OBL2?

There are people in this world who can swear that they attended the funeral of Osama bin Laden many years ago. And yet on 2nd May, 2011 US commandos raided a house in Abbottabad and shot a man they claimed to be OBL and announced that his DNA matched with some of his relatives. Next day as many as his three wives and some children were captured by the Pakistani military who verified that the man was named Osama bin Laden. How is that possible?

Simple enough! Osama might have had a namesake cousin who may have volunteered to act as his double or decoy when he was on the run. After the death of the famous OBL the innocent cousin might have decided to live out the rest of his life in anonymity in Abbottabad and although there was a multimillion dollar head money, those who knew about him decided to keep quiet until the CIA found out that someone by that name was alive and living there. The US leaders obviously thought that political mileage could be gained by having the poor man assassinated and the ugly operation was staged. It is not surprising that the face of the dead man was not shown to any outsider and the body was promptly disposed off out of anybody’s reach.

What a pity that some ten billion dollars that could have been spent on alleviating the misery of suffering humanity were wasted on hunting and killing a simple unsuspecting Beduin.

Just a guess, but it sounds plausible.

HEAT IS ON

Ever since I was taught Newton’s Law of Gravitation at school, “Every particle in the universe attracts every other particle…….,” I had been wondering how the particles know of each other’s existence. The first prerequisite for attracting or being attracted is awareness of the other’s presence. So there must be something being exchanged among all particles of matter in the universe. Some scientists have suggested the existence of a force field around everything that exists; others have proposed the existence of gravitons. But as usual, they all missed the obvious.

Way back in the early 1960s I learnt about thermal radiation and heat transfer and came across the Stefan-Boltzmann Law of Blackbody radiation discovered in late nineteenth century. A black body is a hypothetic body that completely absorbs all wavelengths of thermal radiation incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation given by:

q = σ T4 A (1)

where

q = heat transfer per unit time (W)

σ = 5.6703 10-8 (W/m2K4) - The Stefan-Boltzmann Constant

T = absolute temperature Kelvin (K)

A = surface area of the emitting body (m2)

It was later modified for grey and colored bodies that were not black and for temperature of the environment or other bodies interacting with it. The final simplified equation of net heat transferred from one body to another is of the form:

q = ε σ Fh,c (Th4 - Tc4) Ac

where ε is the emissivity, F the form factor and h and c denote the hotter and colder temperatures.

I had found the answer to my long unresolved conundrum. Every object in the universe makes its presence felt by emitting thermal radiation, the intensity of which is proportional to the fourth power of its absolute temperature, and every object reacts to change in temperature of every other object in its sight.

Obama Gets Osama

Finally we have a story of how the purpose of the existence of US administration and military was fulfilled when in the darkness of night a squadron of US marines in 3 helicopters (symbolizing trinity?) raided an awkward looking building in Abbottabad (named after a British colonialist), shed a lot of blood and captured and shot dead an unarmed man named Osama Bin Laden and dumped his body in the sea a thousand miles away. There is no way of knowing the truth. It might even be a hoax to glorify or discredit someone in the context of USA’s internal politics

Irrespective of the noble purpose of its formation as claimed by its sympathizers, Al-Qaida, the international revolutionary brotherhood headed by OBL had in recent years turned into a demented cult that relished the sight of bloodshed, destruction and misery as much as a super power military organization. It claimed affiliation with Islam but trampled every Islamic virtue. If the assassination of OBL helps to disintegrate that cult, then it certainly is good riddance.

Yesterday a CNN reporter was able to find a lady who had lost her husband in the 9/11 tragedy and tried his best to coax her into making an anti-Islamic or anti-Pakistan statement, but the decent lady stuck to her observation that all this had not brought her husband back. Interestingly enough, on the day when Khalid Sheikh also an Al-Qaida stalwart was put to death by court order, a gentleman who had probably lost his father in that act of violence commented before CNN that it was as sad a day as when his father was killed. That shows the moral and spiritual gap between the American people and the ruling establishment in which the CIA has a lion’s share. Anyone who has lost a loved one in a violent incident shares the grief of the loved ones of another no matter how evil that individual might be.

