Twinkle twinkle little stars how I wonder what you are…. Of course we all sometime or other wondered about the stars, moon and sun, but the same may not be said about the space and time except by few. We all move in space and grow up in time. It is part of our daily existence. We got used to them so much that we hardly think about their existence. Since ancient times man is attempting to use space and time to his advantage. Geometry a branch of mathematics evolved for the measurement and study of solid objects in space. Measurement and study of time resulted in development of astronomy. Earth had a special place, it was considered to be at absolute rest and so was the space around it. Time was linked to the motion of sun and moon. The debate on actual nature of space and time is continuing since antiquity. Study of history is a powerful tool to understand nature. Genesis of all inventions and discoveries lies in the past, to study it, is the best way to understand it. The Geek philosopher Zeno of Elea (490-430 BC) held that space and time are unreal since they could neither act nor be acted upon by matter. Space can be defined only where matter exists. Space and time are just relation between objects. They have no physical existence. They cannot be sensed by our senses. Concept of “empty space” was a contradiction in terms, since if space were truly empty it would be nothing and hence nonexistent. He devised number of paradoxes regarding space and time to prove his views which are known as Zeno’s paradoxes. Scientists and philosophers took thousands of years to resolve these paradoxes and many thinks that they are still unsolved. Zeno’s arguments points to the relative existence of space and events .It was an extreme version of the relational view of space. Aristotle (384-322 BC) linked the space to the sphere of fixed stars and earth as center of such space, the sphere of fixed stars contains space and everything and is therefore immovable. The position and motion of other heavenly bodies are relative to this sphere of fixed stars. Space has no independent existence as existence of vacuum is impossible. Similarly he refused to accept that time exists independent of events as without events there will only be present so time cannot exist. Thus Aristotelian view contains both absolute and relational view about space. Nicolaus Copernicus (1473-1543AD) after careful study of planetary motion concluded that all planets including earth revolves around the sun. Earth is not the center of universe. However he did not attach any absoluteness to position of sun. Space was considered to be flat; all the three independent dimensions are perpendicular to each other. Greek mathematician Euclid (300BC) compiled and developed the geometry for such space which is still in use even after more than two thousand years. His book ‘Elements’ consists of 13volumes. Its method consists of assuming a small numbers of (5nos) of self evident intuitive truths called postulate or axioms and deduced other propositions from it.
1. Given two points ,there is a line segment that joins them.
2. A line segment can be prolonged indefinitely in a straight line.
3. A circle can be constructed when its center and distance [radius] are . given
4. All right angles are equal to one another.
5. The Parallel postulate: If a straight line falling on two straight lines . make the interior angles on the same side less than two right angles, . the two straight lines, if produced indefinitely, meet on that side on . which are the angles less than the two right angles.
Einstein once said that a copy of the ‘Elements’ and a ‘magnetic compass’ were the two gifts he received that had a great influence on him as a boy, referring to the Euclid’s ‘Elements’ as the “holy little geometry book”. ‘Elements’ remained unchallenged till 20th century. In the history of mathmatics no book has influenced the world as it did. But its fifth postulate remained controversial. Mathmaticians believed that it is not an axiom in itself, it can be derived from other four postulate. Alas nobody could prove it. Some of them ruined their life in an attempt to prove it. Galileo (1564-1642) in his “Dialogues on the two chief world systems” which he published in 1632 introduced two principles. 1) Principle of inertia 2) Principle of relativity.He put forward that “there is no absolute motion or absolute rest , all motions are relative. If left undisturbed ,a body in motion will continue to move with same constant speed in same direction”. With this the space lost its absolute character . Issac Newton (1643-1727) in 1687 extended these principles in the famous “Laws of Motion” in his published book “Philosophiae Naturalis Principia Mathematica”.However he tried to reintroduce the concept of absolute space, as phenomenon of acceleration could not be explained by relative motion.He logically concluded the physical existence of space which can be sensed by experiments.He conducted the Bucket experiment(1689) to prove the presence of absolute space (Fig-1).
