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Albert Einstein
All Motion is Relative
 
 
 
Dr V B Kamble

 

Albert Einstein (14 March 1879 – 18 April 1955) was the only son of Hermann and Pauline Einstein. He grew up in Munich, where his father and his uncle ran a small electrochemical plant. Einstein was a slow child and disliked the regimentation of school. His scientific interests were awakened early and at home by the mysterious compass his father gave him when he was about four; by the algebra he learned from his uncle; and by the books he read, mostly popular scientific works of the day. A geometry text which he devoured at the age of twelve made a particularly strong impression.

When his family moved to Milan after a business failure, leaving the fifteen-year-old boy behind in Munich to continue his studies, Einstein quit the school he disliked and spent most of a year enjoying life in Italy. Persuaded that he would have to acquire a profession to support himself, he finished the Gymnasium in Aarau, Switzerland, and then studied physics and mathematics at the Eidgenössische Technische Hochschule (the Polytechnic) in Zurich, with a view toward teaching.


After graduation Einstein was unable to obtain a regular position for two years and did occasional tutoring and substitute teaching, until he was appointed an examiner in the Swiss Patent Office at Berne. The seven years Einstein spent at this job, with only evenings and Sundays free for his own scientific work, were years in which he laid the foundations of large parts of twentieth-century physics. They were probably also the happiest years of his life. He liked the fact that his job was quite separate from his thoughts about physics, so that he could pursue these freely and independently, and he often recommended such an arrangement to others later on. In 1903 Einstein married Mileva Maric, a Serbian girl who had been a fellow student in Zurich. Their two sons were born in Switzerland.

Einstein received his doctorate in 1905 from the University of Zurich for a dissertation entitled, “Eine neue Bestimmung der Moleküldimensionen” (“A New Determination of Molecular Dimensions”), a work closely related to his studies of Brownian motion. It took only a few years until he received academic recognition for his work, and then he had a wide choice of positions. His first appointment, in 1909, was as associate professor (extraordinarius) of physics at the University of Zurich. This was followed quickly by professorships at the German University in Prague, in 1911, and at the Polytechnic in Zurich, in 1912. Then, in the spring of 1914, Einstein moved to Berlin as a member of the Prussian Academy of Sciences and director of the Kaiser Wilhelm Institute for Physics, free to lecture at the university or not as he chose. As it turned out, he found the scientific atmosphere in Berlin very stimulating, and he greatly enjoyed having colleagues like Max Planck, Walther Nernst, and, later, Erwin Schödinger and Max von Laue. During World War 1, Einstein’s scientific work reached a culmination in the general theory.of’relativity, but in most other ways his life did not go well.

Mileva Einstein and their two sons spent the war years in Switzerland and the Einsteins were divorced soon after the end of the war. Einstein then married his cousin Elsa, a widow with two daughters. Einstein’s health suffered, too. One of his few consolations was his continued correspondence and occasional visits with his friends in the Netherlands-Paul Ehrenfest and H. A. Lorentz, especially the latter, whom Einstein described as having “meant more to me personally than anybody else I have met in my lifetime” and as “the greatest and noblest man of our times.”

Einstein became suddenly famous to the world at large when the deviation of light passing near the sun, as predicted by his general theory of relativity, was observed during the solar eclipse of 1919. His name and the term relativity became household words. The publicity, even notoriety, that ensued changed the pattern of Einstein’s life.

In 1933 Einstein was considering an arrangement that would have allowed him to divide his time between Berlin and the new Institute for Advanced Study at Princeton. But when Hitler came to power in Germany, he promptly resigned his position at the Prussian Academy and joined the Institute. Princeton became his home for the remaining twenty-two years of his life. He became an American citizen in 1940.
During the 1930’s Einstein was convinced that the menace to civilization embodied in Hitler’s regime could be put down only by force. In 1939, at the request of Leo Szilard, Edward Teller, and Eugene Wigner, he wrote a letter to President Franklin D. Roosevelt pointing out the dangerous military potentialities offered by nuclear fission and warning him of the possibility that Germany might be developing nuclear weapons. This letter helped to initiate the American efforts that eventually produced the nuclear reactor and the fission bomb, but Einstein neither participated in nor knew anything about these efforts.

