The Structure of Space According to the General Theory of Relativity

According to the general theory of relativity, the geometrical properties of space are not independent;

 but they are determined by matter.  Thus we can draw conclusions about the geometrical structure of the universe only if we  base our considerations on the state of the matter as being something that is known. We know from experience that, for a suitably chosen co-ordinate system, the velocities of the stars small as compared with the velocity of transmission of light. We can thus as a rough approximation arrive at a conclusion as to the nature of the universe as a whole, if we treat the matter as being at rest.

The behaviour of measuring-rods and clocks is influenced by gravitational fields, i.e. by the distribution of matter. This in itself is sufficient to exclude the possibility of the exact validity of Euclidean geometry in our universe. But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the more probable, since calculations shows that the metrics of surrounding space is influenced only to an exceedingly small extent by masses  even of the magnitude of our sun. 

Imagine that, as regards geometry, our universe  behaves analogously to a surface which is  irregularly curved in its individual parts, but which nowhere departs appreciably from a plane:  something like the rippled surface of a lake. Such a universe might fittingly be called a quasi- Euclidean universe. As regards its space it would be infinite. But calculation shows that in a quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be inhabited by matter everywhere; it  would present to us that unsatisfactory picture.

If we are to have in the universe an average density of matter which differs from zero,  however small may be that difference, then the universe cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if  matter be distributed uniformly, the universe would necessarily be spherical ( or elliptical ).  Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in  individual parts from the spherical, i.e. the  universe will be quasi-spherical. But it will be necessarily finite. In fact, the theory supplies us with a simple connection between the space-expanse of the universe and the average density of matter in it;

For the radius R of the universe, obtain the equation: 

                 R² = 2 / Kp

The use of the C.G.S. system in the equation  gives: 

                R² = 2 / K = 108.10³⁷   ;

“ p ” is the average density of the matter and “ k ”

 is a constant connected with the Newtonian constant of gravitation...  

 “ Time and space are not conditions of existence, time and space is a model of thinking. ”

                                   — Albert Einstein   

History of Germany ( From West Germany to East Germany )

The people who lived in what is now Germany and Eastern Europe were Indo-Europeans, originally from the area between the Black Sea and the Caspian Sea. Sometime between 3000 BC and 2000 BC, they had migrated gradually out of that area and all across Europe. The region became associated with the name Germany in the 1st Century BC, when the Romans conquered Gaul.

             18th Century Germany Map 

After the fall of the Roman Empire, the Franks moved into France, but soon conquered Germany as well, so that by 800 AD Charlemagne was able to establish a German Holy Roman Empire that extended over France, Germany and much of central Italy. At first, the Holy Roman Emperors were very powerful, but later they lost power to the smaller German and Italian lords in each region. In the Middle Ages, the dukes and princes  of the empire gained power. The northern states became Protestant in the early 16th Century, while the southern states remained Catholic.

          Clash between Protestants and Catholic 

Protestants and Catholic clashed in the Thirty Year's War (1618—1648). Finally, the war ended with the peace of Westphalia, which is considered  the beginning of the modern nation-state system. 

                         Otto Von Bismarck 

A German Empire was created in 1871 under the leadership of Prussian Chancellor Otto Von Bismarck. Unification was followed by an industrial revolution. By 1900, Germany's economy was by far the largest in Europe, and second only to the US in the world. Germany was declared a republic on 9 November 1918. 

                     Nazis under Adolf Hitler

In 1933, the Nazis under Adolf Hitler gained power and imposed a totalitarian regime. They followed an expansionist foreign policy that led to World War II.

                            Berlín Wall

 After Nazi Germany's defeat, the country was divided into democratic West Germany and  Communist East Germany. It was reunified in 1990. Germany is a federal parliamentary republic of sixteen states. The capital and largest city is Berlin. In recent years, Germany has become increasingly integrated into the European Union.... 

 

Never forget that everything Hitler did in Germany was legal.

                                — Martin Luther King.

History of the United Kingdom ( From East to West )

The British Isles have a rich history going back thousand of years. The first men and women who arrived in the British lsles were hunters and gathers of food, and used simple stone tools and weapons.

