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Floating on Air in Halacha
Hear me out -- this is not meant to be facetious, but I'm asking as an issue of halachic theory.
Let's say a person had the capability to fly (or at least float) -- what would the Shabbos-based halachic problems or challenges be as applied to that person?
Does the tchum get measured straight up?
I saw in another question elsewhere that above a certain point is not considered reshus harabim but the m'kom p'tur seems to be for someone who is elevated on something, not floating independently.
I have looked for relevant halachos but I find a lot about boats and airplanes and less (shocking) about superpowers.
1 answer
Private domains go up to the sky (OC 345:5) but the other three domains stop at 10 handbreadths up (ibid :12, 18, :19).
The Talmud (Eruvin 43a) is unsure if techum extends up beyond 10 handbreadths, and for biblical level questions one should be strict (OC 404).

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