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Essay on the Twin Paradox

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AN ESSAY ON THE TWIN PARADOX
Nwokolo Peter Chidiebere (Nig) pchidiebere@aims.ac.tz April 24, 2016
According to special relativity, time travel into the future is possible. In science fictions, we have time machines which allow us to go anywhere we want either into the past or the future.
But in reality, as far as we know only time travel into the future is possible and it works like this. Imagine we have two identical twins Peter and Paul. Peter gets into a rocket and travels to a star ten light years away. A light year is the distance light travels in one year which is approximately 9.4607 × 1012 km (Crockett, 2013). He moves at 80% the speed of light. When he gets to the star, he turns around and comes back at the same speed. Twenty-five years would have elapsed on earth but only fifteen years for the traveller. When he gets out from the spaceship, he is surprised to see that his identical twin is aged an extra ten years.
Theoretically, if you can get your rocket going near the speed of light and you went as far as one of the galaxies and came back, millions of years would have elapsed on earth, yet the trip might only take you a few weeks. This is because of the assertion in special relativity which says that moving clocks run slow. And that is a great way to remember how things are different between two frames of reference. Vaguely speaking, frame of reference means the world according to you or according to me (Lincoln, 2014). But we have to know that it works both ways. Imagine if I zoom past you in a car. From your point of view, you are standing still and I am doing the moving. So you observe that my clock is running slow. But from my point of view my clock is not running slow. In fact, I am not moving. you are moving past me on the road. I notice that your time is running slow and this is also correct. This has been confirmed with so many experimental evidence and understanding this we can now explain what is the twin paradox.
According to the explanation above each twin should see the other’s clock as running slow
So, why is it that when the trip is over, Paul is ten years older than Peter? One standard explanation is that the symmetry was broken. Peter experiences some forces that speed up, that do the turn around and that slow down the spaceship. Paul never experienced those forces. If things are different, why is it Paul that ages faster? Why is it not the other way around? To make things more complicated, it is concluded that the forces broke the symmetry.
In general relativity, it asserted that accelerating clocks run slow (stackexchange, 2015). But you can have the same acceleration for short trips as for a long trip. The long trip just add more distance. And the way we calculated the age difference between the twins, we only need to know the speed and the distance travelled. In special relativity, we ignore the acceleration and assume that the rocket can change speed instantly. We are only interested in the effects of special relativity. This is the concept that explains the twin paradox (wikipedia, 2015). If each twin would send out a radio signal every second and we count how many signal each one would receive. On departure of the rocket, each twin would receive each other’s signal at the same lowered frequency that is, less than once per second because each other’s clock is running slow. When the Peter gets to the star and does a turn around, at this time he is now getting signals faster than once per second. Meanwhile, Paul continues to get low frequency signals
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for ten more years. After everything is done, we calculate how many signals each one got from the other. Both twins agree that Paul ages the extra ten years. What if we look at it from the rocket’s point of view? That is, it was Paul who is on earth that went out and came back.
And it would be Peter who aged extra ten years. But Peter did a turn around and at the time, they were all these signals spread out in space between the two points going in both directions.
If Peter had stopped transmitting after the turn around, he will continue to get signals for ten more years and they will all be at lowered frequency because they were all transmitted while the rocket was moving away. On the other hand, Peter notices that the signal frequency goes up right away because he just turned around and he is going back into the signals. This explains the twin paradox.
This paradox (in a different form) was first presented in 1911 by Paul Langevin, in which the emphasis stressed the idea that the acceleration itself was the key element that caused the distinction. In Langevin’s view, acceleration therefore had an absolute meaning. In 1913, though, Max von Laue demonstrated that the two frames of reference alone are enough to explain the distinction, without having to account for the acceleration itself (Jones, 2014).
The twin paradox is an important and interesting first step into understanding the nonintuitive world of special relativity (Lincoln, 2014).

References
C. Crockett. A light year. earthsky.org/space/what-is-a-light-year, 2013. [Online; accessed 29-February-2016].
A. Z. Jones.
The twin paradox. http://physics.about.com/od/timetravel/f/ twinparadox.htm, 2014. [Online; accessed 29-February-2016].
D. Lincoln. The twin paradox. http://www.symmetrymagazine.org/article/may-2014/ the-twin-paradox, 2014. [Online; accessed 29-February-2016]. stackexchange. Time in accelerating body. physics.stackexchange.com/questions/112645/ which-clock-is-the-fastest-inside-an-accelerating-body, 2015. [Online; accessed
29-February-2016].
wikipedia. . http://en.wikipedia.org/wiki/Special_relativity, 2015. [Online; accessed
29-February-2016].

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