Creator of the theory of the non-stationary Universe
Alexander Aleksandrovich Fridman(June 16, St. Petersburg - September 16, Leningrad) - Russian and Soviet mathematician and geophysicist, creator of the theory of the non-stationary Universe.
Biography
The first wife of A. A. Fridman (since 1911) is Ekaterina Petrovna Fridman (nee Dorofeeva). Second wife (since 1923) - Doctor of Physics mathematical sciences Natalya Evgenievna Fridman (nee Malinina), their son - Alexander Alexandrovich Fridman (1925-1983) - was born after the death of his father.
see also
- Friedman (crater)
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Notes
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Date of birth: June 16, 1888 Place of birth: St. Petersburg, Russian empire Date of death: September 16, 1925 Place of death: Leningrad, USSR Nau ... Wikipedia
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Fridman Alexander Alexandrovich- A. A. Fridman Fridman Alexander Alexandrovich (18881925) Soviet scientist, one of the creators of modern dynamic meteorology, professor (1918), Doctor of Physical and Mathematical Sciences (1922). Graduated from St. Petersburg University (1910) ... Encyclopedia "Aviation"
Fridman Alexander Alexandrovich- A. A. Fridman Fridman Alexander Alexandrovich (18881925) Soviet scientist, one of the creators of modern dynamic meteorology, professor (1918), Doctor of Physical and Mathematical Sciences (1922). Graduated from St. Petersburg University (1910) ... Encyclopedia "Aviation"
Fridman Alexander Alexandrovich- A. A. Fridman Fridman Alexander Alexandrovich (18881925) Soviet scientist, one of the creators of modern dynamic meteorology, professor (1918), Doctor of Physical and Mathematical Sciences (1922). Graduated from St. Petersburg University (1910) ... Encyclopedia "Aviation"
- (1888 1925) Russian mathematician and geophysicist. In 1922, 24 established that Einstein’s equations of gravity have nonstationary solutions, which formed the basis modern cosmology. One of the creators modern theory turbulence and school of dynamic... Big Encyclopedic Dictionary
Soviet scientist, one of the creators of modern dynamic meteorology. Graduated from St. Petersburg University (1910). In 1913 he began working at the Pavlovsk Aerological Observatory. In 1914 17... ... Big Soviet encyclopedia
- (1888 1925) Soviet scientist, one of the founders of modern dynamic meteorology, professor (1918), Doctor of Physical and Mathematical Sciences (1922). Graduated from St. Petersburg University (1910). From 1913 he worked at the Pavlovsk Aerological Observatory... Encyclopedia of technology
Genus. May 19, 1866 in St. Petersburg; 1889 graduated from St. Petersburg. Conservatory in the composition class of Rimsky Korsakov. Since 1895 he has been the conductor of the string and brass orchestras. Guards Preobrazhensky Regiment, with which in 1897 he traveled to Paris, Rouen, etc. He wrote two... ... Big biographical encyclopedia
- (1888 1925), mathematician and geophysicist. In 1922 1924 he found non-stationary solutions to Einstein's gravitational equations, which formed the basis of the theory of a non-stationary (expanding) Universe. One of the creators of the modern theory of turbulence and domestic... ... encyclopedic Dictionary
Books
- Stress management for a business person, Alexander Fridman, Yuri Viktorovich Shcherbatykh, Dmitry Alexandrovich Galantsev. Stress management for a business person. Stress management technologies proven in corporate wars, legal battles and tough negotiations. Stress management is a skill...
- , Tropp E.A.. Readers are offered a book about the life and scientific work of the classic of Soviet science A.A. Friedman (1888-1925). A prominent place in it is occupied by a biographical sketch, including a number of...
