Brief Resume of the Conference on Einstein(Contd.): Part III

From Mukto-Mona Dhaka Contact

Published in MMon April 01, 2006

Date: September 30, 2005

Venue: Auditorium, Faculty of Business Studies, DU

First Session: Einstein’s World of Physics (9-30 to)

Chaired by: Professor Ajoy RoyAfter the tea break following two papers were presented.

4presented by Prof. Harun ar Rashid, Professor of Physics (retd), DU^{th}paper: ‘Albert Einstein’s General Relativity Cosmology of the Universe’

The paper began with a quotation from Einstein’s letter from Berlin to Arnold Summerfield in Munich on 28

^{th}November, 1915 where in Einstein narrated during this month he had passed through most difficult and critical time of his life. He was then pretty busy developing his equations gravitational theory- and searching for their real basis.He published his paper dealing with what now known as ‘General Relativity’ in Annalen der Physik in 1905 (Ser 4,

17, 769 – 822) under the title ‘Grundalge der allgemeinen Relativistatstheorie’. After reading the paper Max Born was simply charmed stating as human mind’s greatest output in understanding nature of physical world – a unique combination of philosophic sharpness, intuition, and mathematical efficiency. It is an art painted by a great artist. He worked for over a decade to arrive at the ultimate result. His thought began with the idea what was relation between inertial mass and gravitational mass, both concepts were introduced by Newton. In 1911 he showed that both are equivalent. By 1912 he was convinced that Minskowski’s 4 dimensional flat geometry, an extension of Euclidean geometry must break down yielding place to a four dimensional curved space. In order to reach such a decision he had to learn absolute differential tensor calculus with the help of his friend Grossman, mathematics of Gregorio Rickky and Levi Chevita. Once the Minkoski space was reduced to curved space Einstein proposed that Gravitation is nothing but expression of curvature of the space concerned.

In the next year he wrote another paper under the title ‘Kosmologische Betrachtungen zur allgemeinen Relativistatstheorie’ (

Preuessische Akademie der Wissenschaften, Sitzungsberichte,pt I, 142-152, 1917) in which took the first step of understanding cosmology of the universe.

## Principle of Equivalence

In general one distinguishes between weak and strong equivalence. Equivalence between Inertial mass and the gravitational mass is the weak principle of equivalence. Einstein showed these two masses must be identical. Later on it was experimentally verified. According Newtonian mechanics when a mass small is being attracted by a big mass M the acceleration experienced by the small mass is simply g = GM/r

^{2}, G is the gravitational Constant and r is the distance between the particles. Thus principle of equivalence became a fundamental principle, which states: ‘Gravitational mass and inertial mass from the point of physical view are totally equivalent in nature – no physical experiment can distinguish them.’ This in simple term means when a particle is found to moving with accelerated motion it is impossible to if the acceleration arises from inertial or gravitational. The consequence of the principle of equivalence is then that any constant gravitational field could be made to vanish by choosing a suitable accelerated frame of reference. In the language of mathematics the gravitational filed could be ‘transformed away’. As it is interesting from general point of view let us explain it a little bit with the help of an example of moving lift.

1: Let us assume that a lift has been taken to an isolated position in space. A uniform motion is set in to the lift. The observer inside the lift attached to moving frame would see all objects out the lift were moving uniformly.^{st}Stage

2: The lift is now placed under a gravitational field, say at a distance above the surface of the earth. Now let go under free fall. As according to equivalence principle gravitational acceleration is same for all objects, the observer in the lift will not see other situation different from 1. This is means it is not possible to detect gravitational acceleration sitting from a frame of reference that itself falling freely falling under the same gravitational field. The man will feel weightlessness which means either he is rest or in uniform motion.^{nd}Stage

3: The lift is the again taken to a distance space away from any gravitational field. The lift is set to a uniform accelerated motion^{rd}Stageaby an attached rocket. It will appear to the observer in the lift all objects out side the lift are moving with accelerated motion a but opposite direction and same for all objects.

4: We now take the lift to a gravitational field such that g = a (of previous experiment). The observer will not see any different situation as compared to stage 3.^{th}Stage

Only limitation we have to think of is the effect is highly localized i.e. only in a local position in cases 1 and 2, and in cases 3 and 4 equivalence of inertial and gravitational are appreciated. Einstein made this principle universal and applicable to wider range of space. This is what is now termed as ‘strong equivalence principle’.

