How does your smartphone know exactly where you are? The answer lies 12,000 miles over your head in an orbiting satellite that keeps time to the beat of an atomic clock powered by quantum mechanics. Phew. Let's break that down. First of all, why is it so important to know what time it is on a satellite when location is what we're concerned about? The first thing your phone needs to determine is how far it is from a satellite. Each satellite constantly broadcasts radio signals that travel from space to your phone at the speed of light. Your phone records the signal arrival time and uses it to calculate the distance to the satellite using the simple formula, distance = c x time, where c is the speed of light and time is how long the signal traveled. But there's a problem. Light is incredibly fast. If we were only able to calculate time to the nearest second, every location on Earth, and far beyond, would seem to be the same distance from the satellite. So in order to calculate that distance to within a few dozen feet, we need the best clock ever invented. Enter atomic clocks, some of which are so precise that they would not gain or lose a second even if they ran for the next 300 million years. Atomic clocks work because of quantum physics. All clocks must have a constant frequency. In other words, a clock must carry out some repetitive action to mark off equivalent increments of time. Just as a grandfather clock relies on the constant swinging back and forth of a pendulum under gravity, the tick tock of an atomic clock is maintained by the transition between two energy levels of an atom. This is where quantum physics comes into play. Quantum mechanics says that atoms carry energy, but they can't take on just any arbitrary amount. Instead, atomic energy is constrained to a precise set of levels. We call these quanta. As a simple analogy, think about driving a car onto a freeway. As you increase your speed, you would normally continuously go from, say, 20 miles/hour up to 70 miles/hour. Now, if you had a quantum atomic car, you wouldn't accelerate in a linear fashion. Instead, you would instantaneously jump, or transition, from one speed to the next. For an atom, when a transition occurs from one energy level to another, quantum mechanics says that the energy difference is equal to a characteristic frequency, multiplied by a constant, where the change in energy is equal to a number, called Planck's constant, times the frequency. That characteristic frequency is what we need to make our clock. GPS satellites rely on cesium and rubidium atoms as frequency standards. In the case of cesium 133, the characteristic clock frequency is 9,192,631,770 Hz. That's 9 billion cycles per second. That's a really fast clock. No matter how skilled a clockmaker may be, every pendulum, wind-up mechanism and quartz crystal resonates at a slightly different frequency. However, every cesium 133 atom in the universe oscillates at the same exact frequency. So thanks to the atomic clock, we get a time reading accurate to within 1 billionth of a second, and a very precise measurement of the distance from that satellite. Let's ignore the fact that you're almost definitely on Earth. We now know that you're at a fixed distance from the satellite. In other words, you're somewhere on the surface of a sphere centered around the satellite. Measure your distance from a second satellite and you get another overlapping sphere. Keep doing that, and with just four measurements, and a little correction using Einstein's theory of relativity, you can pinpoint your location to exactly one point in space. So that's all it takes: a multibillion-dollar network of satellites, oscillating cesium atoms, quantum mechanics, relativity, a smartphone, and you. No problem.
智慧型手機如何定位你的位置? 秘密就位於你頭頂上方12,000英里, 環繞地球運行的人造衛星上, 搭載著依據量子力學原理設計, 不斷運行的原子鐘。 讓我們先喘口氣,聽我娓娓道來。 首先,為什麼當我們想要知道位置的時候, 也需要知道衛星上的時間? 第一,智慧型手機得先確定 它與衛星之間的距離。 每一個衛星持續不斷地發送訊號, 從太空中,以光速傳送到你的手機。 而手機會記錄收到訊號的時間, 藉此計算與衛星間的距離, 用這個簡單的公式:距離 = c 乘以 時間。 這裡的 c 是指光速, 時間是指訊號傳遞的時間。 但有個小問題, 光速超乎想像的快。 如果我們只能以秒為單位來估算時間, 無論地球上任何一個位置,或是太空中其他地方, 與衛星之間的距離,計算的結果都一樣遠。 所以,為了讓測量到的距離, 能精確到幾英尺之內, 我們得用上至今最精準的時鐘。 原子鐘非常地準確, 即使經過了三億年, 他們依然能分秒不差。 原子鐘的運作原理是量子力學, 所有的鐘都必須有一致的規律性。 也就是說,鐘一定會有重複不斷的運動 用來代表時間的等量累加。 就像老爺鐘的鐘擺, 會因為重力而來回規律擺盪。 原子鐘也有類似時鐘滴答聲一樣的規律, 是根據原子在兩個能階之間的躍遷行為計算而來, 這時量子力學便派上用場。 根據量子力學,原子帶有能量, 但原子的能量總額並不是自由變動的, 而是受限於固定能階, 我們稱之為量子。 打個比方,想像你正在高速公路上開車, 當你加速時,過程中你的車速會持續增加, 例如從時速20英里增加到70英里。 現在,想像你有一輛量子車, 你不會持續地以線性方式加速, 而是會立即的轉變速度, 從某個速度直接變成另一個速度。 對一個原子來說, 從某一個能階跳到另一個能階,稱為躍遷。 根據量子力學, 能量的差異會等於 特性頻率 乘以 常數, 能量的變化會等於 某個固定數值(稱為普朗克常數) 再乘以頻率。 這個特性頻率,就是我們製作原子鐘時所需要的。 GPS衛星仰賴著"銫"和"銣"原子做為頻率的基準。 以銫133為例, 它的特徵頻率為9,192,631,770 赫茲。 也就是每秒大約九十億個週期。 真是個運作非常快速的時鐘。 無論再怎麼熟練的鐘錶匠, 每個不同的鐘擺、發條和石英晶體, 產生的振動頻率都會有些微差異。 但是無論如何,在宇宙中的 銫-133原子 皆以完全相同的頻率進行振盪。 所以多虧了原子鐘, 我們可以測量到1億分之一秒的時間, 以及非常精確地,計算出衛星與物體間的距離。 現在,我們先忽略你在地球上這件事。 我們可以知道你與衛星之間的距離是固定的。 換句話說,你是位在某個 繞著衛星運行的球體表面。 接著測量你與第二個衛星之間的距離, 會得到另一個重疊的球體。 持續做這個動作, 只需要經過四次測量, 並利用愛因斯坦的相對論進行修正, 便可以指出你的位置,就位於空間中的某一點。 這個過程總共需要: 價值數十億美元的衛星網路、 振盪的銫原子、 量子力學、 相對論、 智慧型手機、 還有你。 只要備齊了,一切就都沒問題。