We propose a model for the universe based on Jordan algebras. The action consists of cubic terms with coefficients being the structure constants of a Jordan algebra. Coupling constants only enter the theory via symmetry breaking which also selects a physical vacuum. “Before” the symmetry breaking the universe is in a pre-geometric state where it makes no sense to talk about space or time, but time comes into existence with the symmetry breaking together with a Hamiltonian which can create space from “nothing” and in some cases can propagate the space to macroscopic size in a finite time. There exists symmetry breaking which results in macroscopic spacetime dimensions 3, 4, 6 and 10, based on the Jordan algebras of Hermitian 3x3 matrices with real, complex, quarternion and octonion entries, respectively.

我们提出了基于约旦代数的宇宙模型。该作用由三次项组成，其系数为约旦代数的结构常数。耦合常数仅通过对称破坏进入理论，而对称破坏也选择了物理真空。“在此之前”，打破宇宙的对称处于几何前状态，谈论空间或时间是没有意义的，但是随着对称的打破和哈密顿量一起出现，时间可以存在，哈密顿量可以从“无”到“无”创造空间。在某些情况下，可以在有限的时间内将空间传播到宏观尺寸。基于Hermitian 3x3矩阵的约旦代数（分别具有实数，复数，四分之一和八进制数的项），存在对称破坏，导致宏观时空维数为3、4、6和10。