It is a simple experiment. Half fill a bucket with water and suspend it from a fixed point with a rope. Rotate the bucket in one direction, twisting the rope more and more. After the rope has taken all the twisting that it can take, hold the bucket steady till the water get settled down, then let go. The bucket starts to rotate because of the twisted rope. At first the water in the bucket does not rotate with the bucket but remains fairly stationary. Its surface remains flat. Slowly, as walls of bucket communicate their motion to the water, the water begins to rotate with the bucket and the surface of the water becomes concave. As water gains speed and twisting of rope get reduced the relative motion between bucket and water at one stage become zero. Both rotate as one object. After a while due to the opposite twists generated, the bucket stops. Then it starts rotating, in opposite direction. However water keep rotating in same direction with concave surface. Newton asked the simple question: why does the surface of the water become concave? The fact that the water’s surface gradually assumed a concave shape showed that some forces(centrifugal force) are generated, which is possible if it was spinning with respect to ‘something’, or how else would it know what to do? There is indeed a relative motion between bucket and water specifically during initial stages, but definitely it is not spinning with respect to bucket as surface of water is flat. That “something” is absolute space. It demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space. It even proves that inertia of matter is the direct consequence of the existence of absolute space. One can always decide whether he is rotating with respect to the absolute space by the presence of apparent forces produced. His own Laws of motion tells a different story. All motions in the universe are relative, so there is no absolute position in space. This is what Newton’s laws of motion implied. However he refused to accept the lack of absolute space at personal level. He cleverly proved that all inertial references frames are equivalent as transition from one frame to other can be accomplished by Galilean transformation and there is no way to identify the absolute reference frame. Newtons laws assumes following axioms in their formulation.
1. There exists an absolute space in which Newton’s laws are true.
2.All inertial frames share a universal time.
For Gottfried Wilhelm Leibniz (1646-1716), space is nothing else but an order of the existence of things, observed as existing together.A space exists only as a relation between objects, and which has no existence apart from the existence of those objects. Ernst Mach (1838-1916), who was not convinced by Newton’s bucket argument, wrote in The Science of Mechanics (1883): “No one is competent to say how the experiment would turn out if the sides of the vessel increased in thickness and mass until they were ultimately several leagues thick”. A sufficiently massive bucket, in other words, might carry the local inertial frame of the water around with it, leaving the water’s surface flat. This idea is now known as Mach’s principle. There were no dispute regarding geometrical properties of space and all mathematicians, scientists, philosophers seems to be in complete agreement with each other till the beginning of 20th century, when general theory of relativity is introduced by Einstein. However the physical properties of space were always controversial. Though space was considered to be a separate entity, yet space devoid of any matter i.e. vacuum was unthinkable in ancient and medieval times. Aristotle said ‘nature abhors a vacuum’. With the discovery of vacuum by Italian scientist Evangelista Torricelli in 1643 this controversy was put to rest. Newton considered space to be void where things exist and phenomenon occurs. However discovery of gravitation raised new doubts. Newton’s law of universal gravitation was an elegant mathematical equation, which accurately explains the natural phenomenon but failed to explain the physicals nature of gravity. Newton was uncomfortable with the two aspects of his law 1. Action at a distance 2. Instantaneous action at a distance. In his 1692, letter to Bentley, he wrote: “That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.” Newton’s contemporaries tried to explain action at a distance by the presence of a medium in and around the objects.The action is transmitted by movements or by elastic deformation of this medium. They called this medium aether. Newton himself attempted to put forward his own hypothasis on these lines but remain unimpressed by his own thoughts. In the second edition of Principia he wrote: “I have not yet been able to discover the cause of these properties of gravity from phenomenon and I feign no hypotheses…. It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies.” In 1678 the great Dutch physicist Christian Huygens (1629-1695) wrote a treatise called Traite de la Lumiere on the wave theory of light, and hypothesized that light is a wave propagating through an aether ‘gas’ permeating all space, but Newton rejected this idea, because such a medium would have to extend everywhere in space, and would thereby give resistance to the motion of celestial bodies. Newton postulated the corpuscular theory of light (1704) in which he also considered a “Aethereal Medium” in which light particle could create a localised wave ,this was necessary to expain the phenomenon of refraction and diffraction of light. However, a century later, In the early 1800, the double-slit experiments by Young and Fresnal provided evidence for Huygens’ wave theories. The double-slit experiments showed that when a coherent light from a source is sent through two adjecent narrow slits, the light coming out of those slits togather form a characteristic interference pattern,such pattern is known to be obtained by waves such as water waves. The wavelength of light can be computed from such patterns. Thus Young and Fresnel revived the wave theory of light. They proposed that light could be a transverse wave rather than a longitudinal wave. However, a transverse wave can propogate only in solid medium.It is realized that aberration and polarization of light cannot be explained by longitudenal wave phenomenon. Augustian Fresnel in 1818 argued that light moved through a rigid and stationary aether as a way to explain the existence of transverse wave. The aether is assumed to be a solid which permeate matter and does not interact with any matter. In 1783 French physicist Charles Augustin De Coulomb published the law regarding the interaction between electrically charged particles. “The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each of the charges and inversely proportional to the square of the distance between the two charges”. The magnitude of the electrostatic force (F) between charges (q1) and (q2), is given by