## Equation of motion of a free particle

What Einstein then did he developed a generalized equation of motion of a free particle in a Riemannian curved space in stead Minkoski’s flat space which include a non zero Christofel Tensor, whereas in Minkoski space its components are zero. This is the famous equation of geodesic representing the locus of a freely moving particle in space. This tensor is found to contain a term arising from the inertial acceleration of the particle because of use of non inertial frame and other term from gravitational acceleration. Thus according to principle of equivalence, gravitational term can be expressed as component of Christofel Tensor, which is a sum of acceleration due to inertial and gravitational.

As all over Minkoski space the Christofel Tensor is found to be zero hence, in presence of gravitation field the four-dimensional space could not be flat i.e. the space is curved- which is described as Riemannian curvature. This concept is expressed in general theory of relativity as ‘gravitational field reduces to geometric curvature. This is what is called geometrical transformation of gravity.

Thus there is no inertial frame in general relativity only non inertial frame exists, which means there is no significance of absolute acceleration as absolute velocity has no significance in inertial frame. This is why it is called general relativity. In Riemannian curved space, the Christofel Tensor of a curvature could be made zero by a general transformation- a situation of weightless ness, which we experience in a free fall lift, or space travelers in a rotation free satellite. The astronaut who is attached to a rotating commoving frame of reference would not feel either inertial or gravitational acceleration.

From this follows, showed Einstein, that if a light passes near a uniformly moving lift, the observer in the lift would see that light passes in a straight line unaffected. However if the lift were moving with accelerated motion, say upward, to the observer the light beam appeared to bent away downward. Because with respect to accelerated from attached to the lift bodies outside experiencing inertial acceleration down ward causing a down word bending of beam of light. The effect may be seen from another point of view. As we know we can associate an inertial mass m

_{p}of a photon of energy E = hn = mc^{2}, mp = E/c^{2}= h n/ c^{2}, from the equivalence principle this mass is also a gravitational mass of the photon. Hence light ought to be subject of gravitational attraction by another gravitational mass. For example light rays that passes near the sun must be deflected toward the sun by its gravitational field, just as the path of a planet is deflected.

## Gravitational Field Equations

Einstein then, says the paper, set up field equations valid for material universe. This involves symmetric tensor of rank two and field equations will retain their same form in all frames. The general form of field equation contains a constant known as Cosmological constant.

From general theory of relativity it was predicted the phenomenon of ‘Red Shift’, a relativistic Doppler effect which was verified experimentally by observing galaxies moving away from us appearing as reddish. The theory also successfully explained the observation in advancement of the perihelion of the planet Mercury. Finally prediction of bending of light in a strong gravitational field given by 4M/R, where M is the source of gravitational field, say mass of the sun, and R is the radius of the Sun. If we put the value of R and M for Sun, the deflection of a light beam is ~ 1”.75 (see.). In 1952 an experiment performed during solar eclipse the deviation was obtained 1”.7±0 (

Astronomical Journal, 58, 87, 1953).

Formation of Black holes and cosmology of Universe

The general theory also predicted the possible formation of large heavy mass concentrated in small locality whose gravitational attraction could reach such an extent that all materials objects including light once get into it would not be able to escape. Such object is now termed as `Black Hole’, more extensively explained by Hawking, Penrose, Chandrashekhar and many others. Professor Rashid completed his paper with brief introduction of cosmology of our universe and tried to show how it was hidden in the general theory of relativity. Our universe is made of innumerable number of galaxies and nebulas distributed all over the universe more or less uniformly. When Einstein wrote is paper it was thought the universe is made of stars and the mass of the universe is uniformly distributed. The universe would look alike from all directions. This is what he called ‘Cosmic Principle’. So we can define a cosmic time too and attributes of the universe can be expressed as function of this time and only this time. The density, temperature, curvature of the space and its metric all will be function of this time and same all over the universe. In Einstein’s world the main feature of it is its isotropic nature. The mathematical analysis based on such fundamental attributes to universe leads to the expanding universe under some conditions. Experiment of Hubble on distance galaxies confirmed that universe is expanding. Gammow suggested that if universe were expanding, then these moving galaxies i.e. entire materials contents must have been concentrated at a singular point at certain time, which must had exploded violently at the time of creation of the universe. The phenomenon is now called big bang. If such phenomenon truly occurred then its radiation background must have survived right now. This was precisely experimentally observed.

