作为扩充量子理论的可能性的瓦尔斯特伦反对
The Wallstrom objection as a possibility to augment quantum theory
摘要：
瓦尔斯特伦认为，从马德隆变量$ψ(q)=ρ(q)\exp(\frac{i}{\hbar}S(q))$出发构造波函数的量子解释，特别是纳尔逊随机数的许多变体，并不等同于量子理论。接受这一点，我们明确地添加物理限制$(\forall q\in Q)|ψ(q)|^2>0$的配置空间表示的量子理论。所得到的理论依赖于位形空间$Q$的选择。这种限制增加了证伪这些理论的可能性，使它们在真正被证伪之前，更适合遵循波普尔的经验内容标准。考虑到相对论性标量场的情况下，我们认为，这是合理的预期，基于粒子本体的变体可以（甚至已经）证伪，而证伪基于场本体的变体似乎更难，如果不是不可能的。如果正确的话，转换到一个领域本体论似乎是一个合理的选择解释的基础上马德隆变量，以规避瓦尔斯特罗姆反对。
英文摘要：
Wallstrom has argued that quantum interpretations which construct the wave function starting from Madelung variables $ψ(q)=ρ(q)\exp(\frac{i}{\hbar}S(q))$, in particular, many variants of Nelsonian stochastics, are not equivalent to quantum theory. Accepting this, we explicitly add the physical restriction $(\forall q\in Q)|ψ(q)|^2>0$ in the configuration space representation to quantum theory. The resulting theories depend on the choice of the configuration space $Q$. The restriction adds possibilities to falsify such theories, making them preferable following Popper's criterion of empirical content until they have been really falsified. Considering the case of a relativistic scalar field, we argue that it is reasonable to expect that the variant based on particle ontology can be (or even has been already) falsified, while to falsify the variant based on field ontology seems much harder, if not impossible. If correct, switching to a field ontology seems a reasonable choice for interpretations based on Madelung variables to circumvent the Wallstrom objection.
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