Theme A · Space, Time and Motion · HL only · 8 hours
A.5 Galilean and Special Relativity
How does special relativity change our understanding of motion compared to Galilean relativity?
Higher Level only — no Standard Level content in this topic
For 250 years after Newton, the universe was assumed to work the same way at any speed: a clock on a train ticked at the same rate as a clock on the platform. Galilean relativity said that Newton's laws were the same in all inertial frames, and that was all you needed. But in 1905, Einstein showed that Galilean relativity is incompatible with the constant speed of light — and that something had to give. The answer was space and time themselves.
Special relativity makes two postulates and follows the mathematics wherever it leads. The results — time dilation, length contraction, the relativity of simultaneity — are counterintuitive but experimentally confirmed, most directly by muon decay experiments. Space-time diagrams give a geometric picture of these effects, and the invariant space-time interval is the quantity that all observers agree on regardless of their state of motion.
Einstein's two postulates (1905)
1. The laws of physics are the same in all inertial reference frames.
2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the source or the observer.
A muon is created in the upper atmosphere at a height of 10 km and travels towards Earth at 0.98c. Its proper lifetime is 2.2 μs. Show that it reaches the ground — both from the Earth frame (time dilation) and the muon's frame (length contraction).
Key equations
Lorentz factor: γ = 1/√(1 − v²/c²)
Time dilation: Δt = γΔt₀ (Δt₀ = proper time interval)
Galilean relativity: Newton's laws the same in all inertial frames; Galilean transformations x′ = x − vt, t′ = t
Galilean velocity addition u′ = u − v and its limitation at high speeds
Einstein's two postulates and why they conflict with Galilean relativity
The Lorentz transformation equations (derivation not required)
Relativistic velocity addition (derivation not required)
The space–time interval as an invariant quantity
Proper time and proper length; time dilation Δt = γΔt₀; length contraction L = L₀/γ
The relativity of simultaneity: events simultaneous in one frame are not simultaneous in another
Space–time diagrams: world lines; angle between world line and time axis related to speed by tanθ = v/c
Experimental evidence: muon decay experiments confirm both time dilation and length contraction
Linking questions
How are equations of linear motion adapted in relativistic contexts? → A.1 Kinematics
Why is the Doppler equation for light so different from that for sound? → C.5 Doppler Effect
Special relativity places a limit on speed. What other limits exist in physics? (NOS)
Video Support
Michel van Biezen
Physics 62.1 Understanding Space, Time & Relativity (3 of 55) Is Relativity Real?Physics 62 Special Relativity (18 of 43) A Relativistic Time Experiment
WNY Tutor — worked problems
An astronaut at rest on Earth has a heart rate - time dilationAn electron has a total energy equal to five times its rest energy
Physics with Professor Matt Anderson — full course modules
Module 29 | Relativity | Physics with Professor Matt Anderson