Theory of Relativity and Twin Paradox; #2 Twin Paradox

<Picture 1 ; NASA's Twin Astronauts Scott and Mark>

    

   In the last post The Special Relativity, we talked about the relativity. The main idea was that all motion is relative but the speed of light is the same for all observers.

    

   According to the idea, time can be dilated when you're in the spacecraft moving very fast. In this situation, what would happen if you have a twin sister or brother? Today, we're gonna talk about the twin paradox.

    

 

 

 

1. The Reference Frame

 

<Picture 2 ; Inertial Reference Frame>

   There are three reference frames in the physics. The first one is the stationary frame. For example, you are in the stationary frame when you're on the ground. The environment around you is not moving at all. (In fact, It's not stationary because the earth is rotating but if we assume the ground is stationary it can be a stationary frame.)

    

   The second one is the frame moving at constant speed. For example, you are in this reference frame when you're in the bus moving at constant speed. These two frames are called an inertial reference frame.

    

   Meanwhile, the last one is the frame moving at inconstant speed. It is called non-inertial reference frame.

    

   Do you remember the last post? The motion in a moving bus with constant speed is the same on the ground. It was the explanation of the inertial frame. The special relativity is working on the inertial reference frame.

    

 

 

 

2. Which twin will be order?
 

    

<Picture 3 ; Twin Paradox> 

 

 

   Now, let's talk about the twin paradox. Suppose that there are a pair of twins Dick and Jane. Dick is an astronaut. He is 20 years old when he takes off on a space voyage at a speed of 0.80c to a star 20 light-years away. (c is the speed of light.)

   The equation of the time dilation is as follows.

 

   It means that to Jane, who stays behind, the pace of Dick's like is slower than hers 60%. So Dick returns after 50 years have gone by according to Jane's calendar, but to Dick the trip has taken only 30 years. Dick is therefore 50 years whereas Jane is 70 years old.

   But if we consider the situation from the point of view of Dick in the spacecraft, Jane on the earth is in motion relative to him at a speed of 0.80c. According to it, Jane should be 50 years old when the spacecrafts returns, while Dick is 70 years old. What a paradox?!

   But this two situations are not the same. Dick was not in the inertial frame because he had to change the speed of the spacecraft. However, Jane was in the inertial frame so that the special relativity could work. So, the first calculation is right.

   In conclusion, one of the twin in the spacecraft will be younger after the trip and one of the twin left on the ground will be older after the trip.

    

 

 

 

3. Kelly Twin Experiment

    

<Picture 3 : International Space Station> 

 

 

 

   One of the NASA astronauts Scott Kelly is a twin. His brother Mark is also an astronaut, now retired. In march of 2015, Scott joined a one-year mission to the international Space Station while Mark stayed at home.

    

   The ISS orbits at about 27000km/hr relative to the Earth's surface. According to the special relativity, time will pass more slowly for Scott than for his brother, to the tune of about 28 microseconds a day. But by the general relativity, time will runs slightly faster in spacecraft. But the increase is only about three microseconds a day. So, Scott will become 25 microseconds a day younger than his brother Mark.

  Anyway, the Einstein's great ideas changed the paradigm for that time. Before he explained the relativity, people didn't have a tool for understanding the fast moving things. But he changed the paradigm and it contributed to the modern science including Black Hole and Gravitational Waves.

  In the next posts, we're gonna talk about the Planck's Radiation and Quantum Mechanics. Thank you for reading it.

    

 

 

 

Bibiology

    

Arther Baiser, 2003, Concepts of Modern Physics(6th ed.), Boston : Mcgraw-Hill.

Gideon Lichfield, 2015, "Astronaut Scott Kelly will return from a year in space both older and younger than his twin brother".

Author: J. Kitchener, 2014, "NASA to Conduct Unprecedented Twin Experiment".

2016.04.23. Hankwanghee