Thursday, May 5, 2011

This is how I see - Special and General Relativity Simplified

For all those who are fascinated by physics and would like to know more about theories of relativity, here is a series of posts that will explain what physics is all about. Please note, take in the facts coming up in the video. They will be elaborated in detail with better explanations in the next posts. 

I too am learning. Please put forward any doubts and comments. I will definitely try to get more info on it. Enjoy...





Sunday, May 1, 2011

This is how I see - How Reason Evolves

This is an extract from the book "The Road to Reality" by Roger Penrose.


Am-tep was the King’s chief craftsman, an artist of consummate skills. It was night, and he lay sleeping on his workshop couch, tired after a handsomely productive evening’s work. But his sleep was restless—per- haps from an intangible tension that had seemed to be in the air. Indeed, he was not certain that he was asleep at all when it happened. Daytime had come—quite suddenly—when his bones told him that surely it must still be night.
He stood up abruptly. Something was odd. The dawn’s light could not be in the north; yet the red light shone alarmingly through his broad window that looked out northwards over the sea. He moved to the window and stared out, incredulous in amazement. The Sun had never before risen in the north! In his dazed state, it took him a few moments to realize that this could not possibly be the Sun. It was a distant shaft of a deep Wery red light that beamed vertically upwards from the water into the heavens.
As he stood there, a dark cloud became apparent at the head of the beam, giving the whole structure the appearance of a distant giant parasol, glowing evilly, with a smoky Xaming staV. The parasol’s hood began to spread and darken—a daemon from the underworld. The night had been clear, but now the stars disappeared one by one, swallowed up behind this advancing monstrous creature from Hell.
Though terror must have been his natural reaction, he did not move, transWxed for several minutes by the scene’s perfect symmetry and awe- some beauty. But then the terrible cloud began to bend slightly to the east, caught up by the prevailing winds. Perhaps he gained some comfort from this and the spell was momentarily broken. But apprehension at once returned to him as he seemed to sense a strange disturbance in the ground beneath, accompanied by ominous-sounding rumblings of a nature quite unfamiliar to him. He began to wonder what it was that could have caused this fury. Never before had he witnessed a God’s anger of such magnitude.

