The speed limit
How long does light take to get anywhere?
Predict first. How long will light take to reach the Moon?
Exhibition 3 · Light and Time
Light is the fastest thing there is. Radio is light too, just a colour our eyes can't see, so every message to a spacecraft travels at the same speed. This exhibition has one dial. For now it measures distance: how far light has to go.
Pick somewhere, send light, and wait. These are today's real distances, so the waits are real too. A long wait keeps counting on the progress line while you read on, and a message to Mars is kept on this device until it would arrive.
How long does light take to get anywhere?
Predict first. How long will light take to reach the Moon?
When did the starlight you see tonight set off?
Keep turning the dial outward, past Voyager, to the stars. Out here we measure in light-years. A light-year is a distance, not a time: how far light goes in one year.
Proxima Centauri
4.25 light-years
Its light left in about 2022
The night sky is a picture made of light that set off at different times. Sirius shows you a few years ago; the faint smudge of the Andromeda Galaxy shows you light that left before the first people lived. For some stars even the best telescopes disagree on the distance, so they get a range, not one year.
One light-year is about 9.46 trillion km. Distance from parallax: d (light-years) = 3,261.56 / parallax (milliarcseconds). Year the light left = this year − distance in light-years.
Polaris, Betelgeuse and Deneb have disputed distances: studies of Deneb disagree between about 1,400 and 2,600 light-years.
The dial changes: distance becomes speed
So far the dial has measured how far light has to travel. Now it measures how fast you go, and that changes something different: not when you see a clock, but how fast it actually ticks.
A light delay only makes news late; every clock still keeps its own time. What comes next is not a delay. A fast-moving clock really runs slow.
Does a clock on a fast ship keep the same time as one on Earth?
Here are two identical clocks. Each is a pulse of light bouncing between two mirrors, one tick per bounce. One stays on Earth; the other flies on a ship at the speed you set on the dial. Fly for one hour by the ship's clock, then compare.
Does a clock on a fast ship keep the same time as one on Earth?
Predict first. At half the speed of light, how long does one ship hour last on Earth?
If one twin travels to a star and back, who is older when they meet again?
Now a real trip. One twin stays on Earth. The other flies to a star at the speed on the dial, turns round and comes home. The diagram is a map of space and time: across is distance, up is time on Earth, and each mark is a year of a twin's life.
If one twin travels to a star and back, who is older when they meet again?
Predict first. Who is older when they meet again?
The dial changes again: speed becomes depth
Speed isn't the only thing that changes a clock. Gravity does too: clocks lower down run slower than clocks higher up. Now the dial sets how deep a clock sits in gravity.
Does gravity change how fast a clock ticks?
Move a clock up a mountain, into orbit or close to a black hole, and compare it with one on the ground for a day. In orbit two effects pull against each other: being higher speeds a clock up, and moving fast slows it down. Find the orbit where they cancel.
Does gravity change how fast a clock ticks?
Predict first. A clock on the space station, about 400 km up: faster or slower than one on the ground?
If all of history were squeezed into one year, where would we be?
One last scale, and this one stands outside the dial: no distance, speed or depth changes what has already happened. Squeeze the whole 13.8-billion-year history of the universe into one calendar year. The Big Bang is midnight on 1 January, and now is the stroke of midnight at the end of 31 December.
Each day on this calendar is about 38 million years, and each second about 437 years. The Sun and Earth don't arrive until September, animals spread in mid-December, and the dinosaurs die out on the morning of 30 December. The Moon landing happened a fraction of a second before midnight.
The universe is 13.787 billion years old. Date on the calendar = 1 January + (1 − age ÷ 13.787 billion) × 365 days.
Light takes about a second to reach the Moon, minutes to reach Mars and a whole day to reach Voyager. Our fastest spacecraft are thousands of times slower than light, so those same distances become days, months and decades of travel.
Then how do we go at all?