Physics • Year 12 • Module 7 • Lesson 11
Special Relativity — Inertial Frames and Postulates
Lock in the core vocabulary, Einstein’s two postulates, the significance of the Michelson-Morley experiment, and the Lorentz factor before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: inertial frame, non-inertial frame, special relativity, Galilean relativity, luminiferous aether, Michelson-Morley experiment, Lorentz factor, time dilation, length contraction, postulate. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A reference frame moving at constant velocity in which Newton’s first law holds and no pseudo-forces appear. | |
| 1.2 | A reference frame that is accelerating or rotating, in which fictitious forces (such as the centrifugal force) are observed. | |
| 1.3 | Einstein’s 1905 theory describing the physics of motion in inertial reference frames, founded on the constancy of the speed of light. | |
| 1.4 | The classical principle that the laws of mechanics are the same in all inertial frames and that velocities add simply: $u' = u + v$. | |
| 1.5 | The hypothetical medium through which light was thought to propagate in 19th-century physics. | |
| 1.6 | The 1887 interferometer experiment by Michelson and Morley that found no evidence of Earth’s motion through the hypothetical medium carrying light — a null result that challenged classical physics. | |
| 1.7 | The factor $\gamma = 1/\sqrt{1-v^2/c^2}$; always ≥ 1; quantifies how strongly relativistic effects apply at speed $v$. | |
| 1.8 | The phenomenon whereby a moving clock ticks more slowly than an identical clock at rest, by a factor of $\gamma$. | |
| 1.9 | The phenomenon whereby the measured length of a moving object along its direction of motion is shorter than its proper length, by a factor of $\gamma$. | |
| 1.10 | A fundamental assumption accepted without proof that forms the starting point for a theory; Einstein’s theory of special relativity is built on two of these. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 An inertial frame of reference is any frame that is at absolute rest. T / F
2.2 The Michelson-Morley experiment confirmed the existence of the luminiferous aether by detecting a measurable aether wind. T / F
2.3 Einstein’s second postulate states that the speed of light in vacuum is the same for all observers, regardless of the motion of the source or observer. T / F
2.4 According to Galilean velocity addition, if you throw a ball at 10 m/s forward on a train moving at 20 m/s, a platform observer measures the ball’s speed as 30 m/s. T / F
2.5 The Lorentz factor $\gamma$ equals 1 when $v = 0$ and approaches zero as $v \to c$. T / F
2.6 Time dilation and length contraction are direct consequences of the two postulates of special relativity. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
aether · constant · dilated · identical · inertial · Lorentz · null · postulates
Einstein’s theory of special relativity is built on two ___________. The first states that the laws of physics are ___________ in all ___________ reference frames. The second states that the speed of light in vacuum is ___________ for all observers. This second postulate was motivated partly by the ___________ result of the Michelson-Morley experiment, which found no evidence for the luminiferous ___________. These postulates lead directly to the prediction that moving clocks produce a ___________ time, governed by the ___________ factor $\gamma = 1/\sqrt{1-v^2/c^2}$.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State Einstein’s two postulates of special relativity in your own words.
4.2 Explain what the Michelson-Morley experiment was designed to detect and what its null result implied for the existence of the aether.
4.3 A spaceship travels at $0.6c$. Calculate its Lorentz factor $\gamma$. Show your working.
4.4 A car on a train moving at 20 m/s is driven at 10 m/s relative to the train. (a) What does Galilean relativity predict for the car’s speed relative to a trackside observer? (b) How does Einstein’s second postulate change this for light instead of a car?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “leads to”, “challenged by”, “replaced by”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: Galilean relativity · luminiferous aether · Michelson-Morley experiment · Einstein’s postulates · Lorentz factor · time dilation.
6. Match the formula to its context
Four equations are listed in Column A. Match each to its correct description in Column B by writing the letter A–D. 4 marks (1 each)
| # | Column A — Equation | Column B — Description | Match |
|---|---|---|---|
| 6.1 | $\gamma = 1/\sqrt{1-v^2/c^2}$ | A. Moving clock ticks more slowly; $\Delta t_0$ is the proper time | |
| 6.2 | $\Delta t = \gamma \Delta t_0$ | B. Moving object is shorter along direction of motion; $L_0$ is proper length | |
| 6.3 | $L = L_0/\gamma$ | C. Lorentz factor; equals 1 at $v=0$ and diverges as $v \to c$ | |
| 6.4 | $E = \gamma mc^2$ | D. Total relativistic energy of a moving particle |
Q1 — Term–definition match
1.1 inertial frame • 1.2 non-inertial frame • 1.3 special relativity • 1.4 Galilean relativity • 1.5 luminiferous aether • 1.6 Michelson-Morley experiment • 1.7 Lorentz factor • 1.8 time dilation • 1.9 length contraction • 1.10 postulate.
Q2 — True / false with correction
2.1 False. An inertial frame moves at constant velocity (including zero). There is no such thing as absolute rest in special relativity — any frame moving at constant velocity is inertial.
2.2 False. The Michelson-Morley experiment found no detectable aether wind — a null result. This undermined the aether hypothesis, not confirmed it.
2.3 True.
2.4 True. Classical Galilean velocity addition: $u' = u + v = 10 + 20 = 30$ m/s.
2.5 False. The Lorentz factor $\gamma$ equals 1 at $v = 0$ and approaches infinity (diverges) as $v \to c$. It never approaches zero.
2.6 True. Time dilation ($\Delta t = \gamma \Delta t_0$) and length contraction ($L = L_0/\gamma$) both follow mathematically from Einstein’s two postulates.
Q3 — Cloze paragraph
In order: postulates / identical / inertial / constant / null / aether / dilated / Lorentz.
Q4.1 — Einstein’s two postulates
First postulate (principle of relativity): The laws of physics are the same in all inertial reference frames. No experiment performed entirely within an inertial frame can detect absolute motion. Second postulate (constancy of the speed of light): The speed of light in vacuum, $c \approx 3.00 \times 10^8$ m/s, is the same for all observers, regardless of the motion of the light source or the observer.
Q4.2 — Michelson-Morley experiment
The experiment was designed to detect Earth’s motion through the luminiferous aether by measuring a difference in the travel time of light along two perpendicular arms of an interferometer. The expected aether wind would cause a time difference and produce a fringe shift. The null result (no fringe shift) showed that the speed of light was the same in all directions, implying the aether either did not exist or had no detectable effect.
Q4.3 — Lorentz factor at $v = 0.6c$
$\gamma = 1/\sqrt{1 - (0.6)^2} = 1/\sqrt{1 - 0.36} = 1/\sqrt{0.64} = 1/0.8 = \mathbf{1.25}$.
Q4.4 — Galilean addition vs Einstein
(a) Galilean: speed = $10 + 20 = 30$ m/s relative to the trackside observer. (b) For light, Einstein’s second postulate states that the speed of light is $c$ for all observers. A flashlight on the train does not shine at $c + 20$ m/s; the platform observer still measures $c$. Galilean addition does not apply to light.
Q5 — Sample concept map
Accept any valid labelled arrows, for example:
- luminiferous aether — assumed to be detected by → Michelson-Morley experiment
- Michelson-Morley experiment — null result undermined → Galilean relativity
- Michelson-Morley experiment — motivated → Einstein’s postulates
- Einstein’s postulates — replaced → Galilean relativity
- Einstein’s postulates — determine → Lorentz factor
- Lorentz factor — governs → time dilation
Award 1 mark per valid labelled arrow (maximum 6 marked).
Q6 — Formula matching
6.1 → C • 6.2 → A • 6.3 → B • 6.4 → D.