His Wrst reaction was to blame himself for the design on the sacriWcial cup that he had just completed—he had worried about it at the time. Had his depiction of the Bull-God not been suYciently fearsome? Had that god been oVended? But the absurdity of this thought soon struck him. The fury he had just witnessed could not have been the result of such a trivial action, and was surely not aimed at him speciWcally. But he knew that there would be trouble at the Great Palace. The Priest-King would waste no time in attempting to appease this Daemon-God. There would be sacriWces. The traditional oVerings of fruits or even animals would not suYce to pacify an anger of this magnitude. The sacriWces would have to be human.
Quite suddenly, and to his utter surprise, he was blown backwards across the room by an impulsive blast of air followed by a violent wind. The noise was so extreme that he was momentarily deafened. Many of his beautifully adorned pots were whisked from their shelves and smashed to pieces against the wall behind. As he lay on the Xoor in a far corner of the room where he had been swept away by the blast, he began to recover his senses, and saw that the room was in turmoil. He was horriWed to see one of his favourite great urns shattered to small pieces, and the wonder- fully detailed designs, which he had so carefully crafted, reduced to nothing.
Am-tep arose unsteadily from the Xoor and after a while again ap- proached the window, this time with considerable trepidation, to re-exam- ine that terrible scene across the sea. Now he thought he saw a disturbance, illuminated by that far-oV furnace, coming towards him. This appeared to be a vast trough in the water, moving rapidly towards the shore, followed by a cliVlike wall of wave. He again became transWxed, watching the approaching wave begin to acquire gigantic proportions. Eventually the disturbance reached the shore and the sea immediately before him drained away, leaving many ships stranded on the newly formed beach. Then the cliV-wave entered the vacated region and struck with a terrible violence. Without exception the ships were shattered, and many nearby houses instantly destroyed. Though the water rose to great heights in the air before him, his own house was spared, for it sat on high ground a good way from the sea.
The Great Palace too was spared. But Am-tep feared that worse might come, and he was right—though he knew not how right he was. He did know, however, that no ordinary human sacriWce of a slave could now be suYcient. Something more would be needed to pacify the tempestuous anger of this terrible God. His thoughts turned to his sons and daughters, and to his newly born grandson. Even they might not be safe.
Am-tep had been right to fear new human sacriWces. A young girl and a youth of good birth had been soon apprehended and taken to a nearbytemple, high on the slopes of a mountain. The ensuing ritual was well under way when yet another catastrophe struck. The ground shook with devastating violence, whence the temple roof fell in, instantly killing all the priests and their intended sacriWcial victims. As it happened, they would lie there in mid-ritual—entombed for over three-and-a-half millennia!
The devastation was frightful, but not Wnal. Many on the island where Am-tep and his people lived survived the terrible earthquake, though the Great Palace was itself almost totally destroyed. Much would be rebuilt over the years. Even the Palace would recover much of its original splen- dour, constructed on the ruins of the old. Yet Am-tep had vowed to leave the island. His world had now changed irreparably.
In the world he knew, there had been a thousand years of peace, prosperity, and culture where the Earth-Goddess had reigned. Wonderful art had been allowed to Xourish. There was much trade with neighbouring lands. The magniWcent Great Palace was a huge luxurious labyrinth, a virtual city in itself, adorned by superb frescoes of animals and Xowers. There was running water, excellent drainage, and Xushed sewers. War was almost unknown and defences unnecessary. Now, Am-tep perceived the Earth-Goddess overthrown by a Being with entirely diVerent values.
It was some years before Am-tep actually left the island, accompanied by his surviving family, on a ship rebuilt by his youngest son, who was a skilled carpenter and seaman. Am-tep’s grandson had developed into an alert child, with an interest in everything in the world around. The voyage took some days, but the weather had been supremely calm. One clear night, Am-tep was explaining to his grandson about the patterns in the stars, when an odd thought overtook him: The patterns of stars had been disturbed not one iota from what they were before the Catastrophe of the emergence of the terrible daemon.
Am-tep knew these patterns well, for he had a keen artist’s eye. Surely, he thought, those tiny candles of light in the sky should have been blown at least a little from their positions by the violence of that night, just as his pots had been smashed and his great urn shattered. The Moon also had kept her face, just as before, and her route across the star-Wlled heavens had changed not one whit, as far as Am-tep could tell. For many moons after the Catastrophe, the skies had appeared diVerent. There had been darkness and strange clouds, and the Moon and Sun had sometimes worn unusual colours. But this had now passed, and their motions seemed utterly undisturbed. The tiny stars, likewise, had been quite unmoved.
If the heavens had shown such little concern for the Catastrophe, having a stature far greater even than that terrible Daemon, Am-tep reasoned, why should the forces controlling the Daemon itself show concern for what the little people on the island had been doing, with their foolish rituals and human sacriWce? He felt embarrassed by his own foolishthoughts at the time, that the daemon might be concerned by the mere patterns on his pots.
Yet Am-tep was still troubled by the question ‘why?’ What deep forces control the behaviour of the world, and why do they sometimes burst forth in violent and seemingly incomprehensible ways? He shared his questions with his grandson, but there were no answers.
...
A century passed by, and then a millennium, and still there were no answers.
...
Amphos the craftsman had lived all his life in the same small town as his father and his father before him, and his father’s father before that. He made his living constructing beautifully decorated gold bracelets, earrings, ceremonial cups, and other Wne products of his artistic skills. Such work had been the family trade for some forty generations—a line unbroken since Am-tep had settled there eleven hundred years before.
But it was not just artistic skills that had been passed down from generation to generation. Am-tep’s questions troubled Amphos just as they had troubled Am-tep earlier. The great story of the Catastrophe that destroyed an ancient peaceful civilization had been handed down from father to son. Am-tep’s perception of the Catastrophe had also survived with his descendants. Amphos, too, understood that the heavens had a magnitude and stature so great as to be quite unconcerned by that terrible event. Nevertheless, the event had had a catastrophic eVect on the little people with their cities and their human sacriWces and insigniWcant religious rituals. Thus, by comparison, the event itself must have been the result of enormous forces quite unconcerned by those trivial actions of human beings. Yet the nature of those forces was as unknown in Amphos’s day as it was to Am-tep.
Amphos had studied the structure of plants, insects and other small animals, and crystalline rocks. His keen eye for observation had served him well in his decorative designs. He took an interest in agriculture and was fascinated by the growth of wheat and other plants from grain. But none of this told him ‘why?’, and he felt unsatisWed. He believed that there was indeed reason underlying Nature’s patterns, but he was in no way equipped to unravel those reasons.
One clear night, Amphos looked up at the heavens, and tried to make out from the patterns of stars the shapes of those heroes and heroines who formed constellations in the sky. To his humble artist’s eye, those shapes made poor resemblances. He could himself have arranged the stars far more convincingly. He puzzled over why the gods had not organized thestars in a more appropriate way? As they were, the arrangements seemed more like scattered grains randomly sowed by a farmer, rather than the deliberate design of a god. Then an odd thought overtook him: Do not seek for reasons in the speciWc patterns of stars, or of other scattered arrange- ments of objects; look, instead, for a deeper universal order in the way that things behave.
Amphos reasoned that we Wnd order, after all, not in the patterns that scattered seeds form when they fall to the ground, but in the miraculous way that each of those seeds develops into a living plant having a superb structure, similar in great detail to one another. We would not try to seek the meaning in the precise arrangement of seeds sprinkled on the soil; yet, there must be meaning in the hidden mystery of the inner forces control- ling the growth of each seed individually, so that each one follows essen- tially the same wonderful course. Nature’s laws must indeed have a superbly organized precision for this to be possible.
Amphos became convinced that without precision in the underlying laws, there could be no order in the world, whereas much order is indeed perceived in the way that things behave. Moreover, there must be precision in our ways of thinking about these matters if we are not to be led seriously astray.
It so happened that word had reached Amphos of a sage who lived in another part of the land, and whose beliefs appeared to be in sympathy with those of Amphos. According to this sage, one could not rely on the teachings and traditions of the past. To be certain of one’s beliefs, it was necessary to form precise conclusions by the use of unchallengeable reason. The nature of this precision had to be mathematical—ultimately dependent on the notion of number and its application to geometric forms. Accordingly, it must be number and geometry, not myth and superstition, that governed the behaviour of the world.
As Am-tep had done a century and a millennium before, Amphos took to the sea. He found his way to the city of Croton, where the sage and his brotherhood of 571 wise men and 28 wise women were in search of truth. After some time, Amphos was accepted into the brotherhood. The name of the sage was Pythagoras.