What is Trajectory?

Example 40.2 (Whose trajectory?)

Be careful to name which point you follow. The carousel horse’s nose draws a circle; the whole carousel’s center draws nothing at all — it stays put. A rolling wheel’s hub glides in a straight line while a point on its rim traces graceful hops. One machine, many trajectories: physics follows one point at a time.

Example 5.3 (The walker on the train)

A train travels at $300\,\mathrm{km}/\mathrm{h}$ relative to the ground while a passenger walks toward the front at $4\,\mathrm{km}/\mathrm{h}$ relative to the train.

• In the train frame: the passenger moves at $4\,\mathrm{km}/\mathrm{h}$ down the aisle; the seats are at rest; the trees outside rush backward at $300\,\mathrm{km}/\mathrm{h}$.
• In the ground frame: the seats move at $300\,\mathrm{km}/\mathrm{h}$, the passenger at $304\,\mathrm{km}/\mathrm{h}$, and the trees are at rest.

The same scene, two frames, two entirely different descriptions — and no experiment performed inside the train can declare one of them “the real one”.