{"product_id":"once-before-time-isbn-9780307474551","title":"Once Before Time","description":"\u003cp\u003eIn his introduction to a revolutionary theory of the cosmos, Martin Bojowald shows how the big bang theory may give way to the big bounce theory, which describes our universe as an eternal series of expansions and contractions, with no beginning and no end.\u003cbr\u003e \u003cbr\u003eIn 2000, Bojowald, then a twenty-seven-year-old postdoctoral student at Pennsylvania State University, used a relatively new theory called loop quantum gravity—a cunning combination of Einstein’s theory of gravity with quantum mechanics—to create a simple model of the universe. Loop quantum cosmology, or LQC, was born, and with it, a theory that managed to do something even Einstein’s general theory of relativity had failed to do—illuminate the very birth of the universe.\u003c\/p\u003e“Readers will find undoubted insights into one possible explanation of the universe at its most fundamental and will experience the work of top-level science.”\u003cbr\u003e—\u003ci\u003eThe Wall Street Journal\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“\u003ci\u003eOnce Before Time \u003c\/i\u003etells the story of Bojowald’s discovery and its implications in fascinating, eloquent, even literary prose.”\u003cbr\u003e—\u003ci\u003eNew Scientist\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“Bojowald argues precisely and meticulously.”\u003cbr\u003e—\u003ci\u003eProvidence Journal\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“Bojowald manages to describe these complicated ideas without bogging down in mathematical notation. And like Stephen Hawking, he manages to help readers over the difficult spots with entertaining and literate prose.”\u003cbr\u003e—\u003ci\u003ePittsburgh Post-Gazette\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“Bojowald’s explanations are thorough and logical, and his ideas and metaphors [have] panache.”\u003cbr\u003e—\u003ci\u003eThe Columbus Dispatch\u003c\/i\u003e\u003cp\u003e\u003cb\u003eMartin Bojowald \u003c\/b\u003eis an associate professor of physics at Pennsylvania State University’s Institute for Gravitation and the Cosmos. Originally from Germany, he now resides in Pennsylvania.\u003c\/p\u003e1. Gravitation\u003cbr\u003e\u003cbr\u003eMass Attraction\u003cbr\u003e\u003cbr\u003eShould something from the window fall\u003cbr\u003e\u003cbr\u003e(and if it just the smallest be)\u003cbr\u003e\u003cbr\u003ehow jumps the law of gravity\u003cbr\u003e\u003cbr\u003eas mighty as wind from the sea\u003cbr\u003e\u003cbr\u003eat every ball or blueberry\u003cbr\u003e\u003cbr\u003eand takes them to the core of all.\u003cbr\u003e\u003cbr\u003e-Rainer Maria Rilke, \u003ci\u003eThe Book of Hours\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003eOver  large distances, the universe is governed by the gravitational force.  In physics, the action of a force is the cause of motion or of any form  of change. Complete rest is possible only if no net forces are acting.  One scenario in which this can happen is the absence of any matter  whatsoever-a state called vacuum. But matter quite obviously does exist,  and just by its mass it causes gravitational forces on other masses. To  realize motionless states of rest, at least approximately, all acting  forces must compensate each other. In addition to gravity, there are the  electric and magnetic forces to be considered, as well as two kinds of  forces called weak and strong interactions, reigning in the realm of  elementary particles.\u003cbr\u003e\u003cbr\u003eWhile the electric force is easily  compensated over large distances by the existence of positive and  negative charges, mutually neutralizing each other, the forces that come  into play in the interior of nuclei act only at extremely short range.  What remains over long distances is gravity alone. It rules the general  attraction of masses and energy distributions in space, and thus  dictates the behavior of the universe itself. In contrast to  electricity, there are no negative masses: Gravitational attraction  cannot be fully compensated. Once massive objects such as stars or  entire galaxies form, the resulting gravitational interaction dominates  all that happens. The facets of this commonplace force, often ignored in  recent research and yet-in cosmology and black holes-giving rise to a  rich variety of exotic phenomena, are the topic of this book.\u003cbr\u003e\u003cbr\u003eNewton's law of gravity:\u003cbr\u003e\u003cbr\u003eDistant action and a fatal flaw\u003cbr\u003e\u003cbr\u003eThe  first general law of gravity was formulated by Isaac Newton. As is  typical for many important steps in gravitational research, this  theoretical development required a unified view on well-known phenomena  on Earth with a long list of intricate observations of objects in space:  the moon and some planets. The latter was accomplished thanks to  technologies that, for those times, were highly sophisticated;  conversely, such research has spawned the development of new  instruments. Combining fundamental questions and technological  applications, in many areas of science and in gravitational research in  particular, is a success story that continues into the present day.