Consider the same scenario as in the previous problem: Two twin sisters,Gwen and Jackie,are both 20 years old in the year 2020.Jackie takes off on a round-trip to Vega,25 light-years away.She travels at an average speed of 0.9999c.Which of the following best describes the situation according to Jackie?
A)She stays still,while Earth rushes away from her at 0.9999c and Vega rushes toward her at 0.9999c.Since Vega is 25 light-years away,she says it takes Vega about 25 years to reach her.
B)She says that the 25 light-year trip takes only a few months,and therefore concludes that she is traveling faster than the speed of light.
C)It takes her 25 years to reach Vega.
D)She stays still,while Earth rushes away from her at 0.9999c and Vega rushes toward her at 0.9999c.She sees the distance from Earth to Vega shortened considerably from 25 light-years,and therefore it takes far less than 25 years for Vega to reach her.

Question

Quizplus · Accepted Answer

According to special relativity, as Jackie moves at 0.9999c, she will observe the distance between Earth and Vega to be contracted due to length contraction. From her perspective, the distance between Earth and Vega will be much shorter than 25 light-years. Therefore, Vega will take far less than 25 years to reach her, but for observers on Earth, 25 years will have passed. So, Jackie stays still, while Earth rushes away from her at 0.9999c, and Vega rushes towards her at 0.9999c, and it takes far less than 25 years for Vega to reach her. Option D correctly explains this situation. Option A is incorrect as it takes 25 years from Jackie's frame for Vega to reach her. Option B is incorrect as it violates the speed limit of light. Option C is incorrect as it ignores time dilation due to Jackie's high speed.

Consider the Same Scenario as in the Previous Problem: Two