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- The render distance (observable universe)
- The pixel size (Planck units)
- And the update rate ('speed of light' = speed of information being updated)
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.
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
Pixels (or voxels in this case) are indivisible elements of a larger whole that exist along an evenly spaced grid.
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.
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.
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.
isn’t the most recent explanation on planck’s length saying that we simply can’t observe further down
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.
There is a misconception that the universe is fundamentally divided into Planck-sized pixels, that nothing can be smaller than the Planck length, that things move through space by progressing one Planck length every Planck time. Judging by the ultimate source, a cursory search of reddit questions, the misconception is fairly common. There is nothing in established physics that says this is the case, nothing in general relativity or quantum mechanics pointing to it. I have an idea as to where the misconception might arise, that I can’t really back up but I will state anyway. I think that when people learn that the energy states of electrons in an atom are quantized, and that Planck’s constant is involved, a leap is made towards the pixel fallacy. I remember in my early teens reading about the Planck time in National Geographic, and hearing about Planck’s constant in highschool physics or chemistry, and thinking they were the same. As I mentioned earlier, just because units are “natural” it doesn’t mean they are “fundamental,” due to the choice of constants used to define the units. The simplest reason that Planck-pixels don’t make up the universe is special relativity and the idea that all inertial reference frames are equally valid. If there is a rest frame in which the matrix of these Planck-pixels is isotropic, in other frames they would be length contracted in one direction, and moving diagonally with respect to his matrix might impart angle-dependence on how you experience the universe. If an electromagnetic wave with the wavelength of one Planck length were propagating through space, its wavelength could be made even smaller by transforming to a reference frame in which the wavelength is even smaller, so the idea of rest-frame equivalence and a minimal length are inconsistent with one-another.
Reference: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/
but he’s not saying that the Planck’s length is the pixel size of our universe.
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.