为什么到了午饭时间你的地图就会错

你的手机之所以知道你身处何处,本质上是在窃听太空中的时钟。卫星不间断地播报时间,你的手机根据每个信号到达所花的时间来计算自己的位置。归根结底,这是一个伪装成地图问题的计时问题。

Your phone knows where you stand because it is, in effect, eavesdropping on clocks in space. Satellites broadcast the time, relentlessly, and your phone calculates its position from how long each signal took to arrive. It is, at bottom, a timing problem masquerading as a map.

这里有一个麻烦的细节。那些时钟走得并不和你手腕上的表一样快。离地球质量越远,时间就走得越快一点;在轨道上高速运动,又会把这个速率往另一个方向拉。这两种效应并不能完全抵消,结果卫星上的时钟每天大约会多走百万分之三十八秒。

Here is the inconvenient detail. Those clocks do not tick at the same rate as the one on your wrist. Further from the planet's mass, time runs slightly faster; moving at speed in orbit pulls the rate the other way. The two effects fail to cancel out, and the satellites end up gaining roughly thirty eight millionths of a second every day.

这听起来微不足道。其实不然。光在十亿分之一秒里大约能走三十厘米,所以这种量级的误差如果不加校正,每天累积起来大约会造成十公里的定位误差。地图上代表你的那个蓝点,还没到晚饭时间,就会先飘出街道,再飘出整座城镇。因此,这些时钟被故意设计成在地面上走得不对,这样它们一旦到达轨道,走的速率才恰好是对的。

That sounds like nothing. It is not. Light travels about thirty centimetres in a billionth of a second, so an uncorrected error of that magnitude compounds into roughly ten kilometres of position error per day. Your blue dot would wander off the street, then off the town, before dinner. The clocks are therefore built, deliberately, to run at the wrong rate on the ground, so that they arrive at the right one once they reach orbit.