Einstein received a variety of honours in his lifetime – from the 1921 Nobel Prize in physics to an offer (which he did not accept) of the presidency of Israel after Chaim Weizmann’s death in 1952.

One of Einstein’s last acts was his signing of a plea, initiated by Bertrand Russell, for the renunciation of nuclear weapons and the abolition of war. He was drafting a speech on the current tensions between Israel and Egypt when he suffered an attack due to an aortic aneurysm; he died a few days later. But despite his concern with world problems and his willingness to do whatever he could to alleviate them, his ultimate loyalty was to his science. As he said once with a sigh to an assistant during a discussion of political activities: “Yes, time has to be divided this way, between politics and our equations. But our equations are much more important to me, because politics is for the present, but an equation like that is something for eternity.”

Einstein’s early interests lay in statistical mechanics and intermolecular forces. However, his predominant concern throughout the career was the search for a unified foundation for all of physics. The disparity between the discrete particles of matter and the continuously distributed electromagnetic field came out most clearly in Lorentz’ (1853-1928) electron theory, where matter and field were sharply separated for the first time. This theory strongly influenced Einstein. The problems generated by the incompatibility between mechanics and electromagnetic theory at several crucial points claimed his attention. His strengths with these problems led to his most important early work – the special theory of relativity and the theory of quanta in 1905.

The discovery of X-rays, radioactivity, the electron and the quantum theory brought about a sea change in our ideas and understanding of phenomena at the atomic level. The world of Physics was, however, changing in far reaching ways - with ramifications for our understanding of the very shape of time, space and the universe. This part of the revolution was brought about Albert Einstein, a brilliant and creative theorist and the only thinker ever to be ranked in the same class as Newton. To understand this part of the revolution, we shall need to go back to James Clerk Maxwell (1831-1879) and his ideas about light.

Ether – Unbroken from star to star

Maxwell had introduced a revolutionary set of equations that predicted the existence of electromagnetic fields and established that magnetism, electricity and light were a part of the same spectrum: the electromagnetic spectrum. Light, he maintained, was a wave, not a particle, and he thought that it travelled through an invisible medium he called “the ether”, which filled all space. But physicists began to see a problem, not with Maxwell’s electromagnetic field equations, but with his ideas about the ether.

Maxwell wasn’t the first to come up with this idea that some invisible medium called the ether must fill the vastness of space, extending “unbroken from star to star”. It dated back to the time of ancient Greeks. “There can be no doubt,” Maxwell said in a lecture in 1873, “that the interplanetary and interstellar spaces are not empty but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform, body of which we have any knowledge”. The idea of the ether seemed necessary because, if light was a wave, it seemed obvious that it had to be a wave travelling in some medium. But accepting what “seems obvious” is not the way to do good science; if the ether existed, it should be possible to find some proof of its existence.

The most famous “failed” experiment

Albert Michelson (1852-1931), an American Physicist, had an idea . If the ether that filled the universe were stationary, then the planet Earth would meet resistance as it moved through the ether, creating a current, a sort of “wind”, in the ether. So it followed that a light beam moving with the current ought to be carried along by it, whereas a light beam travelling against the current should be slowed. While studying with Hermann von Helmholtz (1821-1894) in Germany, in 1881 Michelson built an instrument called an interferometer, which could split a beam of light, running the two halves perpendicular to each other, and then rejoin the split beam in a way that made it possible to measure differences in the speeds with great precision.

Michelson ran his experiment, but he was puzzled by his results. They showed no differences in light velocity for the two halves of the light beam. He concluded, “The result of the hypothesis of a stationary ether is …. shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous”.

But may be his results were wrong. He tried his experiment again and again, each time trying to correct for any possible error. Finally, in 1887, joined by Edward Morley, Michelson tried a test in Cleveland, Ohio. Using improved equipment, and taking every imaginable precaution against inaccuracy, this time surely they would succeed in detecting the ether. But the experiment failed again. Let us briefly describe the salient features of this momentous experiment.

