The 17th century science witnessed one of the greatest revolutions for mankind. This revolution was carried out by well known physicist Isaac Newton by proposing the theory of gravity and the laws of motion. These theories were so beautifully explained that no one ever questioned it. But in the end of 19th century, Maxwell’s theory of electromagnetism felt the need to challenge Newton’s well known theory. Newton said that if one can run fast enough, he can catch up with light particles and can run as fast as speed of light. But Maxwell’s theory says that light travel at an enormous speed and one cannot go beyond this limit. Both the theories were accurate but they were mutually incompatible with each other. To resolve this conflict a young clerk at the patent office stepped in giving the humankind the clear idea of our Universe. He was none other than Albert Einstein.
To learn Special Relativity from the roots, we need to clear some basic concepts. Imagine you are in a car and the windows of the car are blocked so that you cannot see what’s going outside. If the car rides with a uniform velocity on the smoothest road with no bumps; it’s hard for you predict your state i.e. you cannot say whether you are at rest or at motion. Now suppose we open the window, you will see trees and buildings passing and you can say that there is motion. But who’s in motion? A distant observer waiting for bus at the bus-stop will say that you are in motion. You can argue that the whole world is moving but you are stationary; no one’s wrong. The reality depends on who is the observer.
Special Relativity is based on following fundamental phenomena:
- Time dilation
- Speed of light
- Length contraction
- Mass-energy equivalence
Time Dilation: Time for an observer in motion slows down with respect to a stationary observer.
Let’s see what this statement means.
Let’s construct a light clock. It can be done by placing two mirrors above one another facing each other. A single photon is placed between the two mirrors and made to move up and down. Because of the mirrors the photon will keep on oscillating up and down and up and down. Let’s take two volunteers for this experiment; George and Caroline. George is standing on the upper mirror and thus in this case George is the part of the system (system in this case are the two mirrors, a photon and George). Caroline is standing at a distant point. Initially the system is at rest.
As shown in the diagram above, Caroline will initially see the system to be stationary (upper part of the diagram). The photon covers a distance of GF in one second (although the photon will make billions of oscillation in one second, let’s consider it takes one second to complete one oscillation for the sake of simpler calculations). Both George and Caroline will agree on the point that the photon takes one second to complete one oscillation. Now let’s set the system as well as George in motion. Since system is in motion, the photon will follow a zigzag path. The up and down motion of the photon is shared by its motion towards the left. But let’s not forget that this condition is true as per Caroline’s view (since she is stationary). George in motion along with the system will see himself as well as the system to be in rest and the whole world in motion. He will not agree that light follows a zigzag path but instead it follows just up and down motion. Let’s have some calculations:
In a stationary system, Caroline and George both agree that photon covers a distance of G to F and again back to G in 1 second. That is a distance of GF in half a second.
When the system is in motion, Caroline will see oscillation of photon from F to H to J (photon will hit the bottom mirror). Surely the distance of F to H is greater than F to G and in Caroline’s watch the time required for the photon to go from F to H will be greater than half a second.
What about George’s perspective? Since he will see the system to be stationary, he won’t agree on zigzag path rather he would rely on up and down path of photon i.e. from F to G and he would measure half second time period for it.
Wait! If both Caroline and George observe same event at same time; how can their measurement of time differ? It seems that George’s clock runs slower and that of Caroline runs faster! The reason is because of George’s motion. If George is having a motion of 3 x 108 m/s, there would be zero time passing for him! This is the concept of Time-Dilation.
Speed of light: Speed of light for all observers is same regardless of their state of motion.
This revolutionary statement brings you to the heart of Special Relativity.
Let’s appoint Caroline and George to carry out a simple experiment.
Let George be the stationary observer in this case and let Caroline be travelling on a train whose speed is 50% the speed of light. Let’s give both George and Caroline a powerful laser which emits a monochromatic light (light with certain frequency). When George shoots the laser, he will measure the speed of light to be 3 x 108 m/s. Since he is stationary there is no doubt of this absolute speed. Since Caroline is in motion with the system (system in this case is referred to train travelling with 50% speed of light), for her the whole world is in motion but herself and the train to be at rest. When she measures the speed of light emitted by her laser, it’s obvious that she will find it to be 3 x 108 m/s. But there is a twist when George measures the speed of light from Caroline’s laser.
