August 5, 2021
PHYSICS LECTURE
EINSTEIN GEOMETRY AS APPLIED TO COSMOLOGY
GEOMETRY and COSMOLOGY
Geometry is the branch of mathematics that defines and relates basic properties and
measurement of line segments and angles (Gantert, 2008). Cosmology is a branch of
astronomy that involves the origin and evolution of the universe, from the Big Bang to
today and on into the future. According to NASA, the definition of cosmology is "the
scientific study of the large scale properties of the universe as a whole.”
SNAPSHOT FROM A COMPUTER SIMULATION OF THE FORMATION OF LARGE-SCALE STRUCTURES IN THE
UNIVERSE, SHOWING A PATCH OF 100 MILLION LIGHT-YEARS AND THE RESULTING COHERENT MOTIONS OF
GALAXIES FLOWING TOWARD THE HIGHEST MASS CONCENTRATION IN THE CENTER. (IMAGE CREDIT: ESO)
During the 1980s observations remained sufficiently crude so that a Universe of critical
density was quite plausible. But more recent observations have made it increasingly
difficult to reconcile a critical Universe with the observations.
It is known that, in addition to the luminous matter seen in the form of stars, the
Universe contains a large amount of "dark" matter, in particular in the halos around
galaxies. The presence of this dark matter is inferred from its gravitational pull on the
surrounding matter. Since the dark matter is distributed in a less clustered manner than
the luminous matter, the apparent average density seems to increase as larger and
larger scales are probed. For a long time it was hoped probing sufficiently large scales
would uncover a critical density of dark matter.
Today it seems unlikely that this hope will ever be realized. It is now possible to probe
the average density of the Universe on scales large enough to compromise a fair
sample of the Universe.
ALBERT EINSTEIN AND COSMOLOGY
Albert Einstein (14 March 1879 – 18 April 1955) was born in Ulm in Germany, but shortly
after his family moved to Munich, where he attended the Luitpold Gymnasium. At the
age of 16 he applied, unsuccessfully, to the Swiss Federal Polytechnic in Zurich, but he
, citizenship to avoid military service in Germany. At the age of 17 he began a four-year
teaching diploma course at the Polytechnic. He became a Swiss citizen in 1901, at
which time he began work at the Swiss Patent Office, where he remained until 1909
following his appointment to a lectureship at the University of Berne. He subsequently
moved to the Charles-Ferdinand University in Prague in 1911; in 1914 he was
appointed director of the Kaiser Wilhelm Institute for Physics. There he remained until
1932, when, with the rise to power of Adolf Hitler, he found himself as a Jew considered
an assassination target. After a brief sojourn in England he took up a position at the
newly created Institute of Advanced Study in Princeton, where he remained to the end
of his life. He never returned to Europe.
Einstein always appeared to have a clear view of the problems of physics and the
determination to solve them. He had a strategy of his own and was able to visualize the
main stages on the way to his goal. He regarded his major achievements as mere
stepping-stones for the next advance. Albert Einstein was according to many the
greatest of all physicists. He was the creator of relativity theory and a founding father of
quantum mechanics. In 1904 he independently laid the foundations of statistical
mechanics, in the manner of Gibbs rather than Boltzmann; in 1905 he created relativity
theory, the theory of Brownian motion, and the theory of quantization of energy,
including the concept of light quanta (photons). It was for the photoelectric effect that he
was eventually awarded the Nobel Prize, in 1921.
At the start of his scientific work, Einstein realized the inadequacies of Newtonian
mechanics and his special theory of relativity stemmed from an attempt to reconcile the
laws of mechanics with the laws of the electromagnetic field. He dealt with classical
problems of statistical mechanics and problems in which they were merged with
quantum theory: this led to an explanation of the Brownian movement of molecules. He
investigated the thermal properties of light with a low radiation density and his
observations laid the foundation of the photon theory of light.
In his early days in Berlin, Einstein postulated that the correct interpretation of the
special theory of relativity must also furnish a theory of gravitation and in 1916 he
published his paper on the general theory of relativity. During this time he also
contributed to the problems of the theory of radiation and statistical mechanics.
In the 1920s, Einstein embarked on the construction of unified field theories, although
he continued to work on the probabilistic interpretation of quantum theory, and he
persevered with this work in America. He contributed to statistical mechanics by his
development of the quantum theory of a monatomic gas and he has also accomplished
valuable work in connection with atomic transition probabilities and relativistic
cosmology. Einstein’s researches are, of course, well chronicled and his more important
works include Special Theory of Relativity (1905), Relativity (English translations, 1920
and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian
Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works,
About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later
Years (1950) are perhaps the most important.
The dawn of the 20th century brought further insights into comprehending the vast
universe. Albert Einstein proposed the unification of space and time in his General
Theory of Relativity. In the early 1900s, scientists were debating whether the Milky Way
contained the whole universe within its span, or whether it was simply one of many
collections of stars. Edwin Hubble calculated the distance to a fuzzy nebulous object in
the sky and determined that it lay outside of the Milky Way, proving our galaxy to be a
small drop in the enormous universe. Using General Relativity to lay the framework,
Hubble measured other galaxies and determined that they were rushing away from the
us, leading him to conclude that the universe was not static but expanding.