Alexander Alexandrovich Fridman was born on June 4 (16), 1888 in St. Petersburg into a family of artists. From 1897 to 1906, Alexander studied at the 2nd St. Petersburg Gymnasium, then until 1910 at St. Petersburg University. In 1913, Friedman entered the Aerological Observatory, where he studied dynamic meteorology. During the First World War he volunteered for an aviation detachment. After graduation, he headed the new Aviapribor plant in Moscow. In 1918–1920, Fridman was a professor at Perm University, after which he returned to St. Petersburg and got a job at the Main Physical Observatory (since 1924 - the Main Geophysical Observatory named after A.I. Voeikov). In 1923, the scientist was appointed editor-in-chief of the Journal of Geophysics and Meteorology, and in 1925 he became director of the geophysical observatory. Friedman died on September 16, 1925 from typhoid fever. After his death, the scientist was awarded the Lenin Prize (1931). However, in 1937, Friedman was recognized as the leader of an anti-Soviet gang of scientist-saboteurs (as a result of which two of his students suffered). Only in the 60s of the last century was he rehabilitated, and the centenary of the scientist’s birth was celebrated on a grand scale.
In 1915 it appeared general theory relativity, and in 1917 Einstein created his cosmological model on its basis. It stated that the Universe is eternal and unchanging, but to achieve this result Einstein had to introduce the so-called cosmological constant. Alexander Friedman was one of the first scientists in the world who perfectly mastered the very complex mathematical apparatus of the general theory of relativity. However, he not only understood how all the formulas of the theory were derived, but realized that these formulas contained a much deeper meaning than Einstein himself put into them. Friedman was a great mathematician and physicist of his time and did not agree with Einstein's conclusion about a static universe. To support his point of view, Friedman published the now classic work On the Curvature of Space in 1922. This work was amazing scientific world. In it, the scientist convincingly showed that several models of the Universe are derived from the formulas of the theory of relativity. At the same time, it turned out that Einstein’s static Universe is only special case, and extremely unlikely. In addition, Friedman criticized the cosmological constant introduced by Einstein, proving its uselessness.
Alexander Friedman was convinced that the Universe is not static and is expanding. However, the scientist was not sure what awaited the world next, and predicted two possible options - either the Universe will expand forever, or after some time the expansion will be replaced by compression. But in any case, it turned out that once upon a time the Universe was a point of infinitesimal volume. In other words, Friedman predicted what we now call the theory big bang. In addition, the scientist even made an assumption about when the expansion began, indicating a time of about 10 billion years ago. The world is now thought to be about 13.5 billion years old, so Friedman was right on that point as well.
Friedman's ideas amazed the world, but Einstein himself categorically disagreed with his colleague - the creator of the theory of relativity did not believe in a non-stationary Universe! That is why, a few weeks after Friedman’s work appeared, Einstein published an article criticizing the idea that our world is not stationary, and pointed out to Friedman an error in his mathematical calculations. Alexander Alexandrovich was not at a loss. On the contrary, he became even more active in his theory and in a personal letter to Einstein in the language mathematical formulas clearly and logically proved he was right. And only then did Einstein realize that he had made a mistake and that the Universe simply could not be stationary!
The German physicist publicly admitted that he was wrong in 1923, adding that Friedmann's work sheds new light on the problem of cosmology and reveals a completely unusual picture of the structure of the Universe. Friedman's work is actually much deeper and more complex than what is described here. They address questions about the curvature of space, the change of this space in time and other properties of the Universe. But the most important thing is that the Soviet scientist not only predicted the expansion of the Universe, but was able to describe the dynamics of this expansion mathematically. Even now, almost nine decades later, Friedman’s calculations remain correct and are in good agreement with observational data.
Unfortunately, Friedman did not live to see the full confirmation of his ideas. This was done in 1929 by American astronomer Edwin Hubble, who discovered the equally famous red shift, which indicates the recession of galaxies. The data obtained by Hubble were in good agreement with Friedman's assumptions. Modern astronomical observations also suggest that Friedman was right in his conclusions.
Alexander Alexandrovich Friedman is the recognized creator of a new cosmology, who pointed out the possibility of the expansion of the Universe and made a significant contribution to the general theory of relativity. Friedman's ideas are also confirmed in the observations of modern astronomers.
>> Alexander Friedman
Biography of Alexander Friedman (1888-1925)
Education: St. Petersburg University
Place of Birth: St. Petersburg, Russian Empire
A place of death: Leningrad, RSFSR, USSR
– Soviet mathematician, creator of modern physical cosmology: biography with photos, the first non-stationary model of the Universe, Einstein.
