Math, Einstein and the Gravity of all that

As a student of physics, I feel extremely happy when people, particularly non-physics people speak about Newton or Einstein even when they do that for the wrong reason. Though the Chandrayan, for whose soft landing 1.3 billion Indians prayed in unison disappointed us, we shall feel happy about the sudden and unexpected resurgence of Physics in our country, which has its genesis in a seemingly casual statement by a central government minister. Good. Very good indeed. Here I am to neither defend the minister’s statement nor disprove it. Some innocuous blab bla bla during this Onam season. Just that.

Caught unawares in the gravitational milieu and the pandemonium that erupted slowly receding, I thought of making the following observations. I will assume  no knowledge in physics for the reader. Yet, a physics student might appreciate me for writing this so that the non-physics too can get a feel of what for, or what not for, they were in the skies for one or two days and can now resign to the gravitational pull and have a terrestrial settlement.

To start with, let us ask the question “Did Newton discover gravity?” The answer should be “yes, indeed. He did.” It is like the answer being affirmative for the question “Did the Wright Brothers discover/invent the airplane?” Though there is only one Isaac Newton, there are three kinds of people associated with his law of gravitation.

(i)          For this category gravitation is all about or it starts and ends with the apple falling on Newton’s head.

(ii)          The second category is the physics student up to the BSc level who understand Newton’s gravitational force as an inverse square law one. The famous formula GmM/R*R is true, very convenient and sufficient enough to calculate the force between two small marbles at a distance of a few centi- meters  or the force between two elephants standing in majestic splendour at the Thrissur pooram. Interestingly the same formula can be used  to calculate the force between the Earth and the Sun. And more interestingly, this force causes the earth to move in the same plane on which it started revolving around the sun when the solar system was formed. If you are a physics student you should know the reason for this –-- the force being central in nature.

(iii)             The third category is the post graduate students of physics. They are introduced into the study of gravitation through the Newtonian theory of the gravitational field (and not just the gravitational force between two masses). One notices that in this theory there is only one potential – the Newtonian field potential. From there they go on to the Einstein’s theory gravitation which is understood in terms of the geometrical structure of the  space-time continuum. The start with the Riemannian metric. Then they have the geodesic equations. Here when they write the full form of the Christofell’s symbols, ten potentials are identified in place of the single potential of the Newtonian theory. I quote from “The Theory of Relativity by R K Pathria”.“....... the fact that the present theory requires ten potentials against one in the Newtonian theory speaks not only of the mathematical complexity but also, perhaps, of its physical profundity”. It should be noted that the theory reduces to the Newton’s theory for slow moving particles in a weak field.

Thus Newton’s theory is right, absolutely right in the limit of weak gravitational fields. But it miserably fails to describe strong fields, for instance, the field of a Black hole,where one certainly needs Einstein's theory of gravitation.

Now  coming back to the cacophony over the minister’s comment over the past two days. The minister, as I have read, is a chartered accountant by training. He need not know about Einstein’s gravity. In all probability it was the proverbial slip of the tongue as the minister himself has admitted. But the interesting thing is that the minister is right, inadvertently though. If you still want to attack the minister do that for his rejection of mathematics. In fact Einstein's General Relativity is a wonderful exhibition of how mathematics can be used to explain mysteries of nature. Be it time dilation, gravitational red or blue shift, precession of planetary orbits or bending of light rays in a gravitational field it is math all the way. And it is a delight to understand how incredibly did Einstein use math to move from the surface of the earth to black holes billions of light years away. As I stated at the outset my intention was not to prove the minister right or disprove him.

Now why did I bring in the Wright brothers earlier? They invented the airplane. But a jet plane or a space craft is not an extension of the airplane. They are two technologies for two different regions of space. Similarly for Newton’s and Einstein’s theory. Both are correct. One in the space where the gravitational field is weak and the other in the space-time continuum where the field is very strong.

The Mystic Einstein

I think, of all the physicists, Einstein is the most mystified and hence most popular. The fact is that he was not the least mystical. Instead he relied heavily on the realities of mathematics. For him truth was what was mathematically true. I write this to narrate a real story. A few years ago an IAS officer visited a school in Kottayam. During his interaction with the students some of them told him about their difficulty with mathematics. Before leaving he told them the story of Einstein. I quote...” Einstein was very poor in mathematics while in school and often failed in the subject. Therefore when he went for higher studies he opted for Physics. Those of you for whom Mathematics is difficult can go for Physics and do well.....”

My Good Heavens! If mathematics is tough for you, go for physics which is very easy!?!

Is there any physics without mathematics? If you know please tell me.