PHYSICS LECTURE
EINSTEIN GEOMETRY AS APPLIED TO COSMOLOGY
GEOMETRY and COSMOLOGY
Geometry is the branch of mathematics that defines and relates basic properties and
measurement of line segments and angles (Gantert, 2008). Cosmology is a branch of
astronomy that involves the origin and evolution of the universe, from the Big Bang to
today and on into the future. According to NASA, the definition of cosmology is "the
scientific study of the large scale properties of the universe as a whole.”
SNAPSHOT FROM A COMPUTER SIMULATION OF THE FORMATION OF LARGE-SCALE STRUCTURES IN THE
UNIVERSE, SHOWING A PATCH OF 100 MILLION LIGHT-YEARS AND THE RESULTING COHERENT MOTIONS OF
GALAXIES FLOWING TOWARD THE HIGHEST MASS CONCENTRATION IN THE CENTER. (IMAGE CREDIT: ESO)
During the 1980s observations remained sufficiently crude so that a Universe of critical
density was quite plausible. But more recent observations have made it increasingly
difficult to reconcile a critical Universe with the observations.
It is known that, in addition to the luminous matter seen in the form of stars, the
Universe contains a large amount of "dark" matter, in particular in the halos around
galaxies. The presence of this dark matter is inferred from its gravitational pull on the
surrounding matter. Since the dark matter is distributed in a less clustered manner than
the luminous matter, the apparent average density seems to increase as larger and
larger scales are probed. For a long time it was hoped probing sufficiently large scales
would uncover a critical density of dark matter.
Today it seems unlikely that this hope will ever be realized. It is now possible to probe
the average density of the Universe on scales large enough to compromise a fair
sample of the Universe.
ALBERT EINSTEIN AND COSMOLOGY
Albert Einstein (14 March 1879 – 18 April 1955) was born in Ulm in Germany, but shortly
after his family moved to Munich, where he attended the Luitpold Gymnasium. At the
age of 16 he applied, unsuccessfully, to the Swiss Federal Polytechnic in Zurich, but he
, citizenship to avoid military service in Germany. At the age of 17 he began a four-year
teaching diploma course at the Polytechnic. He became a Swiss citizen in 1901, at
which time he began work at the Swiss Patent Office, where he remained until 1909
following his appointment to a lectureship at the University of Berne. He subsequently
moved to the Charles-Ferdinand University in Prague in 1911; in 1914 he was
appointed director of the Kaiser Wilhelm Institute for Physics. There he remained until
1932, when, with the rise to power of Adolf Hitler, he found himself as a Jew considered
an assassination target. After a brief sojourn in England he took up a position at the
newly created Institute of Advanced Study in Princeton, where he remained to the end
of his life. He never returned to Europe.
Einstein always appeared to have a clear view of the problems of physics and the
determination to solve them. He had a strategy of his own and was able to visualize the
main stages on the way to his goal. He regarded his major achievements as mere
stepping-stones for the next advance. Albert Einstein was according to many the
greatest of all physicists. He was the creator of relativity theory and a founding father of
quantum mechanics. In 1904 he independently laid the foundations of statistical
mechanics, in the manner of Gibbs rather than Boltzmann; in 1905 he created relativity
theory, the theory of Brownian motion, and the theory of quantization of energy,
including the concept of light quanta (photons). It was for the photoelectric effect that he
was eventually awarded the Nobel Prize, in 1921.
At the start of his scientific work, Einstein realized the inadequacies of Newtonian
mechanics and his special theory of relativity stemmed from an attempt to reconcile the
laws of mechanics with the laws of the electromagnetic field. He dealt with classical
problems of statistical mechanics and problems in which they were merged with
quantum theory: this led to an explanation of the Brownian movement of molecules. He
investigated the thermal properties of light with a low radiation density and his
observations laid the foundation of the photon theory of light.
In his early days in Berlin, Einstein postulated that the correct interpretation of the
special theory of relativity must also furnish a theory of gravitation and in 1916 he
published his paper on the general theory of relativity. During this time he also
contributed to the problems of the theory of radiation and statistical mechanics.
In the 1920s, Einstein embarked on the construction of unified field theories, although
he continued to work on the probabilistic interpretation of quantum theory, and he
persevered with this work in America. He contributed to statistical mechanics by his
development of the quantum theory of a monatomic gas and he has also accomplished
valuable work in connection with atomic transition probabilities and relativistic
cosmology. Einstein’s researches are, of course, well chronicled and his more important
works include Special Theory of Relativity (1905), Relativity (English translations, 1920
and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian
Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works,
About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later
Years (1950) are perhaps the most important.
The dawn of the 20th century brought further insights into comprehending the vast
universe. Albert Einstein proposed the unification of space and time in his General
Theory of Relativity. In the early 1900s, scientists were debating whether the Milky Way
contained the whole universe within its span, or whether it was simply one of many
collections of stars. Edwin Hubble calculated the distance to a fuzzy nebulous object in
the sky and determined that it lay outside of the Milky Way, proving our galaxy to be a
small drop in the enormous universe. Using General Relativity to lay the framework,
Hubble measured other galaxies and determined that they were rushing away from the
us, leading him to conclude that the universe was not static but expanding.