\u003cbr\u003e\u003cbr\u003eEven  before Newton, the initial untidy flood of data, as it was accumulated  by astronomers such as Tycho Brahe, Johannes Kepler, and many others,  was ordered into a model of the solar system. Since Nicolaus Copernicus  and Kepler, this model has largely held the form we know today: Planets  orbit around the sun along trajectories that, by a good approximation,  can be considered as ellipses, or slightly oblong circles. But what is  propelling the planets along their curved tracks? From common  observations we know that a force is necessary to keep a body from  moving stubbornly along a straight line. How can one describe or even  explain the required force in the case of the planets?\u003cbr\u003e\u003cbr\u003eNewton's  groundbreaking insight-the existence of a universal force of gravity  causing not only the motion of all planets around the sun, and of the  moon around the earth, but also the everyday phenomena of falling  objects-is impressive. It is an excellent example of the origin of  scientific explanation: not an answer to a \"why\" question in the sense  of an anthropomorphic motivation, but a plethora of complicated  phenomena, unrelated at first sight, reduced to a single mechanism: a  law of nature. Newton's mathematical description of the situation is  very compact and highly efficient for predictions of new phenomena  described by the same law. In the case of Newton's law of gravity, the  unfathomable power of theoretical prediction has repeatedly been  employed-for instance, to find new planets via small deviations imposed  by their gravitational pull on the trajectories of other planets, or in  planning modern satellite missions.\u003cbr\u003e\u003cbr\u003eSuch success stories, in  which an elegant mathematical description explains and predicts a  multitude of phenomena, can be found throughout physics; they are indeed  the landmarks of its progress. Reliving such insights is often so  gratifying that scientists employ the term \"beauty\"-a pragmatic kind of  beauty whose core, the mathematical formulation, can be seen only by the  initiated, but which in its concrete successes can also be appreciated  by outsiders.1\u003cbr\u003e\u003cbr\u003eConcretely, Newton's law of gravity describes the  attractive force between two bodies caused by their masses. The force  increases proportionally with the amounts of the masses: The attraction  between two heavy bodies is larger than that between two light ones. It  is also inversely proportional to the squared distance between the  bodies; it weakens considerably when the bodies are farther apart. In  addition to these proportionalities, the exact quantitative strength of  the force is determined by a mathematical parameter, now called Newton's  gravitational constant. In this value one can see the unification of  earthly and heavenly phenomena. The gravitational constant can be  derived from the tiny attraction of two masses on Earth, as was first  accomplished in Henry Cavendish's laboratory in 1797 and '98; using the  same value to calculate the force exerted by the sun on the planets  shows exactly the right nudge required to hold the planets on their  observed orbits.\u003cbr\u003e\u003cbr\u003eIn contrast to its clear dependence on distance,  Newton's gravitational force is completely independent of time. Time  independence sounds plausible, for a fundamental law of nature should,  after all, be valid at all times in the same way. It is also consistent  with the dominant understanding of space and time in Newton's age and  long thereafter, not to mention our everyday conceptions of them.  Although one can easily change the positions and distances of objects in  space, space itself appears unchangeable. Also, time seems to pass  simply and uniformly, without being influenced by physical processes or  technical instruments. Since gravity, according to Newton, acts  instantaneously-independently of how far apart the masses are-the force  need be formulated only for the case of two masses not at the same  place, but at the same time.\u003cbr\u003e\u003cbr\u003eDespite its plausible form and  celebrated successes, Newton's theory did have a flaw in its beauty.  