(455) HL Time dilation [IB Physics HL]

Introduction to Time Travel

• Special relativity explores the concept of time travel.

• Reference to the movie "Back to the Future" highlights popular culture's interest in the topic.

Time Dilation

• Definition: Dilation means to open up, in contrast to contraction.

• Explanation of time dilation:

  • Affects how time is perceived based on relative motion.

  • No absolute time exists; time is relative to the observer.

• Example: Traveling fast in a spaceship (near the speed of light) leads to aging differently compared to someone on Earth.

Key Concepts

• Time dilation implies that one can move forward in time relative to someone else.

• The equation for time dilation: ΔT = γΔt₀

  • ΔT: Time measured by a stationary observer (e.g., on Earth).

  • Δt₀: Proper time, or time measured where events happen in the same place.

  • γ (Lorentz factor): γ = 1/√(1 - v²/c²)

Example Calculation

• Scenario: A person travels in space at 0.9c (90% the speed of light) for 10 years (Earth time).

• To find out how long they experienced time, apply the time dilation equation:

  • Identify the proper time and calculate γ validating they experience different time.

Calculation Steps

• Start with the equation: ΔT = γΔt₀

• Proper time is measured in the spaceship; events occur at the same location for the traveler.

• Determine γ:

  • Calculate γ = 1/√(1 - (0.9c)²/c²) → 1/√(0.19) = 2.29 (approx).

• Calculate Δt₀: Δt₀ = ΔT / γ

  • Substituting gives Δt₀ = 10 years / 2.29 = 4.36 years.

Conclusion

• Result shows the traveler aged 4.36 years while Earth aged 10 years.

• Illustrates the mind-blowing concept of forward time travel through relativistic speeds.