The beginning of 20th century was a great time for Albert Einstein because of his excellence in Special Relativity. The whole world was appreciating him for his discovery and his laws, but there was something which made Einstein to worry. Let’s consider a simple example to explain this. Our sun which is 149,600,000 km away from us affects us a lot. We experience its gravitational field as well as we get light. Suppose our sun gets disappeared in a blink of an eye, how long would it take for us to know about it? Light takes 8 minutes to travel this distance, so according to Special Relativity it would take atleast 8 minutes for us to know. But let’s not forget that sun’s gravity holds the Earth in its orbit and sudden disappearing of sun would cause Earth to get thrown off in space. According to Newton’s Law of Gravitation, this would happen spontaneously within no time. But this contradicts Special Relativity that the information of ‘our sun getting disappeared’ has travelled faster than speed of light! To resolve this conflict, Einstein put forward the famous theory of General Relativity.
How about trying out a small experimental version of General Relativity? Have a seat in a car. Make sure you wear the seat-belts. Now suppose the car’s moving at a uniform velocity, you believe yourself to be at rest according to Special Relativity. Now suppose all of a sudden the car accelerates (either increases its speed or changes its direction); no doubt you will feel it. Suppose the car boosts its speed without changing the direction, because of inertia you will be pushed back on seat. If the car changes its direction without affecting its speed you will lean in a tangential way (if car turns left, you will lean right and if it turns right you will lean left). If the car changes its speed as well as direction you will feel both situations; which is risky. In short, acceleration generates a force which says “You are subjected to a force and hence you are not stationary!” This key understanding is one of the most important logic you need to understand General Relativity.
Let’s assign a job for our old known friend George. This time he is confined in a box and he has no way of looking out and predicting what’s in motion relative to what. Let that box be at rest on Earth. We ask George to drop a ball inside the box. No doubt, he will observe the ball to fall because of Gravity of Earth. George concludes “Since the ball is attracted downwards at a same rate as Earth attracts, I must be at rest on Earth.” Now let’s conduct this experiment in a weird sense. We shall now take that confined box along with George at a height of 35,000 feet (6.63 miles) above the Earth’s surface and drop this box. George and the ball are in a free-fall and hence he would measure gravity to be zero. George states “Since the ball which I dropped is suspended in air and since I am feeling weightlessness, I must either be in outer space away from any planet or I must be in free-fall.”
Since George has no way of looking outside, he can’t tell us about his state of motion in both cases. He has to predict his state of motion with the help of dropping ball. This experiment was pretty simple to imagine because it doesn’t involves any kind of acceleration done by the box. But, what if the box in the second case is accelerated?
Let’s perform a similar kind of experiment but this time we take the box in outer space. When the box is in rest the ball dropped by George would keep floating forever and it’s pretty obvious to imagine this because there is no gravity. When the box is in uniform motion, the system (George, ball and box) is in velocity. So if George drops the ball at any given time, the ball would gain the same velocity as that of ship. A distant observer would see the ball to have a uniform velocity equal to that of box but George would see the ball floating.
But complications arise when we make the box to accelerate! When the box accelerates, its speed constantly goes on increasing. Since its speed is increasing with increasing time, the distance covered by the box is also increasing. But the ball is not accelerating. The ball dropped at a given time would exhibit the motion at that time, but not of changing velocity or acceleration as that of box.
To understand this, let the box accelerate at 5m/s2; i.e. after each successive tick of a second by a clock, the speed increases by 5m/s. Let’s say the speed of the box at a given time is 5m/s. At that moment, George drops the ball. Since the system (the ball, George and box) was in motion, the dropped ball will have a motion of 5m/s. But the box is accelerating; the speed before and after any given time will not be the same.
This causes the ball to drop down on the floor. Since the ball falls down, George thinks that he is on a planet with gravitational acceleration of 5m/s2. What if the box accelerates at 9.8m/s2 (acceleration due to gravity of Earth)? If it does so, then the ball would get attracted on the floor at the rate of 9.8m/s2. Hence it would be impossible for George to know about his state; whether he is accelerating or is at rest on Earth! This is the central theme of General Relativity; Acceleration causes Gravity.
