Is It Possible to Create a Perfect Square Using Planck Lengths?

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ianfort
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Hey guys I'm new here. I have a question about Planck lengths that has been bothering me lately. I'm not exactly well versed in the area of quantum physics, learning most of what I know from documentary shows and articles on the internet, so so this may seem like a stupid question, but...

Imagine you have a set of subatomic particles arranged uniformly in the shape of a square. The sides of this square are only a few Planck lengths. Now, if a square's sides are rational in length, then the diagonal between the square's corners MUST be irrational. But that can't be for this square, for that would require a non-integer amount of Planck length to exist between the square's corners.

Does this prove that its impossible to make a truly perfect square physically? If so, then how do Planck lengths fit together uniformly?
 

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The way I've been taught about Plank length is that it isn't the shortest possible length, but is rather, the shortest length that makes sense physically, rather like absolute hot or absolute zero. It isn't a quantisation of distance, rather a limit. So, although you may have technically made something smaller, it isn't signifying anything, so that's fine.

Although I'm sure there's a better explanation.
 
Yes, I agree with Kracatoan. Your argument is more applicable in the context of a quantized minimum length. Quantized space is of interest in many current attempts to quantize gravity, although I don't know what such theories have to say about your suggestion. For one thing, the geometry at that scale ceases to be Euclidean, and so it's not even clear that the irrationality of the diagonal in your case is true.