What is γ when relative speed v is zero?

• 1
• 0
• Infinite

A ship's light-clock mirrors are separated perpendicular to its constant motion. Why does the ground measure a longer tick time than the ship clock?

• The light path is shorter; light speed remains c.
• The light path is longer; light speed remains c.
• The path is unchanged; light speed exceeds c.

After correcting signal-travel delays, each of two inertial frames measures clocks at rest in the other frame as running faster.

One ship clock records 10 s between two ticks. The ship moves at constant speed relative to the ground with γ=2. After correcting signal-travel delays, what ground-frame time elapses between those same ticks, in seconds?

A rod's rest-frame length is 24 m. It moves along its length with γ=2 relative to the ground. Which ground measurement is valid?

• 48 m, using both endpoint positions at one ground time.
• 12 m, using endpoint positions at two different ground times.
• 12 m, using both endpoint positions at one ground time.

Why does time dilation increase the predicted fraction of fast muons reaching the ground, compared with treating their rest half-life as their ground-frame half-life?

• The ground half-life grows by γ, so fewer half-lives pass.
• The muons' rest half-life grows by γ during the flight.
• The ground flight time grows by γ at fixed distance and speed.

For a transverse light clock, (cΔt/2)^2=D^2+(vΔt/2)^2. Here D is mirror gap, Δt is ground tick time and Δτ is ship tick time. A student substitutes D=cΔt/2. Which correction is needed?

• D=vΔt/2, since ship displacement sets the mirror gap.
• D=cγΔt/2, since transverse lengths grow by γ.
• D=cΔτ/2, since the ship tick covers distance 2D.

Muons travel straight down from a production level to the ground at constant speed. The vertical gap H is fixed in ground coordinates. Ground flight time is 6 μs, γ=2 and rest half-life is 1.5 μs. Ignore energy loss. Which row gives consistent ground and muon-frame results?

• Ground half-life 3 μs; muon gap H; muon flight 3 μs; survival 1/4.
• Ground half-life 3 μs; muon gap H/2; muon flight 3 μs; survival 1/4.
• Ground half-life 3 μs; muon gap H/2; muon flight 6 μs; survival 1/4.
• Ground half-life 3 μs; muon gap H/2; muon flight 3 μs; survival 1/2.