Alexander Alexandrovich Fridman born in 1888 on June 16 in the family of two student spouses at the St. Petersburg Conservatory - the future composer Alexander Alexandrovich Fridman (1866-1909) and the future piano teacher Lyudmila Ignatievna Fridman (1869-1953). At the age of 9 (1897), the future scientist’s parents separated, after which he was left to be raised by his father’s new family. He was also raised by his grandfather Alexander Ivanovich Fridman (secretary of the province and part-time medical assistant of the Court Medical District) (1839-1910) and his aunt-pianist Maria Alexandrovna Friedman. A. Friedman began communicating with his own mother almost before his death.
The years of study were spent at the 2nd gymnasium of St. Petersburg. At this time, as well as during his student years, his hobby was astronomy. In 1906, Friedman, together with a classmate named Yakov Tamarkin, published in one of the leading scientific journals"Mathematical Annals" ("Mathematische Annalen") one of the first works on mathematics. In the same year he entered the Faculty of Physics and Mathematics of the University of St. Petersburg in the mathematics department, which he graduated in 1910. He is preparing for a professorship here at the Department of Applied Mathematics. In 1913, he became a practical leader of classes at the Institute of Railway Engineers and gave lectures at the Mining Institute. In the same year he entered the Aerological Observatory in the city of Pavlovsk (near St. Petersburg), where he became interested in geophysical hydrodynamics (at that time dynamic meteorology). In the spring of 1914 he was sent to Leipzig, where in the summer he had the opportunity to fly on an airship, taking an active part in preparing the observation of the solar eclipse in 1914 in August.
When World War I began, Friedman went to the air detachment as a volunteer. From 1914 to 1917 took an active part in the formation of aerological and air navigation services on several fronts, and also acted as an observer during combat flights.
Friedman was the leader in Russia in terms of the idea of the need to establish aircraft instrument manufacturing here. He managed to implement this idea during the times of military devastation and in June 1917 he became the founder and director of the Moscow Aviapribor plant.
From 1918 to 1920 he was a professor at Perm University. Then an employee of the Main Physical Observatory and at the same time a teacher in several educational institutions in Petrograd. In 1923 he became editor-in-chief of the Journal of Geophysics and Meteorology. Shortly before his death, he assumed the position of director of the Main Geophysical Observatory.
A. A. Fridman devoted his main works to the topic of problems in dynamic meteorology - theories of violation of the integrity of the atmosphere, atmospheric gusts and vortices, as well as turbulence in the atmosphere. Also known are his works on the topics of compressible fluid hydrodynamics, relativistic cosmology and physical phenomena in the atmosphere. July 1925 was marked in his life by a scientific flight in a balloon in a team with pilot P.F. Fedoseenko, during which they reached maximum height at that time 7400 m. After mastering the mathematical apparatus of Einstein’s theory of gravity, he reads an introductory course to the theory of relativity in tensor calculus at the university. WITH new physics general public introduced him to the book “The World as Space and Time” (1923). Its second edition was published after the scientist’s death in 1965.
From 1922 to 1924 during scientific research develops non-stationary solutions to Einstein's equations, which was a fundamental factor in the theory of the impermanence of the Universe (its constant expansion). The scientist also conducted other studies, as a result of which he proved that Einstein’s model of the static Universe is a special case. He also refuted the opinion of the general theory of relativity that any space has an end. Later, his theory about the constant expansion of the Universe was confirmed in 1929 by Edwin Hubble as a result astronomical observations behind the spectral lines of galaxies.
In 1925, on September 16, Friedman dies in Leningrad as a result of typhoid fever. His remains rest in the Orthodox Smolensk cemetery.
The personal life of the scientist was also not distinguished by constancy and harmony. He married for the first time in 1911, born. Dorofeeva Ekaterina Petrovna Friedman. In 1923 he became his second wife. Malinina Natalya Evgenievna Fridman (Doctor of Physical and Mathematical Sciences). The date of birth of their son Alexander Alexandrovich Fridman (1925-1983) occurred at a time after the death of his father.
