What is the twin paradox?

twin paradox

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The story of a paradox

twin paradox

There were two scientists of the same age, named Arun and Bob. Bob decided to go for a space journey to reach the closest star, about 5 light-years away from the earth. On the other hand, Arun decided to stay on earth.

They both decided to observe each other from their respective reference frames. The spacecraft accelerated to a velocity of 0.6c. After a certain period, when Bob reached the earth, Arun claimed that Bob is younger than him. Bob didn’t agree to this and claimed that Arun should be younger than him.

“Why are these two observations different?” Let us understand the two different observations made by them. The reason behind this is the different reference frames. 

Arun, who stayed on the earth, considered himself at rest. Bob was the one who’s moving. According to him, Bob reached the star in five years and returned to the earth in another five years. Therefore, Bob completed his space journey in ten years.

Bob, who was the traveler, considered himself to be at rest throughout the journey. According to him, the earth took four years to move away from him, and it took another four years to reach him. He also observed that Arun got affected by the length contraction, which made his journey slower.

This whole argument of the reference frame is called the twin paradox.

 

Is it a paradox? Any statement or observation that contradicts the laws and fundamentals, but they are correct, is known as the paradox. Well, the twin paradox is not a paradox as it is not contradictory now. It can be explained well by physics laws.

Another question that comes up with this case is, “who is right?” The answer is both of them. It is all about the reference frame they have chosen.

Scientist Max Von Laue, in 1913, demonstrated that the traveling between two reference frames is enough for the explanation of the paradox. Before him, Paul Langevin introduced and resolved paradox in 1911, where he described that the acceleration is the correct explanation. 

However, Max Bon & Einstein said that the difference in the aging of the two is because of the gravitational time dilation, which comes as the direct effect of the acceleration. Now, the studies have shown that these two are not absolute explanations, instead, the biological factors and the changes in the human body also affect the aging of the space traveler.

 

The solution to the paradox

They both had a correct point of view in their reference frames. They both can’t disagree with each other. Therefore, to find a possible solution, they decided to make a space-time diagram of the signals they sent to each other throughout the space journey in their respective frames.

twin paradox

Arun’s Frame of Reference

Arun considered the reference frame of the earth, which means, he considered himself at rest. In the left diagram, the time journey of both Arun and Bob shown in Arun’s reference frame. The first signal sent by Bob in the first year of his journey has received by Arun. According to Arun, two years have been passed at that time. Similarly, He received the second signal in the fourth year. But for Bob, only two years have passed. 

The grey line shows that Bob has reached the star. According to Arun, Bob has taken five years to reach there. But Bob took four years to reach there in Arun’s reference frame. At the time of returning, the signal sent by Bob has reached faster than the previous ones. In this way, Arun concluded that Bob reached the earth after ten years in his clock while for Bob, it was eight years. Therefore, Bob must be younger than him. 

 

Bob’s Frame of Reference

In the right diagram, the time journey of both Arun and Bob shown in Bob’s reference frame. The first signal sent by Arun in the first year of the journey has received by Bob. According to Bob, two years have been passed at that time. Similarly, He received the second signal in the fourth year. But for Arun, only two years have passed. 

The grey line shows that Bob has reached the star. According to Arun, Bob has taken three years to reach there. But Bob took four years to reach there in Bob’s reference frame. At the time of returning, the signal sent by Bob has reached faster than the previous ones. In this way, Bob also concluded that Bob reached the earth after eight years in his clock while for Arun, it was ten years. Therefore, Bob must be younger than him. 

So, they both confirmed that Bob is younger than Arun. The physics followed by them to solve the paradox is known as the relativity of simultaneity.

NASA’s real twin experiment

Thinking of space travel and the twin paradox, in 2013, NASA decided to perform a series of tests on the twin astronauts, Scott Kelly & Mark Kelly. In 2015-16, Scott Kelly sent for a 342-days tour at International Space Station while Mark Kelly (retired astronaut) stayed at the earth for observing his brother. 

twin astronauts

In an interview, they were asked about their experiences, so one of the questions was – “Whether Scott younger than Mark when he returned to the earth?” – Well, the ISS is traveling 7.66 km/s, much less than the speed of light. So, the slowing down of time was so minimal that the age difference was calculated to be of a few milliseconds. 

The study of the genes of the twin showed the biological changes, which slows down the aging process. The length of  Telomere (present at the end of the chromosomes) is longer in Scott’s DNA. Actually, the telomere is the indication of the aging of a person, it gets shorter by age. 

The rate of shortening depends upon some of the factors such as food & nutrition, oxidative stress, physical & psychological fitness, and environmental exposures such as air & radiations. So, the space environment increases the length of telomere, which reduces the aging process. 

This biological change in the chromosomal telomere indicates that the space traveler is younger than the one who stayed at the earth. However, if they approach the higher speeds to travel far in the space, the aging would be slower. 

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