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...  

On the Idea of Gravitational Field in Physics

“ If we pick up a stone and then let it go, why does it fall to the ground? ” The usual answer to the question is: “ Because it is attracted by the Earth ”.  Modern physics formulates the answer rather differently for the following reason. As a result of the more careful study of electromagnetic phenomena, we have come to regard action at a distance as a process impossible without the intervention of some intermediary medium. If , for instance, a manget attracts a piece of iron, we cannot be content to regard this as meaning that the magnet acts directly on the iron through the intermediate empty space, but we are constrained to imagine — after the manner of Faraday — that the magnet always calls into being something physically real in the space around it, that something being what we call a  “ magnetic field ”.

In its turn this magnetic field operates on the piece of iron, so that the latter strives to move towards the magnet. We shall not discuss here the justification for this incidental conception, which is indeed a somewhat arbitrary one. We shall only mention that with its aid electromagnetic phenomena can be theoretically represented much more satisfactorily than without it, and this applies particularly to the transmission of electromagnetic waves. The effects of gravitation also are regarded in an analogous manner. 

The action of the earth on the stone takes place indirectly. The earth produces in its surrounding a gravitational field, which acts on the stone and produces its motion of fall. As we know from experience, the intensity of the action on the body diminishes according to a quite definite law, as we proceed farther and farther away from the earth. From our point of view this mean: The law governing the properties of the gravitational field in space must be a perfectly definite one, in order correctly to represent the diminution of the gravitational action with the distance from operative bodies. It is something like this: The body ( e.g. the earth ) produces a field in its immediate neighbourhood directly; the intensity and direction of the field at the points farther removed from the body are thence determined by the law which governs the properties in space of the gravitational fields themselves. 

In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body . For instance, a piece of lead and piece of wood fall in exactly the same manner in a gravitational field in ( in vacuo ), when they start off from rest or with the same initial velocity. This law, which holds most accurately, can be expressed in a different from in the light of the following consideration. 

According to Newton's law of motion, we have: 

( Force ) = ( inertial mass ) × ( acceleration ) 

Where the “ inertial mass ” is a characteristic constant of the accelerated body. If now gravitation is the cause of the acceleration, we then have:

( Force ) = ( gravitational mass ) × ( intensity of                                                  the gravitational field ) 

where the “ gravitational mass ” is likewise a characteristic constant for the body. From these two relations follows: 

( Acceleration ) =  ( gravitational mass ) /                                                  ( inertial mass) × ( intensity                                            of the gravitational field )

If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable choice of units we can thus make this ratio equal to unity.  We then have the following law:  The gravitational  mass of a body is equal to its inertial law  .

 It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following  fact:  The same quality of the body manifests itself according to circumstances as “ inertia ” or as    “ weight ” ( lit “  heaviness ” ). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity...

Galileo Galilei ( Italian astronomer, physicist )

Galileo di Vincenzo Bonaiuti de' Galilei was born on February 15, 1564 in Pisa, Italy. His father was a musician and wool trader. He wanted his son to study medicine. Galileo began his education in   Jesuit monastery  at the age of eleven. By the time he was seventeen, he was enrolled with the University of Pisa to learn medicine.

In University, mathematics became his favourite subject, so much so that he shunned other subjects and began studying only mathematics. Later, to earn his living, he began mathematics tution for other students.

GALILEO, Perhaps more than any other single person, was responsible for the birth of modern science. His renowned conflict with the Catholic Church was central to his philosophy, for Galileo was one of the first to argue that man could hope understand how the world works and, moreover, that we could do this by observing the real world. 

Galileo had believed Copernican theory ( that the planets orbited the sun ) since early on, but it was only when he found the evidence needed to support the idea that he started to publicly espouse it. He wrote about Copernicus's theory in Italian ( not the usual academic Latin ), and soon his views became widely adopted outside the Universities. This annoyed the Aristotlelian professors, who united against him, seeking to persuade the Catholic Church to ban Copernicanism.

Galileo, worried by this, travelled to Rome to speak to the ecclesiastical authorities. He argued that the Bible was not intended to tell us anything about scientific theories and that it was usual to assume that, where the Bible conflicted with common sense, it was being allegorical.

But the Church was afraid of a scandal that might undermine its fight against Protestantism, and so took repressive measures. It declared Copernicanism “  false and erroneous ” in 1616, and commanded Galileo never again to “  defend or hold ” the doctrine. Galileo acquiesced.

In 1623, a longtime friend of Galileo's became the pope. Immediately Galileo tried to get 1616 decree revoked. He failed, but he did manage to get permission to write a book discussing both Aristotlelian and Copernican theories, on two conditions: he would not take sides, and he would how the world worked because God could not place restrictions on God's omnipotence.

The book, “ Dialogue Concerning the Two Chief World Systems ”, was completed and published in 1632, with the full backing of the censors—and was immediately greeted throughout Europe as a literary and philosophical masterpiece. Soon the pope, realizing that people were seeing the book as a convincing argument in favour of Copernicanism, regretted having allowed its publication. The pope argued that although the book had nevertheless contravened the 1616 decree. He brought Galileo before the Inquisition, which sentenced him to house arrest for life and commanded him to publicly renounce Copernicanism. For a second time, Galileo acquiesced.

Galileo remained a faithful Catholic, but his belief in the independence of science had not been crushed. Four years before his death in 1642, while he was still under house arrest, the manuscript of his second major book was smuggled to a publisher in Holland . It was this, referred to as Two New Sciences, even more his support for Copernicus, that was not to be the genesis of modern physics. 

♦ Did You Know?

                      ♣ Galileo wanted to be a monk when he came back from the  Jesuit monastery . His father got angry and withdrew him from there.