F = k q1×q2/ r^2
where r is the distance between the two charges and ‘k’ a proportionality constant. A positive force implies a repulsive interaction, while a negative force implies an attractive interaction. The proportionality constant ‘k’is called the Coulomb constant . This is called electrostatic interaction as it is independent of motion of charged particles. Coulomb’s law deals with charges which have always been static. It is similer to the Newton’s law of gravitation with same shortcommings. It assumes action at a distance and instantaneous action. Just like gravity and electric charge phenomenon, magnetism is also known to generate force at a distance. Serious studies were undertaken in the beginning of 18th century. Hans Christian Oersted discovered that an electrical current gives rise to a magnetic phenomenon that encircles the wire. In 1825, Ampère developed it further and published his Ampere law which provided a mathematical description of the magnetic phenomenon generated by a current. Meanwhile over 2000 years of attempt to prove the 5th postulate of Euclidean geometry leads to the discovery of new geometry later known as non Euclidean geometry. Nikolai Lobachevski, a Russian mathematecian (1792-1856) published it in 1829. This geometry was also developed independently almost at the same time by Janos Bolyai(1802-1860) and Carl Gauss(1777-1855). This is the geometry of curved spaces. Lobachevski called it “imaginary geometry”. This geometry had to wait for about another hundred years before it was discovered that this infact is the real geometry, it is the geometry of nature.Real space is curved. Early on his research on magnetism (1831), Faraday experimented with magnets.He observed the neat continuous curves traced out by iron filings near the magnet.He called them ‘magnetic curves’. Later on he refers to them as ‘lines of force’. These lines of force extending as space was called by Faraday as “magnetic field”. Faraday considered the lines of force as the physical reality of space. Faraday experimentally studied lines of magnetic force and lines of electrostatic force and properties of charge in motion i.e current. He concluded that these lines of force forms a field . He established the causal relation between electricity and magnetism in the form of field. It is now a famous law named after him. “A changing magnetic field, such as a magnet moving through a conducting coil, generates an electric field (and therefore tends to drive a current in the coil)”. This is known as Faraday’s law. “The current created will generate a magnetic field that tends to oppose the change in the magnetic field that induced it”. This is known as Lenz’s law. Faraday was of opinion that force is a substance, and all forces are interconvertible through various motions of the lines of force. He established that electric interaction is not action at a distance nor it is instantaneous.The interaction is by the generated field which travels and takes finite time to interact. So presence of any hypothetical aether permeating all space was not necessary. In 1856 Wilhelm Eduard Weber and Rudolf Kohlrausch performed an experiment to measure the numerical value of the ratio of the electromagnetic unit of charge to the electrostatic unit of charge. The result came out to be equal to the product of the speed of light and the square root of two. Meanwhile, James Clerk Maxwell was working on Faraday’s lines of force. In his 1861 paper “On Physical Lines Of Force” and in 1864 under the title of “A Dynamical Theory Of Electromagnetic Field” he derived expressions for the dielectric constant and the magnetic permeability in terms of the transverse elasticity and the density of this elastic medium. He then equated the ratio of the dielectric constant to the magnetic permeability with a suitably adapted version of Weber and Kohlrausch’s result of 1856, and he substituted this result into Newton’s equation for the speed of sound.He derived a wave equation and shown that it represent a electromagnetic wave that propogate at constant absolute speed which is close to the velocity of light. A changing electric field in space generates a time-varying magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave. In the case of the electric and magnetic fields, the speed is:
c0 = 1 /√ µ0 є0 є0
is the permittivity of free space, μ0 the permeability of free space, c0 is speed of electromagnetic wave in free space. Maxwell discovered that self-propagating electromagnetic waves would travel through space at a constant speed, which happened to be equal to the previously measured speed of light. From this, Maxwell concluded that light was a form of electromagnetic radiation: he gave credit to Faraday’s 1846 paper “Thoughts on Ray Vibrations” for this conclusion. Maxwell wrote: “Faraday discovered that when a plane polarized ray traverses a transparent diamagnetic medium in the direction of the lines of magnetic force produced by magnets or currents in the neighborhood, the plane of polarization is caused to rotate….. The electromagnetic theory of light, as proposed by him, is the same in substance as that which I have begun to develop in this paper”.
