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Yes, this is similar to the twin paradox, but with a few changes:
Two brothers set off from earth to make a round trip of 30 light years in total.
The first brother, say Albert, has a ship that travels at 10% the speed of light so his journey will take him 300 years and, due to time dilation, earth will have aged around 301 years by the time he (or his descendants) gets back.
The second brother, Carl, has a ship that travels at 99.99% the speed of light so his journey will take 30.03 years, however the earth will have aged over 2119 years on his return.
While, to Carl, his journey has been far quicker, he will arrive back to earth over 1800 years after his brothers ship returned.
Therefore, are we not best to be onboard Alberts ship even though his journey will take ten times longer? Unless we are intent on a one-way trip, travelling close to the speed of light would slow us down if our goal was to return to earth.
Yes, the twin paradox is the basis of the question, however, this time, both twins go on exactly the same journey, but somehow the one travelling slower gets back to earth faster. I’m just trying to find out at what point during the journey the twin travelling slower overtakes the one travelling faster?
I appreciate your time and hope that you can clear things up for me
(Andy posted this Question)
I cannot give a clear and final answer here, but we can discuss things over here.
If we are travelling with a 10% the speed of light means we will be going at at speed of 30000000 m/s. If we assume the safe level of acceleration, about 30 m/s2 then we can calculate the time required to accelerate to the speed given starting from rest. This comes to 1 million seconds (around 12 days).
In these 12 days it will travel a distance 15000000000 km which is 1171875 times the diameter of earth and about 100 times the orbital radius of earth around sun.
Thereafter, it goes with constant speed (but where?)
It’s nice to think deep and wide problems like this. I invite visitors to add to this discussion and take this as an opportunity to understand relativity and time travel better.