The Experiment

If there is an ether pervading space, we move through it with at least the 3x104 m/sec speed of the earth’s orbital motion about the sun; if the sun is also in motion, our speed through the ether is even greater (Motions of the Earth through a hypothetical ether). From the point of view of an observer on the earth, the ether is moving past the earth. To detect this motion, we can use the pair of light beams formed by a half silvered mirror (The Michelson - Morley experiment). One of these light beams is directed to a mirror along a path perpendicular to the ether current, while the other goes to a mirror along a path parallel to the ether current. The optical arrangement is such that both beams return to the same viewing screen. The purpose of the clear glass plate is to ensure that both beams pass through the same thickness of air and glass.

If the path lengths of the two beams are exactly the same, they will arrive at the screen in phase and will interfere constructively to yield a bright field of view. The presence of an ether current in the direction shown, however, would cause the beams to have different transit times in going from the half silvered mirror to the screen, so that they would no longer arrive at the screen in phase but would interfere destructively. In essence this is the famous experiment performed in 1887 by Michelson and Morley.

In the actual experiment the two mirrors are not perfectly perpendicular, with the result that the viewing screen appears crossed with a series of bright and dark interference fringes due to differences in path length between adjacent light waves (Fringe Pattern observed in Michelson - Morley experiment). If either of the optical paths in the apparatus is varied in length, the fringes appear to move across the screen as reinforcement and cancellation of the waves succeed one another at each point. The stationary apparatus, then, can tell us nothing about any time difference between the two paths. When the apparatus is rotated by 90°, however, the two paths change their orientation relative to the hypothetical ether stream, so that the beam formerly requiring the time tA (along parth A) for the round trip now required tB (along path B) and vice versa. If these times are different, the fringes will move across the screen during the rotation.

This information can be used to calculate the fringe shift expected on the basis of the ether theory. The expected fringe shift ‘n’ in each path when the apparatus is rotated by 90° is given by

n = Dv2 / ?c2 ;

Here, D is the distance between half silvered mirror and each of the other mirrors (made about 10 metres using multiple reflections), v is the ether speed - which is the Earth’s orbital speed 3x104 (m/s), c is the speed of the light = 3x108 m/sec, and l is the wave length of light used, about 5000Å (1Å=10-10m), one then obtains n=0.2 fringe.

Since both paths experience this fringe shift, the total shift should amount to 2n or 0.4 fringe. A shift of this magnitude is readily observable, and therefore, Michelson and Morley looked forward to establishing directly the existence of the ether. To everybody’s surprise, no fringe shift whatever was found. When the experiment was performed at different seasons of the year and in different locations, and when experiments of other kinds were tried for the same purpose, the conclusions were always identical: no motion through the ether was detected.

The negative result of the Michelson-Morley experiment had two consequences. First, it rendered untenable the hypothesis of the ether by demonstrating that the ether has no measurable properties – an ignominious end for what had once been a respected idea. Second, it suggested a new physical principle: the speed of light in free space is the same everywhere, regardless of any motion of source or observer. As a result, the Michelson-Morley experiment has become the most famous “failed” experiment in the history of science. They had started out to study the ether, only to conclude that the ether did not exist. But if this were true, how could light move in “waves” without a medium to carry it? What’s more, the experiment indicated that the velocity of light is always constant.

It was a completely unexpected conclusion. But the experiment was meticulous and the results irrefutable. Lord Kelvin (1824-1907), said in a lecture in 1900 at the Royal Institution that Michelson and Morley’s experiment had been “carried out with most searching care to secure a trustworthy result,” casting “a nineteenth century cloud over the dynamic theory of light”. The conclusion troubled physicists everywhere, though. Apparently, they were wrong about the existence of the ether – and if they were wrong, then light was a wave that somehow could travel without a medium to travel through. What’s more, the Michelson - Morley results seemed to call into question the kind of Newtonian relativity that had been around for a couple of centuries and by this time was well tested; the idea that the speed of an object can differ, depending upon the reference frame of the observer. Suppose two cars are travelling along on a road. (There weren’t many cars or roads in 1887, but one gets the idea.). One car is going 80 kms per hour, the other 75 kms per hour. To the driver of the slower car, the faster car would be gaining ground at a rate of 5 kms per hour. Why would light be any different?

