GENERAL THEORY OF RELATIVITY

 

 

Part 1: The gravity

 For centuries, ‘Gravity’ has been the most ‘attractive’ word among the scientists and philosophers. It is the very reason for the planets to revolve around the sun as well as the objects falling towards the ground. Well, except you falling for your girl. From Aristotle to Albert Einstein, many great minds have contributed to the mankind’s understanding towards the nature of gravity. Although, Newtonian mechanics define gravity as an attraction force between masses, Einstein changed the whole way of looking into it by his revolutionary theory of general relativity. This is the first part of the general relativity series and we are going to discuss about the gravity.

 The search for the nature of gravity has appeared since the ancient times. Many ancient Greek, Indian, Islamic and European scientists proposed their own theories of gravity. However, they weren’t very significant as like as the one which Aristotle (4th century) had proposed. This guy sat on a rock and put his hand under his chin, told everyone that, a heavier object always falls faster than a lighter object. This statement was later disproved by Galileo galilei (16th century). He conducted an interesting experiment (many historians believe that it was merely a thought experiment) on the leaning tower of Pisa. He dropped two balls of same material but different masses from the top of the tower and noticed that the time of descent for the balls is same, irrespective of their masses. It proved that every object, subjected to free fall, has same acceleration towards the ground. He concluded that the gravity, which causes the objects to fall in same acceleration, is a constant force. 

Indian astronomers like Brahmagupta (7th century) and Bhaskaracharya (12th century) described gravity as an attractive force. Kepler (17th century) proposed that gravity is a force that attracts the bodies mutually. In accordance with Kepler’s laws of planetary motion, Issac Newton (17th century) discovered his laws of universal gravitation. His law states that gravity is an attractive force that acts upon the masses. The force of gravity is proportional to the product of the masses and inversely proportional to the square root of the distance between the masses. 

   Later, Henry Cavendish had proved this law by his experiment and founded the value of the proportionality constant G. Furthermore, It states that the magnitude of the force that exerted by m1 is equal to the magnitude of the force exerted by m2. Which means the gravitational force of a falling apple towards the earth is same as the gravitational force of the earth towards the apple, only the directions are opposite. It is clear that the acceleration of the apple is higher than that of the Earth because of its lesser mass. According to Newton’s second law,

 Where, a is the acceleration of the object and m is the mass of the object. We are standing on the ground because our weight is cancelled by the normal force exerted by the ground. Though, Newton’s law explains gravity well in smaller scales, it failed to incorporate with larger scales. It couldn’t give explanation to the anomalies in mercury’s orbit. Furthermore, Newton himself felt absurd by the question, how the force of gravity was carried in the vacuum space? He even mentioned this in a letter to Bently.

After 2 centuries, Albert Einstein had shown up with his revolutionary theory of general relativity to answer Newton’s question. We shall look into an example before moving into his theory. Imagine some space pirates have stolen our sun within a second. It is not possible for us to get this information for the next 8 mins, because of the constancy of speed of light. However, according to Newton’s gravitation law, as it doesn’t have any time function, we would experience the absence of gravity at the instance. It violates the special relativity theory, because nothing can move faster than light in the observable universe. So, Einstein thought that something should carry gravity in a particular speed. Eventually, He said that space itself is the reason for the presence of gravity. 

He didn’t stop his radical thought. He, further, thought a painter falling from a building. In the painter’s frame of reference, he wouldn’t experience of accelerating towards the ground, rather he would experience like floating in the space and earth is accelerated towards him.

 In another example, a person inside a rocket, which is accelerating at 9.8ms-2, would feel exactly the same gravitational pull that we all are experiencing in our daily life. It is known as equivalence principle.

 Thus, gravity is not a force, actually it is something we experience because of the acceleration of earth in the curved space. Wait, what is a curved space? Well, according to Ehrenfest paradox, consider a disc of radius ‘r’ and circumference of ‘2πr’. Put some measuring scales of length ‘l’ along the circumference. Initially, the total length of the measuring scales will be 2πr. If we rotate the disc about its center, the radius of the disc will be same, but the lengths of the measuring scales will be lesser than before because of length contraction. Due to this effect the circumference of the disc will be greater than 2πr and thus it no longer obeys Euclidean geometry. Euclidean geometry only works in the case of flat surface. As a result, an imaginary observer who stands in the center of this disc, will observe a curved surface.

 This thought experiment led Einstein to say that gravity is an effect caused by the curvature of spacetime. Wait, did I say spacetime? How could time be curved? Well, time curvature refers to time dilation. Time will slow down near the speed of light. In simple terms, higher the acceleration, lower the time ticks. It is known as the time dilation. 

Both length contraction and time dilation are the direct results of special relativity. Though general relativity looks difficult to understand, it has predicted many cosmical phenomena like black holes, gravitational lensing, gravitational waves and so on. Moreover, General relativity plays a crucial role in modern astronomy. 

We shall discuss more about the curvature of spacetime and the explanation of the formula of General relativity in the next article.

STAY TUNED…