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Answer :
Final answer:
The young man will be younger than his twin brother who stayed home due to time dilation caused by his high velocity during the voyage to α Centauri.
Explanation:
Time dilation is a concept in physics that states that time can appear to pass differently for two observers in relative motion. According to Einstein's theory of relativity, the closer an object travels to the speed of light, the slower time appears to pass for that object. This means that if an object is moving at a high velocity, time will appear to pass slower for that object compared to a stationary observer.
In this question, the young man is traveling to α Centauri, which is 4.3 light years away, in a spaceship at a velocity of c/5, where c is the speed of light. To calculate the time dilation experienced by the young man, we can use the equation for time dilation:
Δt' = Δt / √(1 - (v^2 / c^2))
where Δt' is the time experienced by the moving observer, Δt is the time experienced by the stationary observer, v is the velocity of the moving observer, and c is the speed of light.
By plugging in the given values, we can calculate the time dilation factor and determine the age difference between the young man and his twin brother who stayed home.
Learn more about time dilation here:
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Final answer:
In the twin paradox scenario where one twin travels to Alpha Centauri at c/5, the traveling twin would be younger by about 0.89 years due to the effects of relativistic time dilation when compared to their Earth-bound twin after making a round trip.
Explanation:
The subject of this question involves the concepts of special relativity, specifically time dilation and length contraction as described by Albert Einstein. The scenario presented is known as the 'twin paradox,' where one twin travels at a high velocity in space while the other stays on Earth. When the traveling twin returns, they are younger than their sibling due to the effects of relativistic time dilation.
To solve this, the time experienced by the traveling twin must be calculated. The spaceship travels at c/5, or 0.2c, where c is the speed of light. Since Alpha Centauri is 4.3 light years away and the twin is moving at c/5, the time (t) taken for the twin to reach Alpha Centauri as perceived by the Earth-bound observer is:
t = distance / velocity = 4.3 ly / (c/5) = 4.3 * 5c / c = 21.5 years (one way).
Therefore, for a round trip, this time doubles to 43 years as perceived by the Earth-bound observer. According to special relativity, the moving twin's clock runs slower by a factor of gamma (γ), which is [tex]1 / sqrt(1 - v^2/c^2[/tex] c/5, gamma is approximately 1.021. So, the time experienced by the traveling twin is:
t' = t / γ = 43 years / 1.021 ≈ 42.11 years.
Hence, the traveling twin would age approximately 42.11 years while the twin on Earth would age 43 years. The difference in their ages when the traveling twin returns would be roughly 0.89 years, meaning the traveler would be younger by about 0.89 years.
