What does Galilean and Special Relativity cover in IB Physics?

This topic covers how observers in different inertial reference frames describe events in terms of space and time, contrasting Galilean and special relativity. Galilean relativity states Newton's laws are the same in all inertial frames, with x' = x - vt and t' = t. Special relativity is based on two postulates, leading to Lorentz transformations for coordinates and velocities.

Is Galilean and Special Relativity SL or HL?

Galilean and Special Relativity is HL only. SL students are not examined on it.

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Topic A.5 · HL only

Galilean and Special Relativity: notes and practice questions

Q: How do I revise Galilean and Special Relativity for IB Physics?

Start from the core idea: this topic covers how observers in different inertial reference frames describe events in terms of space and time, contrasting Galilean and special relativity. In the exam: hL only. May 2025 HL Paper 2 TZ1 question 7 was a space-time diagram question worth 6 marks: calculate the space-time interval between two events (2), outline what an invariant quantity is (1), sketch the primed axes on the given diagram (2), determine the relative speed (1). Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

10 min read Jump to 16 practice questions

Summary

This topic covers how observers in different inertial reference frames describe events in terms of space and time, contrasting Galilean and special relativity.
Galilean relativity states Newton's laws are the same in all inertial frames, with $x' = x - vt$ and $t' = t$ .
Special relativity is based on two postulates, leading to Lorentz transformations for coordinates and velocities.
Key relativistic effects include time dilation $\Delta t = \gamma \Delta t_0$ and length contraction $L = L_0 / \gamma$ , where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$ .
The space-time interval $(\Delta s)^2 = (c\Delta t)^2 - (\Delta x)^2$ is an invariant quantity.
Space-time diagrams are used to visualize relativistic motion.

How it is examined

HL only. May 2025 HL Paper 2 TZ1 question 7 was a space-time diagram question worth 6 marks: calculate the space-time interval between two events (2), outline what an invariant quantity is (1), sketch the primed axes on the given diagram (2), determine the relative speed (1). That is the shape to imitate. A derivation of the Lorentz equations is not a legitimate question.

Given in the booklet

Galilean and Lorentz transformations, $\gamma$ , relativistic velocity addition, the space-time interval, $\Delta t = \gamma\Delta t_0$ , $L = L_0/\gamma$ , $\tan\theta = v/c$ . The two postulates must be stated in words from memory.

Key ideas

There is no standard level content in A.5.

Not assessed

The derivation of the Lorentz transformation equations and the relativistic velocity addition equations are not required.
The derivation of the time dilation and length contraction equations is not required.

Guiding questions

How do observers in different reference frames describe events in terms of space and time?
How does special relativity change our understanding of motion compared to Galilean relativity?
How are space-time diagrams used to represent relativistic motion?

Linking questions

How are equations of linear motion adapted in relativistic contexts?
Why is the equation for the Doppler effect for light so different from that for sound?
Special relativity places a limit on the speed of light. What other limits exist in physics? (NOS)

Practice questions

16 questions · 1 easy · 13 medium · 2 hard

Showing 16 of 16

Question 1

EasyPaper 2 · calculator2 marks

A spacecraft is designed for interstellar travel and reaches a constant velocity of 0.950 $c$ , where $c$ is the speed of light, relative to a stationary observer on Earth.

(a) Calculate the Lorentz factor, $γ$ , for the spacecraft.

Question 2

MediumPaper 2 · calculator4 marks

(a)

A very long train travels at a relativistic speed $v$ with respect to a station platform. An observer on the platform measures two separate events, a lightning strike at the front of the train (event F) and a lightning strike at the back of the train (event B), to be simultaneous.

(a) An observer is located at the midpoint of the train. Explain, from the perspective of this observer on the train, why the two lightning strikes are not simultaneous.

[3]

(b)

(b) State the condition under which two events that are simultaneous in the platform frame would also be simultaneous in the train frame.

[1]

Question 3

HardPaper 2 · calculator11 marks

(a)

A muon is produced in a particle accelerator at detector D1 and travels towards a second detector, D2. In the laboratory's frame of reference, the detectors are stationary and the distance between them is 900 m.

(a) State the maximum possible distance that can be measured between detector D1 and detector D2.

[1]

(b)

The muon travels at a speed of 0.98c relative to the laboratory. An electron is travelling in the opposite direction at a speed of 0.80c relative to the laboratory.

(b) Calculate the speed of the muon relative to the electron using Galilean relativity.

[1]

(c)

[2]

(d)

(d) Show that the speed of the muon, as measured in the reference frame of the electron, is approximately 0.998c.

[2]

(e)

(e) Calculate the time taken for the muon to travel from D1 to D2, according to an observer in the electron's reference frame.

