Saturday, December 18, 2010
3. THE SCIENTIFIC ERA
Unfortunately, the great debate started by Democritus and Aristotle was halted by political upheavals in the region for nearly a millennium until the scholars of the great Islamic civilization of the Middle East and Central Asia, including Arabia and Persia, revived and translated the great Greek philosophical works. Even today, in the Muslim countries there are schools of thought devoted to the teachings and techniques of Pythagoras and Aristotle, with inevitable adaptations and variations. Nawab Mohammad Yamin Khan in his relatively recent book "God, Soul and Universe in Science and Islam" describes God as a Universal Intelligence that controls all phenomena. Averros (Ibn Rushd, 1126-96 C.E) is said to have believed in the eternity of the world (not as a single act of creation but as a continuous process) and in the eternity of a universal intelligence, indivisible but shared in by all. Similar ideas are attributed to Ibnul Arabi. The pioneering work in physics, chemistry, astronomy, mathematics, optics, medicine etc. by such scientist of those days as Ali Ibn Sina (Avicenna, 980-1037 C.E), Al-Khwarizmi (780-880 C.E), Al-Kindi (800-873 C.E), Jaber bin Hayyan (Geber, 721-815 C.E), Omar Khayyam (1050-1123 C.E), Ibnul Haytham (965-1039 C.E) and Al-Beiruni (973-1048 C.E) etc. paved the way for the European scientists and mathematicians who developed the current scientific vocabulary and techniques. The separation and identification of generic chemicals, the discovery of the principles of optics, the development of algebra, geometry, exponents, polynomials, logarithms and the concepts of calculus, the cataloging of botanical species, indexing of astronomical observations etc. provided a useful information base for scientists in areas where metals and other resources were easily available and working close to fire was relatively comfortable. The initiation of the use of mechanical implements, the exploitation of wind power and techniques of evaporative cooling were, indeed, pointers to things that were to come in future. Alchemy or the attempt to produce gold by combining or altering other substances was, perhaps, the embryonic form of the industrial movement whose object is to add value to insignificant materials. Today, apparently worthless materials are processed to the extent that the final products may exceed the worth of their weight in gold. Many Muslim philosophers of the era, commonly known as Sufis, put forward the notion that the universe consists of an interplay of light and darkness in a continuum of geometric space and time. They chose mostly poetry rather than mathematics as their medium for expression and it takes a complex analytical approach to decode their ideas in contemporary parlance.
From the sixteenth to the nineteenth centuries, Europe saw some very interesting philosophical discussions cutting across the borders of science and religion, on questions such as: whether or not God exists, and if so how he interacts with the material universe; whether or not the soul exists, and if so how it interacts with the body; and whether or not man is free to shape his own destiny. Some of the well-known participants in the debate were Bacon, Hobbes, Descartes, Spinoza, Pascal, Calvin, Luther, Locke, Hume, Leibnitz, Voltaire, Rousseau, Kant, Fichte, Schopenhauer, Schelling and Hegel who, together with such others as Nietzsche, Dante and Goethe etc. produced the bulk of what could be called modern European philosophical heritage. By the end of the nineteenth century, Marx and Engels developed their concept of dialectical materialism that contradicted everything that made sense until then in social, religious, political and economic fields. Science was the only undisputed branch of knowledge. The Marxist reaction does not seem altogether incongruous when one considers the fact that many serious intellectuals of those days were convinced that mankind had finally evolved into two distinct species discernible as the ruling and working classes. Some other examples of dichotomacious illusion are Christian-nonchristian, Muslim-nonmuslim, Jewish-nonjewish and Aryan-nonaryan -- both Indian and German varieties.
During the 16th and early 17th centuries, the works of Copernicus, Brahe, Kepler and Galileo established that the earth and other planets rotate and revolve around the Sun in elliptical orbits and telescopes revealed the distances and motions of the stars. The principle of gravitational acceleration was deduced and the invention of the telescope paved the way for the calculation of the distances of various stars from the earth. Simply by measuring the change of the angular bearings of a star over a six month interval and dividing the diameter of the earth's orbit around the Sun by this quantity, it became possible to calculate its distance from the earth or the sun. Apparently fixed stars were used for reference. Today we believe that the universe consists of thousands of galaxies, millions of light years apart, which in turn comprise of thousands of star systems and that Aristotle's crystal spheres do not exist.