Justice would have been done if Osama bin Laden had been kept alive and tried in a court of law and the allegations of his involvement in various terrorist acts proven in a fair manner. Assassination by presidential order is by no mean justice.

As far as I am concerned, my private war on terror is going to continue with efforts to make terrorist leaders, generals and presidents renounce their lust for death and destruction.

Some More Definitions

Address = Location in space

Point = Address without content

Line = String of addresses without content

Motion = Change in address

Absolute motion = Change in address relative to a fixed address

Relative motion = Difference of absolute motions of two bodies

Straightening the Space

The algebraic function y = 1/x is unique and had fascinated scientists and mathematician of the 19th century. The graph of the function is called a hyperbola which is a perfect example of an asymptote. It is shown below:

For those who are not familiar with mathematical jargon it can be explained in terms of numbers. The values of y for various values of x are as in the table below:

It is clear that as the value of x decreases the value of y increases, so much so that when the value of x becomes zero, the value of y becomes infinity. However it is interesting that if you proceed from x=1 toward x=0 the value of y increases to plus infinity, while if you approach from x=-1 towards x=0, the value of y decreases (or increases in the negative direction) until it becomes minus infinity. Thus at x=0, y exists simultaneously at plus and minus infinity. From the common concept of infinity it is mind boggling. How can something exist at both extremes of the universe at the same time? Such a thing could only happen if the space was a curved continuum. To put it simply, if two persons started walking in opposite directions an d continued to do so without deviating one day they would meet face to face on the other side of the earth. Hence came the idea of the curved space and the donut shaped universe.

But the scientists who must have been euphoric at the brilliant idea which must have been dubbed a great discovery seem to have missed out on the relationship between algebra and geometry. y=1/x can be written as x*y=1 which is the equation of a rectangle of unit area. As x decreases, y increases and the shape changes from square to oblong and gradually a thinner and longer rectangle until x approaches zero and y approaches infinity. But when x becomes equal to zero, the rectangle ceases to exist. It becomes a straight line. There is what one might call a geometrical phase change. Just like gas laws can not be applied after the gas has condensed into a liquid, the equation of a rectangle can not be applied to a straight line. X=0 is a straight line which extends from minus to plus infinity along the y axis. Is anything wrong with that?

So it seems that the notions of space being a curved continuum and the universe being donut shaped are mere illusions and any mathematical deductions based on these notions would produce more profound illusions.

If I live long enough or get an opportunity to devote full time to the subject, I would certainly like to remove as many illusions as possible.

Star Flirt

It was a pleasant summer night. The full moon was constantly smiling as usual. The stars were showing off their radiation and the planets were dancing in their orbits with ecstatic abandon. It was party night for nature. The Earth was looking great in its shades of blue and green.
One of the stars winked at Earth and whispered, “Your green leafy wig looks wonderful.”
“Aha!” Chuckled Earth and splashed a big wave in the Atlantic. “Do you know what’s inside?”
“No,” said the star,” Can you tell me what resides in there?”
“Oops,” shrieked the earth and a streak of lightning flashed.
“What was that?” asked the startle star.
“Naughty lice!” the earth tried to regain its composure.
“What do you mean?” wondered the star.
“There are many of them under my beautiful green leafy wig and each more troublesome than the other, especially the two legged ones. They live to give me pain. Sometimes they bury powerful explosives under my skin and ignite them. It is really painful.”
“So why don’t you get rid of them?” asked the star with a touch of sympathy.
“How can I?” replied Earth, “They are my life and I must live with them.”
And the party continued.

6. DISTANT WORLDS

So far, we have discussed the development of those parts of the science of Physics which relate to the understanding of the universe around us. Theorization from a mass of data collected from observation and experimentation, or theoretical analysis resulting in the prediction of what would be discovered later, are the two main modes by which Science grows. However, there is no dearth of anomalies in Science, some of which have been occasionally highlighted in the preceding text.

