Imaging with clocks

Making pictures by timing

It's possible to build up a picture of the world just from a series of times. That's what bats do, by a process of active sensing: a bat sends out a pulse, then times how long until the echo arrives back. The longer the delay, the further away the object that produced that delay. (That's not all bats do – they can also map the velocities of things from the altered frequency of the pulse, but that's another story – they use the Doppler effect. More on that later.)

Ultrasonic rulers perform much the same simple trick. A pulse of sound is sent out, and the time between this emission and the detection of the echo provides information about the distance.  You could use electromagnetic waves, but then the times would be much much shorter, and so you'd need a very accurate clock, unless the distance was very long. So radar is used to find out how far away the Moon is, and the distance to Venus. Much beyond that and the reflections are too dim: the amplitude is too small to be detected by any instruments we have so far managed to build.

If you do have a very accurate clock then you can use a series of electromagnetic pulses to build up a map of any planet, so long as you can put a satellite in orbit around it. Just time the interval between the emitted pulse and the reflection arriving back at the satellite to get information about the distance between the satellite and whatever is doing the reflecting (the planet's surface?). As you can use any part of the electromagnetic spectrum for the pulses, you can choose to image even where there is continuous cloud cover: that is how a topographic map of Venus was made.

Medical ultrasonic imaging is another example of active imaging, where the time between a pulse and its echo is interpreted as a distance, thus building up a map of what lies in front of the probe, which contains both source and detector.

In all these cases, you use distance travelled = speed × elapsed time.

Geological sensing is less subtle, as the emitted pulse is often a controlled explosion. However, the analysis required to interpret these collected reflections is considerable as there may be many different materials through which the vibrations have travelled, all with different speeds of propagation.

If only there were a universal speed that converted distance to time at a constant rate. There is: the speed of electromagnetic waves, which is a constant – always and everywhere. So any distance can now be mapped as a time. That's the beginning of Einstein's theory of relativity. More later.  Passive imaging is not so good at revealing distance information: you simply don't know when the pulses were emitted. Unless you can do some kind of echolocation, more indirect methods have to be used. So for estimating the distances to the galaxies, for example, the reflected pulses would simply be too low in amplitude to be detected, and, as it turns out, you'd have to wait several years for such a pulse to return (a deliberate understatement – it may well be several million years). The distances turn out to be huge.

How do we know? Justified guesswork: we see how bright things appear and then make assumptions about the brightness of the source. Then the inverse square law can be used to figure out just how far away the object is.