A.5.2 (HL)—Galilean relativity

State the principle

Galilean relativity says that Newton’s laws have the same form in every inertial reference frame. An observer moving at constant velocity therefore uses the same Newtonian mechanics, provided speeds are far below the speed of light and the frame is non-accelerating.

Relate the observations

The same event occurs in both frames, but the observers can assign different positions. In the classical model, time is absolute: both observers use the same $t$ , while the moving frame changes the position coordinate according to $x′=x-vt$ .

Check the boundary

Use Galilean relativity for inertial frames in the non-relativistic limit. It is not the correct model for measurements involving speeds comparable with $c$ , where the assumptions of absolute time and unchanged light speed fail.

Common trap

“Same laws” does not mean that all observers measure the same position or velocity. It means the equations of Newtonian mechanics keep the same form after changing between inertial frames.

How it is assessed

Questions use a moving frame or a length/time comparison and ask you to apply or explain the classical transformation. Marks depend on recognizing the inertial-frame assumption and the Newtonian absolute-time model.

Command terms

State / Explain / Outline

What earns marks

Identify both frames as inertial, state that Newton’s laws retain the same form, and distinguish the classical assumptions of absolute time and Galilean coordinate transformation from the later relativistic model. Use the given frame velocity and sign convention consistently.

Watch for

Applying Galilean relativity to a relativistic situation without checking that the non-relativistic assumptions are appropriate.

Representative question

[Maximum number: 1]

Write down the length of the space station according to Galilean relativity.

Choose the model

State the inertial reference frame first. Galilean relativity uses x′=x−vt, t′=t and u′=u−v. Special relativity uses the two postulates, Lorentz transformations and u′=(u−v)/(1−uv/c²).

Track what changes and what is invariant

In special relativity, use γ=1/√(1−v²/c²), the invariant interval (Δs)²=(cΔt)²−(Δx)², proper time, proper length, Δt=γΔt0 and L=L0/γ. Separate measurements of space and time can change between frames, while the interval and vacuum light speed do not.

Read the evidence

On a space–time diagram, world-line angle gives tanθ=v/c, frame axes determine simultaneity, and no world line exceeds the light line. Muon survival provides experimental evidence: time dilation explains the longer Earth-frame lifetime, while length contraction explains the shorter atmospheric distance in the muon frame.

Final retrieval check

For every calculation, identify the frame, select the proper quantity if one is given, keep signed velocities and units consistent, and check the result against c, γ≥1, or the invariant interval. The syllabus requires applying the transformations and equations, not deriving them.

A.5.2 (HL)—Galilean relativity

Apply Galilean Relativity

A.5.2 (HL) Exam Analysis

Assessment in practice

Retrieve the A.5 Galilean and Special Relativity Model

Question 1