In the period spanning the 17th and early 18th centuries, a group of brilliant scientists and mathematicians, notably Newton, Leibnitz, Huygens, Hooke, and Boyle produced calculus and the laws of mechanics, optics, thermodynamics and observations on magnetism and gravitation with experimental verification that transformed the face of the earth. Things would no longer happen by the will of the gods or kings, but by the laws of physics and other sciences to be developed in subsequent years; in spite of the fact that Newton himself is stated to have "considered that God had made the universe from `small indivisible grains of matter'." Newton perceived the formula for gravitational forces between objects also known as `Newton's Law of Gravitation' F=G.m1.m2/d^2 where F is force between two bodies of masses m1 & m2, a distance d apart and G the universal gravitational constant and measured it from experiments with brass balls and torsional pendulum now believed to be 6.673x10^-11 Nm2/Kg2. From this and the value of the acceleration due to gravity on earth's surface as 9.81 meters per second per second (9.81 m/s2) it is possible to calculate earth's mass as 5.97x10^24 Kg. By equating the gravitational force between Earth and the Sun with the centripetal force (F=mrω2 where m is mass of Earth, r is distance between Earth and Sun and ω the angular velocity of Earth around Sun) it was possible to determine the mass of the Sun and similarly all other heavenly bodies.
It is common observation that cohesive forces among the molecules of a body weaken as its temperature rises and become neutralized when it turns into liquid. The force further weakens with increase in temperature until it becomes repulsive when the substance turns into a gas, and the repulsion continues to grow with temperature. It is not clear whether gravitation is modified by temperature or thermal repulsion is a different phenomenon.
Although not commonly highlighted, perhaps, the greatest contribution of Newton and his contemporaries was the development of the consciousness that momentum and energy - kinetic and potential - are essential components in the existence of matter. Momentum is given by the product of mass and its velocity or the integration of force over time; whereas energy is produced by the integration of force over distance. Conversely, the differentiation of momentum with respect to time produces force and so should the differentiation of energy with respect to length or distance: an idea not yet fully developed although it is quite apparent in pulling and pushing and the effects of receiving or emitting radiation at one surface. In simple terms, it is this author's assertion that applying force at a point is nothing but creating an energy differential across it and motion from a higher energy state or location towards a lower energy state or location in a dynamic or kinematic sense is similar to the thermodynamic process of convection. Heat itself does not have a physical existence, but is a measure of energy level with a specific transfer mechanism. The same could be said of electricity, except for its sign i.e positive and negative. Both momentum and energy are considered indestructible. While momentum can only be transferred from one body to another, energy can manifest itself in many forms i.e kinetic, potential, thermal, light, sound, electrical charge, magnetism etc. Although momentum and energy are both derived from velocity, they do not reconcile if all the energy and momentum of one body is transferred to another of differebt mass ( v2/v1=m1/m2 from momentum and (m1/m2)^0.5 from energy).
Integration over time is like collecting water flowing from a hose into a bucket. The water flow rate is the differential and the bucketful the integral. Now it is not possible to reverse the conditions in the hose and bucket, except on paper by differentiation or in reality by applying a new set of appliances; although a new differential can be created by tilting the bucket. However, in elastic systems a certain amount of reversal in distance is possible by virtue of the stored elastic energy which is often dissipated by oscillation; but reversal in time is not possible. It should be noted that if the flow-rate in the aforementioned hose is not constant, and differs with the time of the day then the amount of water collected in the bucket in say five minutes will be different depending on whether it was collected in the morning, noon or evening of a particular day. It is, therefore, important that the symbol representing the result of integration must indicate the relevant limits of integration. It is interesting that scientists have been so preoccupied with Pythagoras' theorem that they are convinced that velocities can be added vectorially because they can be represented by straight lines and not as the consequence of the summation of kinetic energies related to the velocity components in two perpendicular directions (0.5mV^2 = 0.5mVx^2 + 0.5mVy^2). Similarly, the resultant of numerous forces acting on a body is not a game of arrows but the identification of the sum of components in a unique direction in whose normal plane the projections of all the forces add up to nothing.
