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Calling Planck units "pixels" is extremely reductive. This is just naively applying video game concepts to physics with a poor understanding of both.
I took an entire graduate course in QM and a quantized Universe does, in fact, seem pixelated. That's exactly how I explain it to people. There's simply a finite level to how closely you can zoom in. Space, time, and energy are all quantized, and maybe even gravity though we haven't figured that one out yet.
Why can’t you cut a Planck unit in half?
The why is not really known. But we simply cannot. There is not line where one particle ends and another particle begins. The best you can do is give a probability distribution, but some of the particles will be in places where they're not really supposed to be. This is actually what drives the fusion processes in stars. The nuclei don't actually have enough kinetic energy to fuse--but she is the protons in one hydrogen nucleus just magically appear in the nucleus of a neighboring hydrogen atom.
You literally can't have distances that are smaller than these probability distributions.
Wikipedia's description quotes Bernard Carr and Steven Giddings as saying that any attempt to investigate the possible existence of shorter distances [via particle accelerator] would result in black holes rather than smaller objects
Why, though?
You have probably heard of the Heisenberg uncertainty principle? It's the one about how you can't both know the position and the speed of an electron or photon, because the observation itself changes the outcome of the other.
Something similar exists for length. If we try to observe things at Plancks length, we introduce issues about whether the thing or space even exists there. The observation of infinitely small space requires infinitely large energy in this space causing a black hole or something. I'm not really sure I get it.
There are several good YouTubes on it, but this video sort of made sense to me: https://youtu.be/snp-GvNgUt4
this was one of the better descriptions for why nothing smaller than that can be measured, but I'm aware that my pop-sci joke post is starting to annoy actual students of physics - so who knows if this discussion stays up.
A finite level to how close you can zoom in is very different from pixels. Pixels (or voxels in this case) are indivisible elements of a larger whole that exist along an evenly spaced grid. The universe doesn't have a Cartesian coordinate system measured in Planck lengths
That's exactly what a Planck unit of spacetime is. And yes, the Universe--like a screen--is divided into an evenly-spaced grid any time you choose a coordinate system.
I took an entire graduate course in QM and a quantized Universe does, in fact, seem pixelated. That's exactly how I explain it to people. There's simply a finite level to how closely you can zoom in.
isn’t the most recent explanation on planck’s length saying that we simply can’t observe further down, but it is hypothesised that smaller lengths actually exist?
Just searched a bit, looking into how the length came to be and found this from wikipedia. https://simple.m.wikipedia.org/wiki/Planck_length "The Planck length does not have any precise physical significance, and it is a common misconception that it is the inherent pixel size of the universe." What I found elsewhere was that it's the only length one can get out of the universal constans of G, c and h. So as far as I know with my limited know how is that the planck length is useful or more convenient than other lengths in quantum physics.
No. The math has the indivisibility built right into it, and our countless observations agree. There's no smaller length, because then the probability distributions between different particles start overlapping. There's a limit to how closely you can zoom in, and we can describe that limit mathematically. We don't know why it's there, but it's certainly there.
can you post a source for this?
I can't post a source for all of QM, no. I can share my class notes with you, but you might as well look into it. There are lots of quality online classes about it. You can go digging for info about Planck's constant, that's where it's "built into" the math.
Here's a good explanation from PBS Spacetime https://youtu.be/tQSbms5MDvY
but he’s not saying that the Planck’s length is the pixel size of our universe.
Reference: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/
And neither was I. But what he IS saying is that there's a limit to how closely you can measure length in any dimension. Thinking of it like pixels is a useful metaphor because that's an indivisible unit, and it's what's behind Planck's constant. But a Planck length is really only relative to quantum gravity, not QM generally.