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.
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.
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.
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.
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.