量子几率的不合理成功I：作为均匀涨落的量子测量
The Unreasonable Success of Quantum Probability I: Quantum Measurements as Uniform Fluctuations
摘要：
我们引入了一个“均匀张力约化”（UTR）模型，它允许表示与任意测量情况相关的概率，并使用它来解释量子概率（玻恩规则）作为“均匀”波动出现在这种测量情况。该模型利用单纯形的几何形状来表示的状态，在某种程度上，测量概率可以推导出适当定义的凸子区域的单纯形的“勒贝格措施”。我们考虑一个非常简单和令人回味的物理实现的抽象模型，使用一个材料点粒子，这是由弹性膜，通过打破和崩溃产生不同的可能结果。这种易于可视化的机械实现允许人们获得对任意测量过程的可能隐藏结构的相当深入的了解。我们还表明，UTR模型可以进一步推广到一个“一般紧张减少”（GTR）模型，描述的条件下，缺乏知识所产生的“非均匀”波动。在这个放大器的框架，特别适合于描述认知科学的实验，我们定义和激励的概念“普遍测量”，描述最一般的可能条件下缺乏知识的测量，强调均匀波动表征量子测量也可以被理解为平均在所有可能的形式的非均匀波动，可以实现在测量的上下文中。这意味着量子力学的玻恩定则可以被理解为更一般的非均匀理论的一阶近似，从而解释了量子概率在描述现实的不同领域中的巨大成功的一部分。这是一个两部分的文章的第一部分。
英文摘要：
We introduce a 'uniform tension-reduction' (UTR) model, which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform' fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states, in a way that the measurement probabilities can be derived as the 'Lebesgue measure' of suitably defined convex subregions of the simplexes. We consider a very simple and evocative physical realization of the abstract model, using a material point particle which is acted upon by elastic membranes, which by breaking and collapsing produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of an arbitrary measurement process. We also show that the UTR-model can be further generalized into a 'general tension-reduction' (GTR) model, describing conditions of lack of knowledge generated by 'non-uniform' fluctuations. In this ampler framework, particularly suitable to describe experiments in cognitive science, we define and motivate a notion of 'universal measurement', describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. This is the first part of a two-part article.
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