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When the twins are 20 years old, Speedo, sets out on an epic journey from the Earth to Planet X, located 20 light-years away. One light-year is the distance light (EM waves) travels through free space in 1 year. Speedo travels at a speed of 0.95c relative to the inertial frame of his twin brother; Goslo, back home on the Earth. After reaching Planet X, Speedo becomes homesick and immediately returns to the Earth at the same speed 0.95c. Upon his return, Speedo is shocked to discover that Goslo has aged 42 years and is now 62 years old. Speedo, on the other hand, has aged only 13 years and is now 33 years.

When the twins are 20 years old, Speedo, sets out on an epic journey from the Earth to Planet X, located 20 light-years away. One light-year is the distance light (EM waves) travels through free space in 1 year. Speedo travels at a speed of 0.95c relative to the inertial frame of his twin brother; Goslo, back home on the Earth. After reaching Planet X, Speedo becomes homesick and immediately returns to the Earth at the same speed 0.95c. Upon his return, Speedo is shocked to discover that Goslo has aged 42 years and is now 62 years old. Speedo, on the other hand, has aged only 13 years and is now 33 years.

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Using mathematical proofs, show that the paradox presented on the image is true. Explain and Show full working.         

THE TWIN PARADOX • When the twins are 20 years old, Speedo, sets out on an epic journey from the Earth to Planet X, located 20 light-years away. • One light-year is the distance light (EM waves) travels through free space in 1 year. • Speedo travels at a speed of 0.95c relative to the inertial frame of his twin brother; Goslo, back home on the Earth. After reaching Planet X, Speedo becomes homesick and immediately returns to the Earth at the same speed 0.95c. • Upon his return, Speedo is shocked to discover that Goslo has aged 42 years and is now 62 years old. Speedo, on the other hand, has aged only 13 years and is now 33 years.
Transcribed Image Text:THE TWIN PARADOX • When the twins are 20 years old, Speedo, sets out on an epic journey from the Earth to Planet X, located 20 light-years away. • One light-year is the distance light (EM waves) travels through free space in 1 year. • Speedo travels at a speed of 0.95c relative to the inertial frame of his twin brother; Goslo, back home on the Earth. After reaching Planet X, Speedo becomes homesick and immediately returns to the Earth at the same speed 0.95c. • Upon his return, Speedo is shocked to discover that Goslo has aged 42 years and is now 62 years old. Speedo, on the other hand, has aged only 13 years and is now 33 years.
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