- Special Relativity And Riemannian Geometry 1 (76.72 KiB) Viewed 47 times
Special Relativity and Riemannian Geometry
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Special Relativity and Riemannian Geometry
Special Relativity and Riemannian Geometry
QUESTION 1 Two twins, Alice and Bob, are 30 years old. Alice gets on a rocket and travels at 0.75c, for what she experiences to be 6 years. Bob remains on Earth during this time. Ignore all effects of acceleration and assume Alice traveled at a constant speed with respect to Bob for the entire journey. (Hint: A lightyear is the distance traveled by light in one year, which is just c multiplied by one year, or 9.46 x 1012 km. In many problems it is simpler to write it as le. year, since c often cancels out.) a) How old is Bob when Alice reaches her destination? (5) (3) b) What was the distance of the journey according to Alice? c) What was the distance of the journey according to Bob? d) Which twin measured the proper distance of the journey? (3) (1) e) Which twin measured the proper time of the journey? (1) f) Alice gets back in her rocket and returns to Earth at the same speed as the outbound journey. Draw a rough spacetime diagram for Bob's frame indicating clearly: Alice's departure from Earth (Event A) - Alice reaching her destination (Event B) Alice's return to Earth (Event C) Both Alice's and Bob's worldlines between Events A and C. (5)
QUESTION 1 Two twins, Alice and Bob, are 30 years old. Alice gets on a rocket and travels at 0.75c, for what she experiences to be 6 years. Bob remains on Earth during this time. Ignore all effects of acceleration and assume Alice traveled at a constant speed with respect to Bob for the entire journey. (Hint: A lightyear is the distance traveled by light in one year, which is just c multiplied by one year, or 9.46 x 1012 km. In many problems it is simpler to write it as le. year, since c often cancels out.) a) How old is Bob when Alice reaches her destination? (5) (3) b) What was the distance of the journey according to Alice? c) What was the distance of the journey according to Bob? d) Which twin measured the proper distance of the journey? (3) (1) e) Which twin measured the proper time of the journey? (1) f) Alice gets back in her rocket and returns to Earth at the same speed as the outbound journey. Draw a rough spacetime diagram for Bob's frame indicating clearly: Alice's departure from Earth (Event A) - Alice reaching her destination (Event B) Alice's return to Earth (Event C) Both Alice's and Bob's worldlines between Events A and C. (5)