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Date May 2018 Marks available 1 Reference code 18M.3.SL.TZ2.5
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term Calculate Question number 5 Adapted from N/A

Question

Observer A detects the creation (event 1) and decay (event 2) of a nuclear particle. After creation, the particle moves at a constant speed relative to A. As measured by A, the distance between the events is 15 m and the time between the events is 9.0 × 10–8 s.

Observer B moves with the particle.

For event 1 and event 2,

Explain what is meant by the statement that the spacetime interval is an invariant quantity.

[1]
a.

calculate the spacetime interval.

[1]
b.i.

determine the time between them according to observer B.

[2]
b.ii.

Outline why the observed times are different for A and B.

[1]
c.

Markscheme

quantity that is the same/constant in all inertial frames

[1 mark]

a.

spacetime interval = 272 – 152 = 504 «m2»

[1 mark]

b.i.

ALTERNATIVE 1

Evidence of x′ = 0

t′ «\(\frac{{\sqrt {504} }}{c}\)» = 7.5 × 10–8 «s»

ALTERNATIVE 2

γ = 1.2

t′ «= \(\frac{{9 \times {{10}^{ - 8}}}}{{1.2}}\)» = 7.5 × 10–8 «s»

 

[2 marks]

b.ii.

observer B measures the proper time and this is the shortest time measured

OR

time dilation occurs «for B's journey» according to A

OR

observer B is stationary relative to the particle, observer A is not

[1 mark]

c.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.2 – Lorentz transformations
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