So c = c0 = 1/√ µ0 є0
Where ‘c’ is the velocity of light. Later in 1888 Heinrich Hertz demonstrated the emission of electromagnetic waves by a high-frequency electric oscillator. This spectacular discovery confirmed the correctness of Maxwell’s theory. There was need for a propagation medium for such a wave, as electric field is not known to sustain itself without the presence of electric charge and associated matter. Just as waves in water uses water as a medium to move across, and audible sound waves uses solid liquid or gas as medium to move through, so light waves also require a medium, the “luminiferos aether”. Because light can travel through a vacuum, it was assumed that the vacuum must contain the medium of light. The second reason which was necessating the presence of such a medium was the violation of Galilian relativity principle.
Consider a stationary inertial reference frame O (Fig-2)and a lamp at rest in the free space of O. If lamp is switched on , the rays of light will start propogating in all directions with same velocity given by Maxwell’s equation. As permittivity and permeability of free space is same everywhere the velocity will be independent of place and direction so velocity of light will propagate with constant velocity ‘c’ in all directions. Now consider another inertial reference frame O’ moving parallel to O with uniform velocity ‘V’ as shown. The permittivity and permeability of free space being independent of motion, it will be uniform and isotropic in O’ frame also. So the velocity of light in O’ will also be ‘c’ every where and in all directions as per Maxwell’s equation. So when light is switched on and each observer in O and O’ make measurement of light velocity , both will get same value given by maxwell’s equation i.e ‘c’. Which implied that the velocity of light is independent of frames of reference. During those period Galilean principle of relativity was well established and it is understood that all laws of mechanics must conform to Galilean transformation in order for them to be true. In the reference frame O the light will propagate with constant velocity ‘c’ in all direction. Now if we apply Galilean principle of relativity, what would be the value of velocity of light emitted by the lamp at O when measured from O’? As all motions are relative we will get different velocity in different directions, e.g the velocity of light ray traveling parallel along x axis in same direction is given by (c-V). Light ray traveling In opposite direction along x axis will be (c+V). This is contradictory to the result obtained through Maxwell’s equations, which predicts a absolute velocity for light. Now the law of electrodynamics which is well established and experimently proven not conforming to universal law of mechanics is quite distrubing. How to reconcile it?To have absolute velocity there must be an absolute rest, a frame of reference which cannot be moved. It was hypothesized that a ‘luminiferous aether’ permeate all space and self propogating electromagnetic wave like light, travel through it as mechanical disturbance. So aether becomes a immobile and unique frame of reference which is uniform throughout universe in which Maxwell’s equations holdes true, all electromagnetic phenomenon occur in this absolute frame only.The relationship between other reference frames remain as given by Galilian transformation. Maxwellian space has thus become more like the absolute space of Newton.Maxwell himself proposed several mechanical models of aether. Now how to detect that special frame of reference of aether or the frame of absolute rest? We all experience the flow of wind on our face from opposite direction while travelling by bus even when atmosphere is calm and air is still. Our earth is in motion around the Sun, it is hurling at speed of 108000km/hr. Sun is also in motion within the galaxy, and galaxy as well is moving with tremendous speed in the universe.Earth is also rotating on its axis. So actual speed and direction of motion of any point on earth relative to aether is uncertain. For the purpose of clarity if just for a moment we assume that sun is stationary relative to aether frame, then our earth is moving with the said speed in the sea of aether. Can we detect the aether wind on our face? The very definition of aether does not allow this. Aether does not interact with matter readily,has undetectable density, rigidity etc. However there is a easy way out as also pointed by Maxwell. With in the aetheral frame, light travels with same speed in all direction so when measured from earth as reference, light travelling along the direction of motion of the earth would have a different speed than light traveling backward.