Newton's laws of motion are regarded as a breakthrough in science, and paved the way to the eventual landing of man on the moon. However, some very interesting situations arise if one analyses the motion of things as one observes on earth, and as they would appear from outside the earth. Let us take a seemingly stationary brick of one kilogram mass and apply a force of one newton to it so that it is accelerated by one meter per second per second for a period of two seconds, at about noon on a clear sunny day close to the equator. During these two seconds, the brick will attain a linear velocity of two meters per second and a kinetic energy of two joules. The work done by one newton over a distance of two meters would also be two joules. So everything works out fine. But the earth, due to its daily rotation around an axis and annual revolutionary motion around the sun, has a surface linear velocity of nearly 29,336 meters per second, which also applies to any person or object on the earth. Hence, to an observer outside the earth, the brick had an initial velocity of 29,336 meters per second which was increased to 29,338 meters per second. This should result in a kinetic energy increase of 1/2x293382-1/2x293362 = 58,674 joules. Similarly, the extraterrestrial observer would also notice that the brick moved a total of 58,674 meters during the two seconds, 58,672 meters with the earth and 2 meters on it under the force of one newton; so that the work done should be force times distance i.e 58,674 joules. By the same token, an observer beyond the solar system would get even larger figures for the same phenomenon as he would also add the drift of the solar system. The question, therefore, is: Who is right? Obviously, the earth-based observer can support his calculation with the muscular or mechanical energy spent in the exercise which compares with the two joules figure. Similarly, the extraterrestrial observer might notice a slowing down of the earth or a change in the entropy of the overall solar system comparable with his own observation of changes in velocity and kinetic energy of the brick. One could satisfy himself by saying that whereas the earth-based observer is accounting for events relative to the time when the brick started accelerating, the observer out in space is doing the same with reference to the time when the parent system, the earth started moving. But such a statement would be neither mathematically nor philosophically convincing. Only it can be said with certainty that in a moving reference frame if the primary and secondary motions are parallel, then the apparent work done equals the apparent change in kinetic energy whether one considers the relative or the absolute motions. The primary motion defines the positive direction. If the secondary motion is at an angle to the primary motion then its components parallel to the primary motion and at right angles to it should be treated separately for the application of the conservation principle. Now, could it be that for a very modest expenditure of energy by us, nature sometimes has to pay significantly more in overheads? The problem can be looked at in two different perspectives by analogies. The first analogy is that of delivering a parcel to someone in another city. One can do it himself by taking a taxi to the airport, then a plane to the other city, then again a taxi to the address where the parcel is to be delivered. This would involve a considerable expenditure, not counting the return journey. The same result can be achieved much cheaply by walking to the nearest courier service or post office and making a relatively small payment. The difference in cost seems intriguing until one finds out that the courier who travels to deliver the parcel carries many other parcels also with him, or there is a complex but well organized postal system which makes the job so cheap.
The second analogy is that of driving a car. To a nontechnical person it involves the filling of fuel tank with petrol, turning the ignition key, moving the steering wheel, manipulating the pedals, changing gears by moving a lever and giving signals by operating the indicators. It all involves such an insignificant amount of effort and energy. Most of us have observed the child who jumps on the driving seat and enthusiastically swings the steering wheel hoping that it would move the car because that is what his observation has been limited to. Similarly, a naive researcher may spend a lifetime studying the behavior of cars and succeed in drawing only a few conclusions about when the blinking lights occur and so on; but ever thing may seem quite simple if he talks to drivers and mechanics or reads the highwaycode and the car manual. However, the automobile engineer sees the motion of the car in terms of the flow of currents, the flow of fuel and air into the engine, the movement of the butterfly in the carburetor and other valves, the ignition of the mixture in the cylinders, the thrust on the pistons, the torque on the crank shaft, the transmission of forces through the gearbox, connecting rod, and differential, the multiplication of forces and movements in the steering mechanism and so on. The designer has his own considerations in terms of thermodynamics, mass flow, kinematics, aerodynamics and strength of materials, to name a few topics. Could it be that our perception of the universe, in spite of all our scientific knowledge, is of the order of the comfortable driver rather than the automobile engineer who sees many a horsepower at work in the engine? In any case, the above observations are enough to caution us that an immodest manipulation of forces or energies on earth could create a considerably magnified effect somewhere to cause instability in one of the systems essential for our survival.
Another divergence that one comes across in the same era of scientific investigation is in the theories of light as put forward by Newton and Huygens. Newton, on the basis of the observations of reflection and refraction of light by Kepler, Descartes, Snell etc. suggested that light consists of minute corpuscles given out by a luminous body. Different colors of light were assigned to different sizes of the corpuscles. Huygens, on the other hand, studied the diffraction of light and was convinced that light is a sort of wave generated by a luminous body in ether, an all pervading elastic substance which filled the entire universe including the intermolecular spaces of solids. A number of optical phenomena that could not be explained by the corpuscular theory were found to yield to analysis based on the wave theory. Maxwell's development of the theory of electromagnetic radiation in the nineteenth century confirmed the wave theory of light and brought the concept of ether to the forefront of scientific investigation.
