Why is a vacuum balloon impossible? According to Can Impossible Vacuum balloon be possible with this idea?, a vacuum balloon is impossible. Why is that?
 A: A simple vacuum balloon that consists just of a spherical shell of uniform thickness is not possible at all in air at 1 atm. I only know how to prove it can't be done with a material with uniform properties such as an amorphous solid but I believe it can be shown that it can't be done with any material. Suppose you have a vacuum balloon that's a spherical shell of an amorphous material. The problem is not that it doesn't have the strength to support the pressure difference. The problem is that the vacuum balloon would be in an unstable equilibrium because the material doesn't have a high enough shear modulus to stabilize it shape. The YouTube video Railroad tank car vacuum implosion shows that a solid steel tank car can implode when it's nowhere near thin enough to float in air. For a spherical shell of a given thickness to support 1 atm on the outside and 0 atm on the inside, the sheer modulus it must have varies as the inverse cube of the thickness. I once read that water is 800 times denser than air. If the shell is thin enough to float in air, then in order for it to support 1 atm on the outside and 0 atm on the inside, it must have a shear modulus of about 1,000,000,000 atm or more. I also read that diamond has the highest shear modulus of any material at 535 GPa which is far below the required shear modulus.
