| Vocademy |
In the third chapter, Einstein discusses space and time in classical mechanics. He starts by stating that it is not clear what is to be understood by "position" and "space."
He starts by noting that if he drops a stone from the window of a moving train, he will see the stone drop straight down to hit the moving ground (disregarding the effect of air resistance). An observer standing by the track will see the stone follow a parabolic curve. The question is, what is the actual path of the stone? He then asks what is meant by motion in space.
We have already seen that we cannot define points in space without referencing a known point on a rigid body or system of coordinates. We are forced to say that the stone travels in a straight line relative to a system of coordinates rigidly attached to the train carriage but travels in a parabola relative to a system of coordinates rigidly attached to the ground. We then see there is no "true" trajectory but only a trajectory relative to a particular body of reference.
Furthermore, to describe the trajectory, we must describe each point of the trajectory as it relates to time. The time data must be described so that the values can be expressed as some magnitude resulting from some measurement. To make such measurements, Einstein imagines two identical clocks, one possessed by the person on the train and the other possessed by the person by the track. Each observer determines the position of the stone relative to their own reference body at each tick of the clock (compensating for the time delay due to the propagation of light).
| Vocademy |