                  Map of the Old England 

Nearly 2000 years ago, the Romans came to Britain and changed the country. Even today, the ruins of Roman buildings, forts, roads, and baths can be found all over Britain. They established medical practice, and a language of administration and law. Many English words are derived from the Latin launguage of the Romans.

Around AD 410, when the Roman army left, the Anglo-Saxon tribes invaded. In AD 800s, the island was divided among several small Kingdoms. In AD 886, the Anglo-Saxon leader Alfred The Great  united these kingdoms into one nation, which he called Angleland. This would later be changed to  England.

                            Alfred The Great

The Middle Ages in Britain saw some devastation and war. One of the most exciting periods of Britain history was from 1485 to 1603, during the rule of the Tudors, a Welsh-English family. The United Kingdom came into being on 1 May 1707, as a result of the political union of the Kingdom of England ( which included Wales ) and the Kingdom of Scotland.

                            Queen Victoria

 Another period of enormous change was during 1837 to 1901, the reign of Queen  Victoria. Registration of births, marriages and deaths came into practice; Mines Act ended child  labour; and the first post boxes were built.

                          King Edward VII 

Queen Victoria died in 1901 and her son Edward  VII became king. The new century was characterized by a feeling of great optimism.  Things such as motion pictures, automobiles, and  airplanes came into use. The United Kingdom is a constitutional monarchy with Queen Elizabeth II  as  the head of state. It is governed by a  parliamentary system with its seat of government  in London, its capital... 

“ HEAVEN TAKE THY SOUL, AND ENGLAND KEEP.                           MY BONES! ”

                                      - William Shakespeare.

History of Russia ( From St. Petersburg to Siberia )

The History of Russia begins around 1200s BC, with the arrival Cimmmerians , normads of Indo-European origin, in what is today called Ukraine. They were defeated by the Scythians, an Iranian tribe.In 200 BC, the Scythians were conquered by the Samaritans bringing Greek and Roman influence that would continue for many centuries. 

In the 800s, the Eastern Slaves were settled in different regions in Russia. The Slavs were an ethnic group that eventually split into the Russians, Ukrainians, and Belarusians.

In 862 , Rurik, a Varangian prince ruled the region which became known as the Land of the Rus. Around 1200, Russia was conquered by the Mongols led by Genghis Khan.

 In 1480, Ivan lll freed Russia from the Mongols. In 1547, Ivan lV, also known as Ivan the Terrible, became the first Tsar. In the 18th century, the principality of Muscovy had become the huge Russian Empire,  Stretching from Poland eastward to the Pacific Ocean.

Successive régimes of the 19th century responded to such pressures with a combination of half- hearted reform and repression. Russian serfdom was abolished in 1861. In 1898, the Russian Social Democratic Labor Party was established by the Marxists.

In 1903, Lenin became the leader of the Bolsheviks. In the World War I, the Russians fought the Germans and Austrians. But, in 1917, the revolutionaries overthrew the Russian government.

The next year, Czar Nicholas Il and his family were murdered, and Russia became the Russian Soviet Federative Socialist Republic which eventually formed the Union of Soviet Socialist Republic ( USSAR ).

Russia has existed as a state for over a thousand years, during most of the 20th century Russia was the core of the Soviet Union.

 Russia lost its superpower status as it faced serious challenges in its efforts to forge a new post-soviet political and economic system. Russia today shares much continuity of political culture and social structure with its Tsarist and Soviet past...

“ Без труда́ не вы́тащишь и ры́бку из пруда́ ”

                                      — Russian Proverb 

The Black Hole Explosions

The lower the mass of the black hole, the higher its temperature is. So as the black hole loses mass, its temperature and rate of emission increase. It therefore loses mass more quickly. What happens when the mass of the black hole eventually becomes extremely small is not quite clear. The most reasonable guess is that it would disappear completely in a tremendous final burst of emission, equivalent to the explosion of millions of Thermonuclear bombs.