But that’s just what the Michelson and Morley experiment had shown; Light does behave differently. The velocity of light is always constant – no matter what. Astronauts travelling in their spaceship at a speed of 2,90,000 km/sec alongside a beam of light (which travels at 3,00,000 km/sec) would not perceive the light gaining on them by 10,000 km/sec. They would see light travelling at a constant 3,00,000 km/sec. The speed of light is a universal absolute!

 

The Four Dimensions

According to Einstein's views, space and time are more intimately connected with one another than it was supposed before and with in certain limits, the notion of space may be substituted by the notion of time and vice versa. To make this statement more clear, let us consider a passenger in a train having his meal in the dining car. The waiter serving him will know that the passenger ate his soup, meals and dessert in. the same place, that is, at the same able in the dining car. But, from the point of view of a person on the ground, the same passenger consumed the three courses at points along the track separated by many kilometres. We Can hence make the following trivial statement: Events taking place in the same place but at different times in a moving system will be considered by a ground observer as taking place at different places.

Now, following Einstein's idea concerning the reciprocity of space and time, let us replace in the above statement the word "place" by the word "time" and vice versa. The statement will now read: Events taking place at the same time but In different places in a moving system will be considered by a ground observer as taking place at different times. This statement is far from being trivial. It means that if, for example, two passengers at the far ends of the dining car had their after-dinner coffee sipped simultaneously from the point of view of the dining-car waiter, the person standing on the ground will insist that the coffee was sipped at different times! Since according to the principle of relativity, neither Of the two reference systems should be 'preferred to the other (the train moves relative to the ground or the ground moves relative to the train), we do not have any reason to take the waiter's impression as being true and ground observer's impression as being wrong or vice versa. Of course, this would not be apparent to you If you were the ground observer. This is so because the distance of, say, 30 metres between two passengers sipping their after dinner coffee at opposite ends of the dinning car translates into a time interval of only 10-8 seconds, and there is no wonder that this is not apparent to our senses. It would become appreciable when the train travels close to the speed of light.

The transformation of time intervals into space Intervals and vice versa was given a simple geometrical interpretation by the German mathematician H. Minkowski. He proposed that time or duration be considered as the fourth dimension supplementing the three spatial dimensions (x, y, z) and that transformation from one system of reference to another be considered as a rotation of co-ordinates systems in this four dimensional space. A point in these four dimensional space is called an event. Relativistic effects like the length contraction and the time dilation then become consequences of the rotation of these space-time coordinates.

These effects being relative, each of the two observers moving with respect to one another will see the other fellow as somewhat flattened in the direction of his motion and will consider his watch to be slow!

The Special Theory of Relativity:

Surprisingly, Einstein never received a Nobel prize for the most important paper that he published in 1905, the one that dealt with a theory that came to be known as the special theory of relativity.

He also tossed out the idea of the ether, which Michelson and Morley had called into question. Maxwell needed it because he thought light travelled in waves, and if that were so, he thought, it needed some medium in which to travel. But what if, as Max Planck’s (1858-1947) quantum theory stated, light travels in discrete packets or quanta? Then it would act more like particles and wouldn’t require any medium to travel in.

By making these assumptions — that the velocity of light is a constant, that there is no ether, that light travels in quanta and that motion is relative — he was able to show why the Michelson - Morley experiment came out as it did, without calling the validity of Maxwell’s electromagnetic equations into question. But, where does “relativity” enter?