[3]

(f)

(f) State and explain the reference frame in which the proper time for the muon's journey from detector D1 to detector D2 is measured.

[2]

Question 4

MediumPaper 2 · calculator10 marks

(a)

A spaceship departs from a space station, which is at rest in an inertial reference frame S. The spaceship travels at a constant velocity $v$ . The clocks on the station and the spaceship are synchronized to zero at the moment of departure ( $t = t' = 0$ ). At a later time, the spaceship emits a distress signal. According to an observer on the space station (frame S), this emission event occurs at a distance of 12 ly from the station and at a time of 13 years after departure.

(a) State what is meant by the spacetime interval between two events.

[2]

(b)

(b) Calculate the value of the spacetime interval between the departure of the spaceship and the emission of the signal, according to the observer on the space station.

[2]

(c)

(c) The emission of the signal occurs at the location of the spaceship. Determine the time elapsed on the spaceship's clock between departure and the emission of the signal.

[2]

(d)

(d) Explain why the time interval measured on the spaceship is known as the proper time interval.

[2]

(e)

(e) Calculate the velocity $v$ of the spaceship relative to the space station, as a fraction of the speed of light $c$ .

[2]

Question 5

HardPaper 2 · calculator9 marks

(a)

The spacetime diagram below shows two events, P and Q, as observed in a reference frame $S$ . Each event emits a light signal.

Spacetime diagram showing axes ct/ly on vertical axis from 0 to 7 and x/ly on horizontal axis from 0 to 8. A grid with major increments of 1 ly is shown. Event P is plotted at (x = 2, ct = 2). Event Q is plotted at (x = 7, ct = 5).

Calculate the time between event P and event Q, according to frame $S$ .

[2]

(b)

Calculate the time taken for the light signal leaving event P to arrive at the position of event Q, according to frame $S$ .

[2]

(c)

Calculate the location of a stationary observer in frame $S$ who receives the light signal from event P simultaneously with receiving the light signal from event Q.

[2]

(d)

Determine the velocity of a moving frame of reference in which event P and event Q occurred simultaneously.

[3]

Question 6

MediumPaper 2 · calculator10 marks

(a)

An interstellar civilization monitors two distant space probes, "Voyager Alpha" (event P) and "Explorer Beta" (event Q), from their stationary reference frame S. The spacetime coordinates of these events, representing the moments they transmit unique data packets, are observed as:

Event P: $(x_P, ct_P) = (1.0 \text{ ly}, 1.0 \text{ ly})$

Event Q: $(x_Q, ct_Q) = (5.0 \text{ ly}, 2.0 \text{ ly})$

A spacetime diagram illustrating these events is shown below.

Calculate, according to frame S, the time difference between the transmission of data packets from Voyager Alpha and Explorer Beta.

[2]

(b)

Determine the time taken for a light signal (representing data) from Voyager Alpha's transmission location to reach Explorer Beta's transmission location, as observed in frame S.

[2]

(c)

Find the spatial coordinate in frame S of a stationary alien observation post that receives the data packets from Voyager Alpha and Explorer Beta at the exact same moment.

[3]

(d)

Calculate the velocity of a hypothetical alien spacecraft (a moving reference frame) in which the transmissions from Voyager Alpha and Explorer Beta would be observed to occur simultaneously.

[3]

Question 7

MediumPaper 1A · calculator1 mark

An observer on a stationary space station sees two probes, P1 and P2. P1 is moving away from the station at a speed of $0.60c$ . P2 is moving away from the station in the opposite direction, also at a speed of $0.60c$ .

What is the speed of P2 as measured by an observer on P1?

A. $0$

B. $0.88c$

C. $c$

D. $1.20c$

Question 8

MediumPaper 1A · calculator1 mark

A hypothetical unstable particle has a proper lifetime of $2.5 \times 10^{-6} \text{ s}$ . The particle is moving at a speed of $0.92 c$ relative to a stationary laboratory observer.

What is the lifetime of the particle as measured by the laboratory observer?

A. $0.98 \times 10^{-6} \text{ s}$

B. $2.5 \times 10^{-6} \text{ s}$

C. $6.4 \times 10^{-6} \text{ s}$

D. $4.0 \times 10^{-6} \text{ s}$

Question 9

MediumPaper 1A · calculator1 mark

A spacecraft travels from a space station to a distant planet at a relativistic speed $v$ . The journey takes a proper time $T$ as measured by an astronaut on the spacecraft. What is the distance between the space station and the planet in the reference frame of the space station?

