Relativity for All Contd.!! (The General theory of Relativity)

On the 140^th birth anniversary of Albert Einstein it is our great pleasure to revisit one of his greatest masterpiece, the General theory of Relativity (GR) (arguably the best theory of Einstein). Today we discuss GR in his memory and ponder over the extraordinary genius of the man who redefined Physics in the 20^th century.

Albert Einstein

Background

After his miraculous year in 1905, when he laid the foundation of 4 groundbreaking theories of nature (Photoelectric effect, Brownian motion, special theory of relativity and “the world’s most famous equation, E= mc2”), Einstein came to the limelight. 

World’s most famous equation

From a patent clerk in Bern, Switzerland Einstein became a lecturer in the University of Bern in 1908. The following year he was appointed as an associate professor of theoretical physics in the university of Zurich. Einstein became a full professor in the Charles-Ferdinand university in Prague in April, 1911. In 1912 he returned to Zurich as a professor of theoretical physics in ETH, Zurich. He decided to move to Germany and on 1^st April, 1914, he joined the Berlin University.

During all these switch overs from one institute to the other Einstein kept nourishing his original idea of generalizing the theory of relativity that he proposed back in 1905. It was as situation of crisis to humanity. First world war was about to break out. But all these seemed to have minimal effect on the genius. A sense of incompleteness kept haunting him through days and nights.

General theory of Relativity

                                       The Problem 

If we recall our last discussion of Special theory of Relativity we will note that the theory was valid only for inertial (non-accelerated) frames of references. But in reality almost all frames are accelerated . A moving car needs to accelerate or de-accelerate. Similarly a cyclist has to use brakes while cycling. A football rolling on the ground de-accelerates due to friction. All these are non-inertial (accelerated) frames of references where special theory of relativity is not applicable. 

So we need a general theory of relativity that will be applicable to all frames of references (both inertial and non-inertial frames).

Why a theory of Gravity?

In the attempt to generalize his theory of relativity, Einstein knew that he has to incorporate acceleration in his theory. Now acceleration comes from force. In a great insight Einstein understood two things which he stated as the Principle of Equivalence.

1)  The equivalence of inertial and gravitational mass.    

2)  The gravitational force experienced locally while standing on a massive body like Earth is the same as the pseudo force experienced by an observer in a non-inertial frame of reference.

He had the feeling that this can really be a theory of gravity. He started to consider the problem of gravity seriously. He consulted Max Planck (who laid the foundations of Quantum mechanics in 1900) and told him about his intentions to work out the gravity problem. 

The legend says that Planck told him “There are two possibilities: (1) The gravity problem is so difficult that probably you will never succeed.  (2) Even if you are able to find a solution to the problem nobody will believe you.”

Max Planck

The weak link of the prevailing Newton’s theory of Gravitation

The first comprehensive theory of gravitation was stated by Isaac Newton in the 17^th century. It stated that:

Any two masses separated by a certain distance will attract each other by a force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

The theory seemed to be fine at that time with no flaws and was universally accepted. Newton became the God and very few people had the guts to question his intellect. Moreover the problem of gravity was very difficult to address and so only a few showed any further interest and believed in Newton.

Isaac Newton

But some natural questions arise:

What is the source or the origin of the force?

What is creating it?

Why is it present at all?

Newton was silent to these questions. He did not have any logical answer to it. 

The Theory that answered the above questions

Einstein’s theory of General Relativity is a geometric theory of gravitation that answered the prevailing questions of the critics.

Einstein argued that space-time (space and time together) is like a stretched fabric.  Now when we put a mass on such a fabric naturally it will create a curvature around itself. This is warping (curving, bending or twisting) of space-time that gives rise to a gravity well around the mass. Now when a second mass comes within the curvature quite naturally it moves towards the first body due to the gravity well produced. 

Curvature in space-time

Einstein argued this is what gravitation is!! It is not a force at all as Newton had proposed almost 250 years back. It is a phenomenon that is created by the geometry or curvature of the space-time.

Greater the mass greater the curvature on the space-time fabric

What a masterstroke indeed!! What a beautiful insight!! The common mind can only bewilder and get lost in its aura!! Such was the extraordinary genius of a curious mind.   

The Race to Glory

Einstein had developed the physics of the theory back in 1912, but he did not have any clue about the Mathematics. He needed sufficient knowledge about the geometry of curved space-time (Non-Euclidean geometry) before he could proceed towards developing any meaningful mathematics of the theory. 

