Gravitation

 Let’s start with a famous story in science…

                Newton was sitting under an apple tree investigating the nature of force which makes moon go around the earth. All at a sudden an apple fell from the tree and this raised a question in Newton's mind ‘what made the apple fall down and not go up?’ This gave rise to a very important concept in physics called Gravitation.

                Now let’s discuss what Newton said about Gravity. Two bodies in this universe attract each other with a force which is directly proportional to the product of mass of both the objects and inversely proportional to the square of distance between them. Let’s put it in an equation:

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What’s that ‘G’? G is gravitational constant which is 6.67 x 10-11 Nm² kg^-2.

                Now let’s think about a situation. All at a sudden sun disappears! Sounds stupid isn’t it? As per Newton the planets will immediately start moving tangential to its orbit. This is because gravitational field will disappear and planets, which rotates around the sun due force of gravity, will be free to move and hence will move tangential.

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                However Einstein disagreed with this. As per Einstein the fastest possible speed in our universe is that light (which is approximately 3 x 10⁸ ms^-1) and is the same for everyone. Let's say there are two person, one at rest while the other one travelling at a very high speed with respect to the first person. Both of them will measure the speed of light as 3 x 10⁸ ms^-1 as it is not relative to the observer. Let’s call it cosmic speed limit. Even speed of gravity is slower than that light.

                We all know that it takes 8 min for light from sun to reach our earth.  Then we can say that gravity from sun take more than 8 min to reach earth. Then how will earth start moving tangentially immediately? So even if sun disappears the earth will be moving in its orbit for more than 8 min.

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                Einstein said that heavy objects such as planets and stars caused curve in space-time, considering space-time like a trampoline. Now let’s take the curve caused by our sun in the fabric of space-time. Planets follow the path formed by the curve caused by the sun.

                Now look at what will happen if sun suddenly disappears, with the new understanding of gravity proposed by Einstein. If sun disappears, the gravitational disturbance caused by this incident will form a wave, similar to that of ripple in a lake when a pebble is dropped in it. When this gravitational wave passes the earth we will find a sudden change is our orbit and only then the planet will start moving tangential to the orbit.

Spacetime

Space-time is defined as a mathematical model in which space and time are interwoven into one single continuum. The space-time of our universe in interpreted to that of a Euclidean space, with 4 dimensions, space consisting of 3-dimensions and time is taken as the fourth dimension. A unique position in a unique time in a space-time is defined as an event. Event is the basic concept of space-time.

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          All of us are familiar with the concept of planes i.e. 2-D plane, 3-D plane etc. A point in a 2-D plane is denoted as (x,y) and that in a 3-D plane is given as (x,y,z). Here x, y and z can be identified as the unique distance between the point and x-axis for x, y-axis for y and z-axis for z.

          An event in space-time can also be defined similarly as (x,y,z,t),  x, y and z here refers to the unique position of the point in the space while t denotes the unique time of the event. This way the coordinates specify where and when event occur. However the question which arises now is why do we need to include time and make it complex?

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          In classical mechanics, the non-relativistic model, time is considered as an independent and is treated as universal with constant passage irrespective of the motion of the observer. However in relativistic model, time is considered to be inseparable from the three dimensions of space as it has been noticed that time slows at higher speeds of a reference frame with respect to another reference frame. This phenomenon is referred as time dilation.

          However the number of dimensions required for analyzing our universe is a question among scientists. Speculative string theory predicts the number of dimensions to be 10 or 26, with M-theory predicting 11 dimensions, 10- spatial and 1- temporal). The widely accepted model is that of 3- spatial and 1- temporal, which is space-time. Increase in number of dimensions from four would have significant difference only in sub-atomic level.