One of the topics which has not been discussed at any considerable length in spite of being significant to the aims and objects of this work is Cosmology which combines astronomy with the more recently developed techniques of radiotelescopy and spectroscopy. With these techniques, it is now established that the Sun, like other stars, is a dense mass of plasma with a core temperature of about thirteen million degrees Centigrade consisting mainly of hydrogen and small amounts of heavier elements formed by nuclear fusion which constantly releases heat energy producing the blinding illumination. It is also believed that planets have formed due to the separation of small quantities of spinning gaseous clouds containing heavier elements which gradually cooled and condensed into bodies such as the Earth.

However, it is curious that while ninety two elements and hundreds of isotopes are formed in the complex process of nuclear fusion, transmutation and, probably fission in stars, the dozen elements of the man-made trans-Uranic series are not formed naturally.

Even more curious is the fact that the steady state theory of the formation of the universe assumes that stars were formed by the gravitational collapse of very large clouds of hydrogen gas which created such high temperatures and pressures that nuclear fusion reactions took place in them without any external detonation. But regular hydrogen found abundantly in the water of our oceans and whose nucleus has only one proton does not take part in nuclear fusion no matter what you do with it. Only isotopes of hydrogen such as deuterium whose nucleus has both a proton and neutron and tritium whose nucleus has one proton and two neutrons take part in nuclear fusion. So it seems that the original gas clouds would have had predominantly deuterium and tritium and so would be the case with our Sun. And since our Earth is believed to have originated from the Sun, the waters in our oceans should have been mostly heavy water in the beginning which may have transformed into normal or light water over billions of years. But then the same would have happened in the stars including our Sun and the fuel for the fusion reactions should have ended ages ago.

The advances in the techniques of radio transmission and reception during the first half of the twentieth century, and the invention of radar and eventually radio telescopes resulted, during the 1960's, in the discovery of some unique phenomena called Quasars, Pulsars and Black Holes. The quasars are very large stars, though much smaller than galaxies, at great distances beyond the limits of our own galaxy (The Milky Way which is known to be so large that light takes a hundred thousand years to travel across it; and containing roughly a hundred thousand million stars) which are not only visible with optical telescopes but also emit radio waves and ultraviolet radiation. Scientists are unable to explain how such relatively small objects can generate such inconceivably large amounts of energy that they appear bright at such huge distances. Pulsars are celestial bodies, again at very great distances, but estimated to have planet (Earth) size dimensions characterized by the emission of regular pulses of radio waves every second or fraction thereof.

Our knowledge about the Earth, the Solar system and the Universe as a whole has been considerably augmented by the data obtained from satellites equipped with sophisticated electronic gadgetry sent into outer space, earth orbit and orbit around the Sun with the help of powerful rockets developed initially for military purposes. The paths of these satellites have, however, remained within the range of the orbital planes of the planets of our Solar system.

To explain the complex cosmological phenomena, a new science of astrophysics has come into existence which correlates the known facts of other disciplines particularly physics with astronomical observations. For instance, several mathematical models of the universe's evolution and lives of stars have been based on Einstein's general relativity. The equations represent such fundamental canons of physics as preservation of the sum total of mass and energy in the universe, the conservation of momentum, the balance of forces etc., and are solved starting with the initial condition that all matter and energy was concentrated at a point in a boundless vacuum where it suddenly exploded, expanded and eventually diluted into what we see as the universe around us, which is still believed to be expanding.

Thus although the void of the universe is assumed to be infinite, the expanded material part must always have a dynamic boundary within which all our observations are limited, enveloped by a larger expanding sphere of radiation energy which must have escaped in all directions at the speed of light; a sort of universe within universe within universe, the radius of the radiation envelop being about twenty thousand million light years if the current estimate of the age of the universe is correct.

As for what came out of the big bang initially, it is obvious that the vital fundamental particles were formed which then combined in their own ways to form subatomic particles and so on.

