Theory of Relativity and Twin Paradox; #1 The Special Relativity

 

 

<Picture 1 ; Albert Einstien>

 

  In the last post, we talked about the Big Bang Theory and its proof. The first evidence was the Doppler effect and the second one was Cosmic Background Radiation.

  In a following series of post, I'm gonna tell you the basic knowledge of relativity and the Twin Paradox. Today's topic is the Einstein's theory of Special Relativity.

 

1. Galileo's Relativity

<Picture 2 ; The ball's motion in a moving bus>

   In fact, the relativity is a familiar concept in our life. For example, we take a bus everyday. If you throw a ball upwards in a moving bus, the ball will be fallen on your hands not behind your hands. The movements in a moving bus are exactly same as the movements on the ground.

   In a bus travelling at a constant speed, all motion is exactly same as on the ground. So if you don't look outside, you will never know whether the bus is moving or not. This is the relativity. All motions are relative.

2. Einstein's Imagination

<Picture 3 ; The possibility of seeing my face with mirror>

  When Einstein was young, he wondered whether he would be able to see his face in a mirror if he was sitting in a train travelling constantly at the speed of light. It's not just a simple question. If you want to see your face in a mirror, the light reflected from your face has to go to the mirror and be reflected to your eyes (of course with the speed of light). But if the train travels with the speed of light, the light will never touch the mirror because it constantly fade away with the speed of light. Then you will never see your face in the train.

  The problem is that you will be able to know whether the train is moving or not without looking outside if you have a mirror. It's different from the bus' case. It's braking the law of relativity.
  
  However, he found that it was wrong. The speed of light is the same in all frames. So, in the train, you can see your face with a mirror because the speed of light is constant regardless of the frames. Now, the Einstein's theory can be simplified to a sentence.

  All motion is relative but the speed of light in free space is the same for all observers.

  

3. Time dilation

   This simple idea can change our whole concepts of time. Not only the measurement of motions but also time intervals can be affected by relative motion between an observer and what is observed. As a result, a clock that moves with respect to an observer ticks more slowly than it does without such motion. This effect is called time dilation(to dilate is to become larger).

 

<Picture 4 ; Clock on the grounds>

  Suppose there is a clock shown in the Picture 4. In the clock, a pulse of light is reflected back and forth between mirrors L apart during t0. So, on the ground, the equation is as follows because 'time=distance/velocity.'

  (t0 is the time at the ground and c is the speed of light.)

<Picture 5 ; Clock in the spacecraft>

   

   Meanwhile, if someone in the spacecraft travels with the same clock, the formular will be as follows.

  t is the time of the clock moving with spacecraft in terms of the ground.

   Because the quantity is

always smaller than 1 for a moving object, t is

always greater than t0. So, the moving clock in the spacecraft appears to tick at a slower rate than the stationary one on the ground, as seen by an observer on the ground.

4. Conclusion

 

<Picture 6 ; Twin Paradox?>

   For a man in a moving spacecraft, time goes slowly. Is it possible? And Does it mean he can be younger if he travel with the spacecraft? And If he has a twin sister left on the earth, what will happen to his sister? In the next post, I'm gonna talk about the Twin Paradox. Thank you for reading it.

Bibiology

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

2016.04.17 Hankwanghee