According to Princeton University professor Igor Klebanov, “if Friedman had lived a little longer, he would certainly have been awarded the Nobel Prize. After all, he was the first scientist to come up with a solution to the equation of general relativity for the Universe, which is constantly growing and expanding.” Nowadays, modern scientists have conducted a number of scientific experiments, the results of which confirmed the correctness of his decision.
The world is not fully created: the heavens are always being renewed, astronomers are always adding new ones to the old stars. If I discovered a star, I would call it Friedman - better means I can’t find it to make everything clearer.
Friedman! Until now he is a resident of only a few bookshelves- an amateur mathematician, a young meteorologist and military aviator on the German front somewhere, and later - the organizer of Perm University at the dawn of Soviet power. Member of Osoaviakhim. Having caught typhus in the Crimea, unfortunately, he did not return from Crimea. Died. And they forgot about him. Only a quarter of a century later they remembered the man and seemed to revive him: “Young, full of boldness, he did not think without ideas. It is a fact that in some ways he went further than Einstein himself: sensing the inconstancy of forms in this hurricane world, he saw galaxies scattering in the curvature of space.” – “Expansion of the Universe? We need to figure this out!”
They begin to bicker.
But the fact is undeniable: this Friedman was a scientist with a very enviable future. Oh, shine above the sky a new star, Friedman!
Some inaccuracies do not at all spoil the poems of Leonid Martynov, dedicated to the mathematician, physicist, meteorologist Alexander Alexandrovich Fridman, who succeeded despite short life, leave a noticeable mark on world science.
Academician P. L. Kapitsa argued that Friedman was one of the best Russian scientists. “If it had not been for his death from typhoid fever at the age of 37... he certainly would have done a lot more in physics and mathematics and would have achieved the highest academic ranks. IN at a young age He was already a professor and was world famous among specialists in the theory of relativity and meteorology. In the 20s, while in Leningrad, I often heard reviews of Friedman as an outstanding scientist from professors Krutkov, Fredericks, and Bursian.”
While still a high school student, Friedman (together with Ya. D. Tumarkin) published two short articles on number theory. Both received an approving review from the famous mathematician D. Hilbert. Friedman’s widow wrote: “...In childhood, the most severe punishment, which pacified his rebellious temper: he was left without an arithmetic lesson, and he remained that way for the rest of his life. While still a student he published several mathematical studies; one of them was awarded a Gold Medal from the Faculty of Physics and Mathematics.” The widow was referring to work on number theory - again done with Tumarkin.
In 1910, Friedman graduated from St. Petersburg University and was retained at the mathematics department to prepare for a professorship. At the same time, he taught classes in higher mathematics at the Institute of Railways and the Mining Institute. For many years, Friedman maintained a trusting relationship with his teacher, Academician Steklov. The correspondence of scientists is of undoubted value, since it allows not only to see their interests, but also to understand the atmosphere that reigned in mathematics of that era.
“Dear Vladimir Andreevich,” Friedman wrote in 1911, “I had to remember the saying that you spoke about this spring: “Do as you know, you will still regret it.”
The fact is that I decided to get married.
I already told you in general outline about his bride. She is taking a course (mathematics); her name is Ekaterina Petrovna Dorofeeva; a little older than me; I think that marriage will not have an adverse effect on my studies...”
In the same letter, Friedman reported:
“...Our classes are with Yak. Dove. (with Yakov Davidovich Tamarkin, a student of V.A. Steklov and friend of Friedman) are going, it seems, quite favorably. They, of course, consist solely of reading the courses and articles recommended by you for the master's exam. We have already finished hydrodynamics and are starting to study the theory of elasticity. We have several questions, but it’s better to find out when we meet with you.”
In 1913, Friedman passed the exams for a master's degree in pure and applied mathematics. Having become interested in mathematical aerology, he got a job at the Aerological Observatory in the city of Pavlovsk, but at the end of the summer of 1914 the first World War. Friedman volunteered to join an aviation detachment operating on the Northern Front. Starting as a private, he quickly rose to the rank of corporal, and in the summer of 1915 he received his first officer rank - warrant officer. Friedman not only established air navigation and aerological services on the Northern Front, but also took part in combat missions more than once as an observer pilot.
