Characterization, Optimum Estimation, and Time Prediction of Precision Clocks

摘要

St. Augustine asked 'What then, is time. If no one asks me, I know what it is. If I wish to explain it to him who asks me, I do not know.' We have learned a few things since St. Augustine, Einstein has taught us a lot. But still there are a lot of unanswered questions. In particular, how do you measure time. It intrigues me that we never measure time; we measure time differences, i.e. the time difference between two clocks. I know of no way to measure the time of a clock. I can measure the time of an event with references to a particular clock. Another intriguing question is, if time cannot be measured, is it physical or is it an artifact. We conceptualize some of the laws of physics with time as the independent variable. We attempt to approximate our conceptualized ideal time by inverting these laws so that time is the dependent variable. The fact is that time, as we now generate it, is dependent upon defined origins, a defined resonance in the cesium atom, interrogating electronics, induced biases, and random perturbations from the ideal. Hence, at a significant level, time -- as man generates it by the best means available to him -- is an artifact. Corollaries to this are that every clock disagree with every other clock essentially always, and no clock keeps ideal or 'true' time except as we may choose to define it. Frequency or time interval, on the other hand, is fundamental to nature; hence, the definition of the second can approach the ideal. Noise in nature is also fundamental. Characterizing the random variations of a clock opens the door to optimum estimation of environmental influences and to the design of optimum combining algorithms.