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The Contemporary Cosmos
Scientifically, what all the denizens of the Universe have in common is that not a single one of them, from the Moon out to the Sun, the planets, the stars, the galaxies and out to the most distant quasar, are in the place where and when we see them. For example, at dawn, the Sun has already risen 8' 19''(8 minutes, 19 seconds) before we see it rise on Earth's Eastern horizon, and again has set 8' 19'' before we see it set on our Western horizon. This is due to the single most significant and controlling factor in the workings of the universe - the speed of light. It not only has a limit of 299,800 kilometers per second (186,283 miles per second,) it is also independent of the motion of its source, or its observer. What does it mean when we say the speed of light is independent of the motion of its source or the observer? To understand this phenomenon, we must first bear in mind that ordinarily we see things from the Newtonian system's definition of force, space (distance) and time, where everything, from falling apples to orbiting planets, are under the influence of the force of gravity, and subject to the same laws of motion. These laws are applied logically and consistently everywhere in the Universe irrespective of underlying circumstances. The foundations of this logical world are space (distance) and time. Newton himself defined time and space in this way in his Principia "Absolute, true and mathematical time, of itself and from its own nature, flows equably, without relation to anything external, and by another name is called duration." Likewise, "absolute space, in its own nature, without relation to anything external remains always similar and immovable." In other words, space and time are absolute. And so it seems to us. Why? Consider the following: Suppose you are standing on a pavement and I am sitting in a car traveling at 100 km/hr. when you look at me in the car, you see me traveling at 100 km/hr. Now if you are blind folded and placed in another car going at 100 km/hr alongside me, and remove your blindfold, you see me alongside you at all times, i.e. my speed relative to you is zero. But, if I travel in the opposite direction as your car, the distance between us in one hour would be 200 kilometers, i.e. my speed relative to you, or yours speed relative to mine would be 200 km/hr. Similarly, suppose I am sitting in a car going at 100 km/hr, and throw a stone out the window of the car at a speed of 100 km/hr in the direction the car is traveling. Relative to you standing on the pavement, the stone would have a speed of 200 km/hr. Because, being in the car, the stone already has a speed of 100 km/hr which, when added to the speed my hand gives it, would make the speed of the stone relative to you 200 km/hr. By the same reasoning, if I throw the stone at the speed of 100 km/hr in the opposite direction of the travel of the car, the speed of the stone relative to you would be zero. This is called "relative motion," and Newton's classical physics deals with it quite satisfactorily. However, if I were holding a flashlight and turned it on, no matter in what direction I aim it, unlike the stone, the speed of its light relative to you would not change. It would be 299,800 km/sec irrespective of the speed of the car, not even if the car were traveling at near the speed of light. For light, or at the speed of light, the speed of the car becomes irrelevant. Clearly, something strange happens when speeds get near that of light. Since speed is a defined quantity equal to distance divided by time, both of which are supposed to be absolute, either distance or time should depend on speed (i.e. be relative) in order for the speed of light to remain absolute. Not until 1860s, when Maxwell's electromagnetic wave theory of light revealed a problem with Newton's classical mechanics when it came to the speed of light on moving objects, did anyone question the validity of the absoluteness of space and time. The doubts most dramatically became real by the results of the Michelson-Morley experiment. The two scientists performed an experiment in 1887 in an attempt to determine the speed of the Earth through space[1]. They split a beam of light and sent both beams toward a common target, one beam at the direction of motion of the Earth, and the other at right angle to it. The time delay in the arrival of the two light beams was to have provided the value of the speed of the Earth through space. Why? Because the speed of the light beam traveling in the direction of motion of the Earth was expected to have been faster than the speed of the second beam by a factor equal to the speed of the Earth through space. Much to their surprise, however, both beams arrived at the target at exactly the same time. That is, in defiance of the laws of Newtonian mechanics (not to mention common sense), the speed of the Earth appeared to make no difference in the speed of light. Furthermore, since no matter how fast a source of light traveled the speed of light remained constant, it followed that the speed of light must be an impassable limit. Classical physics was in deep trouble. Obviously a whole new mechanics were needed where the speed of light would become an impassable limit, and either time or space, or both were relative.
