The Relativity Of The Idea Of Distance

What is the distance between the points A and B in the train in Section 9?

We need a body of reference to measure it.

• If our viewpoint is the train, then a man in the train measures the distance by using his measuring-rod to mark the distance on the floor as many times as is needed to take him from A to B.
• If our viewpoint is the embankment, then we measure A' and B' at time t using the definition of time at Section 8. The distance between A and B is gotten by the repeated application of the measuring-rod along the embankment.

These two measurements will not be the same. This means that the train as measured from the embankment may be different from that obtained by measuring in the train itself.

This leads to a second objection to Section 6= the man walking in the train covers the distance w in a unit of time measured from the train. This distance as measured from the embankment is not necessarily equal to w.