Like the beauty of the theory itself, this flaw, too, can be understood  completely only with a sufficient amount of background knowledge. But  even on the surface, it is a good example of the progress of theoretical  physics. Newton himself had reportedly been uneasy about the  \"animalistic\" tendencies of his law of gravitation: As an animal is  attracted from far away by the expectation of food or companionship, a  massive body appeared to move toward another one from a distance. This  action at a distance, apparently without the more intuitive type of  local interactions as realized for bodies pushing each other at close  contact, was considered a serious conceptual weakness in spite of all  concrete successes.\u003cbr\u003e\u003cbr\u003eIt is extremely difficult to correct this  weak spot by constructing a theory only of local interactions that, of  course, should otherwise remain compatible with the astronomical  successes of Newton's theory. To start with, one will have to consider  the time dimension, too, for such a local interaction must take some  time to propagate from one body to the other. As it turned out, a  consistent reformulation is possible only by radically changing  Newton's-and our-intuitive conceptions of space and time. It requires  much more highly sophisticated mathematical machineries and substantial  efforts, but these efforts are rewarded by a theory of unprecedented  beauty in the sense described above. All this required dedicated  physical research and, not least, a strong mathematical grounding. The  flaw in Newton's theory was to be corrected only long after Newton-by  Albert Einstein.\u003cbr\u003e\u003cbr\u003eRelativity of space and time:\u003cbr\u003e\u003cbr\u003eSpace-time transformers\u003cbr\u003e\u003cbr\u003eAll this took a long time, or a short time: for, strictly speaking, no time on earth exists for such things.\u003cbr\u003e\u003cbr\u003e-friedrich nietzsche, Thus Spoke Zarathustra\u003cbr\u003e\u003cbr\u003eIn  physics, as in all of science, it is important to distinguish between  properties that depend on the person making an observation and  properties independent of an observer. The mass of a particle refers  only to the particle itself and will, if the particle remains unchanged,  always be measured as the same value. Except for unavoidable  experimental inaccuracies, it does not matter who is doing the  measurement. A particle's velocity, on the other hand, appears  different, and sometimes drastically so, depending on whether an  observer is moving with respect to the particle. An observer moving  along with the particle at exactly the same speed would perceive the  particle as being at rest, well known from two cars cruising side by  side along a straight stretch of highway. To the driver of one car, the  other one seems not to be moving. Any other observer would see the car  (or the particle) move and attribute to it a nonzero velocity.  Relativity in general terms is the mathematical analysis of such  relationships; it ultimately tells us what we can learn about nature in a  fully objective, observer-independent way.\u003cbr\u003e\u003cbr\u003eFor many centuries,  space and time were thought of as observer- independent. Distances  between points and durations of temporal periods appeared absolute, no  matter how an observer would be positioned or move. But the first fault  lines in this worldview opened up toward the end of the nineteenth  century, eventually leading to special relativity. In this new view,  space and time cannot be seen in separation but are intertwined,  interchangeable, and observer-dependent. Like the velocity of a  particle, the values measured for them depend on the motion of an  observer. In abstract terms, they describe different dimensions of a  single physical object: space-time; and only space-time concepts, but  not space or time themselves, are independent of the person making a  measurement.\u003cbr\u003e\u003cbr\u003eHow can this be demonstrated by physical means? To  answer this question and to explain the role of dimensions, we first  consider space alone. Space has different dimensions, namely three: we  can move sideways, back and forth, and up or down. Here, one might ask  why these should be considered as three dimensions of a single space,  rather than three completely independent directions: width, depth,  height. The answer is simple. Width, depth, and height are not absolute  and independent properties; they can be commuted into one another. We  have only to turn around in space to make the height of a cube appear as  its width, and in this sense height and width can be interchanged. This  is not a transformation by a physical process, like a chemical  reaction, but a much simpler one by means of changing our viewpoint.  What we see as height, width, and depth depend on the place of an  observer (or on conventions such as the use of Earth's surface along  which to measure width and depth); they cannot be considered properties  of space itself as a physical object. For this reason, one speaks of  three-dimensional space, not of the existence of three independent  one-dimensional directions.