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Everett’s Missing Postulate and the Born Rule
Foundations of Physics ( IF 1.5 ) Pub Date : 2020-04-26 , DOI: 10.1007/s10701-020-00338-4
Per Arve

Everett’s Relative State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are formulated. In short they are (1) for a system with continuous coordinates $${\mathbf {x}}$$ x , discrete variable j , and state $$\psi _j({\mathbf {x}})$$ ψ j ( x ) , the density $$\rho _j({\mathbf {x}})=|\psi _j({\mathbf {x}})|^2$$ ρ j ( x ) = | ψ j ( x ) | 2 gives the distribution of the location of the system with the respect to the variables $${\mathbf {x}}$$ x and j ; (2) an equation of motion for the state $$i\hbar \partial _t \psi = H\psi$$ i ħ ∂ t ψ = H ψ . The first postulate connects the mathematical description to the physical reality, which has been missing in previous versions. The contents of the standard (Copenhagen) postulates are derived, including the appearance of Hilbert space and the Born rule. The approach to probabilities earlier proposed by Greaves replaces the classical probability concept in the Born rule. The new quantum probability concept, earlier advocated by Deutsch and Wallace, is void of the requirement of uncertainty.

中文翻译:

埃弗雷特的缺失假设和出生规则

由于理解退相干作用的进展,Everett 的相对状态解释越来越受到关注。为了实现其作为对物理世界的现实描述的承诺,制定了两个假设。简而言之,它们是 (1) 对于具有连续坐标 $${\mathbf {x}}$$ x 、离散变量 j 和状态 $$\psi _j({\mathbf {x}})$$ ψ j 的系统( x ) ,密度 $$\rho _j({\mathbf {x}})=|\psi _j({\mathbf {x}})|^2$$ ρ j ( x ) = | ψ j ( x ) | 2 给出了系统位置相对于变量 $${\mathbf {x}}$$ x 和 j 的分布;(2) 状态 $$i\hbar \partial _t \psi = H\psi$$ i ħ ∂ t ψ = H ψ 的运动方程。第一个假设将数学描述与物理现实联系起来,这在以前的版本中是缺失的。导出标准(哥本哈根)公设的内容,包括希尔伯特空间的出现和玻恩规则。Greaves 早先提出的概率方法取代了 Born 规则中的经典概率概念。多伊奇和华莱士较早倡导的新量子概率概念没有不确定性的要求。
更新日期:2020-04-26
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