You may think that the speed of light would be greater than usual speed just because the speed of light and speed of train gets summed up. If so then you are wrong, but not completely.
Your way of thinking is in the sense half. The resultant speed of light is the addition of speed of light and speed of train but let’s not forget time-dilation! Since speed of train is half the speed of light, the clock of Caroline would run 50% slower as compared to clock owned by George. Caroline and photons from her laser both are experiencing slow flow of time. Since the time for photon gets slowed down by 50%, their speed gets slowed down by 50%. But Caroline’s travelling on the train which has a top speed of 50%speed of light! The fast speed of train and the slow speed of photons (because of time-dilation) exactly cancel out leaving a fixed constant i.e. speed of light which is 3 x 108 m/s. Thus, no matter what’s the state of motion of George, he will measure the speed of light by Caroline’s laser to be constant.
Length Contraction: If any object posses motion, its length gets contracted.
This statement can be proved true with the help of the following example.
Let’s appoint George to be head chief of army troops going for an inter-galactic war. Let Caroline be a stationary observer on a planet. There are 3 space-ships moving in a linear direction with uniform velocity, one behind the other. George is present on the second, i.e. between two space ships. Since George is in motion along with his and other two space ships, for himself he is in rest and the whole Universe is in motion. He is the part of the system which includes the three space-ships. Initially the system is normal as their velocity is uniform. George commands the two space-ships “As soon as you receive this signal, boost your engines and we all shall accelerate uniformly.” Since the two ships before and after him are stationary (for him), when he sends the signals in the form of light the two space-ships receive it at the same time and all three of them accelerate uniformly keeping the distance between the three ships to be constant. But what about Caroline’s perspective? Since she is stationary on a planet, she would observe the three ships to be in motion. She would see the distance between those three to be constant but she would spot an error when the ships accelerate.
As shown in the above figure, the ship C is moving towards the signal i.e. towards ship B and ship A is moving away from the signal i.e. away from ship B. When ship B gives out signal, ship C captures it very quickly and it is the first to accelerate. But when ship B releases signal, it takes time for ship A to capture it and it is last to accelerate. Since ship C accelerates first and ship A accelerates last, the distance between the starting tip of ship A to the tail of ship C gets reduced! Or we can say that the whole system is contracted on acceleration as per Caroline’s view. But for George, nothing’s change and he is ready to battle.
This is the unique phenomena of Length contraction.
Mass-energy equivalence: Mass is a form of condensed energy. We can turn mass into energy or vice-versa.
George is travelling in a space-ship having 50% speed of light. On the other hand Caroline is moving in a space-ship with hardly any speed noticeable. Let’s consider that George’s ship is just flowing above Caroline’s ship. At a perfect timing if George throws a ball towards Caroline’s ship, the ball will get bounced and if George maintains his speed, there’s a possibility that he may catch it. The view for George in this case is similar, i.e. for him he is a rest and the whole Universe around him is in motion. He will see no special problem when he throws the ball, it gets bounced back and he catches it. But Caroline would spot an error! Since George is moving at 50% speed of light, because of time dilation she would see the movements inside or on the ship to happen slowly, even with the ball. The speed, the bouncing and his catching of ball would appear to be slowed; as if the ball is having a huge mass! If the speed of George’s ship increases, the ball would appear to slow down and as if the ball has gained more mass.
Let’s think it in a different way. George needs huge amount of energy to boost his ship to 50% speed of light. This huge amount of energy gets compensated with mass. Greater the applied energy (greater will be the amount by which ship increases its velocity) greater will be the mass. Or in other words, we can convert energy to mass or vice-versa. How can we transform mass to energy? One of the greatest examples is ‘Nuclear fission bombs’. In this, the mass is transformed to an enormous amount of energy.
This is Einstein’s theory of Special Relativity. This theory rocked the world and gave humans the most important element; reality of nature!