Inertial Frames and the Laws of Physics Revision Notes | A Level AQA Physics

1. The Central Puzzle: Does Physics Change When You Move?

Picture two physicists: Aisha is sitting still in a train station, and Mohammed is on a train moving at a steady 200 km/h. Both perform the same experiment — they drop a ball and measure how it falls. Do they get different results? Do the laws of physics look different to each of them?

This question sits at the very heart of special relativity. The answer — and it is a profound one — is no. The laws of physics look identical to both observers, provided neither of them is accelerating. That single insight, formalised as the principle of relativity, is the foundation on which Einstein built his entire theory.

To understand why this matters, you first need a precise grip on what physicists mean by a frame of reference — and specifically, what makes a frame inertial.

2. Frames of Reference: Choosing Your Vantage Point

A frame of reference is the coordinate system an observer uses to assign positions and times to events. When Aisha watches the ball drop, she measures its position relative to the platform. When Mohammed watches the same ball drop inside the train, he measures its position relative to the carriage. Both are valid descriptions — they are just different frames of reference.

The key insight is that the numbers an observer measures — such as the velocity of a ball — depend on the frame. But the laws governing those numbers should not. That distinction is everything in relativity.

Now here is the critical question: are all frames of reference equally valid for doing physics? The answer is no — and that is where the concept of an inertial frame becomes essential.

3. Inertial Frames of Reference

Think of Mohammed's train again, but now consider two scenarios. In the first, the train moves at a perfectly steady 200 km/h on a straight track. In the second, the train brakes sharply. In the first scenario, Mohammed is in an inertial frame — he feels no push or pull, and a ball placed on a smooth table stays put. In the second scenario, the ball slides forward as the train decelerates. Mohammed is now in a non-inertial frame.

The operational test for an inertial frame is Newton's first law. Place an isolated object — one with no forces acting on it — in your frame. If it stays at rest or moves with constant velocity, your frame is inertial. If it accelerates without any apparent cause, your frame is non-inertial.

• A train moving at constant velocity on a straight track — inertial frame
• A train accelerating out of a station — non-inertial frame
• A car cornering at constant speed — non-inertial frame (centripetal acceleration)
• A laboratory on Earth's surface — approximately inertial for most experiments (Earth's rotation introduces tiny non-inertial effects, but these are negligible at the scale of most A-level problems)
• A spacecraft drifting at constant velocity far from any gravitational source — inertial frame

Notice that 'at rest' is itself a relative concept. Aisha standing on the platform is at rest relative to the platform, but moving at 200 km/h relative to Mohammed's train. Both frames are inertial — neither is accelerating. This is a crucial point: there is no single 'truly stationary' frame that is more correct than any other inertial frame.

4. The Principle of Relativity: Same Laws, Every Frame

With inertial frames defined, the central principle of special relativity can be stated precisely. This is the first of Einstein's two postulates, and it is the one rooted in classical physics going back to Galileo.

Return to Aisha and Mohammed. Mohammed drops a ball inside the train carriage. From his perspective, the ball falls straight down — it obeys $F = ma$ with the gravitational force acting vertically. Aisha, watching from the platform, sees the ball follow a parabolic path because it also has the horizontal velocity of the train. The trajectory looks different in each frame. But the law — Newton's second law — works perfectly in both frames. The form of the equation does not change.

This is what 'same form' means in practice. The symbols and the relationships between them — $F = ma$, conservation of momentum, the wave equation for light — are written identically in every inertial frame. The numerical values of quantities like velocity will differ between frames, but the structure of the law does not.

The principle has a powerful implication: there is no preferred inertial frame. No observer in an inertial frame can claim to be 'truly at rest' in any absolute sense. All inertial frames are physically equivalent — a statement that directly contradicts the idea of a fixed 'aether' that physicists once believed light needed to travel through.

5. Why Non-Inertial Frames Break the Principle

The principle of relativity applies specifically to inertial frames. To see why the restriction matters, consider what happens in a non-inertial frame — and why the laws of physics appear to change there.

Chloe is sitting in a car that suddenly accelerates forward. She feels pressed back into her seat. From her perspective inside the car, it looks as though a force is pushing her backwards — yet nothing is physically touching her from behind. This apparent force is called a fictitious force (sometimes called a pseudo-force). It only appears because Chloe's frame is accelerating; it has no physical agent causing it.

In Chloe's accelerating frame, Newton's first law appears to fail: objects accelerate without any real force acting on them. The form of Newton's laws changes — extra fictitious-force terms must be added to make the equations work. This is precisely what the principle of relativity says should not happen in an inertial frame. The principle holds only where no acceleration is present.

6. Galilean Relativity and the Road to Einstein

The idea that physical laws are the same in all inertial frames did not originate with Einstein — it goes back to Galileo in the seventeenth century. Galileo argued that a sailor below decks on a smoothly sailing ship could not perform any mechanical experiment to tell whether the ship was moving or at rest. This is Galilean relativity, and it works perfectly for mechanics.

The problem arose in the nineteenth century when Maxwell derived his equations for electromagnetism. Those equations predict that light travels at a fixed speed $c = 3.0 \times 10^8$ m/s. But fixed relative to what? Under Galilean relativity, velocities add: if Mohammed throws a ball at 10 m/s on a train moving at 200 km/h, Aisha sees the ball moving at the sum of those speeds. If the same rule applied to light, then the speed of light measured by different observers would differ — and Maxwell's equations would take a different form in different inertial frames.

That would violate the principle of relativity for electromagnetic laws. Einstein resolved this tension by insisting that the principle of relativity must hold for all physical laws — including electromagnetism — and that the speed of light must therefore be the same in all inertial frames. That second postulate, combined with the first, generates the full framework of special relativity. The lesson here is that the principle of relativity is not merely a convenient assumption; it is a deep constraint on what any correct physical theory must satisfy.

7. Exam Technique and Mark-Winning Precision

Questions on inertial frames and the principle of relativity tend to test whether you can apply these ideas to unfamiliar scenarios, not just recall definitions. The following guidance targets the specific ways marks are won and lost on AQA papers.

When asked to define an inertial frame, the mark-winning phrase is 'a frame that is not accelerating' or 'a frame moving at constant velocity (which includes being at rest)'. Saying 'a frame moving at constant speed' is insufficient — speed is scalar and does not capture direction; constant velocity is the correct term.

When asked to explain why the laws of physics have the same form in all inertial frames, structure your answer as: state the principle, give a concrete example of a law (such as Newton's second law or conservation of momentum), and then confirm that the form of that law is unchanged even though numerical values of quantities may differ between frames.

Extended-response questions on this topic often ask you to evaluate the significance of the principle of relativity. A strong answer will: (1) state the principle precisely, (2) explain that it applies to all physical laws including electromagnetism, (3) note that it rules out a preferred 'absolute rest' frame, and (4) connect it to Einstein's resolution of the conflict between Newtonian mechanics and Maxwell's equations. That four-point structure maps directly onto the marking criteria for higher-band responses.

Together, the definition of an inertial frame and the principle that physical laws take the same form in all such frames form the conceptual bedrock of special relativity — every result that follows, from time dilation to length contraction, rests on these two ideas.