On measuring velocity

It's not easy to measure velocity

Just how fast am I going? Seems an easy question, but appearances are very definitely deceptive.

Here's a snippet of conversation between a young child (about six years old) and his dad, both passengers on a train.

Boy: When will it go fast?

Dad: It is going fast.

Boy: It's not going fast.

Dad: You might not feel it's going fast. Don't you remember being in an aeroplane? That didn't feel fast either.

The boy mumbles something inaudible and looks unimpressed with this line of argument.

But Dad's position is a difficult one. There are no reliable guides to sensations of velocity. We simply do not have a built-in velocity meter, comparable to our built-in acceleration meter.

And this lack of a built-in meter is not really accidental as there are good reasons to believe such a thing could not be engineered. Velocity all depends on a point of view, as we'll see shortly. For now it's enough to notice that the boy and his dad were not moving apart, so from one point of view (the child's?), their velocity was zero. However, they were definitely getting closer and closer to London, so from another point of view their velocity could not be zero.

So another line of attack with the child's initial question, likely to have left him even less impressed, would be:

Dad: Well, it all depends on your point of view.

And so it does – always. Simple questions about how fast one is going may not have simple, unique answers. One has to ask a less simple question to get a more simple answer. An essential additional component of the enquiry is to make explicit the point of view. To miss that out, like this:

Innocent: How fast am I going?

makes lots of hidden assumptions. Only a more comprehensive question can better define the answer space.

Learning: How fast am I moving away from that fencepost?

or

Egocentric: How fast is that fencepost moving away from me?

And later you'll see that a more sophisticated and complete approach still might begin here:

Sophisticate: By how much is the distance between me and the fencepost increasing each second?

Measurements of How fast? don't always depend on first measuring distance and time

But we get ahead of ourselves. Here, just remember that you need to agree on a point of view before you can settle a How fast? question. Often the point of view is implicit: this may or may not lead to confusion – it depends on whether others share your implicit assumptions.

There is one curiosity about measurements of velocity that's worth mentioning here – we can do it remotely. In some cases, very remotely. This relies on the Doppler effect. This is worth dwelling on because you don't have first to measure distance and then time. Instead you simply count.

Bats and policemen are both interested in velocities of approach and recession, and both use similar physics, although very different technologies.

Speed enforcement officer: What's the velocity of that car?

Bat: What's the velocity of that insect?

Or, even:

Physics bat: What's the velocity of that tree?

Bats do this by engaging in active sensing – firing out a burst of vibrations and then measuring the shift in frequency of the reflections.

Doctors use a similar active sensing technique for measuring blood-flow, but planetary scientists use a variation. They're obliged to, because the trip time is huge: the interval between the emitted and reflected beams could be years.

Full details are in the SPT: Radiations and radiating topic.