A. $vT$

B. $vT\sqrt{1-\frac{v^2}{c^2}}$

C. $\frac{vT}{\sqrt{1-\frac{v^2}{c^2}}}$

D. $\frac{vT}{1-\frac{v^2}{c^2}}$

Question 10

MediumPaper 1A · calculator1 mark

A space-time diagram shows the coordinate axes of an inertial reference frame S ( $x, ct$ ) and another inertial reference frame S' ( $x', ct'$ ) which moves at a constant velocity relative to S. Four events, P, Q, R, and X, are shown on the diagram.

Space-time diagram showing S(x, ct) and S'(x', ct') frames. The S' axes are tilted. Event X is shown. A line through X parallel to the x' axis passes through P. A line through X parallel to the ct' axis passes through Q. A line through X parallel to the x axis passes through R.

Which row correctly identifies an event that is simultaneous with event X in frame S', and an event that occurs at the same position as event X in frame S'?

	Simultaneous with X in S'	Same position as X in S'
A.	P	Q
B.	P	R
C.	R	P
D.	Q	P

Question 11

MediumPaper 1A · calculator1 mark

The proper length of a spaceship is $L_0$ . The spaceship travels at a constant speed of $0.6c$ relative to a space station. An observer on the space station measures the length of the spaceship to be $L$ .

What is the ratio $\frac{L}{L_0}$ ?

A. $\frac{3}{5}$

B. $\frac{4}{5}$

C. $\frac{5}{4}$

D. $\frac{5}{3}$

Question 12

MediumPaper 1A · calculator1 mark

A muon is created by a cosmic ray interaction at an altitude $H$ above the Earth's surface, as measured in the Earth's reference frame. The muon travels vertically downwards with a constant speed $v$ relative to the Earth.

What is the time for the journey as measured by an observer on Earth and the time as measured in the muon's reference frame?

Option	Time in Earth frame	Time in muon's frame
A	$\frac{H}{v}$	$\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$
B	$\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$	$\frac{H}{v}$
C	$\frac{H}{v}$	$\frac{H}{v}$
D	$\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$	$\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$

A. Time in Earth frame: $\frac{H}{v}$ , Time in muon's frame: $\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$

B. Time in Earth frame: $\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$ , Time in muon's frame: $\frac{H}{v}$

C. Time in Earth frame: $\frac{H}{v}$ , Time in muon's frame: $\frac{H}{v}$

D. Time in Earth frame: $\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$ , Time in muon's frame: $\frac{H}{v}\sqrt{1-\frac{v^2}{c^2}}$

Question 13

MediumPaper 2 · calculator3 marks

A probe travels at a constant relativistic speed $v$ relative to a planetary base along the $x$ -axis. A scientist on the base records two sensor malfunctions, Event 1 and Event 2, as occurring simultaneously.

Explain, by referring to the Lorentz transformation equations, the condition under which the computer on the probe will also record Event 1 and Event 2 as occurring simultaneously.

Question 14

MediumPaper 2 · calculator12 marks

(a)

An observer $A$ on a space station is at rest. A spacecraft carrying observer $B$ travels at a constant velocity $v$ relative to the space station. The origins of their coordinate systems coincide at $t = 0$ for observer $A$ and $t' = 0$ for observer $B$ .

According to observer $A$ , an explosion occurs at $x = 6.0 \text{ ly}$ at $t = 10.0 \text{ yr}$ .

Outline what is meant by the spacetime interval between two events.

[2]

(b)

Calculate the spacetime interval between the explosion and the coincidence of the origins.

[2]

(c)

According to observer $B$ , the explosion takes place at the origin of their reference frame.

Determine the time of the explosion according to observer $B$ .

[2]

(d)

Explain, with reference to your answer in (c), the concept of time dilation.

[3]

(e)

Determine, in $\text{m s}^{-1}$ , the velocity $v$ of the spacecraft relative to the space station.

[3]

Question 15

MediumPaper 1A · calculator1 mark

A spaceship travels with speed $\frac{3c}{4}$ with respect to the Earth. A comet travels in the same direction as the spaceship with speed $\frac{c}{2}$ with respect to the Earth.

What is the speed of the comet in the spaceship's reference frame?

A. $\frac{c}{4}$

B. $\frac{2c}{5}$

C. $\frac{10c}{11}$

D. $\frac{5c}{4}$

Question 16

MediumPaper 1A · calculator1 mark

A radioactive particle travels at a constant velocity relative to a laboratory. Observer X measures the proper time interval between the creation and the decay of the particle. Which statement is correct?

A. Observer X is at rest relative to the laboratory.

B. Observer X is at rest relative to the particle.

C. Observer X measures the longest possible time interval between the two events.

D. Observer X measures the two events to occur at different positions in space.

Every Galilean and Special Relativity question, marked for you

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Galilean and Special Relativity: notes and practice questions

How it is examined

Guiding questions

Linking questions