一个离散的有限的多重宇宙
A discrete, finite multiverse
摘要：
多世界解释（MWI）避免了波函数坍缩的问题。表示相同量子事件的不同MWI树可以具有不同的拓扑，这取决于观察者。然而，它们都同构于包含所有事件的所有结果的块宇宙群，因此，在这个意义上，块宇宙群是一个更基本的表示。MWI树的不同分支代表MWI中的不同宇宙，最终在共同的祖先分支中共享相同的量子态。这种分支拓扑与闵可夫斯基块宇宙的拓扑不相容;解决方案是用离散的平行块宇宙代替分支，每个块宇宙从主干延伸到最外面的树枝。分支中宇宙的数量与其厚度成正比，而厚度又取决于该分支中状态概率振幅的绝对平方。每个量子事件都可以用一个宇宙核来表示，这是将再现该事件结果的量子概率的最小宇宙组。通过考虑任何事件的结果的概率比率，可以表明每个内核中的宇宙数量必须是有限的，就像多元宇宙中的宇宙总数一样。此外，多元宇宙中的每个宇宙在空间和时间上都必须是有限的。另一个结果是量子概率必须是理性的，这表明量子力学只是离散理论的近似。一个必然的结论是，并非所有可以想象的宇宙都存在于多元宇宙中，这无疑会让那些喜欢交替历史小说的人失望。
英文摘要：
The Many Worlds Interpretation (MWI) famously avoids the issue of wave function collapse. Different MWI trees representing the same quantum events can have different topologies, depending upon the observer. However, they are all isomorphic to the group of block universes containing all of the outcomes of all of the events, and so, in that sense, the group of block universes is a more fundamental representation. Different branches of the MWI tree, representing different universes in MWI, ultimately share the same quantum state in a common ancestor branch. This branching topology is incompatible with that of the Minkowski block universe; the resolution is to replace the branches with discrete, parallel block universes, each of which extends from the trunk to the outermost twigs. The number of universes in a branch is proportional to its thickness which, in turn, depends upon the absolute square of the probability amplitude for the state in that branch. Every quantum event may be represented by a kernel of universes, which is the smallest group of universes that will reproduce the quantum probabilities of the outcomes of that event. By considering the ratios of the probabilities of the outcomes of any event, it can be shown that the number of universes in every kernel must finite, as must be the total number of universes in the multiverse. Further, every universe in the multiverse must be finite both in space and time. Another consequence is that quantum probabilities must be rational, which suggests that quantum mechanics is only an approximation to a discrete theory. A corollary is that not every conceivable universe exists in the multiverse, no doubt to the disappointment of those who enjoy alternate-history novels.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
