Brief Resume of the Conference on Einstein

From Mukto-Mona Dhaka Contact

Published in MM on 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 Roy 

In all five papers were presented as reported earlier.  

First paper: ‘Einstein’s dynamical theory of Brownian Motion’ presented by Dr, Showkat Akbar of AEC, Bangladesh.  

Summary: Brownian motion was discovered first by a British scientist in 1827, when he was looking at a glass of water with suspended pollen grains. He found that pollens were as if full of life moving in random manner in all directions inside the liquid medium, water. This motion of non-soluble material particles mixed in a liquid was known as ‘Brownian Motion’. The problem was not understood and left unattended till Einstein looked to the problem very seriously in 1905, no 2 of his three celebrated papers in Annal der Physik in 1905. In earlier, some studies tried to explain it as a phenomenon of surface tension of the liquid concerned, others attributed it such properties of the liquid as viscosity, uneven temperature distribution within the liquid, chemical reaction etc. But all attempts failed.

Einstein considered particles of very minute size only visible under a moderately high power microscope i.e. of 10-2 to 10-3 cm or so immersed in a chemically inert liquid. Einstein’s explanation is based on two assumptions:  

    • The liquid consists of innumerable number of its molecules (water molecule) of medium, which are at random motion in a thermodynamical equilibrium state due to thermal agitation.
    • These molecules randomly in motion at certain instant of time collide with the pollen grains or any other non-soluble dust-particles suspended in the liquid. These collisions between water molecules and pollen grains create the random motion found in pollen grains.

 Next problem is to apply statistical method to understand the collision problem, which he did. Obviously number of molecules far exceeds number of pollens, so we may consider each pollen grain is surrounded but a large number of water molecules. As the water molecules are in random motion the impact on a pollen is not same as a result of which a non zero resultant force all the time acts on a particular grain causing a motion in any direction. This effect on each pollen gives an over all random motion picture. If the particle size is big enough then impact on the grain from all other sides by molecules tend to cancel each other – so non equilibrium force exists. This diminishes the random motion. In analyzing this intricate problem Einstein brought in

 

    • The concept of osmotic pressure in a liquid and phenomenon of diffusion instead of using Equipartition theorem of energy. He set up a diffusion equation now known by his name. 
    • Statistical physics which he applied to calculate root mean square velocity of the supended grains.
    • Molecular kinetic theory of heat and macroscopic theory of dissipation.

 

He finally from his analysis predicted the magnitude of size of a molecule. Thus Einstein theoretically predicted the existence of the entity of molecule, very much a physical reality rather than metaphysical concept confined so far in the mind of philosophers.  French physicist named Jean Perrin, after about a decade made a detail study of suspended particles experimentally from which he estimated the size of a molecule. This study under the name of ‘discovery of the equilibrium of sedimentation’ brought him Nobel Prize in Physics in 1926.

 Einstein-Perrin effect not only stimulated research works in various modern fields of physics such as Fractal theory, voltage fluctuation for quantum effects which led to the discovery of Quantum fluctuation dissipation theorem due to Callen & Welton and Nyquist & Johonson, Statistical non linear dynamics, Thermal equilibrium system etc. 

In technological and applied sciences, this phenomenon has been applied successfully:

Medical Imaging, Robot technology, Estimation of ferocity of flood and drought, Market analysis, Decision-making process, Aerosol spray etc. 

2nd  paper: ‘Photo Electric Phenomenon’ presented by Prof. H. M. Sengupta, Professor of Physics (retd.), DU 

The phenomenon of Photo electricity shows that when a beam of light falls on a metallic surface a stream of electrons escape from the metal surface. According to classical theory of electromagnetic there is nothing strange in it. When light falls on metal surface it absorbs light energy and as energy is built up the electrons get out of the surface overcoming the surface barrier characteristic of the material. But this explanation offered by classical theory does tally with experimental facts. As for example: 

    • For emission of electron one needs a light of minimum wave length ( ), called threshold frequency. Below threshold frequency no emission of electrons takes whatever might be the Intensity of incident light.
    • The peak of kinetic energy of electrons is independent of intensity of light but depends on frequency of light (above threshold frequency). The maximum peak value linearly increases with the increase of frequency of light.
    • The distribution of energy of photoelectrons is again independent of intensity of light used, but once again depend on the frequency of light used. The intensity only increases the number of photoelectrons.
    • According to classical theory there must be some time lag between the fall light on the surface and emission of electrons, but experiment shows that the process is almost instantaneous.

