Special relativity thought experiment

Time Dilation

Explore how relative motion can produce different elapsed times for two people and, in this simplified scenario, close an initial age gap.

What this model assumes

The older person travels at a constant fraction of the speed of light while the younger person remains in the reference frame used for the calculation.

  • The birth dates define only the initial age difference.
  • The result uses special relativity and idealized constant motion.
  • Acceleration, turning around, gravity and travel distance are not modeled.

Inputs

β = v = c

Results

Ship time is the proper time experienced by the traveler. Earth-frame time is the elapsed time experienced by the person who remains behind.

Initial age difference Δ — Absolute difference between the two birth dates
Lorentz factor γ — γ = 1 / √(1 − β²)
Traveler's elapsed time t′ — Proper time: t′ = Δ / (γ − 1)
Earth-frame elapsed time t — Reference-frame time: t = γ · t′

How to read the calculation

Time dilation relates Earth-frame time t to the traveler's proper time t′:

t = γ · t′

To close an initial age difference Δ, the person who stays behind must age by exactly Δ more than the traveler. Therefore:

Δ = t − t′ = (γ − 1) · t′

This is an educational idealization, not a practical travel model. At everyday speeds, γ is extremely close to 1, so the required time becomes extraordinarily long.

Show calculation details 

          

        

      

    


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