Special Relativity for beginners

Physics

 

In 1905, When Einstein published his Theory of Special Relativity, many believed his ideas were insane. Indeed, it was insane but true. If it were not for these crazy people, we wouldn’t have progressed much in science. Einstein with his theory changed the way we think about our world.  Nature behaves in the way unimaginable. It was Einstein’s genius and his courage to defy establishment that the theory of relativity came in to existence

 

Before we start Special Theory of Relativity, we must know what we mean by a frame of reference. Let us suppose, I am standing at my Hostel gate and happen to measure the distance from my Hostel to college with a device. Let the distance I measure be 200 meters. Then I would say “According to my frame of reference the distance to the college is 200 meters”. In this case my Hostel serves as the origin. Similarly, another person named Samvedana measures the distance to the college standing at a bus stop and finds it to be 100 meters. Then we would say “According to Samvedana’s frame of reference the distance to the college is 100 meters where the origin in this case is the bus stop”. It is more of an observer’s perspective kind of thing.

 

I can ask Samvedana to walk towards me with a speed of 5 km/hr. Then I would say, Samvedana’s reference frame is walking at 5 km/hr towards my reference frame.  Now if Samvedana walks with a constant speed of 5km/hr throughout   her journey, without changing her direction then I would call her frame to be an “inertial” one.  Simply putting Inertial frames are non- accelerating frame. Here, by “frame of reference”, we would only refer to “Inertial frames”.  We won’t dig deep into the meaning of reference frame. For us this should suffice.

 

 

We are now equipped to start learning Special Theory of Relativity very roughly. I mean it.

Einstein’s Special Theory of Relativity revolves round the nature of time and the speed of light. Two of the postulates of this theory are

  • There is no preferred inertial frame of reference i.e. Laws of physics are same for each observer in inertial frame.
  • The speed of light has a fixed constant value in every inertial frame.

Let me explain them one by one

First Postulate

It tells us that whether it be for Me or Samvedana , the laws of physics will remain same . For example we know from Newton’s law of motion that “Force = Mass * Acceleration”. Then this formula will always remain in the same form for Samvedana as well as for me.

Second Postulate

This is a bit tricky one. Let us first do a simple high school velocity addition problem. Say, Samvedana is walking towards me with a speed of 5 km/hr and has a tennis ball in one of her hand. When I measure the speed of the    ball, I would find it to be 5 km/hr, same as that of Samvedana’s walking speed but for Samvedana, the ball is always in her hand  i.e. the ball is not moving . Hence she would measure the ball’s speed to be 0 km/hr i.e. at rest. Now, While Samvedana is still walking, I ask her to throw the ball at me. Samvedana throws the ball and measures its speed. She finds the speed of the ball to be 30 km/hr. When the ball is travelling towards me, I too measure its speed but I find the speed of the ball to be 35 km/hr. This was expected as Samvedana was walking, her walking speed was added to the ball’s speed and we know 30 km/hr+ 5 km/hr =35 km/hr.  That’s what we learned at school. The velocity gets added.

Now we can understand second postulate. For this let us now put a torch light in the hand of Samvedana instead of a tennis ball. I ask Samvedana to turn on the torch light while she is still walking .She measures the speed of light and she finds it to be 3 lakh Km/hr. Now  I measure the speed of the same light emitting from Samvedana’s torch  .Then using the same logic as used before in the above paragraph while solving high school problem, we should expect the result to be 3 lakh Km/hr + 5 km/hr = 3 lakh and 5 Km/hr . But this is not what happens.  Instead I get the same value for speed of light as Samvedana i.e. 3 lakh Km/hr, no matter how fast Samvedana is walking.  Therefore the postulate: the speed of light is frame independent. Sounds weird? That is what makes it more lovable.

Let’s talk about some of its consequences. Just don’t panic. Keep calm and read.

  1. Length Contraction
  2. Time Dilation
  3. Relativity of simultaneity
  4. Equivalence of mass and energy

These consequences are noticeable only at very high speed. For low speed Newton’s mechanic is sufficiently accurate.

Let us break them one by one

1). Length Contraction:

To explain this, we will have to bring back Samvedana . Say, Samvedana is at rest and is holding a rod. She then measures its length and finds it to be 1 metre. Now I measure its length and would find it to be the same i.e. 1 metre. No surprise there but now suppose Samvedana starts running holding rod in her hand with a speed of 0.5 times the speed of light. We repeat the measurements.  When Samvedana measures the length of the rod it’s still 1 meter. But when I measure its length, I find it to be less than 1 metre. That is length contraction. This implies length of objects gets contracted along the direction of motion.  As a matter of fact, Samvedana would also shrink a bit in my frame.

2.) Time Dilation

Let us get straight to the example.  Suppose Samvedana and I both have a big clock which reads the same time when we both are at rest i.e. when Samvedana is not moving. Now  Samvedana  carries that big clock along and starts running very fast (near the speed of light) . Then I would see that Samvedana’s clock is running very slow compared to mine.  Suppose Samvedana starts running at 10 a.m. After an hour, I ask Samvedana to stop running. My clock would then show 11 a.m. whereas Samvedana’s clock would show somewhere between 10 a.m. and 11 a.m. For Samvedana the time runs at normal speed. It is only when we compare a moving frame to another stationary frame we notice the difference.  This what time dilation is; Time slows down for moving frame.

3.) Relativity of Simultaneity

Suppose Samvedana is at rest and she is standing on the road joining two cities, Sabaila and Janakpur. Sabaila is near to her than Janakpur .She then hears two explosions, first from sabaila and then from Janakpur . She uses the speed of sound and the distance formula to calculate the time at which the explosions took place. She finds that even though she heard the explosions at different time they took place at the same time. Let the explosions took place at 9 a.m. Since she was nearer to sabaila and sound travels at some finite speed, she heard the explosion from sabaila first and then from Janakpur. Now say, I am also standing on the road connecting sabaila and Janakpur. But I am closer to Janakpur than Sabaila. I would hear the Janakpur’s explosion first and then from Sabaila. I then calculate the time of explosion at these two cities .But again the time of explosion would be same as found by Samvedana i.e. 9a.m. Therefore, I would say “When I and Samvedana were relatively at rest the explosions took simultaneously”. i.e Explosions took place at the same time .  Now, if Samvedana starts running very fast on the road and then calculates the time of explosions in  Sabaila and Janakpur  , she would find that one explosion took place after another . i.e For her,  In Sabaila it might be at 9 a.m and 9:15 a.m in Janakpur . Explosions are not simultaneous for Samvedana but for me, since I am not moving, the explosions will still be simultaneous as before. Hence we say that “two frame may not necessarily agree on the simultaneity of an event”. This is what we refer to as relativity of simultaneity.

 

 

 

4.) Equivalence of mass and energy

This is perhaps the most famous consequences of all. E = MC2  ,  is not something anyone hasn’t seen. This says that mass is equivalent to energy and related by the above formula.  This lead to the development of nuclear bombs and those monstrous bombs proves how much energy we have got even in a tiny chunk of matter. We also see its numerous applications in particle physics where particle turns in to energy and vice-versa.

Though we have many other consequences of Special Relativity, we have discussed most important ones. In this article, I have only scratched the surface of this theory but if anyone wants to master Special Relativity, they need to be fully acquainted with electromagnetism, tensors and linear algebra.   Special Relativity revolutionized physics and has stood the test of time. Though we never know when Einstein might be proven wrong, we continue to enjoy his view and most importantly his theories.

This article was first published on April 28, 2018 but due to some technical issue it has been republished

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Surya Kiran Yadav

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Last modified: July 18, 2019

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Special Relativity for beginners

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