Choosing a point of view
Teaching Guidance
for 14-16
Recording a process and agreeing on the recorded measurements
Wrong Track: Everyone agrees on durations and locations, surely. Where things are and when they happen everyone has to agree on.
Right Lines: If you want to be accurate you have to be more careful: when something happens and where it happens depend on point of view. But your basic idea is right – there are some things that everyone will agree on.
Snippets and suggestions
Thinking about the learning
Here is a telling snippet of conversation:
Six year old: How long until the train gets in?
Dad: Five minutes.
Six year old: But how long is five minutes?
Looks like being a long five minutes for the dad.
Thinking about the teaching
Indicating where things are and when they happened turns out not to be so trivial. It took some time before Greenwich was adopted as the agreed zero of longitude, and even longer before the clocks all over the UK agreed with each other (this had to wait for the railways, which carried timepieces from one station to another).
The Airy Transit Circle at Greenwich (1851) was agreed as the zero of longitude for the world in 1884, largely because of the accumulation of existing practice. Many countries had their own origins, but the tonnage of shipping using the Greenwich meridian provided a significant factor in the debate.
Now it's been supplemented by a GPS-based system, which doesn't quite agree with the older standard. You can find out by how much by visiting Greenwich and turning on your own GPS unit.
But there's more:
Distances between different positions feel as if they ought not to depend on the point of view, assuming the journey from one to the other follows the same route.
Differences in clock times from the start to the end of a journey (the duration) also feel as if they should be invariant – that is, not depend on the point of view.
It took the simple, but deep, analysis of an Einstein to show that our common-sense reasoning here does let us down. Both the journey distance and the journey duration depend on the point of view – that's an important insight from the theory of relativity (even in his theory some things don't change – there are some invariants). These effects are only noticeable at very high speeds.