Oddly enough, all the estimated matter and energy in the universe fails to account for all the gravitational forces that are supposed to be acting in it; and hence the existence of large quantities of some sort of speculative dark matter beyond perception is suspected, perhaps similar to the apparitions of some religious beliefs. However, there is a spectrum of solutions to the equations of general relativity that range from a continuous and indefinite expansion at the present rate to an eventual slowing and subsequent contraction to a dense state. Identical analyses can be carried out for either the entire universe or a single star or galactic system. The pulsars, thought to be the remnants of such collapsed stars are also called neutron stars and are believed to consist largely of tightly packed neutrons with a density that is a few billion times that of earth such that a cubic centimeter of their matter would weigh a few million tons on earth.

Many astrophysicists believe on theoretical grounds that the gravitational collapse of a star could create a high density object whose gravitational field would be too strong to allow anything -- including light waves -- ever to leave the body. Such hypothetical objects are called "black holes", because light and other signals being unable to emerge from them, their matter has literally disappeared from view, although they continue to influence the motion of other stars in their vicinity. Based on irregularities in star movements and the emission of very short wavelength radiation, a number of black-hole locations have been conjectured by astrophysicists. What is more interesting is that scientists believe that the normal laws of physics would not be applicable in the vicinity of black holes which are said to be capable of "devouring" any matter that approaches them and loses its physical structure.

We thus find that an extension of our knowledge of Physics and Astronomy brings us to a point where we must start looking for a new set of physical laws which could naturally bifurcate into two sets of physical laws, one governing the events in our galaxy, and the other in the vicinity of the black holes. For those who believe that the laws of physics are universal and everlasting, this must be a minor shock. On the lighter side, blackholism seems to have existed among people for some considerable time in the form of persons who are always ready to grab but never willing to give away anything, and somehow they seem impervious to all norms and laws.

Democracy

After years of correlation of information I have come to the conclusion that democracy can and should be defined as follows:

Democracy is that form of government in which all lands of the country along with its assets, state treasures and right to make laws other than religious tenets belong to the people; no individual including the heads of state and government has the right to spend state or public funds at his or her discretion; and all citizens including holderes of high office, public representatives, civil servants and military are bound by the rules and instructions collectively issued by a body of elected representatives of the people on an equal basis while having the right to exercise basic human rights and a universal obligation to accept and obey the judgment of courts of law.

Conversation in Heaven – 2

 Is the Earth maintaining its course and orientation?


Yes. All the volcanoes fired at the right time and course and attitude corrections have been taking place automatically.


How do volcanic eruptions affect life on Earth?


In the old days animals used to panic and some would be killed or injured by the lava, debris and smoke. Now human beings too suffer losses of life and property. Sometimes entire town are flattened.


Can they find a way to protect themselves?


Human beings have been trying to unveil the secret causes of natural disasters by scientific investigation. They have set up warning stations so that areas likely to suffer may be evacuated.


Has it affected the evolution process?


Yes, we upgraded the genetic code to ensure that human beings sympathize with and help each other in the case of natural disasters overriding their tribal differences.

5. THE QUANTUM LEAP IN SCIENCE

The dawn of the twentieth century heralded a new era in intellectual and experimental pursuits of understanding the nature of the universe around us. Not only did man achieve a long cherished dream of flying in the air, but nature was seen from viewpoints previously unimagined. In 1901, Max Plank in connection with "black body" radiation, proposed the quantum theory of radiation, which was definitely formulated by Einstein in 1905. According to the Quantum theory radiation occurs, not continuously permitting all possible values as assumed by the wave theory, but in a discrete quantified form, as integral multiples of an elementary quantum of energy. This means that energy should be considered atomic in nature like matter. The concept was verified by Compton in connection with the scattering of X-rays and Plank's hypothesis was extended to the extent that radiation is considered corpuscular in nature, made up of discrete quanta, which are shot out in space with the velocity of light. This, however, did not nullify the previous proofs that light and other radiations are waves. The quantum is now known as photon, and its energy is given by hf or more accurately (1/2+n)hf, where n is an integer, h the Plank's constant having an accurately determined value of 6.624x10-34 joule-second, and f the frequency of radiation. (Looking at the construction of the energy expression and the unit of the Plank's constant this author is tempted to suggest that it could be an integral of energy with respect to time. It is dimensional problems like this that have resulted in the introduction of dimensionless expressions in thermodynamics and fluid mechanics.) The photon is said to have no mass of its own for reasons to be discussed later. The quantum theory has been instrumental in explaining the photoelectric effect, commonly observed in solar cells which would have worked just as well even without the quantum theory, though their development may not have been as rapid.

