No, by our current understanding there is no length smaller than a Planck length, and any distance must therefore be divisible by an integer. That is, the length is made up of discrete quanta. Pi, or any other irrational number, is by definition not divisible by an integer, or it would be a ratio, making it rational. This has nothing to do with the accuracy or precision of our measures.
Comment on Irrational
themeatbridge@lemmy.world 2 weeks agoWe could make an object that is exactly pi meters long. Make a circle of 1 meter in diameter, and then straighten it out. We would not be able to measure the length more accurately than we can calculate it (that might be the larges understatement ever) but to the tolerance with which we could make a 1 meter dismeter circle, you should have the same tolerance to the circumference being pi.
aberrate_junior_beatnik@midwest.social 2 weeks ago
BluJay320@lemmy.blahaj.zone 2 weeks ago
Planck length isn’t the smallest possible distance. It’s simply the smallest distance at which our current understanding of physics still holds up. Beyond that, our current models break down, but our current models are very incomplete
wholookshere@lemmy.blahaj.zone 2 weeks ago
Mmmmmm don’t know about that.
The Planck length is the minimum resolvable accuracy of the universe. That doesn’t mean it’s a building block like the electron is.
themeatbridge@lemmy.world 2 weeks ago
I believe you’re mistaken. A Planck length is the minimum length we can extrapolate down before physics gets weird, but that doesn’t mean it is the smallest possible length anything can be.
And an irrational number does exist as a discrete unit, it simply cannot be described as a fraction. Case in point, if you could create a spherical particle that was exactly 1 Planck length across, it would have a circumference of exactly π Planck lengths.
By your logic, such a theoretical particle could not exist because the circumference includes an irrational number in the size of the body.
Ziglin@lemmy.world 1 week ago
Two issues:
- Planck length The resolution of the circle would be too low to be precisely pi. (I’m not sure whether everything moves only in Planck lengths or whether we live in a voxel world but either way it’s not as precise as however many digits of pi we know.
- Matter waves Assuming that the circle has energy (which it must due to Heisenberg’s uncertainty principle(I haven’t actually read this but I assume that like a vacuum according to the unruh effect matter can’t be devoid of energy)) the particles making up that circle would have a wavelength in which they can interfere with other particles and also have an area in which they might be.
Donkter@lemmy.world 2 weeks ago
I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.
themeatbridge@lemmy.world 2 weeks ago
Right, by my point is that your accuracy and precision are the same whether you are making a 1 meter length object or a π meter length object. Your meter stick is not accurate to the width of a hydrogen atom, either.
But if we accept the precision of our manufacturing capabilities as “close enough,” then it is equally as close to exactly π as it is to exactly 1.
Donkter@lemmy.world 1 week ago
Not to reiterate what other people have said here. But you can make an object 1 meter long by defining that object as 1 meter (hell, you don’t have to, but you can define 1 meter as the length that light travels in a specific amount of time or something silly). Then, to create something two meters long, you can have two of those one-meter lengths. To make something π meters long, you would need infinite precision, that is not true for 1 meter or even 1/3 as you mention later in this thread. There is no way to divide anything into exactly π length. There is an easy way to divide something into a number that can be expressed as a fraction, such as 1/3, or any fraction you care to come up with, even if it can be represented as .3 repeating.
mexicancartel@lemmy.dbzer0.com 2 weeks ago
The precision of our manufacturing capabilities might be limited as QM has this discreete nature. It might be limited in this universe. So pi may only exist theoretically
themeatbridge@lemmy.world 2 weeks ago
But you could make that same argument for a lot of fractions. 1/3 doesn’t exist because you cannot divide a quantum in three. 0.333 repeating means that eventually you have to divide an indivisible foundational particle in thirds.
IsoSpandy@lemm.ee 1 week ago
Sure. But how about a plank length instead of width of H atom. That would be great.