Refer Fig-3 if ‘c’ is the absolute velocity of light in aether and ‘v’ is the absolute velocity of earth at certain point relative to aether ( absolute velocity will vary from point to point in orbit). Two rays of light comes to earth from two opposite direction along the direction of motion. The instrument at earth will read velocity of light from upstream side as (c+v) and that of downstream as (c-v). On this line of thinking in 1887 Albert Michelson and Edward Morley devised an experiment using apparatus of very high accuracy. It cannot measure the velocity of light , it was designed to detect any change in light velocity due to aether wind. It was so designed that it can be rotated to any direction and can continuously measure the velocity difference over a period of time, this was necessary as magnitude and direction of aether wind is uncertain. However no aether wind was detected. More accurate similar experiments and also experiments based on other principles were carried out , all gave null results.This made scientists more and more obsessed with aether. Many magical, invisible and strange properties of aether were assumed to explain the null result. Lorentz introduced a revolutionary idea, aether is completely motionless, nothing can move it or disturb it mechanicaly. Electromagnetic property is the property of aether not of matter, electric and magnetic field represent the states of aether like state of matter solid, liquid and gas. Material bodies are made of elementry charged particles (electron) spaced togather, however there is strict separation between matter (electrons) and aether, elementry particles are only responsible for carrying and movement of charges the electromagnetic field of the aether is the communication mode between the electrons. Thus an abstract electromagnetic aether replaces the older mechanistic aether models. Thus Lorentz’s aether has only two properties 1)- It is the seat of electromagnetic field 2)- It is immobile. To explain the null result of Michelson and Morley experiment ,he introduced the concept of physical length contraction of body in motion and to explain the aberration of light and Fizeau experiment he introduced concept of local time in 1895. These resulted in what is now known as “Lornetz transformation equation”. Albert Einstein(1879-1955) on the other hand was fascinated by the constant velocity of light as predicted by Maxwell’s equations. However assuming existence of absolute reference frame for this theory to holds true, was unacceptable to him. Only simple and logical way he thought was to abandon the aether theory. But how to resolve the two issues now related to aether ? 1- Existence and propogation of electromagnetic field in space. 2- Violation of Galilean principle of relativity. He reasoned that, the assumption that a universal medium aether is present is unnecessary. The electromagnetic fields are not states of a medium, and are not carried by anything. But they are independent realities which are not reducible to anything else, exactly like the atoms of ponderable matter. Electromagnetic radiation, like ponderable matter, brings impulse and energy with it, and both matter and radiation are but special forms of distributed energy. To resolve the second issue, he revolutionized the very concept of space and time. In 1905 he published what is now called Special Relativity. He treated space and time as dependent on velocity and discovered that free space and time has flexible existance like a rubber.The space can be contracted and time can be stretched. He linked this flexibility to limiting velocity of light. He established that space, time and motion is related by Lorentz transformation equation. The Galilean transformation is just a special case of Lorentz transformation. He further revolutionized the concept of space-time in his General theory of relativity. He established that matter deforms the space-time geometry around it. Geometry of space is not Euclidean , but curved. The shortest distance between two points is not straight line, but a curve. The objects moves along this curved space time.We call this phenomenon “gravity”. As space is considered to be curved, light coming to us from stars travels along these curved paths. So it can be concluded that the position of stars as we see in the sky are not real position, but the apparent positions ( Fig- 4) as projected by light.
However the curvatures in space is not as steep as is shown here, otherwise we will be seeing multiple images of star in different directions everywhere. Most of the universe is devoid of any matter. The density of interstellar space is only 10-24 gram per cubic centimeter of space. Distance between stars is very large; the nearest star the Proxima Centuari/Alpha centuari is around 40000000million kilometer from Sun. Strength of Gravitational field reduces as the inverse square of the distance from bodies, so gravitational fields are very weak within inter stellar and intergalactic space. More over gravitational field itself is considered to be a weak field with long range, unlike magnetic, electric or nuclear field. These are strong field with low ranges. You can very well compare the strength of a horse shoe magnet and earth’s gravitational field. The attractive force of magnet is much stronger near the magnet though the weight and size of magnet is negligible compared to earth, however you may not detect any magnetic field a few meter away. You see the moon thousands of kilometer away held in the orbit by gravitational field of earth. So strong gravitational forces can be encountered only near the surface of massive bodies or large scale stellar clusters. The curvature of space is much higher near the surface of massive bodies. And such effects which we have discussed are measurable when light from stars passes near the surface of massive bodies like our Sun. Such phenomenon has actually been observed.
There is other phenomenon like gravitational lens effect (Fig- 5) which produces multiple distorted images of stars. This also has been discovered during astronomical observations. All these occurrences in universe prove the existence of curved space around us. Unlike space, the existence of time always had a mysterious aspect throughout the ages. Few philosophers and scientists have raised doubt about its physical existence. It is visible in Zeno’s arrow paradox and in St Augustine statement when he said “What then is time? If no one asks me, I know. If I wish to explain it to one that asketh, I know not.” However concept of time was less controversial in its application. There was no doubt about its absoluteness until the publication of special theory of relativity. How long this flip flop of space and time will continue nobody knows.
(c) all rights reserved. An excrapt from book ‘ Into The World of Relativity’
http://pothi.com/pothi/book/sarada-world-relativity
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