The above discussion brings us to a very important principle of physics, which, unfortunately, is not discussed at all in high school. This principle is too important and beautiful for students to remain ignorant of it. The basic idea is this. The world looks the same if I look at it from here or from there, or if I look at it now or later.

 

Here is an example. The force of gravity does not change over time. Suppose it did change, and got stronger. We do work lifting an object, and recover the energy when we drop it. If gravity is stronger later, we will get more energy back than we gave in. We see a connection between conservation of energy and time symmetry.

 

In a similar fashion, there is symmetry in positions. Consider a physics experiment moving objects, measuring the speeds and such. If things were different to someone else at a different point, we could never do any physics experiments. This is called space symmetry.

 

When we discuss forces and motion, we draw a graph of, say, position of an object versus time. The origin of the graph is arbitrary. Usually we rush over this point. My suggestion is that we stress that this arbitrary nature of the origin is called symmetry, and is a powerful concept in modern physics.