None of the above characteristics associated with photoelectric effect could be explained with electromagnetic theory of light. Einstein first in his famous paper published in Annalen der Physik, ( ser 4), 17,132-148, 1905 gave a satisfactory explanation of the phenomenon. Instead of treating light as wave of periodic vibration of electric and magnetic vectors, he used light as a stream of concentrated energy-particles called quanta, each having energy E = hn in his analysis. But first he established the fact that light is in reality made of quanta i.e. photons he tackled the problem of radiation inside a black body using thermodynamical as well statistical methods. He used Boltzman’s fundamental law connecting entropy of the system and the thermodynamic probability. Einstein used Wien law to obtained for the probability of finding total energy by chance compressed in a fraction of volume of the total volume. This leads that the quantum character of light. He applied this concept to explain the photoelectric effect. He treated the phenomenon as collision of photons and bound electrons in a metal. Since an electron is bound up with the metal surface, to liberate it a photon of minimum energy equal to that barrier is required. So if we use a photon of energy (hn) greater than barrier energy, some portion of energy of the photon would spent to overcome the barrier (hno) and rest energy would appear as kinetic energy of the escaping electron. The simple interaction  may be expressed as in equation form, known as Einstein’s photoelectric equation. 

hn =   hno + Tm

The emitted electrons do not have same kinetic energy because the electrons within metal escapes from deep inside the metal, not only from the surface. Deeper electrons would have lesser kinetic energy as photon would more energy to get them liberated. In fact distribution of kinetic energy ranges from zero to a maximum value (Tm ).  

It may be stressed that Einstein’s theory of photon is more fundamental in as sense light not only absorbed or emitted as quantum of energy, but they travel too as particles in all medium. On the other hand Planck was very conscious of his statement- he thought light maintains its continuous character of flow of energy in the form of Electromagnetic wave. Only during emission or absorption by an atomic system it behaves as quantum of energy i.e. as particles. According to Einstein’s principle intensity of light is the measure of number of photons falling on a unit area per second time, whereas its energy is associated with the corresponding frequency of light in question E = hn; energy of photon thus does not depend on its intensity- this is the fundamentality of Einstein’s concept.       

 

3rd paper: ‘Space-Time-Content (Sthan-Kal-Patra : Ż’vb - Kvj - cvÎ)’ presented by Prof. Ahmed Shafi, Professor of Physics, DU

Briefly introducing the contradiction that existed between classical dynamics formulated by Newton (1687) and Electromagnetic field Equations introduced by Karl Maxwell (1888), which unified electricity, magnetism and light in one fold through his celebrated four field equations. The scientists at that time that the similar existence of time and space in those equations. But no further progress was made, even theoretically to unify the concept of time and space. On the other hand Newton’s concept about these two entities were that both were independent of each other and absolute. Newton himself however shown that absolute space and time could not be measured, we have to deal with relative space and relative time. The scientists at that time introduced a novel idea of a medium called ether through which Maxwell’s electromagnetic waves propagate. It seems search for an absolute frame of reference ended because this ether spreading over the entire universe through which from microscopic particles to giant celestial bodies were moving. Question arose are the Maxwell’s equations too invariant under Galilean-Newtonian transformation. Mechanical laws were, but Maxwell’s equations were not found to be.

