Name: Charles
Status: student
Grade: 9-12
Country: Canada
Date: Spring 2012

Question:
Why is a Planck area defined as the Planck length squared? That would imply that the Planck area is a square with side lengths of the Planck length. On top of that, it is said that no two points in the Planck area can be differentiated from each other. This clearly contradicts with the Planck area being a square because the diagonal of the square is longer than one Planck length. In that case, should not the Planck area be a circle instead? This also goes for Planck volume. Should it not be a sphere instead of a cube (Planck length cubed)?
Replies:
I would categorize this as non-quantum reasoning applied to a quantum
world. Since the Planck length is the smallest meaningful length,
fractions of a Planck length don't have meaning. 1.41 Planck lengths
doesn't have different meaning from 1 Planck length. Thus,
effectively, a Planck (square) area is indistinguishable from a Planck
circle.

Hope this helps,
Burr Zimmerman
You have to be very careful when considering Planck dimensions. When the Planck “length” is inserted into various physical quantities it turns out that these quantities can be recast into dimensionless forms!! So you get the same result whatever shape or form you choose. The explanation is too long to put here but it is explained well on the web site: http://en.wikipedia.org/wiki/Planck_units

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