TIME DILATION
It was Albert Einstein who came up with the answer. Time, he concluded, just wasn't the same for every observer when speeds approached the speed of light. It slows down as velocity of the traveler approaches the speed of light, and becomes zero at the speed of light. This is the concept known as "time dilation," and one of its consequences is the famous "twin's paradox:" One of two twins remains on Earth while the other embarks on a journey into space at a speed near that of light. According to the concept of time dilation, when the space traveler twin returns to Earth, he would have aged much less than the twin who stayed behind. Why? Because time for the space traveler brother had slowed down throughout his journey, while his brother had aged at his "normal time." The formula for measuring the effect of time dilation is: T = T'(1-v2/c2)1/2 Where: T = Time of the moving observer. T' = Time of the stationary observer. v = Speed of the moving observer. c = Speed of light. Since c is very large (300,000 km/sec), for values of v which are within human experiences even traveling at present spacecraft speeds when in orbit (7.8 km/sec), the term v/c is so negligible that the difference between T and T' is nearly imperceptible. Only when v begin to approach single digit percentages of light speed (for 1% and higher) that the effects of time dilation become appreciable. The following are the values of T/T' vs. values of v from 0.5% to 100% of c. v/c T/T' 0.005 0.9999874 0.01 0.9999499 0.10 0.9949874 0.25 0.9682458 0.50 0.8660254 0.60 0.8000000 0.70 0.7141428 0.80 0.6000000 0.90 0.4358898 0.95 0.2738612 0.99 0.1410673 0.999 0.0447213 0.9999 0.0141421 1.0000 0.0000000 As this table shows, if one is traveling at 50% the speed of light, each second of his time is equal to 0.8660254 second of a stationary person. However, as his speed is increased, this fraction becomes increasingly smaller and smaller until his speed reaches that of the speed of light, when time stands still for him completely.
RELATIVISTIC MASS:
Newtonian mechanics dictates that as a force acts steadily on a body, its momentum (mass * speed) increase indefinitely. When the speeds are small there is no problem, however as the speed reaches near the speed of light it can no longer increase, but momentum does. This can happen only if the mass of the object increases to the point that the applied force can no longer accelerate the body. The formula for this change is: M = M'/(1-v2/c2)1/2 Where: M = The relativistic mass. M' = Mass of the object at rest. An intuitive way of expressing this idea comes from the definition of mass as inertia, the resistance to acceleration exhibited by a body that is being acted upon by a force. The increase of the inertia implies that the resistance to applied force increases (or the effect of the force progressively decreases) to the point that the speed of light cannot be attained.
ALBERT EINSTEIN AND THE THEORY OF RELATIVITY:
Einstein formulated this concept in his special theory of relativity, which deals with uniform motion. It was published in 1905 when Einstein was only 26 years old and working as a clerk in the Swiss patent office. Einstein's ideas about the nature of time were so against common sense that many just couldn't understand them. And a few who did, wouldn't take them seriously because they meant the end of physics as they knew them. The most important and troublesome change was that three-dimensional geometry could no longer describe the space we call universe. A new form of geometry, which took account of time, was needed. In other words, the universe could no longer be described as "where," but more like "where-when." One man who took Einstein's ideas seriously was Minkowski, his former mathematics teacher at the Zurich Polytechnic who had called him "a lazy dog." He recognized the revolutionary nature of Einstein's ideas, and set about filling some of the gaps in the theory, which had been left open by Einstein. These gaps were more mathematical in nature, a science, which was not one of Einstein's forte. In 1907 Minkowski wrote a book called Space and Time, in which he treated time as a fourth dimension. He demonstrated that time and space could not be separated, and that they were intertwined with each other, and existed only as space-time. We could no longer state "where" we are in the Universe without specifying "when" we are. Soon, scientists all over the world, including Einstein himself began to work out its mathematical implications. The results pointed to further strange and astonishing results: When applied to Maxwell's electromagnetic theory of light, it showed that as a particle's speed approached the speed of light, its mass, i.e. resistance to notion, increased, thus requiring ever bigger amounts of energy to push it forward. Furthermore, its dimensions decrease until it vanishes at the speed of light.
