In "Upside Down", what happened after Eden gave birth to Adam's children? Will they belong to the "Up" or the "Down" world?
The short answer is a combination of "We don't know" and "It doesn't matter".
We don't know because it is not explained to us. The science in the movie is sketchy at best. That said, even Adam and Eden wouldn't have known until the twins were born (which at the risk of sounding macabre, is not a given either).
It doesn't matter because regardless of which world they are born of, they can live anywhere, thanks to Adam's (and Bob's) innovations.
Trying to predict what will happen using reason is difficult thanks to the whole "third law" business which is, IMO, too gimmicky. From Wikipedia:
After some time in contact, matter in contact with inverse matter burns.
We are not informed what exactly Bob did to "negate" the gravitational effects. We don't know if it also negates the third law. But that is unlikely. If it doesn't, then there are a few points to consider:
- In light of the third law, how did Adam impregnate Eden in the first place? How did she get fertilised?
- Presumably, those from Up can only eat Up grown food. This would mean that Eden will only be able to eat Up food and thereby, the twins too. It would then follow that the twins will be made of Up matter.
- But why twins? IMO, the writer wants us to believe that one twin will be an Up while the other will be a Down. This unfortunately does not solve the nutrition problem from above.
- The twins were conceived when Adam and Eden had sex in the "neutral zone" between worlds. We will have to assume that the "third law" doesn't really have an effect in this region, which would mean that the twins are "neutral zone" citizens. Furthermore, this might render them immune to all three laws and capable of living on either world. Perhaps all "interracial" couples will then go to the neutral zone to conceive.
IMO, the neutral zone theory is the least problematic solution to the problem. But let's hope that there are no plans for a sequel :)