Lecture Notes on Time Dilation and "Interstellar"

Introduction to Time Dilation

• Miller's Planet: Closest planet to black hole Gargantua in "Interstellar."
• Concept: Time dilation explained using "Interstellar" as context.
• Fundamentals of Relativity:
  • General Relativity: Strong gravitational fields slow down time.
  • Special Relativity: Time slows down for moving objects.

Key Concepts

• Strong Gravitational Fields:
  • Closer to massive objects, time experienced slower.
  • Example: Walking up stairs increases speed of time slightly as distance from Earth's gravity increases.
• Gravitational and Motion Influence:
  • Being further from gravity speeds time, but motion slows it.

Gravitational Redshift

• Example case:
  • Person A near a massive object sends light to Person B in space.
  • Light loses energy escaping gravitational pull, decreasing frequency.
  • A green laser (600 trillion vibrations/sec) becomes a microwave radio beam (10 billion vibrations/sec).
• Conclusion: Clocks run at different rates due to gravitational impact.

Biological Effects

• Person A: Normal perception of time.
• Person B: Observes Person A in slow motion.

"Interstellar" and Time Dilation

• Einstein's Insight:
  • Acceleration and gravity influence time dilation.
  • Greater gravity slows time significantly (e.g., black hole's surface).
• Miller's Planet: Extreme time dilation due to proximity to Gargantua.
  • Earth's time runs faster compared to Miller's Planet.

Real-world Application

• International Space Station (ISS):
  • Time on the ISS runs slower than on Earth.
  • Requires adjustment using Einstein’s equations.

Interpretation in Film

• Filmmaker Techniques:
  • Use of music with ticking elements to symbolize time dilation.
  • Each tick on Miller's Planet equals a significant time on Earth.
  • Example: 61,400 Earth seconds per one Miller's Planet second.

Realism of Extreme Time Dilation

• Gravity Comparison:
  • Miller's Planet gravity is 130% of Earth's.
  • Extreme dilation (1 hour equals 7 years) requires a massive gravitational field, like near a black hole's event horizon.
  • Realistic depiction impossible; it’s science fiction for cinematic effect.

Conclusion

• Science Fiction vs Reality:
  • Artistic liberties in "Interstellar" to create compelling narrative.
  • Film uses time dilation concept creatively yet unrealistically.

Summary Quote

• "We'll find a way professor. We always have." - Highlighting human perseverance and optimism.