I was thinking that, in an alternative universe, there's no reason why they should have the same number of spatial dimensions as us. So why not four, or five, or ten?
Because if you traveled to four-dimensional space, then you would find your skin insufficient to contain all of the air, blood, half-digested food, and maybe even internal organs that now find an extra degree of freedom within which to diffuse.
Five and higher dimensions makes it worse; the many things inside of you that keep you alive would disperse and splatter even faster.
So far I have discovered that to have any sort of meaningful adventure in a parallel universe, it must have the same number of spatial dimensions as we do (namely 3), it must have at least one time-like dimension, the electromagnetic interaction must exist and must recognize and interact with your electrons and protons. Gravity would be nice, and I don't know enough about weak and strong interactions to know if they would be necessary.
There are most likely other limitations and dangers in such fantastic travel that have not yet come to mind.
In short, the inter-universe questing of children from our universe can never be to any world truly alien from our own. Which is very sad.
Update: spam bots kept specially favoring this multi-year-old post in particular with travel blog advertisements disguised as comments, so I have disabled comments on this post.