It may be stated here that zeros are basically of two kinds -- the subtractional zero which can be obtained by repeated subtractions and represents nothingness, and the divisional zero which is obtained by repeated divisions and represents a negligible fraction. The quantum theory, in a way, defined the ultimate fraction or arithmetical atom that could be treated as a basic unity; thus doing away with the divisional zero that could have diverse negligible values. Mathematical propriety dictates that if a=0 and also b=0 then you cannot write a=b since it would lead to a/b=1 or 0/0=1 which amounts to making something out of nothing. Indeed, many such situations arise due to taking x^0, whose value is unity, as a function or part of a function of x. In fact, a constant numerical term in a function definition indicates origin relocation.

In 1905, Einstein theorized the constancy of the speed of light irrespective of the motion of the source or the observer by putting forward his famous theory of Special Relativity. The two fundamental postulates used in the theory are:

a) Measurement of absolute motion is impossible to an observer stationed on a moving system.

Comment: The measurement of absolute motion requires reference to a permanently fixed or unmoving point within the field of observation or perhaps the universe which we do not seem to have discovered yet because we have not looked for it. Equally it is impossible to conceive relative motion without assigning absolute motion to the observer or the observed or both.

b) The velocity of light is constant, independent of the relative motion of the source and observer.

Comment: It would apply perfectly to waves generated in a vast medium such as water (the ether is undone) in which two persons may be rowing their boats, but when you consider a travelling source throwing corpuscular projectiles being observed by another moving observer it becomes complicated to say the least. Waves possess velocity of propagation which can not be compared with the velocity of transportation possessed by particles.

He then went on to set up the constitutive equations of motion for two sets of reference frames having a uniform relative translatory motion with respect to an event visible from both reference frames, using independent time and space variables for each system with the speed of light as a constant. He used a unique technique of implied division by masked zeros developing equations of the form ax0=bx0 which, depending on progressive manipulations, can give various solutions of the type a=bxc where the sign and value of the constant c would depend on other constants and intermediate mathematical operations. By dexterous manipulation of these equations he deduced the interrelationships of the time and space variables in the two systems, which turned out to be identical to the Lorentz's transformation equations. Later scientists have used different mathematical tools to arrive at the same conclusions. In a nutshell, these equations mean that simultaneous time and distance measurements made from two vantage points moving relative to each other will have different values, and events that appear simultaneous to one observer may not seem so to the other. The two should agree to disagree. However, they do not contradict the fact that a particular event should instantaneously appear exactly the same to any observer irrespective of his speed and direction if occupying a particular location in space at a particular time, e.g. pictures taken with a high speed camera.

Since the variables are related to each other by a numerical quantity given by (1-v^2/c^2)^1/2 where v is the relative speed of the systems and c the speed of light, and since it is inconceivable for the term to be an imaginary quantity, v cannot be faster than c; or in other words, nothing can move faster than light. A corollary of the theory also gives an equation for the addition of velocities which ensures that the resultant will not exceed the velocity of light, so that two photons linearly approaching one another, each travelling with the speed of light have a relative velocity equal to the velocity of light, not twice. Such a postulate can only be satisfied by adjusting or redefining the unit of time as a half of the normal second with reference to the specific situation. This compression of the second would, of course, be only a mathematical manipulation and not affect any natural phenomena. The basic flaw in the time dilation concept seems to be that time lag or observation delay due to the time taken by light to reach an observer, which is an aberration and changes with distance irrespective of speed of travel, has been confused with real time.

