Time Dilation

• What phenomenon occurs when objects travel close to the speed of light?

  Time dilation

  
• How does an observer moving relative to a fast object perceive its clock?

  It appears to tick slower
• What does observer H see on their clock while moving close to the speed of light?

  It ticks at a regular pace
• What time does observer G measure on observer H's clock?

  14:45 instead of 15:00
• How does observer H perceive observer G's clock?

  As ticking slower
• What does a stationary observer see regarding moving clocks?

  They run slower in the moving frame
• What is the gamma factor symbolized as?

  γ
• What does the gamma factor account for in time dilation?

  Transformation between reference frames
• What is the formula for the gamma factor?

  γ = $\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$
• Why is the gamma factor always greater than 1?

  Because $v$ is always less than $c$
• What does the time dilation equation relate?

  Proper time and observed time
• What is a light clock composed of?

  Two mirrors facing each other
• How does an observer on a train platform see the light clock's operation?

  Light reflects between mirrors
• What is the distance between the mirrors in a light clock denoted as?

  L

  
• What is the time interval for light to travel in a stationary light clock?

  Δt0 = $\frac{2L}{c}$
• How does the light clock on a moving train differ from the stationary one?

  It travels a longer path, D
• What geometric principle is used to relate distances in the moving light clock scenario?

  Pythagoras' theorem
• What is the formula derived from Pythagoras' theorem in this context?

  D² = L² + (vΔt)²
• What does the observer on the train platform see regarding the light ray's travel?

  It travels at an angle
• What is the time interval measured by the stationary observer on the platform?

  Δt = $\frac{2L}{c\sqrt{1 - \frac{v^2}{c^2}}}$
• What is the relationship between D and Δt in the light clock scenario?

  D = $\frac{cΔt}{2}$
• What does the equation Δt = γΔt0 signify?

  Time interval in moving frame
• What does it mean if γ > 1?

  Δt > Δt0
• How do observers perceive each other's clocks?

  Each sees the other's clock as slower
• Why does the light beam not speed up to hit mirrors at the same frequency?

  Due to Einstein's second postulate
• What must both observers measure regarding the speed of light?

  It must be c
• What is crucial about the time measured in the light clock scenario?

  It is measured at the same position
• What is the distance from the base station to the star according to Emma?

  14.2 light years
• What speed is Alex's spacecraft traveling at?

  0.7c
• How long does it take light to travel 14.2 light years?

  14.2 years
• What is the formula to find the time taken according to Emma?

  Δt = $\frac{s}{v}$
• What is the calculated time taken according to Emma?

  20.29 years
• What is the proper time interval Alex measures for her travel?

  14.5 years
• Why does Emma measure a longer time for Alex's journey?

  Because Alex's clock is moving
• What is a helpful mnemonic for time dilation?

  Moving clocks run slower
• What is the significance of 'proper time' in this context?

  It depends on the reference frame
• What mathematical concepts are used in the derivation of time dilation?

  Speed = distance/time and Pythagoras' theorem