## Unified Field Theory

Finally the author mentioned about Einstein’s dream of unified field theory, though he did not succeed in transforming Maxwell’s electromagnetic field in to space-time curvature, as was done for Newtonian gravitational field. Though not in Einstein’s way unification of three fields namely electromagnetic, weak nuclear and strong nuclear have been unified in Grand Unified Theory (GUT). Only illusive gravitational field discovered by Newton is still left out. Would String theory succeed, only time can say?

5written by Prof. Jamal Nazrul Islam, UGC Professor of Mathematical Physics, Chittagong University.^{th}paper: ‘Present and Future of the Universe’

As Professor Islam was away, the chairman of the session Prof. Roy presented his paper in brief on his behalf. The salient feature of his paper was that the Universe is mainly made of galaxies and dust particles distributed uniformly over the universe. The galaxies of various sizes and shapes are really made of starts living in different stages. Some are white dwarfs, some are black dwarfs, some are neutron stars and illusive black holes. Name of our galaxy is Milky Way in which our sun is just another star out of millions. In time our sun will turn into a white dwarf and then a black dwarf after giving up radiation. Famous astrophysicist Chandra Shekhar theoretically showed that the stars having mass greater than 1.4 times the mass of sun will not turn into a white dwarf. As the mass of a star increases to the critical value its radius reaches to zero. This is what we call Chandra Shekhar limit. Later works showed massive stars lying within mass limit (1.4 – 3) M, M being the mass of the sun, may become neutron starts after being blown up through violent explosion called Supernova. The still massive stars become ‘Black holes’ because of collapse on a small volume due to severe gravitational pull. The characteristic of these invisible celestial bodies are- any objects including electromagnetic radiations when pass near by fall into it and nothing could come out of the body, except a kind of radiation called Hawking radiation, once absorbed. In 1929 because of a series of celebrated experiments performed on distance galaxies by Edwin Hubble, which showed appearance of those galaxies as reddish. Conclusion was these galaxies must be moving away from our galaxy, the Milky Way, appearing red because of Doppler shift as predicted by Einstein’s General Relativity. From this idea of expanding universe led scientists to think and calculate back that about 15000 millions of years ago all these materials must have been concentrated in the form dense energy (hot super dense state) into a singular point, which suddenly exploded into a ‘big bang’- the moment of creation of space-time. Physicists opined that even up to 10

^{-40}sec. all four fundamental forces were unified in the form of a ‘super force’. Elementary particles like quarks, electrons, protons and neutrons came into being after ~ 1 sec. and then after a few seconds a nucleus consisting of a proton and a neutron was formed, and then gradually Hydrogen and Helium, the first simple atomic system came into existence. And after about hundred thousand years matter was formed, and then after a period two hundred million years galaxies and other big celestial bodies were formed. Our sun was created inside our own galaxy milky way about 500 crore years ago, and then about 450 crores of years back our solar system including mother earth was born. What was before the big bang is a metaphysical question which physicists bother least to answer?

What is the present status of our universe? Experimental observations show it is expanding – the distance galaxies are moving away faster than the nearer ones. The value of the Hubble constant i.e. present rate of expansion of the universe is ~ 23 km per second per mega light year (23 ± 3 s-1 Mly-1). Whether the universe continuously expands for indefinitely or it will start contracting after some time depends on many elements. The major element is the average density of the matter in the universe. It has been shown that there is a critical value of such density r

_{c}~ 1.1x10^{-26}kg per cubic meter, whereas present lowest density as estimated is something like 0.015 x 10^{-26}kg per cubic meter. The ratio of the real density and the critical density (w) determines the fate of the universe. If w <1, the universe will be open and expanding, if w > 1 then it is a closed universe and contracting. The present ration is ~ .014, much less than the critical value 1, so universe is an expanding one at present. But there is a sign of retardation of this expansion. The physicists are of opinion that other than visible matters there are dark matters more or less uniformly distributed in the universe, which may be undetected black holes, intergalactic sea of hydrogen and neutrino-ocean. If those hidden matters are taken into account, the value of w may well exceed 1 paving the path of retraction. The universe might then reach a singularity point similar to that of at the time of creation collapsing into a big crunch, the end of universe. There is another possibility however, instead of collapsing into a big crunch, it may bounce back overcoming the gravitational attraction because of tremendous opposite pressure generated during the process of contraction. In this way we might get an oscillating universe, which will never die away.