You drop a ball inside a car traveling at a steady \(50 \mathrm{~km} / \mathrm{h}\) in a straight line on a smooth road. Does it fall in the same way as it does inside a stationary car? How does this question relate to Einstein's special theory of relativity?

Imagine you're inside a train, sitting comfortably as you watch the scenery go by. You decide to toss a ball straight up in the air. To you, it seems to go up and come back down to your hand. But to an observer outside, the ball is traveling in a curved path, going forward with the train while it goes up and down. What causes these different observations?
The answer lies in the concept of 'reference frames'. A reference frame is a perspective from which we measure and observe motion. It's like choosing a camera angle in a movie; the action can look quite different depending on where the camera is placed. In physics, reference frames are essential for describing how objects move relative to one another.
In the exercise, both the moving car and the stationary car act as reference frames. Inside the moving car, the dropped ball falls straight down just as it does in a stationary car. This is because, inside the car, we're in the ball's reference frame. To the ball, it doesn't matter if the car is moving or not; it experiences the same laws of physics and falls straight down due to gravity.

It's all a matter of perspective! Relativity of motion is the concept that motion is not absolute but rather, it's relative to the observer's frame of reference. This idea is crucial to understanding why different observers can see the same event differently.
For example, if you're standing on the side of the road watching a car go by, you'll say the car is in motion. But what if you were in the car? From your new vantage point, you're at rest, and it's the world that's moving past you. Both perspectives are valid; they are simply relative to different frames of reference.

Everyday Examples

Take the exercise we're considering. For an observer inside the car, the ball drops straight down because both the observer and the ball are part of the same moving frame. To an observer outside the car, the ball seems to take a different path, traveling forward as well as down. This shows relativity of motion: the ball's path looks different depending on the observer's frame of reference.

No matter where you are, whether lounging on a sofa or hurtling through space on a spaceship, the laws of physics that apply to you remain consistent. This wonderful uniformity means that the same principles that govern the fall of an apple from a tree on Earth would also apply to an astronaut letting go of a toolkit in the zero-gravity environment of space, albeit with some variations due to different forces acting in each scenario.
In Einstein's Special Theory of Relativity, this consistency is a fundamental postulate. It states that the laws of physics are invariant (i.e., they have the same form) in all inertial frames of reference. This idea is profound as it implies the laws of physics don't change regardless of how fast you're going or in what direction, as long as you're not accelerating.

Understanding Through the Exercise

In the textbook exercise, the ball falls in a way that is consistent with the laws of gravity. Both a stationary and a moving car witness the ball falling straight down because the laws of physics being applied are unchanging across both scenarios.

Inertia is the tendency of objects to keep on doing what they're currently doing — either staying still or moving at a consistent speed in a straight line. An inertial frame of reference, then, is a perspective from which an observer sees objects obeying the law of inertia — no forces like friction or air resistance are causing acceleration.
These frames are key in understanding Einstein's Special Theory of Relativity, which only applies in inertial frames. When we consider the exercise with the ball in the car, we're working within an inertial frame of reference because the car is moving at a constant speed on a smooth road.

Why It Matters

It's in these inertial frames that the laws of physics are consistent, a point that is beautifully illustrated by the behavior of the ball as seen by the observer. Acceleration changes the game by introducing additional forces, which is why inertial frames — where acceleration is absent — are so important in physics.