Einstein was far from being an expert in such a geometry. But one man by the name of David Hilbert was. He was a mathematical giant of that era. Hilbert took up the problem and started developing the mathematics, which came as a terror to Einstein. His theory was in danger of being credited to somebody else. He had to act and act fast.

David Hilbert

Einstein’s friend Marcel Grossmann (a great mathematician) came to his rescue. With his help Einstein learnt the concepts of Riemannian (Non-Euclidean) geometry and started developing the mathematics of his theory. Hilbert on the other hand continued his effort silently but swiftly. 

As the race to glory became more and more intense the scientific community watched the battle of the two scientific giants (one physicist, the other mathematician) and waited eagerly for a result.

By the grace of God, it so happened that both these great minds reached their destination independently and almost simultaneously. By 1915 both had their own versions of the mathematics of GR ready. On careful scrutiny it was found that both were correct.

Hilbert accepted that the contributions to the theory was far more loaded in favour of Einstein and the theory of general relativity must go by the name of Einstein. This ended all confusions if at all there was any. Finally in 1916, Einstein published his theory of general relativity in the Annals of Physics.

It is difficult to contemplate the feelings of the great man. During his quest, at some point he must have felt that he was losing the battle. After all Hilbert was a great mathematician and matching him was a herculean task. Therefore after the publication, it could have felt like winning a battle once thought to be lost. But it should be remembered that the physical basis of the theory was solely laid by Einstein and probably that’s enough to retain the credit. 

The Equations of General Relativity

This is a relation between mass and spacetime geometry.

Equation of GR

The Reaction from the scientific community

Accepting this theory was not at all easy for the scientific community. The theory will shake the very foundations of physics. Shock-waves were abundant and far reaching. Scientists had many years of scientific career jeopardized. Isaac Newton’s theory of gravitation was in danger. So it happened as Max Planck had predicted some years back. Everybody demanded a proof for the theory.

The radical nature of the theory was criticized by many great minds. Some even thought that GR is not a theory of physics, but the whims and fantasies of Einstein, who is living in a fantasy world.

Experimental physicists like Philipp Lenard (Nobel Laureate, 1905) went into direct confrontations with Einstein and mocked him publicly. He said that physics is a subject of experiments and observations. We believe what we see. There is no place for dreamers like Einstein in the scientific community. Science got really ugly!!

Einstein retaliated but he understood that he had to give a proof to save his theory from being demolished by the critics (specially nazi).

The Proof of General Relativity

The paper was published. The theory was complete. But it didn’t matter to anybody because nobody believed it. Now the genius of Einstein faced a bigger challenge. How will he provide a proof for the theory for which he fought for over a decade. Moreover he was not an expert in experimentation at all. It was an uphill task for him.

But again his extraordinary genius came out with an extraordinary idea. He proposed the bending of starlight around the solar limb (gravitational lensing) as a possible proof for general relativity. 

He argued that the light from the distant stars that pass by the sun before reaching us on Earth will bend while their journey near the sun. The sun being a massive mass will create a huge curvature in the space-time around it. The starlight while passing by the sun will follow this curvature and get bent. As a result multiple images of the star will be formed in the sky. This is in complete compliance with general relativity.

So if Einstein’s theory is correct starlight will bend around the sun and if it is not then the light will pass unaffected. Einstein requested the astronomers all over the world to go and check it.

Many astronomers including Arthur Eddington, a renowned British astronomer took up the challenge. Watching the faint starlight in the presence of powerful sunlight was always going to be difficult. So they chose total solar eclipse for their observations.

In 1919, Eddington’s observations of a total solar eclipse provided concrete proofs in favour of Einstein’s general theory of relativity. 

A British proof to a German theory provided a thrust towards world peace in the post first world war era. Einstein dreamt of a peaceful world without any wars. Even his greatest scientific theory advocated his humane feelings.

In 1921, Einstein was awarded the Nobel prize, not for his general theory of relativity, but for his discovery of the photoelectric effect (may be to his disappointment).

General theory of relativity has been termed as ‘the most beautiful theory of physics’ ever. Till date it remains arguably the best theory of nature not to win a Nobel prize.

I am not a genius. I am just curious...I ask many questions and when the answer is simple, then God is answering.     

         --Albert Einstein.

By Prabir Rudra