The eighteenth and nineteenth centuries saw prolific developments in physics and chemistry combined with a very rapid rate of innovation and invention. The progress in basic sciences led to the development of better and more precise equipment and machines which in turn enhanced the capabilities of scientists to conduct experiments and make new discoveries. Some of the notable scientists of the era include Pascal, Benjamin Franklin, Galvani, D'alembert, Volta, Faraday, Joule, Charles, Gauss, Carnot, Ampere, Kelvin, Hertz, Mendelyev, Coulumb, Rankine, Roentgen, and the Curies. Although their work did not directly influence the theories about the universe, the increase in knowledge and understanding of the properties of matter and the scope of their application indirectly contributed to the developments that took place in the twentieth century. John Dalton of this period is credited with the formulation of the modern chemical atomic theory. J.J. Thomson, in 1897, discovered the electron and postulated that atoms consisted of two parts; the spherical shell that contained most of the mass and uniformly distributed positive charges with negatively charged electrons embedded in it. Experiments with Thomson's cathode ray discharge tube and Millikan's oil drop apparatus helped to determine the vital statistics of the electron as being a mass of 9.1x10^-31 kilogram, a radius of 2.8178x10^-15 meter and a charge of 31.85x10^-16 coulombs equal to 1.6x10^-19 joule also known as one electron volt. The electron, thus, has a mass density of 9.721x10^12 kilogram per cubic meter i.e. a liter of electrons would weigh about one hundred million tons if packed closely. This, of course, would never happen as even in the common electrical wire the charge only flows in a thin outer skin because of the repulsion of like charges.
Romer in 1673 determined the velocity of light as approximately 3x10^8 meters per second from observations on the eclipses of the satellites of Jupiter. Bradlay was able to calculate the velocity of light in 1726 from the apparent displacement or aberration of the fixed stars, which he discovered, due to the earth's orbital velocity of about 18.5 miles per second which yielded the value of 185,000 miles per second. Fizeau, using a toothed wheel to interrupt at very fast intervals a light beam which was reflected along the same path, measured the velocity of light as 3.13x10^8 meters per second in air. Foucault using a rotating mirror to produce an image shift measured the velocity of light to be 298,000 kilometers per second. Using laboratory sized equipment and a tube filled with water he found that "light traveled more slowly in water than in air." Later, Michelson with similar apparatus showed that the ratio of the velocities of light in air and water was equal to 1.33 - in good agreement with the value of the refractive index. The velocity of light in water is thus 2.26x10^8 meters per second. However, Michelson found that the velocity of yellow light was 1.76 times greater in air than in carbon bisulphite; the corresponding refractive index of carbon bisulphite is 1.64. This resulted in the discovery of dispersion and the concept of wave velocity and group velocity in dispersive media. As a result of these experiments the wave nature of light was established.
However, neither the corpuscular nor the wave theory explained all the phenomena related to light; although each explained some. Similarly, the assumption of the presence of ether created it's own problems. Michelson and Morley (1881-1887) carried out an ingenious experiment to verify the existence or otherwise of ether by splitting a beam of light into two beams at right angles and then making the two component beams converge at one point to produce interference patterns. But the rotation of the system to align one or the other beam with the orbital movement of the earth (30,000 meters per second) in concurrent and opposite directions did not cause any change in the interference fringe pattern. It was thus concluded that the ether did not really exist and that the velocity of light is invariant in a given medium or empty space where it is maximum and remains constant in all directions. It was also argued that Maxwell's equation did not necessarily require the existence of a hypothetical medium, but could be interpreted in terms of geometrical space. The void was back in place. Until then, time was regarded as a universally invariant phenomenon and distances were considered absolute. However, Lorentz starting with Maxwell's line of reasoning and introducing a moving observer came up with a set of equations that could only be true if time and space were to dilate or become nonabsolute, having different values for different observers.
The realization of the finite velocity of light resulted in the recognition of an obvious element of uncertainty in observed phenomena. A physical change would not be regarded as existing until light from it reached an observer, and even then he would only know the state of affairs that existed when the light reaching him had started from the subject of observation. There is, thus, a time lag between the occurrence and observation of any phenomenon, no matter how small this time lag is.