MASS, ENERGY, AND THE SPEED OF LIGHT
Another crucial inference of the theory pointed to the most sensational and far reaching conclusion regarding the nature of quanta. It showed that light quanta were simply particles that somehow had shed their mass, and transmuted into a form of pure energy traveling at the speed of light. This meant that mass and energy were interchangeable, and the speed of light was somehow involved in their relationship with each other. It took Einstein almost two years before he could work his way through the mathematics of this concept. But, when he did, the result was the formulation of the most famous (or infamous, depending on ones point of view) equation in physics: E=mc2 where E is energy, m is mass and c is the speed of light. This earth-shattering formula implies that matter is merely solidified energy, and that given the enormity of the value of the speed of light, a tiny amount of mass could be converted into a gigantic amount of energy. It turns out that there is enough energy in one kilogram of matter to lift 300,000 tons of rock from Earth to the surface of the Moon. No other equation or scientific principal has imparted a greater understanding of the workings of the universe, or impacted the life, and threatened the existence of man more than this equation. It has shown us why stars shine, and provided the impetus for the development of atomic power, the atom bomb, and the hydrogen bomb. Indeed, the universe was created according to this equation, at the event we call the Big Bang - the moment the unimaginably vast amount of primordial energy began to be transformed into matter.
THE NATURE OF GRAVITY:
Minkowski, more than any other well-known scientist of that time, including the renown Max plank, seems to have inspired Einstein, and induced him to go on. He provided Einstein with the insight that resulted in his development of the general theory of relativity. It looked at the nature of gravity in a way that was vastly different from what Newton had described it as. Einstein formulated his conclusions in two theories. Special relativity, published in 1905, which deals with uniform motion, and general relativity, published in 1915, which deals with accelerated motion. Both describe motion at speeds near that of light, and are reduced to Newton's laws of motion for speeds that are small compared to the speed of light. Other than their failure to predict motion at speeds near that of light, Newton's formulas, while ascribing the motion of the planet to gravity, fail to show how the force is being instantly transmitted through empty space. Action at a distance was a concept hard to fathom, so the idea of the ether was invented. It was to have been an odorless, mass-less, colorless, friction free, unchanging, something that permitted unimpeded motion through itself - namely light and gravity. Einstein never liked the idea of the ether, and was also disturbed by the fact that relativity could be applied to every physical phenomenon except gravity. It seemed to him that since gravity depends on the mass of the bodies upon which it acts, and the precise numerical value of mass is relative (depends on the speed), then gravity should be relative. But, it is not. Furthermore, since nothing can move faster than the speed of light, how can gravity be transmitted instantaneously across the vast distances of the cosmos. Einstein had been thinking about all this after he had published his special theory of relativity. One day in November 1907, while sitting in a chair at the patent office at Bern where he worked as a second class clerk, an idea occurred to him which he later called "the happiest thought of my life." "If a person falls freely," he thought, "he will not feel his own weight." The reason, he realized, was because every molecule in his body was being accelerated at the same exact rate by gravity. This fact had been known since the time of Galileo. It could also be said that the man is stationary and his surrounding is accelerating upward. Gravity, therefore, seemed to him to be relative. This meant the principals of relativity developed for uniform motion may be applied to accelerated motion as well. Taking his cue from the fact that Newton's inertia mass was equal to gravitational mass, and arguing that if electro-magnetic field could transmit magnetic force, then he concluded, a gravity field could transmit gravitational force. And the field was the result of the effect a mass has on its surrounding space. Under such a circumstance, space and time are no longer absolute - they are united in a flexible continuum that responds to the presence of mass.
