Back to Special Relativity

Table of Contents

1. Scenario
2. The Paradox
3. The Paradox using Proper Time
4. Legitimate Use of Δ𝛕 = Δt /γ
5. Back to the Paradox
6. Spaceship’s Worldline in Earth’s Reference Frame
7. Calculating the Proper Time Interval for the Spaceship’s Worldline
8. Problem with the Calculation
9. Two Solutions
   1. Extending Δ𝛕 = Δt /γ to Flat Spacetime
   2. Using Multiple Inertial Reference Frames
   3. Resolution of the Paradox

Scenario

The Paradox

The Paradox using Proper Time

Legitimate Use of Δ𝛕 = Δt /γ

A scenario where each of two passing spaceships legitimately uses Δ𝛕 = Δt /γ to calculate proper time intervals on the other.

Back to the Paradox

Spaceship’s Worldline in Earth’s Reference Frame

Calculating the Proper Time Interval for the Spaceship’s Worldline

Problem with the Calculation

Two Solutions

Extending Δ𝛕 = Δt /γ to Flat Spacetime

Sean Carroll, Spacetime and Geometry: an Introduction to General Relativity

Don Koks, Where is the Boundary between Special and General Relativity?

Using Multiple Inertial Reference Frames

Resolution of the Paradox