花粉与电子：随机性研究
The pollen and the electron: a study in randomness
摘要：
花粉粒在一杯水中的随机运动只是表面上如此。它是由一种基本的确定性运动--水分子与颗粒碰撞的运动--的粗粒化引起的。在较小尺度上不观察自由度会使确定性进化在较大尺度上显得不确定。在这篇文章中，我们试图使情况下，量子不确定性产生类似的方式，从粗粒化的确定性（但非幺正）在普朗克尺度的演变。基本的演化是由迹动力学理论描述的，迹动力学是一种确定性的矩阵动力学，量子理论及其不确定性是由此产生的。该理论的一个结果是Karolyhazy不确定性关系，这意味着计算速度的普遍上限，正如其他研究人员所指出的那样。
英文摘要：
The random motion of a pollen grain in a glass of water is only apparently so. It results from coarse-graining an underlying deterministic motion - that of the molecules of water colliding with the grain. Not observing degrees of freedom on smaller scales can make deterministic evolution appear indeterministic on larger scales. In this essay we attempt to make the case that quantum indeterminism arises in an analogous manner, from coarse-graining a deterministic (but non-unitary) evolution at the Planck scale. The underlying evolution is described by the theory of trace dynamics, which is a deterministic matrix dynamics from which quantum theory and its indeterminism are emergent. One consequence of the theory is the Karolyhazy uncertainty relation, which implies a universal upper bound to the speed of computing, as noted also by other researchers.
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