is not impossible as an effective description, but it cannot be fundamental.
A hidden geometry beneath light
If light propagates on a two-dimensional interface, the next question is unavoidable: what geometry can support this without introducing preferred directions or inconsistencies? Not all grids are equal. Square lattices introduce directional bias. Irregular structures introduce location-dependent behaviour.
Here, several independent arguments converge on the same answer: hexagonal geometry. Hexagonal tilings are maximally isotropic in two dimensions, suppress anisotropy under coarse-graining, and hide their discreteness more efficiently than any other regular structure. This is why hexagons appear so often in nature — from honeycombs to graphene — and why they reappear here, not from chemistry or biology, but from causal consistency.
Importantly, this hexagonal structure isn’t perfectly hidden. If it exists, it should leave an extremely small but specific imprint.
A concrete, testable consequence
A hexagonal substrate predicts a six-fold directional pattern in how light propagates — not large enough to notice in everyday life, but potentially detectable in ultra-precision experiments. A square structure would instead produce a four-fold pattern. A perfectly smooth continuum would produce none at all.
This makes the idea experimentally sharp: six-fold symmetry supports the framework; four-fold symmetry falsifies it; continued null results push the underlying scale smaller. This is the crucial difference between a speculative idea and a physical one — the ability to be wrong in a specific, testable way.
A different way to think about light and space
Seen this way, light is not just something that moves through space. It is part of the mechanism by which space is inferred. The speed of light becomes more than a numerical constant — it becomes the maximum rate at which the universe can commit new, irreversible facts into existence.
Whether this picture is ultimately correct is for experiment to decide. But it fits into a broader shift in modern physics: away from spacetime as a fixed background, and toward spacetime as something that emerges from deeper causal and informational structure. In that sense, the idea that light may be fundamentally two-dimensional is not isolated — it is one concrete expression of a much larger rethinking of what space really is.