Matrix Theory and Linear Algebra (562420), страница 18
Текст из файла (страница 18)
After Einstein’s work of 1917, several scientists, including the abbé Georges Lemaître in Belgium, Willem de Sitter in Holland, and Alexander Friedmann in Russia, succeeded in finding solutions to Einstein’s field equations. The universes described by the different solutions varied. De Sitter’s model had no matter in it. This model is actually not a bad approximation since the average density of the universe is extremely low. Lemaître’s universe expanded from a “primeval atom.” Friedmann’s universe also expanded from a very dense clump of matter, but did not involve the cosmological constant. These models explained how the universe behaved shortly after its creation, but there was still no satisfactory explanation for the beginning of the universe.
In the 1940s George Gamow was joined by his students Ralph Alpher and Robert Herman in working out details of Friedmann’s solutions to Einstein’s theory. They expanded on Gamow’s idea that the universe expanded from a primordial state of matter called ylem consisting of protons, neutrons, and electrons in a sea of radiation. They theorized the universe was very hot at the time of the big bang (the point at which the universe explosively expanded from its primordial state), since elements heavier than hydrogen can be formed only at a high temperature. Alpher and Hermann predicted that radiation from the big bang should still exist. Cosmic background radiation roughly corresponding to the temperature predicted by Gamow’s team was detected in the 1960s, further supporting the big bang theory, though the work of Alpher, Herman, and Gamow had been forgotten.
| III | THE THEORY |
The big bang theory seeks to explain what happened at or soon after the beginning of the universe. Scientists can now model the universe back to 10-43 seconds after the big bang. For the time before that moment, the classical theory of gravity is no longer adequate. Scientists are searching for a theory that merges quantum mechanics and gravity, but have not found one yet. Many scientists have hope that string theory will tie together gravity and quantum mechanics and help scientists explore further back in time (see Physics: Unified Field Theory).
Because scientists cannot look back in time beyond that early epoch, the actual big bang is hidden from them. There is no way at present to detect the origin of the universe. Further, the big bang theory does not explain what existed before the big bang. It may be that time itself began at the big bang, so that it makes no sense to discuss what happened “before” the big bang.
According to the big bang theory, the universe expanded rapidly in its first microseconds. A single force existed at the beginning of the universe, and as the universe expanded and cooled, this force separated into those we know today: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. A theory called the electroweak theory now provides a unified explanation of electromagnetism and the weak nuclear force theory (see Unified Field Theory). Physicists are now searching for a grand unification theory to also incorporate the strong nuclear force. String theory seeks to incorporate the force of gravity with the other three forces.
One widely accepted version of big bang theory includes the idea of inflation. In this model, the universe expanded much more rapidly at first, to about 1050 times its original size in the first 10-32 second, then slowed its expansion. The theory was advanced in the 1980s by American cosmologist Alan Guth and elaborated upon by American astronomer Paul Steinhardt, Russian American scientist Andrei Linde, and British astronomer Andreas Albrecht. The inflationary universe theory (see Inflationary Theory) solves a number of problems of cosmology. For example, it shows that the universe now appears close to the type of flat space described by the laws of Euclid’s geometry: We see only a tiny region of the original universe, similar to the way we do not notice the curvature of the earth because we see only a small part of it. The inflationary universe also shows why the universe appears so homogeneous. If the universe we observe was inflated from some small, original region, it is not surprising that it appears uniform.
Once the expansion of the initial inflationary era ended, the universe continued to expand more slowly. The inflationary model predicts that the universe is on the boundary between being open and closed. If the universe is open, it will keep expanding forever, even though the rate of expansion will gradually slow. If the universe is closed, the expansion of the universe will eventually stop and the universe will begin contracting until it collapses. Whether the universe is open or closed depends on the density, or concentration of mass, in the universe. If the universe is dense enough, it is closed.
| IV | SUPPORTING EVIDENCE |
The universe cooled as it expanded. After about one second, protons formed. In the following few minutes—often referred to as the “first three minutes,” combinations of protons and neutrons formed the isotope of hydrogen known as deuterium as well as some of the other light elements, principally helium, as well as some lithium, beryllium, and boron. The study of the distribution of deuterium, helium, and the other light elements is now a major field of research. The uniformity of the helium abundance around the universe supports the big bang theory and the abundance of deuterium can be used to estimate the density of matter in the universe.
From about 300,000 to about 1 million years after the big bang, the universe cooled to about 3000° C (about 5000° F) and protons and electrons combined to make hydrogen atoms. Hydrogen atoms can only absorb and emit specific colors, or wavelengths, of light. The formation of atoms allowed many other wavelengths of light, wavelengths that had been interfering with the free electrons, to travel much farther than before. This change set free radiation that we can detect today. After billions of years of cooling, this cosmic background radiation is at about 3° K (-270° C/-454° F).The cosmic background radiation was first detected and identified in 1965 by American astrophysicists Arno Penzias and Robert Wilson.
