Most people know helium, hydrogen, and hot air can be used for lighter-than-air flight because they are ... lighter than air. But the more basic concept is that a volume of matter in a container having a total density less than the density of its surrounding will be pushed up by the pressure of that surrounding matter beneath it. So I thought... instead of the container holding a matter with less density at the same pressure as its surrounding, what if it held a vacuum?
Granted, the container would have to be quite strong to withstand the external pressure and still light enough that it doesn't increase the total density beyond that of its surrounding matter. But if those requirements were met, it should rise, right?
And then my imagination really wandered and I thought... what if we were able to build a spherical structure as big as the moon out of a super-light and super-strong material that contains a vacuum. Would it float in Earth's atmosphere rather than falling all the way to the ground? And wouldn't that be a freaky sight?
And pondering in the other direction... wouldn't it also be possible to fill a non-stretchy balloon with enough helium that the pressure and density goes up to the point that the balloon would be heavier than air?