A black hole with a mass a few times that of the sun would have a temperature of only one ten-millionth of a degree above absolute zero. This is much less than the temperature of the microwave radiation that fills the universe, about 2.7 degrees above absolute zero — so such black holes would give off less than they absorb, though even that would be very little. If the universe is destined to go on expanding forever, the temperature of the microwave radiation will eventually decrease to less than that of such a black hole. 

 The black hole will then absorb less than it emits and will begin to lose mass. But, even then its temperature is so low that it would take about 10⁶⁶ years to evaporate completely. This is much longer than the age of the universe, which is only about 10¹⁰ years.

There might be primordial black holes with a very much smaller mass that were made by the collapse of irregularities in the very early stages of the universe. Such black holes would have a much higher temperature and would be emitting radiation at a much greater rate. A primordial black hole with an initial mass of a thousand million ton would have a lifetime roughly equal to the age the universe. Primordial black holes with initial masses less than this figure would already have completely evaporated. However, those with slightly greater masses would still be emitting radiation in the form of X rays and gamma rays. These are like waves of light, but with a much shorter wavelength. Such black holes hardly deserve the epithet black. They really are white hot, and are emitting energy at the rate of about ten thousand megawatts.

 

One such black hole could run ten large power stations, if only we could harness its output. This would be rather difficult, however. 

The black hole would have the mass of a mountain compressed into the size of the nucleus of an atom. If you had one of these black holes on the surface of the Earth, there would be no way to stop it falling through the floor to the center of the Earth. It would oscillate through the Earth and back, until eventually it settled down at the center. So the only place to put such a black hole, in which one might use the energy that it emitted, would be in orbit the Earth would be to attract it there by towing a large mass in front of it, rather like a grass in front of a horse. This does not sound like a very practical proposition, at least not in the immediate future...

We can calculate the temperature of black hole, By using this equation:  

The General Relativity And Quantum Mechanics ( From The Black Hole )

Radiation from black holes was the first example of a prediction that depended on both of the great theories of this century, general relativity and quantum mechanics. It aroused a lot of opposition initially because it upset the existing viewpoint: “ How can a black hole emit anything?  ” When Stephen Hawking first announced the results of him calculations at a conference at the Rutherford Laboratory near Oxford, Hawking was greeted with general incredulity. At the end of Hawking talk the chairman of the session,  John G. Taylor  from Kings College, London, claimed it was all nonsense. He even wrote a paper to the effect. 

However, in the end most people, including John Taylor, have come to the conclusion that black holes must radiate like hot bodies if our other idea about general relativity and quantum mechanics are correct. Thus even though Hawking have not yet managed to find a primordial black hole, there is fairly general agreement that if Hawking did, it would have to be emitting a lot of gamma and X rays. If Hawking do find one, He will get the Noble Prize.

The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as we once thought. If an astronaut falls into a black hole, its mass will increase. Eventually, the energy equivalent of that extra mass will be returned to the universe in the form of radiation.

Thus, in a sense, the astronaut will be recycled. It would be a poor sort of immortality, however, because any personal concept of time for the astronaut would almost certainly come to an end as he was crushed out of existence inside the black hole. Even the types of particle that were eventually emitted by the black hole would in general be different from those that made up the astronaut. The only feature of the astronaut that would survive would be his mass or energy. 

The approximations, Hawking used to derive the emission from black holes should work well when the black hole has a mass greater than a fraction of a gram. However, they will break down at the end of the black hole’s life, when its mass gets very small. The most likely outcome seems to be that the black hole would just disappear, at least from our region of the universe. It would take with it the astronaut and any singularity there might be inside the black hole. This was the first indication that quantum mechanics might remove the singularities that were predicted by classical general relativity. However, the methods that Hawking and other people were using in 1974 to study the quantum effects of gravity were not able to answer questions such as whether singularities would occur in quantum gravity. And Hawking radiation equation has a blackbody spectrum: 

From 1975 onward, Hawking therefore started to develop a more powerful approach to quantum gravity based on  Feynman’s  idea of a sum over histories. We shall see that quantum mechanics allows the universe to have a beginning that is not break down at the origin of the universe. The state of the universe and its contents, like ourselves, are completely determined by the laws of physics, up to the limit set by the uncertainty principle. So much for free will...