The National Aeronautics and Space Administration’s Cosmic Background Explorer (COBE) spacecraft mapped the cosmic background radiation between 1989 and 1993. It verified that the distribution of intensity of the background radiation precisely matched that of matter that emits radiation because of its temperature, as predicted for the big bang theory. It also showed that the cosmic background radiation is not uniform, that it varies slightly. These variations are thought to be the seeds from which galaxies and other structures in the universe grew.
| V | REFINING THE THEORY |
Evidence indicates that the matter that scientists detect in the universe is only a small fraction of all the matter that exists. For example, observations of the speeds with which individual galaxies move within clusters of galaxies show that there must be a great deal of unseen matter exerting gravitational forces to keep the clusters from flying apart.
Cosmologists now think that much of the universe—perhaps 99 percent— is dark matter, or matter that has gravity but that we cannot see or otherwise detect. Theorized kinds of dark matter include cold dark matter, with slowly moving (cold) massive particles. No such particles have yet been detected, though astronomers have given them names like Weakly Interacting Massive Particles (WIMPs). Other cold dark matter could be nonradiating stars or planets, which are known as MACHOs (Massive Compact Halo Objects). An alternative model includes hot dark matter, where hot implies that the particles are moving very fast. The fundamental particles known as neutrinos are the prime example of hot dark matter. If the inflationary version of big bang theory is correct, then the amount of dark matter that exists is just enough to bring the universe to the boundary between open and closed.
Scientists develop theoretical models to show how the universe’s structures, such as clusters of galaxies, have formed. Their models invoke hot dark matter, cold dark matter, or a mixture of the two. This unseen matter would have provided the gravitational force needed to hold large structures such as clusters of galaxies together. The theories continue to match the observations, though there is no consensus on the type or types of dark matter that must be included. Supercomputers are important for making such models.
Astronomers are making new observations that are interpreted within the framework of the big bang theory. Scientists have not found any major problems with the big bang theory, but the theory is being constantly adjusted to match the observed universe.
Trapezoid
Trapezoid, in plane geometry, quadrilateral (four-sided) figure with two parallel sides, or bases, of unequal length. The perpendicular distance between the bases is known as the altitude. The sides that are not parallel are called legs, and a line from the midpoint of one leg to the midpoint of the other is called the median; the multiplication of the altitude and the median yields the area of the trapezoid. When the legs of a trapezoid are of equal length, the figure is called an isosceles trapezoid.
Trapeziod
A trapezoid is geometrical figure with two parallel sides. In an isoceles trapezoid, the two non-parallel sides are equal in length. In a rectangular trapezoid, one of the non-parallel sides is perpendicular to the two parallel sides.
Ellipse
Ellipse, in geometry, closed plane curve, one of the conic sections (see Cone), formed by a plane that cuts all the elements of a right circular cone. A circle, which is formed by a plane perpendicular to the axis of the cone, is a specialized form of ellipse.
An ellipse may be defined as the locus of all points, P, the sum of whose distances, d1 and d2, from two fixed points is a constant (see Fig. 1). The two fixed points that define an ellipse are known as its foci and are labeled F and F’ in Fig. 1. This property of an ellipse is often used for drawing the figure. If pins are placed in the drawing surface at the two foci and a length of string is tied loosely between them, a point holding the string taut will trace an ellipse as it moves.
|
|
Any ellipse is symmetrical with respect to its major axis, which is a straight line passing through the two foci and extended to meet the curve at each end. It is also symmetrical with respect to its minor axis, a line perpendicular to the major axis at the midpoint between the two foci. In a circle the two foci of the ellipse coincide, and the major and minor axes are equal.
The eccentricity of an ellipse, that is, the ratio of the distance between the foci to the length of the major axis, is always less than 1. The eccentricity of a circle is 0.
The ellipse is one of the most important curves in physical science. In astronomy, the orbits of the earth and the other planets around the sun are ellipses. It is used in engineering in the arches of some bridges and the design of gears for certain types of machinery such as punch presses.
Archimedes
Archimedes (287-212 bc), preeminent Greek mathematician and inventor, who wrote important works on plane and solid geometry, arithmetic, and mechanics.
Archimedes was born in Syracuse, Sicily, and educated in Alexandria, Egypt. In pure mathematics he anticipated many of the discoveries of modern science, such as the integral calculus, through his studies of the areas and volumes of curved solid figures and the areas of plane figures. He also proved that the volume of a sphere is two-thirds the volume of a cylinder that circumscribes the sphere.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