Another expression derived from the principles of relativity is of the form m = m0/(1-v2/c2)1/2; where m0 is the rest mass i.e the mass of a body measured when at rest relative to the observer, m the "effective mass" i.e. mass of the body measured when it is moving with a velocity v relative to the same observer, and c is the velocity of light. Since v is always less than c, m will always be greater than m0 except when v itself has an imaginary value which is regarded as impossible. It can be shown that the increase in mass is approximately equal to the kinetic energy divided by c squared.

This brings us to the most famous of Einstein's deductions -- the mass-energy relationship given by E = mc2, where E is the energy equivalent of mass m. In other words, one kilogram of any substance is equal to 9x10^16 joules or 2.51x10^10 kilowatt-hours of energy and vice versa. This means that even if all the earth's known resources of energy production were utilized, no more than a few tons of matter would be produced in a year. However, it is this conversion of matter into energy that produces all the heat in the nuclear fission reactors. But of course, the reactors would have worked the same even if the equation was not known. The mass-energy relationship was verified by Kaufman and Bucherer using the electrons of Beta rays from radium with widely different velocities, ranging up to as high as 0.99c. The mass-energy relationship carries interesting implications for the elastician. If the velocity of electromagnetic waves or light c is taken as the equivalent of distortional waves in a solid elastic medium, and the energy equivalent of mass as strain energy, then mass becomes a function of strain in the medium.

The confirmation of special relativity and its corollaries ushered in a new era of natural philosophy. The classical theory of mechanics in which the sums of forces and moments at a point had to be separately zero and matter and energy had to be conserved individually was superseded. It was obvious that accurate results could only be obtained by balancing the accounts of the energy equivalent of mass as well as the other forms of energy such as kinetic, potential, inertial, deformational etc., or the mass equivalent of the energies as the case might be.

Rutherford carried out experiments on the scattering of alpha particles, which are the positively charged bare helium nuclei, by thin foils of matter and found that although most of the alpha particles suffered only small deflection due to multiple scattering, yet there were a certain number that were scattered through much larger angles. To accommodate this phenomenon he proposed, in 1911, the nuclear atom model in which most of the mass and positive charge was concentrated at the center forming the nucleus, and the electrons revolved in circles around the nucleus in a manner similar to the planets revolving around the Sun. Although this model solved Rutherford's immediate problem, it was found to be in conflict with the electromagnetic theory, as revolving electrons must emit radiation at all times, and constantly consume energy which would compromise the stability of the atomic structure. Twelve years later in 1923, Niels Bohr applied the quantum theory to the Rutherford atom model and developed his theory of atomic structure which is now widely accepted in a further modified form as it resolves many of the dilemmas faced by earlier physicists. The theory is based on two postulates reproduced below as stated by Rajam:

i) The first postulate referring to the electronic structure, states the electrons cannot revolve in all possible orbits as suggested by the classical theory, but only in certain definite orbits satisfying quantum conditions. These orbits may, therefore, be considered as privileged orbits, non radiating paths of the electron.

ii) The second postulate referring to the origin of spectral lines states that radiation of energy takes place only when an electron (instantaneously) jumps from one permitted orbit to another (without existing in any intermediate location - hence the phrase quantum leap). The energy thus radiated which is equal to the difference in the energies of the two orbits involved must be a quantum of energy hv.

The mathematical deduction based on the above postulates produced quantitative results which agreed with available experimental data, and thus the assumptions were accepted as physical laws.

Bohr's simple theory of circular orbits, in spite of its many successes, was unable to explain certain fine details of the hydrogen spectrum such as the Balmer series, suggesting that for each quantum number there might be several orbits of slightly different energies. Somerfeld, in 1915, modified Bohr's theory by introducing the ideas of motion of electrons in elliptical orbits and of the consequent relativistic variation of the mass of the electron. By the application of the relativistic mass energy relationship, he found the path of the electron to be a complicated curve, known as a rosette -- a precessing ellipse, doubly periodic. In interpreting the observed fine structure of spectral lines, he was forced to introduce a selection rule to preclude some of the orbits permitted by his mathematics. The Rutherford-Bohr-Somerfeld atom model was only a partial success as it could only predict three out of five components of the H-alpha line. Nevertheless, Somerfeld was able to underscore the concept of "Spatial Quantization" i.e not only distances and forms, but also directions must have discrete values with permissible conditions. Nature's limitations were getting more and more exposed. The void was beginning to develop holes. In 1923, Uhlenbeck and Gouldsmit in order to explain satisfactorily the intricate spectral phenomena such as the fine structure and the Zeeman effect i.e the splitting of spectral lines under the influence of an applied magnetic field, put forward the hypothesis of the spinning electron, with a spin quantum number which is always 1/2 for an electron although most other quantum numbers are integral. Plank's joule-seconds had to be multiplied with something having time in the denominator to give straight forward energy.