But there is some extra-ordinary behaviour of light! When George shines a beam of light from one end of the box to other under uniform velocity, there is nothing abnormal behaviour. Since the photons of the light experience no acceleration, the light goes straight to the other end.
When you look closely at this figure, you may compare it with figure 2. Under uniform velocity, the point P (point at which light hits other end of the box) is just shifted vertically. To a distant observer, the beam of light has covered some distance but not for George. For our volunteer George light travels straight.
Now suppose all of a sudden the box accelerates. This causes abnormal behaviour of light. Since light from George’s laser shoots at that moment when the speed of box is say 5 m/s, when the light would hit the other end of the box, the speed of box would have been 10 m/s and it would have covered some distance when the beam was on its way!
Just like in figure 3 where the ball was attracted on the floor, light also gets attracted downwards causing the path to be curved. Although for acceleration like 5 m/s2 this bending of light is negligible, but if the acceleration is large enough, one can notice this effect. Thus one can conclude that acceleration causes the light ray to bend. But acceleration produces gravity! Thus the final statement is: Gravity causes light to follow a curve path. This is true for all bodies having mass. Even our Earth curves the path of light rays inwards which are coming from distant star. Greater the mass of the body, greater is the curvature of light. Our sun bends the light of a distant star at a greater curvature as compared to Earth. What if the mass of the body is so massive that even light can’t escape? That’s the theory of black holes! Black holes have so massive mass that light is curved so inward that it lands on the surface of black hole. Thus no light can escape the gravity of black hole.
But it’s a bit difficult to construct a model of Space where the straight moving light rays suddenly gets curved in the vicinity of Gravitational field. It’s difficult only if we see space (space-time to be precise) as just empty stretch of nothingness. What if I say our Space-time is like a piece of fabric? A fabric of cosmos; a stretched cloth which explains the workings of the Universe. Yes it’s true. Space-time is like a vast spread sheet of cloth like fabric. When there is absence of mass or energy this fabric is pretty smooth and flat; but when there is a presence of mass or energy it curves the surrounding space-time. To demonstrate this imagination, take a big piece of a cloth (most preferably a rubber spread-sheet) and just stretch it tightly from all the corners. Since it is being stretched easily, the fabric is nice and flat. Now place a heavy object (baseball, golf ball or cricket ball) right in the centre. Observe the curvature of this fabric. There is a depression seen in this fabric. Now take a small ball with less mass (ball bearing) and just leave this object in this curved fabric. You will notice that this small ball actually follows an elliptical orbit before hitting the big ball; just like a meteor hitting any planet. Thus it can be concluded that the big ball curves space-time fabric causing the small ball to attract towards itself. It forces this small ball to follow an elliptical orbit before hitting, just like gravity does in functioning of our Universe. Thus Mass and energy distorts Space-Time fabric giving rise to Gravity.
What about the orbital motion of planets like Earth around Sun? Recall the 5th figure. Although George shoots the beam of light straight, it goes curved. That’s wholly because of gravitational effect. Similarly, Earth and other planets follow a straight path but because of Sun’s gravity it appears to be elliptical or curved. Not only they follow straight path but they follow least energy path. It’s that orbit where planets require no special energy to accelerate. Thus this is the reason why planets don’t fall on sun! Think it in a geometrical way; take a flat paper and draw a straight line on it. Now curve this paper in a spherical way, just like a sphere (although it’s tough but just imagine). Now the straight line no-longer seems straight but rather it looks like ‘curved’. This is the effect of curved space on a straight line motion. Let’s get back to the question which launched General Relativity. ‘If sun disappears, how we would come to know about this? Would light inform us or gravity?’ The answer is “both.” Solving mathematics of General Relativity one comes to the point that light and gravity travels at a same speed. No matter how big or small that object is, gravity travels with light. Thus preventing Special Relativity being violated.
Einstein’s General Relativity was a biggest clue for humans about how our Universe works. It framed the idea of space-time and cosmos for beings like us. Today GPS satellites and space exploration projects use General Relativity. Without this, we would have been absolutely nothing.