THE SPACE-TIME CONTINUUM:
Thus, what Newton attributed to the force of gravity is nothing more than the curvature of the space-time continuum around any given mass such as the Sun. The planets simply follow the easiest path in the warped space-time that surrounds the Sun. Similarly, the Moon simply follows the curvature of the space-time continuum created around the earth by its mass. In all cases, the tendency to fall down the space-time continuum is attributed to gravity, but here, no force of gravity is implied or hypothesized. In fact, one might say that the planets and the moon are not following a curved path, nor are they falling. They are simply following just as straight a path as the shape of the space-time continuum allows. By this time, the mathematical intricacies of four-dimensional geometry had been worked out, but it was quite difficult and considered arcane. Einstein, who had spent his college years thinking instead of doing his mathematics homework, reached for his friend Marcel Grossman[2], and with his assistance, finally worked out the complexities of his space-time concept. By, it had taken him thirteen years to do so. He published the results in March 1916 as his "general theory of relativity," and the world of science was never the same again. Einstein's formulations immediately cleared up the mystery of the observed perturbations of the orbit of the planet Mercury, which could not be explained by Newtonian mechanics. However, this was not sufficient proof of a theory with such far reaching consequences, and overwhelming conclusions. A much more dramatic proof in the form of observation and measurement of one of the theory's more outlandish predictions was needed. It came three years later in during an eclipse of the Sun. If the theory is correct and the force of gravity gives way to the geometry of space-time itself, then it follows that light and all other forms of radiation should also follow the curved path of space-time around any heavy celestial object. And, if the object is massive enough, then the deflection of the path of a far off star passing through its strong gravitational field could be large enough to be measurable from the Earth. As it happens, the Sun is just massive enough to bend the light of any star that passes near it to the point that it is measurable from the Earth. But, this could be done only during an eclipse of the Sun when far off stars behind it becomes visible. The opportunity came in May 29, 1929, when a total eclipse of the Sun took place in the western equatorial coast of Africa. Arthur Stanley Edington, a prominent British scientist and Einstein's most ardent supporter had mounted an expedition to a cocoa plantation in the Principe Island off the nose of west Africa specifically to test Einstein's theory. On the day of the eclipse, clouds obscured the sun much to the despair of astronomers. But at the instant of the total eclipse, as if by magic or some divine intervention, a hole opened up in the clouds allowing Edington to photograph the stars of the Hyades cluster surrounding the blocked out sun. He developed the photographic plates that night in his tent and "...as the last lines of the calculations were reached," he later wrote, "I knew that Einstein's theory had stood the test and the new outlook of scientific thought must prevail." When Edington reached England after a few months, he developed his remaining plates and verified his preliminary calculations that indeed the light of the distant stars had been deflected by an amount exactly as predicted by Einstein's theory. He made the announcement on November 6, 1919, at a meeting of the Royal Society in London while he stood under the portrait of Newton. The news was conveyed to Einstein by a telegram from his close friend Lorentz. Einstein showed the telegram to a student who asked him, "What would you have said if there had been no confirmation?" "I would have had to pity our dear Lord," Einstein replied. "The theory is correct." Headlines all over the world heralded the news, and Einstein became an instant celebrity and a hero. Soon, A handful of scientists and mathematicians who could grasp the intricacies of general relativity, began to expound on it, and out of their scrutiny came a whole slew of conclusions and answers to some of the outstanding questions regarding the nature of the universe. One such question was with regards to the shape of the universe.
THE SHAPE OF THE UNIVERSE:
So long as space and time had been regarded as unchanging, there was no escaping the conclusion that the universe is either finite, or infinite, both of which seemed equally illogical and absurd. If it were final, what lay beyond it? And the idea of it being infinite just doesn't sit right. Presumably one could sit by the bank of a river and contemplate an infinite universe until the cows came home, and he would still be where he started. But relativity demonstrated that in the vast distances between galaxies, space and time could be distorted until the entire universe could be said to be rolled in on itself. An astronaut could conceivably circumnavigate the universe, visiting every galaxy, and finally end up right here in the Milky Way. Just like an ant traveling the surface of the Earth from the North to the South Pole, and from the east to the west, could pass through every square millimeter of the surface of the Earth and end up where he started. The idea of a finite but unbounded space, according to Max Born, "is one of the greatest ideas about the nature of the world which has ever been conceived."
THE EXPANSION OF THE UNIVERSE:
When Einstein put forth his concept of relativity and the nature of gravity, his formula showed that the universe should be expanding. This was not only a brand new idea, but given the state of our knowledge at the time seemed totally absurd to him. So, caught in a momentary lack of confidence in his theory, he did what every red-blooded theorist always does to bring renegade equations into line. He introduced a "fudge factor" in it, calling it the "cosmological term," in order to prevent his formula from reaching such a conclusion. That same year, an American astronomer named Vesto Slipher, working at Lowell Observatory in Arizona (established by the rich eccentric Boston millionaire Percival Lowell to chart the canals of Mars), noticed a large shift towards the red end of the spectral lines of stars in the spiral arms of galaxies. This meant that they were moving away from the Earth at very high speeds. But, he didn't yet know how far away they were, or even if they belonged to other galaxies. That proof was supplied by Edwin Hubble, who detected a special type of star among them, known as Cepheid variable. The discovery enabled him to calculate the star's distance. Since they turned out to be farther away than the dimensions of the Milky Way, he concluded that they belonged to other galaxies. Hubble then calculated the recession velocity of twenty-five galaxies from the magnitude of the red shift of their spectrum, and plotted them against their distance obtained from their Cepheid variable stars. This relationship turned out to be a straight line. This was proof that the universe was expanding, and that the farther away a galaxy is, the faster it is moving out. The slope of this line was soon dubbed the "Hubble Constant," and was thereafter used to calculate the distance of farther galaxies. Hubble had not known of Einstein's "cosmological term," but as soon as Einstein heard about Hubble's work, he got on a ship and came to California to meet him. After reviewing Hubble's data, Einstein called his "cosmological term" the worst mistake of my life." Einstein's "worst mistake" represented nothing more than sort of antigravity force acting over long distances. Eighty five years later, it would become the only explanation for a phenomenon which astronomers would observe, but, except for Einstein's work, would have neither believed their eyes nor their calculations. In the year 2001, observations determined that the expansion of the universe has been accelerating for the last 6 billion years instead of continuing to decelerate under the force of the gravitational attraction of its denizens. The only explanation was Einstein's cosmological term.