                      ♣ Galileo built his first telescope in 1609, which featured three times magnification. Later, he developed models that could see up to 30 times magnification.

                       ♣ Galileo was a well-known and accomplished musician.

Galileo Galilei died on March 8, 1642 following a prolonged illness...

Issac Newton ( English mathematican, physicist )

Sir Isaac Newton was born on December 25, 1642 in Lincolnshire, England. Newton was named after his father — Isaac Newton, who died three months before his birth. He was a premature child and was raised by his maternal grandmother. Newton went to The King's School, Grantham; When he turned twelve. In 1661, he enrolled with the Trinity College, Cambridge. He obtained his degree in 1665. Later, he joined the same college as a mathematics professor. 

Sir Isaac Newton was not a pleasant man. His relations with other academics were notorious, with most of his later life spent embroiled in heated disputes. Following publication of  Principia Mathematica  (1687) —  surely the most influential book ever written in physics —  Newton had risen rapidly into public prominence. He was appointed president of the Royal Society and became the first scientist ever to be knighted. 

Newton soon clashed with the Astronomer Royal, John Flamsteed, who had earlier provided Newton with much needed data for  Principia, but was now withholding information that Newton wanted. Newton would not take no for an answer:  he had himself appointed to the governing body of the Royal Observatory and then tried to force immediate publication of the data. Eventually he arranged for Flamsteed's work to be seized and prepared for publication by Flamsteed's mortal enemy, Edmond Halley. But Flamsteed took the case to court and, in the nick of time, won a court order preventing distribution of the stolen work. Newton was incensed and sought his revenge by systematically deleting all references to Flamsteed in later editions of  Principia. 

A more serious dispute arose with the German philosopher Gottfried  Leibniz. Both Leibniz and Newton had independently developed a branch of mathematics called calculus, which underlies most of modern physics. Although we now know that Newton discovered calculus years before Leibniz, he published his work much later. A major row ensued over who had been first, with scientists vigorously defending both contenders. It is remarkable, however, that most of the articles appearing in defense of Newton were originally written by his own hand — and only published in the name of friends!  As the row grew, Leibniz made the mistake of appealing to the Royal Society to resolve the dispute. Newton, as president, appointed an " impartial " committee to investigate, coincidentally consisting entirely of Newton's friends!  But that was not all: Newton then wrote the committee's report himself and had the Royal Society published it, officially accusing Leibniz of plagiarism. Still unsatisfied, he then wrote an anonymous review of the report in the Royal society's own periodical. Following the death of Leibniz, Newton is reported to have declared that he had taken great satisfaction in " breaking Leibniz's heart ". He also did some important work in optics.

During the period of these two disputes Newton had already left Cambridge and academe. He had been active in anti-Catholic politics at Cambridge, and later in Parliament, and was rewarded eventually with the lucrative post of  " Warden of the Royal Mint ". Here he used his talents for deviousness and vitriol in a more socially acceptable way, successfully conducting a major campaign against counterfeiting, even sending several men to their death on the gallows. 

Sir Isaac Newton died on March 31, 1727 during his sleep...

Albert Einstein ( German—born Theoretical physicist )

Albert Einstein was regarded as the founder of modern physics, Albert Einstein was born to Hermann Einstein,a salesman and an engineer,and Pauline Kochon on 14 March 1879, in Ulm, Kingdom of Württemberg, German Empire. He received his education at the Luitpold Gymnasium in Munich. His grades in physics and mathematics were always excellent. He completed his schooling at the Argovian Cantonal School, Aarau, Switzerland, and at the age of seventeen he joined the Zürich Polytechnic for a physics and mathematics teaching diploma programme.

Einstein received his degree in 1900 but failed to get a suitable teaching job. With his friend's help, he joined the Federal Office for Intellectual Property as an assistant examiner – level lll .

Einstein secured a permanent position at the Swiss Patent Office in 1903. His conclusions about the space-time connection and the nature of light were aided by his work and experiments during this job.

Einstein completed his Ph.D. from the University of Zürich in 1905 and published four papers in the scientific journal named ″ Annalen der Physik ". The year was miraculous for him as these papers on photoelectric effect, Brownian motion, special relativity, and mass-energy equivalence ( E= mc² ) were significant contributors to the foundation of modern physics. They reformed the views on time ,  space, and matter. In the next few years, Einstein came to be recognized as a major scientist.

In 1908 he joined the University of Bern as a lecturer and the next year he was appointed as an associate professor at the University of Zürich. Two years later, in 1911, he was appointed as a professor at the Charles-Ferdinand University, Prague. Here he wrote several scientific works. Einstein returned to Zürich the next year, and for the two years that followed, he joined ETH Zurich as a professor of theoretical physics.

Einstein was appointed as the director of Kaiser Wilhelm Institute of Physics in the year 1914 and as the president of the German Physical Society in 1916. He developed the general theory of relativity between 1907 and 1915. It was published in 1915. In 1916, Einstein published " Relativity: The Special and the General Theory " in German. Its first English translation was published in 1920. Divided into three parts, the special theory of relativity, the general theory of relativity, and the consideration on the universe as a whole. It is considered a groundbreaking scientific work.

In 1921, Einstein was awarded the Nobel prize in physics " for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect. " 

 In the year that followed, he travelled extensively. In 1933, he joined the Institute for Advanced Study in the United States, and by 1940 he became an American citizen.

Einstein published numerous scientific and non-scientific works. Some of his published works include: Sidelights on Relativity (1922), Cosmic Religion: With Other Opinions and Aphorisms (1931), Essays in Science (1934), The World as I see It (1949), Out of My Later Years (1950), and Ideas and Opinions (1954). 

Einstein died on 18 April 1955, aged seventy-six, in Princeton, New Jersey.