算法控制实验中的测量极限
Limits to measurement in experiments governed by algorithms
摘要：
我们提出以下问题：如果物理实验完全由算法控制，那么算法会对实验实现的物理测量产生什么影响？在一个研究物理系统以及与物理系统相结合的算法可能的计算性质的计划中，我们已经开始分析（i）实验过程的算法性质，以及（ii）使用物理实验作为图灵机的预言的想法。为了回答这个问题，我们将扩展我们的实验预言理论，以便使用图灵机来模拟控制物理实验进行的实验程序。首先，我们指定一个实验，测量质量通过碰撞在牛顿动力学;我们检查它的性质，准备使用它作为一个预言。我们开始使用非均匀复杂性类对多项式时间图灵机的计算能力进行分类。第二，我们表明，模拟实验者和实验程序的算法施加了限制，什么可以测量的设备。事实上，这些定理为我们在简单物理实验中测量的物理量的知识提供了一种新形式的不确定性原理。我们认为，在这里建立的结果是一个巨大的一类实验的代表。
英文摘要：
We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment? In a programme to study the nature of computation possible by physical systems, and by algorithms coupled with physical systems, we have begun to analyse (i) the algorithmic nature of experimental procedures, and (ii) the idea of using a physical experiment as an oracle to Turing Machines. To answer the question, we will extend our theory of experimental oracles in order to use Turing machines to model the experimental procedures that govern the conduct of physical experiments. First, we specify an experiment that measures mass via collisions in Newtonian Dynamics; we examine its properties in preparation for its use as an oracle. We start to classify the computational power of polynomial time Turing machines with this experimental oracle using non-uniform complexity classes. Second, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on what can be measured with equipment. Indeed, the theorems suggest a new form of uncertainty principle for our knowledge of physical quantities measured in simple physical experiments. We argue that the results established here are representative of a huge class of experiments.
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