Soap Bubbles to Einstein: an article by Bernhard List
But children are not the only ones who are interested in soap bubbles. These fragile entities have captured the imagination of mathematicians, as well. From their physicist colleagues, mathematicians know which forcesact on a soap bubble. Namely, there are tension forces between the molecules of the soapy skin, aimed at keeping the surface of the bubble as small as possible, while the volume of the bubble stays constant.
Mathematically speaking, the question of what shape the surface of a soap bubble should have is aminimization problem (the surface area must be as small as possible) with a constraint (the volume must remain constant). For this kind of problem, mathematics offers versatile tools, collectively known as the calculus of variations, with which mathematicians can derive an equation that characterizes the surfaces of soap bubbles. From these equations, one can derive that the only solutions in ordinary three-dimensional space (more precisely: in Euclidean space) are spherical surfaces. That is the mathematical reason behind the fact that soap bubbles are spherical.
That's why, at institutes like the Albert-Einstein-Institute, you can find mathematicians working on both superficially dissimilar problems - on abstract models of the universe and on questions from the world of soap bubbles.
Further InformationFor background information on basic relativity relevant for this text, see Elementary Einstein, in particular the chapter on General relativity.