The Twin Paradox - Time Travel

Once upon a time

There lived twins Sheldon and Missy who lived pretty happily on earth. Sheldon, decides to make a trip to a distant planet (cause why not?) , which is in rest with respect to earth and come back. He boards the spaceship "Soyuz", going towards the planet in uniform velocity. When he reaches the planet, he jumps from the space ship to another "Soyuz.2" which is going towards the earth. When he reaches the earth, he jumps out and meets his sister.

Now the question.

Are they of equal age?

To keep things simple lets take this data:-

Distance between the earth and the planet = 8 Light years

Speed of Soyuz wrt earth = 0.8c

Speed of Soyuz.2 wrt earth = 0.8c

These speed are wrt Missy, who is on earth.

When Sheldon is on Soyuz, he is moving and all his clocks run slower because of time dilation (dont know what that is? CLICK HERE!).

Heart beat is the number of beats taken by heart per minute. As his heartbeat, pulse beat etc represent clocks in themselves - they too run slower.

Missy calculates that Sheldon will take 8light years/ 0.8c = 10 years to reach the planet.

But all these 10 years, time is passing slowly in on Soyuz and the clocks will read only 6 years. Hence the number of breaths taken by Sheldon corresponds only to 6 years.

Sheldon jumps onto Soyuz.2 . For the return journey too, though according to Missy it will again take another 10 years to return, according to Sheldon only 6 more years have passed.

Through the entire journey, Missy has aged by 20 years and Sheldon by 12.

This aging is in real sense, Missy will have twice the white hair than Sheldon etc.

Now this was all with respect to the sister, The paradox arises when we analyse the events from the point of view of Sheldon.

When he is in the space ship, to him the distance between earth and the planet is not exactly 8 light years. The earth and the planet are moving with repect to him and hence he is measuring contracted length. The separation is therefore 8 light years * 0.6 c = 4.8 light years only.As the planet is approaching Sheldon at 0.8c, time taken to reach = 4.8 light years / 0.8c = 6 years. According to his clock, he is jumping onto Soyuz.2 , 6 years after the journey started. After he is on Soyuz.2 both the planet and earth are moving with the same speed 0.8c according to him. Again the earth is 4.8 lightyears from the planet and is appraoching at 0.8c. So another 6 years

Now real problem arises when Sheldon tries calculating Missy's age.

The earth is going away from the Soyuz with a speed of 0.8c. According to Sheldon, the time on earth will be slower! So according to him, Missy should be aging slower than he is. The same is true during his return journey. So according to Sheldon, he calculates that only 7.2 years have passed for Missy.

He will expect to see Missy 4.8 years younger than him

THIS my dear readers, Is the PARADOX.

According to Missy, Sheldon's clocks are running slowly but according to Sheldon, it is Missy's clock which is slower.

So who is right?