A rocket with a proper length of 100 m travels past a space station at v = 0.866c (γ = 2). What length does the station observer measure for the rocket?
A200 m — the rocket appears stretched because it is moving away at high speed
B100 m — length is an intrinsic property of the rocket, unaffected by relative motion
C50 m — the station observes the contracted length L = L₀/γ = 100/2
D70.7 m — applying a factor of 1/√2 to the proper length
Length contraction gives L = L₀/γ. At γ = 2, the station measures half the proper length: 50 m. Option A reverses the direction of the effect. Option B is the pre-relativistic intuition that length is frame-independent — exactly what special relativity overturns. Option D applies the wrong factor; γ at v = 0.866c is exactly 2, not √2.
Question 2 Multiple Choice
The station observer measures the passing rocket as contracted. An observer on the rocket simultaneously measures the station's rulers. What does the rocket observer find?
AThe station's rulers appear normal length — only the rocket is moving, so only the rocket contracts
BThe station's rulers appear longer — the rocket's contraction is compensated by ruler stretching
CThe station's rulers appear contracted by the same Lorentz factor — the effect is fully symmetric
DThe measurement is impossible to interpret because simultaneity prevents comparing ruler endpoints across frames
Length contraction is symmetric: each inertial frame measures the other's objects as shortened by the same factor γ. There is no privileged 'truly moving' frame — in the rocket's frame, the station is moving, so the station's rulers contract. This seems paradoxical but is consistent because 'measuring both endpoints simultaneously' involves different spacetime events in each frame, and simultaneity is frame-dependent.
Question 3 True / False
A moving rod oriented perpendicular to its direction of motion is measured by a stationary observer. The observer finds the rod's length in that perpendicular direction is unchanged.
TTrue
FFalse
Answer: True
Length contraction only affects the dimension parallel to the direction of motion. Transverse dimensions are invariant. A symmetry argument shows why: if perpendicular lengths contracted, a moving ring could not pass through a stationary ring of the same radius, and neither frame could be preferred for deciding which ring is 'smaller' — a contradiction.
Question 4 True / False
Length contraction means the atomic bonds in a moving rod are physically squeezed together, compressing the rod's material structure from the rod's own perspective.
TTrue
FFalse
Answer: False
Length contraction is a geometric property of spacetime, not a mechanical compression. In the rod's own rest frame, its internal structure is completely unchanged — atoms and bonds are at their normal separations. The contracted length is what a stationary observer measures; it reflects the frame-dependence of simultaneous endpoint measurements, not any physical force acting on the rod.
Question 5 Short Answer
Length contraction is symmetric — each frame measures the other's rods as shortened. Why doesn't this symmetry lead to a logical contradiction?
Think about your answer, then reveal below.
Model answer: The symmetry is consistent because measuring a rod's length requires determining the positions of both endpoints simultaneously, and simultaneity is frame-dependent. What counts as 'the same moment' differs between frames. Each frame's length measurement involves different pairs of spacetime events, so both frames can consistently report the other's rod as shorter — they are not measuring the same physical situation from different perspectives.
This is the heart of understanding length contraction: it is not about physical change but about the geometry of spacetime measurements. The relativity of simultaneity ensures the two frames make fundamentally different measurements, and each is correct within its own frame. The spacetime interval — not length alone — is what is truly frame-independent.