论新量子方法中的玻恩规则
On the Born rule in a new quantum approach
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中文总结 AI 辅助
该研究在新量子基础方法中，通过跃迁概率原理这一弱条件证明了玻恩规则，并提出了比传统更简单的态概念。
中文摘要 AI 辅助
在新量子基础方法的背景下，玻恩规则在弱条件下通过若干步骤被证明。玻恩规则背后的唯一弱条件被称为跃迁概率原理，它与统计学的似然原理密切相关。该条件从多个角度进行了讨论。整个方法导致了比有限维量子力学中传统态概念更简单的态概念。
英文摘要
In the context of a new approach towards quantum foundation, the Born rule is proved under weak conditions through several steps. Some of the steps turn out to have connections to statistical theory. One step gives a generalized likelihood principle, a result of independent interest. The sole additional assumption behind the Born rule is a consequence of the likelihood principle of statistics. This principle is discussed from several points of view. The whole approach towards quantum foundation advocated here, leads to a simpler and more intuitive pure state concept than the traditional one in quantum mechanics. It also provides links to statistical theory and to Andrei Khrennikov's macroscopical quantum-like models, in particular, models connected to cognition and decisions. Finally, the approach has connections to relativity theory and to quantum field theory. It is a hope that this approach now can be seen as a good alternative to the traditional formal foundation of quantum theory. The approach is here discussed in the case of finite-values variables, but continuous variables and variables taking a countable set of values can be included in the theory by approximating them with finite-valued ones.
发表机构
- University of Oslo（奥斯陆大学）
机构由 AI 辅助整理，请以论文原文为准。
