In digital devices, we have pixels, which represent the smallest unit of size anything can be in a digital program. Something that is a single pixel in size in every dimension cannot get smaller. Depending on the software, though, sometimes their shape is not consistent with one another; a pixel could be square, hexagonal, etc.
Suppose you’re envisioning the universe’s equivalent of that, the absolute smallest total area that it is possible to envision something as. A pixel of the universe if you will, or a grain of space. If what you’re envisioning has absolutely no geometrical features it doesn’t need, what shape is it? What shape would an absolute grain of space or a pixel of the universe be?
Intrigued to ask because each shape I envision as the shape of a pixel of the universe comes with what appears to be issues; 1) if pixels are spherical, they don’t seem like they’d fit together 2) if pixels are cubes, then the universe has to answer for dimensional/directional bias as the corners would change based on perspective 3) if it’s triangular, how would light exuding from a single point work 4) if it’s hexagonal, that implies a sixfold dimensional system which seems to run us into geometrical issues again.
Reality isn’t a grid of pixels of any shape. If it were, I suspect the Michelson-Morley experiment would’ve gone differently.
But if it were, the pixels would be some at-least-4-dimensional shape.
Fun fact: many early video games didn’t have pixels (even in the CRT sense of the word)
Answer this definitively, and win yourself a Nobel prize!
Many of the leading physicists in today’s age think the shape is a little ‘string,’ if you will.
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I don’t think it’s likely that there is a minimum volume, at least not a discrete quantized one. It would have to be a [regular honeycomb tessellation](https://en.wikipedia.org/wiki/Honeycomb_(geometry\)) that shows no bias towards any particular direction (i.e. no corners). There are no shapes that fulfill both of those conditions in 3D space.
Why is #1 an issue? You’re assuming physics at a subatomic level works the same as that at a macroscopic level, but they don’t. Things don’t have well defined boundaries.
In 3D space it’s called a voxel
Hexagons are the bestagons.
I think the premise of a „pixel“ being the smallest entity in software is not right. Rasterization, i.e. translating (actually reducing) a defined subset of the software state into a 2D grid of colored pixels, is only a very limited view on that software.
This might be the reason for the different answers we‘re getting here. Most aim for subatomic physics, it we could also go to light theory (photons and wave frequencies/resolution) and human retinas, general optics and electron microscopes, which again would end up at subatomic physics (you got my circle-train of thought here).
See the other answers for why this isn’t really right, but given 4 dimensional spacetime, if that ‘pixel’ did exist, it would look like a hypercube/tessaract. A constantly stretching and twisting but approximate one, anyway.