对冯·诺意曼“量子概率论”的两点质疑

本文对于公认的量子力学数学基础—冯·诺意曼概率论提出了两点质疑。从物理上讲,它将导致“粒子的势能以一定的概率超过总能量”这种违背能量守恒原理的结论。从数学上讲,它在某些方面还不如玻恩的概率解释(即常被物理学家称为“经典概率论”的数学意义的概率论)。因此,量子力学的数学基础似乎需要进一步发展和完善。

Two Queries About von Neumann's "Quantum Probability

The paper raises two queries about the generally accepted mathematical foundation of quantum mechanicsvon Neumann's quantum probability. From the point of view of physics, von Neumann's theory will lead to the result that "the potential energy of a particle may be over the total energy with a definite probability", it contradicts the law of conservation of energy. From the point of view of mathematics, in some branches von Neumann's theory is not as good as the Born' s probabilistic interpretation (i. e. the so-called "classical probability", or the probability in mathematical sense). Consequently, it looks as if the mathematical foundation of quantum mechanics needs to be further developed and perfected.