\u003cbr\u003e\u003cbr\u003eTime is similar, although its  transformation is harder. By simply turning around one can influence  only one's view on space; the change of the angle of view (or, more  precisely, the tangent of the angle as a mathematical function, which  does not differ much from the angle when it is small) is expressed by  the ratio of spatial extensions, such as the height before and after  changing the viewpoint. By changing the angle, one can only transform  spatial extensions into one another. If we want to transform space into  time, we must vary a quantity given by a ratio of spatial and time  extensions: a velocity. Traversing a certain distance in some period of  time means that one moves at a velocity obtained as the ratio of that  distance to the required time.\u003cbr\u003e\u003cbr\u003eThis consideration does, in fact,  lead to the basic phenomenon of special relativity. If we are moving  faster than a second observer while viewing a certain scene, spatial and  time distances appear different to each of us. As changing the angle of  view transforms spatial extensions, changing the velocity of an  observer commutes spatial distances to timelike ones and vice versa.  Distinguishing space and time extensions is thus dependent on the  viewpoint (or the \"viewtrack,\" if we are indeed moving); it cannot have a  physical basis independent of observers' properties. Instead of  separate space and time, there is only one joint object: space-time.  Special relativity is the theory of these changing viewtracks (also  called inertial observers) in the absence of the gravitational force.\u003cbr\u003e\u003cbr\u003eAs  an illustration, these considerations are certainly no proof; not every  ratio implies a transformation when it is changed. For instance, the  birthrate of a country is the ratio of newborns to the total population,  but a change in the birthrate does not mean that inhabitants are  transformed into newborns. An important difference from the previous  example is the role of observers: Changes are caused by observers taking  different positions and states of motion; and since physical laws must  be independent of the special private and personal properties of those  making the observations, concepts distinguished only by viewpoints must  be discarded. In special relativity, this \"transformability\" of space  and time, forcing us to deny them separate meaning, has not only been  substantiated mathematically; it has also been verified experimentally  myriad times, especially in reactions of elementary particles. While the  Newtonian concepts of a rigid space and an independent time would not  agree with many measurements made in the last century, in a special  relativistic view no inconsistencies arise.\u003cbr\u003e\u003cbr\u003eNewton's view was  able to enjoy great success for such a long time because noticeably  transforming space and time requires very large observer velocities.  Unless measurements are extremely refined and precise, in order to see  an effect, speeds must be close to the immense velocity of light:  roughly 300,000 kilometers per second. In everyday life, this makes the  transformability of space and time imperceptible.2 For an observational  verification, one needs either very high velocities or very precise time  measurements in order to notice the tiny time changes at low  velocities. Both methods have been developed in the past century.\u003cbr\u003e\u003cbr\u003eVery  precise time measurements are achieved by atomic clocks, making  space-time transformations detectable even at the typical speeds of  airplanes. (Since planes have to move at a certain height, additional  effects arise due to a reduction of gravity acting on the clock farther  away from the center of the earth. This general relativistic effect,  depending on the gravitational force, is introduced below.)\u003cbr\u003e\u003cbr\u003eAt  velocities close to that of light, space-time changes drastically: As an  observer at rest would describe it, time is transformed almost  completely into space, and thus passes ever more slowly. Once the speed  of light is reached, which is possible only for massless objects such as  light itself, all timelike distances vanish. Going beyond that speed  limit is impossible, for all time has already been used up when we reach  the speed of light. No signal can move faster than light. Delays in any  transmission of information must always occur; they may be small, but  they do become noticeable at large distances. (This maximum speed is  that of light in a vacuum. In transparent media such as water, light  usually moves more slowly than in a vacuum.Translated by the author","brand":"Vintage","offers":[{"title":"Default Title","offer_id":46303878152421,"sku":"NP9780307474551","price":18.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780307474551.jpg?v=1767734135","url":"https:\/\/k12savings.com\/es\/products\/once-before-time-isbn-9780307474551","provider":"K12savings","version":"1.0","type":"link"}