A universe with a total mass of zero would lack gravitational interactions, rendering it fundamentally different from our own. The discussion explores the implications of negative matter, which could theoretically balance out positive matter to achieve a zero mass universe, but raises concerns about annihilation between matter and antimatter. General relativity does have solutions for massless universes, such as the Milne Model, which does not involve antimatter. The consensus is that a truly massless universe would contain nothing at all, as any form of matter or antimatter would still exert gravitational influence. Overall, the conversation highlights the complexities of mass and gravity in theoretical physics.