Experimental Setup

• Identical twin astronauts Terra and Stella volunteer for experiment on 20th birthday
• Terra remains on Earth, Stella travels in spaceship
• Stella's journey: 86.6% speed of light to star 10 light years away, then return at same speed
• Expected journey time: 23 years based on distance calculation

Special Relativity Principles

• Faster objects move through space → slower movement through time (relative to stationary observer)
• Lorentz factor equation quantifies this relationship
• Length contraction: moving object contracts by same factor as measured by stationary observer
• At 86.6% speed of light: Lorentz factor = 2
  • Time passes twice as slowly aboard spaceship
  • Stella won't notice time slowing (all processes slow equally: clocks, devices, biological activities, aging, perception)
  • Only inertial (non-accelerating) observers like Terra can detect time difference

The Apparent Paradox

• Terra's perspective: she'll be older when reunited (Stella ages slower)
• Stella's counterargument: spaceship stands still, universe (including Terra) moves around her
  • In this view, Terra ages slower, making Stella older
• Contradiction: both can't be older than the other
• Known as "twin paradox" - not true paradox, just misunderstanding of special relativity

Light Burst Communication Experiment

• Each twin sends light burst every year that passes for them
• Light speed constant regardless of observer's reference frame
• Observation includes: time for other twin to experience one year + light travel time between them

Graph Analysis - Terra's Perspective

• X-axis: distance from Earth, Y-axis: time passage
• Terra's path: vertical line (distance = 0, each tick = 1 year)
• Stella's path: origin to 11.5 years time + 10 light years distance, then back to 0 distance at 23 years
• Terra's first light pulse: 45-degree diagonal line (light takes 1 year per light year)
• Stella moving away: light catches up after 7 total Terra years, 4 Stella years
• Second burst reaches Stella during return journey
• Stella moving toward light source: receives bursts more frequently
• Result: Stella observes Terra aging slowly first half, rapidly second half

Stella's Perspective

• Universe appears to move around her spaceship
• Length contraction factor of 2: distance between Earth and star shrinks by half
• Each leg takes ~6 years from Stella's perspective
• First signal to Earth: 2 Terra years have passed
• 4 more outbound signals sent from increasing distances
• Terra receives first inbound pulse after 21+ years
• Terra receives multiple bursts per year during Stella's return

Observational Asymmetry

• Terra observes Stella aging slowly for ~90% of 23 years apart, rapidly last 10%
• Stella sees even split between slow/fast aging periods
• Asymmetry explains why paradox isn't real paradox

Final Results

• Space voyage duration: 23 Earth years, 11.5 ship years
• Reunion ages: Terra 43 years old, Stella 31 years old
• Age difference: 12 years (Terra older)

Resolution of Paradox

• Stella's error: assuming equal claim to being inertial observers
• Inertial observer requirements: constant speed and direction relative to universe
• Terra: constant zero velocity (truly inertial)
• Stella: changed direction for return journey → entered different reference frame
• Only Terra maintained inertial reference frame throughout