- #1
aliens123
- 75
- 5
I was hoping I could get some help on wrapping my head around the twin paradox. The problem is I have never seen the following "contradiction" addressed. I understand (at least on paper) that events simultaneous in one frame needn't be simultaneous in another. But consider the following argument:
Consider three observers, Oscar, Beth, and Jim.
Jim is tasked with retrieving a rare mineral from the planet near the star Alkaid. Alkaid is 99-light years from Earth. Jim knows that with the technology available he can travel at a speed of .98c. The trip to Alkaid will therefore take him 20 years in his frame. However, to observers on Earth, it will take 101 years.
Beth stays at home on the Earth. Jim travels to Alkaid. Oscar is in the same reference frame as Jim. Jim gets in a rocket and travels to Alkaid. The Earth and Alkaid synchronize clocks with respect to one another. Jim gets in a rocket and travels to Alkaid. When he leaves his frame, his clock, Earth’s clock, and Alkaid’s clock all read 0.
When Jim arrives at Alkaid he finds that the clock on Alkaid which was synchronized to Earth reads 101 years. Oscar however, who was in the same frame as Jim, is present whizzing over Earth at the time Jim reaches Alkaid. He looks down at the clock on Earth and it reads 3.96 years! This is because the Earth bound clock was moving relative to their frame.
Imagine Beth, when her clocks reads year 3.96, looks upward. She sees Oscar whizzing by over her, and sees that his clock reads a time of twenty years. She reasons that this means Jim has already reached Alkaid. She is able to send a message to Oscar (because Oscar is right above her) to reverse the direction of the ship. Oscar does this nearly instantaneously. Jim returns home another 3.96 years later. This means that he returned home to Earth in 7.92 years (as measured by the clocks on earth), with the rare mineral intact.
But to observers on Earth this trip should have taken a total of 202 years.
Consider three observers, Oscar, Beth, and Jim.
Jim is tasked with retrieving a rare mineral from the planet near the star Alkaid. Alkaid is 99-light years from Earth. Jim knows that with the technology available he can travel at a speed of .98c. The trip to Alkaid will therefore take him 20 years in his frame. However, to observers on Earth, it will take 101 years.
Beth stays at home on the Earth. Jim travels to Alkaid. Oscar is in the same reference frame as Jim. Jim gets in a rocket and travels to Alkaid. The Earth and Alkaid synchronize clocks with respect to one another. Jim gets in a rocket and travels to Alkaid. When he leaves his frame, his clock, Earth’s clock, and Alkaid’s clock all read 0.
When Jim arrives at Alkaid he finds that the clock on Alkaid which was synchronized to Earth reads 101 years. Oscar however, who was in the same frame as Jim, is present whizzing over Earth at the time Jim reaches Alkaid. He looks down at the clock on Earth and it reads 3.96 years! This is because the Earth bound clock was moving relative to their frame.
Imagine Beth, when her clocks reads year 3.96, looks upward. She sees Oscar whizzing by over her, and sees that his clock reads a time of twenty years. She reasons that this means Jim has already reached Alkaid. She is able to send a message to Oscar (because Oscar is right above her) to reverse the direction of the ship. Oscar does this nearly instantaneously. Jim returns home another 3.96 years later. This means that he returned home to Earth in 7.92 years (as measured by the clocks on earth), with the rare mineral intact.
But to observers on Earth this trip should have taken a total of 202 years.