Foundation lesson
A sign records direction
Choose right as positive and left as negative. Opposite displacements can cancel without either particle staying still.
Written for this edition, not translated from Einstein.
How can movement add up to zero?
On the ruler below, the starting point is zero. A final mark three units to the right has displacement +3; one three units to the left has displacement −3. Adding the signed displacements gives zero. Adding the distances from the start gives six.
Displacement compares where something ends with where it started, whatever it did in between. A walker who goes three units right and comes back has displacement zero after walking six, which is the lower pair of arrows in the drawing.
Worked example: Two walkers, opposite directions, average zero
Two walkers both finish one unit from their start, one at −1 and the other at +1. The signed average is zero. The average distance is one.
The ruler, with both journeys on it
Zero is where each journey starts. Every arrow has a length, and the arrowhead says which way it went.
What it shows, in words
On the upper band two arrows leave zero in opposite directions and each is three units long. Their signed displacements, +3 and −3, add to zero; the distances they cover, three and three, add to six. On the lower band a single walker goes out three units and comes back along the same three units. That walker ends where the journey began, so the displacement is zero, and six units of ruler passed underneath.
In neither picture did anything stay still. A total of zero is a statement about where things ended, and the arrows are what it leaves out.
Where this lesson stops
The sign names a direction relative to a chosen axis; it does not mean a negative distance.
If you came here from a passage, Back returns you to the exact place you left.