Thus came into being the Quantized vector atom model which was further developed by Pauli, Stern and Gerlach with the help of a host of others. Although this is not the last word in atom models, we will stop here and take a look at some of the parallel developments.

Minkowsky, using the principles of special relativity and the four dimensional geometry of Rieman was able, in 1908, to present to the world a new and unique concept of four dimensional space time continuum which is represented mathematically by the second order differential equation ds2 = dx2 + dy2 + dz2 + c2dt2. The square of time has no practical significance by itself, but multiplied by the square of velocity it represents an area like the other terms of the equation. Similarly, in the Cartesian coordinate system x*y, y*z and z*x represent area but x*x means nothing. In terms of 20th century physical science this means that the minute displacement represented by ds is not completely described by the three coordinate dimensions dx, dy and dz, as in classical Euclidean geometry; but in addition by the time dimension dt also, forming the fourth coordinate of relativistic geometry. The quantity ds is renamed as a "point event" and is not exactly a distance in space, but an element in the four dimensional Minkowsky space-time continuum which is `simultaneously finite and boundless.' However, in this continuum, matter is able to assert itself as "the pressure of matter distorts the curvature of the four dimensional space-time continuum which is the physical universe." Einstein was able to correlate the idea with the balancing of centripetal and centrifugal forces in a string and stone respectively, which are attached and whirled giving the stone a curvilinear motion. In 1915, he extended his special theory of relativity that was limited to systems with uniform linear motion, to encompass systems moving in any way, even with accelerated velocity, and in particular to a special case of accelerated motion that is involved in the most common phenomenon of gravitation. Using, in turn, Minkowski's model, Einstein in his General Theory of Relativity worked out the law governing the motion of a body in a distorted and curved space-time continuum using the advanced mathematical tool of tensor calculus. He was able to show that Newton's inverse square law of gravitation is a first approximation of his relativistic law which is claimed to have been successfully tested in several astrophysical phenomena, such as the advance of perihelion of the planet mercury, the shift of spectral lines in the light received from the companions of Sirius etc. Now, if space can be pulverized (quantized) and curved under pressure, it can hardly be a void; it seems more like a personality.

With the advent of the quantum theory, physicists were obliged to admit a dual nature, wave and particle, for radiant energy for the simple reason that the Plank energy equation contains a frequency term for the photon that is assumed to be a massless particle. In 1924, Louis de Brogli took a bold step forward and suggested that matter, like radiation, has dual nature i.e particles believed to possess discrete rest mass such as molecules, atoms, protons, electrons and the like might exhibit wave-like properties under appropriate circumstances. There was a certain amount of initial pessimism about the theory of matter waves which later came to be known as de Brogli waves because of their difference from electromagnetic waves as their velocity of propagation is given by u = c2/v, where v is the velocity of the moving matter and c the velocity of light. The de Brogli waves have a wavelength L=h/mv, where h is Plank's constant and m the mass of the matter particle. However, the discovery of the diffraction of electrons in 1927 by Davisson and Gremer provided experimental confirmation of the theory. Dempster (1927) and Esterman (1930) obtained diffraction effects with hydrogen and helium atoms, thus lending support to the matter wave theory. The only snag is that u can be greater than c since v is less than c which, oddly enough, Einstein did not mind. So, in view of the rule that wave velocity is the product of wave-length and frequency, it may be said that every particle of matter has a characteristic frequency given by f = mc2/h, for notations defined earlier or a characteristic time period of 1/f.