DARK ENERGY:
Cepheid Variable stars can be detected only as far as about 20 million light-years out into space. Therefore, there was no way to directly determine the distance of objects beyond this point. In fact, astronomers multiplied the value of the Hubble constant with the recession velocity of objects beyond this point to calculate their distance. In late in 1998, however, two groups of astronomers tried independently to use the Hubble Space Telescope, to refine the value of Hubble's constant by detecting a special type of supernova, called type-Ia supernova. This type of supernova, like Cepheid variable stars, have the same intensity, except that they can be detected in the much deeper parts of space, where Cepheid variables cannot. Much to astronomer's surprise, the data of both groups showed that the light of the supernovas were dimmer than expected, or the rate of expansion of the universe is increasing. That is, as if some force is pushing galaxies apart, while the expectation had always been that their gravitational attraction should be pulling them together so that the rate of expansion should be decreasing. Naturally, the first instinct of astronomers was to question the data, speculating that perhaps intergalactic dust dims the light of the supernova, thus introducing errors in the data. Others went in search of scientific explanations in the form of an as yet undiscovered force responsible for the acceleration, calling its source "dark energy," or "negative energy." They found it in the original "cosmological term" of Einstein's equations. If it should have a negative value, they concluded, the expansion should be accelerating. The debate went on until early in the year 2001, when astronomers at the Space Telescope Science Institute - the home of the Hubble Space Telescope - found an old Hubble photograph of deep space. The image quite by accident contained the image of a supernova that had taken place 11 billion years ago. The photograph showed the light of the supernova to be bright enough not to have been distorted by intergalactic dust. Also, calculations showed that the rate of expansion then was much lower than it is now. Since that gravitational force is attractive in nature and decreases with increasing distance, while the force of the dark energy is repulsive in nature and increases with increasing volume, it seems that earlier in the life of the universe when its volume as well as the distances between galaxies were much less than they are now, gravitational force was dominant. Therefore, the rate of expansion of the universe was decreasing. However, some 6 billion years ago, both the distances between galaxies, and the volume of the Universe had increased to the point that the force of the dark energy took over from gravity, accelerating the expansion. The most significant ramification of this discovery is in ascertaining the final fate of the Universe. Before all this, it was believed that the fate of the universe depended on its current density. If this density is more than one atom of hydrogen per square meter of space, gravity will eventually stop and then reverse the expansion, collapsing the universe on itself in a moment of the "Big Crunch," followed by another Big Bang, and on and on. Now it looks like this density will not be the determining factor, and that regardless of its value, the dark energy will be increasing for ever and ever due to the increasing volume of the Universe, pushing galaxies forever farther and farther apart. It seems that we are doomed in a universe where billions of years from now, the Milky Way galaxy will be all that we shall see in our sky, the others being much too far away. In the end, all the stars in all the galaxies will simply burn out, and the universe will end not with a Big Crunch, but with a whimper. So it is that after eighty-five years, relativity is still capable of confounding us by revealing more of the mysteries of the Universe. And, fifty years after his death, Einstein is sending physicists to their yellow pads (computer screens these days) and their particle accelerators to try and figure out how and where this new force we are calling dark energy has come from. The true lesson of Einstein's theory of relativity is that we cannot trust our senses. He believed in, and used science as means to explore natural phenomenon that are not readily apparent to us, and are beyond our perceptions. Einstein has made us not believe our eyes, or trust our instincts.
[1] In the late 19th Century, the vast spaces of the Universe was thought to have been permeated by an imaginary substance called "the luminiferous ether." [2] Whose class notes always helped Einstein at the last minute to pass his examinations.
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