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How does the twin paradox work? explained in detail:

Twin paradox
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Twin paradox, an important paradox of special theory of relativity states that if one of two twins travels to any nearby star with the speed of light and with almost the same speed when he comes back to the earth, he is younger than his twin brother. This is a weird and unexpected event. But, in the eyes of Science, it’s a very very interesting & reasonable event. Let’s know-how. Today askedweb will teach you how does the twin paradox works?

Twin Paradox
Twin Paradox

Back in 1905, in Einstein special theory of relativity, there are three important conclusions-

Time dilation:

Time becomes slow for an object when it has a velocity comparable to the speed of light.

Length Contraction:

Length contracts for the observer when the object gains a speed comparable to light.

Relative mass gain:

we all know that mass is a constant physical property of an object, but it’s true until it has no speed almost the same as the light. When any object runs with a velocity comparable t light, it gains its mass, and then its mass does not remain constant and it depends on its speed.

However, we have to remember that these three phenomena, i.e. special theory of relativity take place for an inertial frame of reference. Now, what is an inertial frame of reference? An inertial frame of reference is a frame of reference which is either slow or has a constant velocity. Just when it accelerates or retards, it becomes the non-inertial frame of reference and for this frame of reference special theory of relativity is not acceptable.

Twin Paradox
Twin Paradox explanation

Now, come to the point to explain Twin Paradox-

Let’s imagine two twin brothers-A & B. Again assume A for astronaut and B for businessman. At the age of 20, A becomes an astronaut and he gets a chance to go to space, where on the other hand at this age B is a successful businessman.

After spending 50 years on the earth at the age of 70 years B sees A to return back. but, looking at him, A seems to be younger than B. Asking A, B comes to know that A is 50 years old. B comes to know that A is 50 years old. B becomes astonished. He says, brother, I know, you have spent 50 years I space but did you forget you went at the age of 20 when we were of the same age. A smiled and says, no brother, I know, I have spent only 30 years in the space. B did not believe it. A starts to explain it to him. We also should listen to him.

A says that his space-ship has a velocity of 0.8c i.e. 80% of the speed of light. The speed was almost comparable to the speed of light and at this speed, he and his space-ship felt time-dilation, i.e. normal time for B became slow for A. That’s why A spent 30 years when B spent 50 years on the earth. He also showed his calculations-

t=t0/√(1-(v/c)²) equation, where t was 50 years, the time with respect to the earth frame, v was his space-ship speed=0.8c, and c is the speed of light.

However, after calculation we get t0, the time A spent with his frame of reference= 30 years.

It was very simple.

Now, you can ask, what was if we consider space-ship as rest frame. i.e. if we observe the whole event from the space-ship. The earth looks going away when A started his journey and the earth looks returning back when A was returning back.

No, you can not. You can not observe the scene from the space-ship frame, because it is not an inertial frame of reference. When it returns back it retards, then it Is a non-inertial frame.

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