Learn English – A word for ‘something more’ or ‘missing from life’

The sensation you describe occurs when you're in free fall, as described on HowStuffWorks:

But in the "free-fall" state, there is hardly any net force acting on you. In this case, the various pieces of your body are not pushing on each other as much. They are all, essentially, weightless, each falling individually inside your body. This is what gives you that unique sinking feeling in your stomach.

Unfortunately, there doesn't seem to be a specific term for it. (Unless there's a really technical medical term that involves your vestibular system somehow.)

On the other hand, that falling sensation (and accompanying twitch) you sometimes get when you're falling asleep? That's a hypnagogic myoclonic twitch.

Maybe it could be "likewise". It can be used in many cases, when someone expresses some feeling/opinion, and you want do say that you feel/think the same.

E.g.: A: It was a pleasure talking to you. B: Likewise. (it was a pleasure for me as well)

A: I feel sad for this. B: Likewise. (I feel sad too)

Etc.