Question

In the so-called twin paradox, one twin (A) travels away from the Earth to a distant star at high speed while the other (B) stays behind. When twin A arrives at the star, she is 19 years older than when she left Earth. Twin B on Earth knows from the local astronomers that the star is 49 light-years away.

When twin A arrives at the star, how much older is twin B on the Earth than twin A? More specifically, find the time coordinate on Earth for the event "twin A arrives at the star" and calculate the difference in ages.

Answer 1

The twin paradox involves time dilation where the traveling twin A ages less than twin B on Earth. By applying the relativistic factor, when twin A arrives at the distant star after 19 years, twin B on Earth is 551 years older than twin A.

Step-by-step explanation:

In the twin paradox, twin A travels to a distant star at a high velocity while twin B stays on Earth. The scenario involves time dilation, a concept from Einstein's theory of relativity, which predicts that the moving twin A would age less compared to the twin B who stays on Earth. Considering twin A travels at a velocity where γ is 30.0, if the trip takes 2 years in twin A's frame, it would take 60 years in twin B's frame due to time dilation.

Calculating the Age Difference: If the star is 49 light-years away and twin A ages 19 years during the trip, and assuming twin A travels at a constant speed where 1 year in her frame corresponds to 30 years on Earth, twin B on Earth will age 19 × 30 = 570 years during twin A's journey. Therefore, when twin A arrives at the star, twin B on Earth will be 551 years older than twin A.