Your Phone Does Not Know What Time It Is
Part 5 finished with a gap in the system. Latitude counts from the equator, and nobody had to decide where the equator goes — the Earth's spin puts it where the ball is widest, and that is that. Longitude has no such line. Nothing about a spinning ball marks out one place and calls it zero.
So the last piece of your address is not a measurement at all. It is a decision, and it was made in a meeting.
Half of your address was voted on
For most of the age of sail, every country counted longitude from its own capital. French charts started from Paris. Spanish ones had started from an island in the Canaries. British ones counted from the Royal Observatory at Greenwich, in London. There were others.
That was survivable while ships mostly carried their own nation's charts, and a growing nuisance once railways, telegraphs and international trade meant everybody had to agree what a printed number meant.
In October 1884 twenty-five countries sent delegates to Washington for the International Meridian Conference. They picked Greenwich. Not because there is anything special about that hill in south London, and everybody in the room knew it. They picked it because roughly seven ships in every ten already carried charts drawn from it, and changing the other three was cheaper than changing the seven.
The vote was twenty-two in favour, one against, two abstaining. France was one of the abstainers and went on printing longitude from Paris for another twenty-seven years.
A phone finds itself in about a second
Now the modern answer, which turns out to be this book's first four parts wearing new clothes.
High above you — about twenty thousand kilometres up, which is far higher than any space station — a few dozen satellites are going round the Earth twice a day. Each one carries an atomic clock, the most accurate kind of clock there is, and each one is doing nothing but broadcasting the same short message over and over:
I am at this exact point. It is exactly this moment.
Your phone listens. And what it does with the message is Harrison's trick, one more time.
Four things have to be true before a phone can put a dot on a map. Choose each one.
- The satellite knows where it is, and when — its orbit is tracked from the ground and predicted ahead, and the atomic clock on board keeps time to about a billionth of a second. Everything downstream depends on that clock being right, so each satellite carries several and they check each other.
- The journey takes time — a radio signal travels about thirty centimetres every billionth of a second. So if your phone knows when the message was sent and when it arrived, the gap between them times the speed of light is the distance to that satellite. One distance puts you somewhere on a huge sphere. Three of them cross at a point.
- Your phone's own clock is hopeless — it is a cheap quartz crystal, out by thousandths of a second. At thirty centimetres per billionth, being a thousandth of a second wrong makes every distance three hundred kilometres wrong. A phone cannot simply read the travel time, because it does not know when the message arrived.
- So it listens to a fourth — and this is the clever part. Three satellites would be enough if the phone knew the time. It does not, so the time is a fourth unknown alongside north, east and up. A fourth satellite gives a fourth measurement, and now there are four facts and four unknowns. The phone works out what time it is in the same breath as it works out where it is.
Read that fourth point again and you are back on the deck of an eighteenth-century ship. The device does not know the time at the reference place. The whole problem is getting the time at the reference place. Harrison solved it by carrying a clock so good it could not go wrong. Maskelyne solved it by reading a clock nobody could take away. Your phone solves it by admitting it has no idea and working the time out from the answer, several times a second, for as long as the map is open.
Why does a phone need signals from four satellites rather than three?
- Because it does not know what time it is, so time is a fourth unknown to be solved for
- Because one satellite is always broken
- Because three satellites cannot cover the whole sky at once
- Because the fourth one carries the map
Where this leaves you
Go back to the first page of this book, and to the free half of the answer.
That half has not changed at all. The pole star is still where it was, still sitting at an angle above your horizon that is your latitude and nothing else, still readable by anybody standing outside on a clear night with no equipment and no permission. It worked for Phoenician sailors and it works for you. Nothing anybody has built since has made it any less true.
The other half took four hundred years, a wrecked fleet, an Act of Parliament, a carpenter's whole life, a book of tables published every year since 1767, five miles of glass tubes on a heath, and eventually a ring of atomic clocks in orbit. All of it to answer the same small question:
What time is it, over there?
Next time a map opens on a phone and drops a blue dot on you, that is what just happened. It is not magic and it is not new. It is the oldest hard question in navigation, asked again, and answered before you have finished looking at the screen.