A spaceship moves at 0.9c relative to Earth. A crew member's onboard clock measures a journey of 10 years. How much time passes on Earth clocks during this journey?
ALess than 10 years — the Earth clock runs slow from the crew member's perspective
BExactly 10 years — time dilation only applies to the moving frame
CMore than 10 years — the ship clock is dilated relative to Earth, so Earth clocks tick faster
DThe question is unanswerable — time dilation is symmetric, so both frames are equally valid
The crew member's clock measures proper time Δτ = 10 years (they are present at both events: departure and arrival). The Earth observer measures dilated time Δt = γ·Δτ, which is greater. At v = 0.9c, γ ≈ 2.29, so about 22.9 years pass on Earth. Option A confuses which observer measures which time. Option D is wrong because the symmetry is broken when the ship turns around — the traveling twin must accelerate, which breaks the equivalence of the two frames.
Question 2 Multiple Choice
Which observer measures the proper time between two events?
AThe observer who is moving fastest relative to the events
BThe observer in the frame where the two events occur at the same spatial location
CThe observer who is stationary relative to Earth's surface
DAny observer — proper time is the same in all inertial frames
Proper time is measured by a clock that is physically present at both events — meaning the events occur at the same location in that clock's rest frame. This clock reads the minimum elapsed time between the two events. Any other observer in relative motion measures a longer (dilated) time Δt = γΔτ. The proper-time clock is the one that 'travels with the process' being timed.
Question 3 True / False
An astronaut traveling at 0.99c would subjectively notice their onboard clock running slowly.
TTrue
FFalse
Answer: False
False. Each observer always experiences their own clock as ticking normally — at one second per second. The astronaut's clocks, biological processes, and perceptions all proceed at the usual rate from their own perspective. Time dilation is not a subjective experience of the moving observer; it is an observation made by another frame when comparing clocks. This is perhaps the most common misconception about time dilation: it is a relational phenomenon, only observable when comparing two frames.
Question 4 True / False
The twin paradox is fully resolved by noting that from the traveler's perspective, the stay-at-home twin's clock runs slow — so both twins age less than the other, which is a contradiction.
TTrue
FFalse
Answer: False
False. The apparent symmetry breaks when the traveling twin accelerates to turn around. Only the stay-at-home twin remains in a single inertial frame throughout the journey. The traveling twin must change inertial frames, and this asymmetry resolves the paradox: the traveling twin is the one who genuinely ages less. The result is not a contradiction but an asymmetric outcome predicted by both special and general relativity.
Question 5 Short Answer
Why is proper time called the 'minimum' elapsed time between two events, and who measures it?
Think about your answer, then reveal below.
Model answer: Proper time is measured by a clock present at both events (the events occur at the same location in its rest frame). It is the minimum because any observer in relative motion measures a dilated (longer) time Δt = γΔτ, where γ ≥ 1. The traveling clock follows the most direct path through spacetime between the two events; clocks in other frames follow longer spacetime paths and accumulate more coordinate time.
This minimum property reflects the geometry of spacetime: the inertial (straight-line) path maximizes proper time, while a 'bent' path (changing direction, i.e., accelerating) accumulates less proper time. This is the opposite of spatial geometry, where the straight path is the shortest — in spacetime geometry, the inertial path corresponds to the maximum elapsed proper time for a traveler moving between two events.