We mentioned earlier the role of the ether as a universal frame of reference with respect to which light waves were supposed to propagate. Whenever we speak of “motion”, of course, we really mean motion relative to a “frame of reference”. The frame of reference may be a road, the earth’s surface, the sun, the center of our galaxy; but in every case we must specify it. Stones dropped in New Delhi and in Washington both fall “down”, and yet the two move in opposite directions relative to the earth’s center. Which is the correct location of the frame of reference in this situation, the earth’s surface or its center? The answer is that all frames of reference are equally correct, although one may be more convenient to use in a specific case. If there were an ether pervading all space, we could refer all motion to it, and the inhabitants of New Delhi and Washington would escape from their quandary. The absence of an ether, then, implies that there is no universal frame of reference, so that all motion exists solely relative to the person or instrument observing it.

The theory of relativity resulted from an analysis of the physical consequences implied by the absence of a universal frame of reference. The special theory of relativity treats problems involving the motion of frames of reference at constant velocity (that is, both constant speed and constant direction) with respect to one another; the general theory of relativity, proposed by Einstein a decade later, treats problems involving frames of reference accelerated with respect to one another. The special theory has had a profound influence on all of physics.

The paper in which the young Albert Einstein in 1905 set out the special theory of relativity confronted common sense with several new and disquieting ideas. It abolished the ether, and it showed that matter and energy are equivalent. The new ideas derive from the central conception of relativity: that time does not run at the same pace for every observer. This bold conception lies at the heart of modern physics, all the way from the atomic to the cosmic scale. Yet it is still hard to grasp, and the paradoxes it pose continue to puzzle and to stimulate each generation of physicists.

Two Axioms

The special theory of relativity is based upon two axioms. The first states that the laws of physics may be expressed in equations having the same form in all frames of reference moving at constant velocity with respect to one another. This axiom expresses the absence of a universal frame of reference. If the laws of physics had different forms for different observers in relative motion, it could be determined from these differences which objects are “stationary” in space and which are “moving”. But because there is no universal frame of reference, this distinction does not exist in nature; hence the above axiom. Consequently, this axiom implies that two observers, each of whom appears to the other to be moving with a constant speed in a straightline, cannot tell which of them is moving.

The second axiom of special relativity states that the speed of light in free space has the same value for all observers, regardless of their state of motion. This axiom follows directly from the result of the Michelson - Morley experiment, and implies that when both observers measure the speed of light, they will get the same answer.

Neither of these axioms was new in itself. The first axiom had long been implicit in the accepted laws of mechanics. The second one was beginning to be accepted as the natural interpretation of Michelson and Morley’s experiment in 1887. What was new, then, in Einstein’s analysis was not one axiom or the other but the confrontation of the two. They form the two principles of relativity not singly but together. This is how Einstein presented them jointly at the beginning of his paper.

So basically, in the special theory of relativity Einstein revamped Newtonian physics such that when he worked out the formulas, the relative speed of light always stayed the same. It never changes relative to anything else, even though other things change relative to each other. Mass, space and time all vary depending upon how fast you move. As observed by others, the faster you move, the greater your mass, the less space you take up and the more slowly time passes for you! The more closely you approach the speed of light, the more pronounced these effects become. Let us have a look at some of the consequences of the theory of relativity.

Time Dilation

It follows at once from the two axioms combined that we have to revise the traditional idea of time. By tradition we take it for granted that time is the same everywhere and for everyone. Why not? It seems natural to assume that time is a universal “now” for every traveller anywhere in the universe. But, according to the theory of special relativity, time cannot run at the same pace for two observers, one of whom is moving relative to the other, if they are to get the same speed (that is for light) when they time a beam of light that is moving with one of them. Consider this example.

If you were an astronaut travelling at 90 percent of the speed of light (about 2,70,000 kms per second), you could travel for five years (according to your calendar watch) and you’d return to Earth to find that 10 years had passed for the friends you’d left behind. Or, if you could rev up your engines to help you travel at 99.99 percent of the speed of light, after traveling for only 6 months you’d find that 50 years had sped by our Earth during your absence!

Clocks moving with respect to an observer appear to tick less rapidly than they do when at rest with respect to him. If we, in the S frame, or the stationary frame of reference,