Under this backdrop, after industrial revolutions when sophisticate scientific instruments such various kinds high resolution microscopes, optical interference instruments were fabricated to observe minute optical phenomenon of microscopic world and giant telescopes to see the Macroscopic world of universe. Michelson and Morley performed a historical experiment to detect ether current both in the direction in which earth was moving (in fact opposite to earth’s motion) in the space around sun as well as perpendicular to the direction of motion. He used a big interferometer with special arrangement based on the principle of Michelson Interferrometer. Their attempt failed because in both directions time of arrival of reflected light from the distance perpendicular mirrors showed no difference, as it should have been from a simple calculation. It was a perplex, which meant light travels with similar speed in all directions whether along ether current or perpendicular to it. Classical concept of relative motion so far light was concerned was not applicable. This indirectly meant that we have to abandon the existence of ether. This paved the new thought in the form Special theory of relativity invented by Einstein, which he published in 1905 (Annalen der Physik, (ser 4), 17, 891-921, 1905). However Lorentz tried to explain the null result of Michelson on the basis of contraction of the apparatus length in the direction of motion of the earth. This ad hoc hypothesis could explain the result of Michelson experiment, but this was simply an empirical solution. 

Einstein’s paper of 1905 brought the solution in a general way. His analytical approach based on two basic postulates:  

    • In all inertial frame of reference light travels with constant speed, whether an observer is at rest in one frame or an observer is on a train moving with an uniform speed does not matter.
    • All physical laws – Mechanical as well Electromagnetic laws, must remain invariant

Under these two axioms, meaning of Lorentz’s contraction comes out to be that `length is frame dependent – i.e. if Lo is the length of an object (such as length of the spectrometer arm along the direction of motion) with respect to a frame at rest, and L is the length of the same object that is fixed in a uniformly moving reference frame with respect to the fixed frame. In general Lo ą L but could related as : L =  LoÖ(1- v2/c2 ). This means a moving object would appear to be shortened by the factor (1- v2/c2 ) 1/2 . In a similar way it has been shown that it was established that time interval between two events dt in a fixed frame would not be the same interval in a uniformly moving frame, but say dt`. This means time is not an invariant entity, but observer dependent. In this case time interval is lengthened in the moving system which could be expressed in a simple mathematical relation :   dt` =  dt/ (Ö(1- v2/c2 ).  This means if we have two clocks synchronized to each other when both systems were at rest, then as one system starts moving with uniform speed, the observer at rest frame would see that clock at moving frame tickling slowly. This is what we call time dilation. The time dilation has been experimentally verified in meson decay process.

Prof. Shafi then introduced the concept of four-dimensional world and gave some brief description through four dimensional geometrical analysis involving space and time due to Minkoski and Poincare. In the light of relativistic approach when a particle moves near velocity of light, Newtonian mechanics which was modified by Einstein now known as relativistic mechanics from which his famous equation E = mc2 was obtained showing the mass–energy equivalence.

The author then tried to explain the very well known twin paradox in a lucid language to non-conversant audience. He narrated a story, in the context of his Bengali audience, of a twin sister Mona and Lisa; Lisa under took a space journey in rocket nearly moving with speed of light. As they are in relative motion, not knowing who are at rest, both sisters will see that other sister’s clock is moving slowly. After some time, Lisa returned to his sister Mona; Mona saw that her sister has come back after 8 years i.e. her age has increased by as against Lisa’s age only 4 years. On the other hand Lisa will notice that her age increased by 8 years (in her own frame of reference) and Mona’s only by 4 years. Both can’t be true – so it is a paradox. Where lies the mystery? Explanation is not that difficult. Mona’s reference frame always remained unaltered. But when Lisa started her journey her frame was moving away from Mona, but on her return path she was not in the same reference frame, it was now moving opposite direction towards Mona, so it is a different frame, although Lisa thought she was at rest always. Hence Lisa would see Mona’s clock behaving differently as compared to when she was moving away. In return path Lisa would see that her sister Mona is approaching to her with same speed. The net result is Lisa would see that Mona’s clock has recorded eight years more as compared to her clock. So time traveler Lisa would conquer the time by four years and look younger compared to her sister Mona who spent all the time on earth in inertia. So one who wants to longer old age our doctor should prescribe for space travel.

The author finally held responsible Jewish race including Einstein for Hiroshima and Nagasaki first atom bomb catastrophe in which thousands of innocent lives were vanquished, and thousands died because of its long time fall out after suffering from various deceases including cancer. Out of this pathos writer dedicated his article to this victims who were the victims of modern atomic science. One may not agree with the final comments of the author singling out a suffering community throughout the history of civilization the unfortunate Jewish race holding responsible for Hiroshima – Nagasaki disaster.

(contd to next part)