“...My life flows quite smoothly,” he wrote to Steklov on February 5, 1915, “except for such accidents as: the explosion of shrapnel at 20 steps, the explosion of the fuse of an Austrian bomb in half a step, which ended almost safely for me, and falling on my face and head that ended in a rupture upper lip and headaches. But, of course, you get used to all this, especially when you see things around you that are a thousand times heavier...”
After the October Revolution, Friedman returned to teaching.
In 1918, he was given the position of extraordinary professor at the department of theoretical mathematics of the young Perm University.
Friedman taught at Perm University for two years.
Only in 1920 did he return to Petrograd.
In a hungry, cold capital, a young scientist got a job at the Main Physical Observatory. At the same time, he gave lectures at several universities, including Petrograd University. In 1922, Friedman derived a general equation for determining the velocity vortex, which later became fundamental in the theory of weather forecasting. At the Naval Academy, he gave a course of lectures “Experience in the hydromechanics of compressible fluid”, deciding difficult task about the movement of liquid or gas with very high speeds, when a liquid or gas cannot fundamentally be considered ideal and their compressibility must be taken into account. In those same years, together with L.V. Keller, he indicated a system of characteristics of the structure of a turbulent flow and constructed a closed system of equations, connecting the pulsations of speed and pressure at two points of the flow at different times. In 1925, for research purposes, he ascended in a balloon with the famous Soviet stratonaut P. Fedoseenko to a record height for that time - 7.4 kilometers.
Friedman’s two small works on cosmology attracted particular attention: “On the Curvature of Space” (1922), and “On the Possibility of a World with Constant Negative Curvature” (1924), published in the Berlin Physical Journal. In these works, Friedman showed that the geometric properties of the Universe on large scales should change dramatically over time, that is, all such changes should be of the nature of “expansion” or “compression.” A few years later, the American astronomer Hubble actually discovered the effect of the recession of galaxies - a consequence of the expansion of the Universe.
Before Friedman’s work, the belief in a static Universe was so great that even Einstein, when developing the general theory of relativity, introduced into his equations the so-called cosmological constant - a kind of “anti-gravity” force, which, unlike other forces, was not generated by any physical source , but was embedded in the very structure of space-time.
On September 18, 1922, Einstein published “Remarks on the work of A. Friedman “On the curvature of space.” The summary of this remark read: “...The results regarding the non-stationary world contained in the mentioned work seem to me suspicious.” However, already on May 31, 1923, having understood the work of the Russian scientist, Einstein hastened to announce: “... In the previous note, I criticized Friedman’s work. However, my criticism, as I became convinced... was based on an error in calculations. I think Friedman's results are correct."
Friedman proved that the matter of the Universe does not necessarily have to be at rest. The Universe cannot be stationary, he believed. The universe must either expand or contract.
In arguing this, Friedman proceeded from two assumptions.
Firstly, he pointed out, the Universe looks absolutely the same everywhere, no matter in what direction we observe it, and, secondly, this statement always remains valid, no matter from what place we observe the Universe.
The models considered by Friedman said that at some point in time in the past, naturally - cosmic time, that is, billions and billions of years distant from us (time that human brain difficult to perceive as something real), the distance between all galaxies should have been zero. At this moment (usually called the Big Bang), the density of the Universe and the curvature of space should have been infinite. Since mathematicians cannot actually handle infinitely large quantities, this meant that, according to the general theory of relativity, there had to be a point in the Universe at which none of the laws of this theory itself could apply.
Such a point is called singular.
Analyzing the concept of singularity, the French mathematician Lemaitre proposed calling the state so high concentration substance as a “primary atom”. He wrote: “The word “atom” should be understood here in its original form, Greek meaning. An atom is something so simple that nothing can be said about it and not a single question can be asked about it. Here we have a completely incomprehensible beginning. Only when the atom decayed into a large number of fragments, filling the space of a small but not exactly zero radius, physical concepts began to acquire meaning.”
Friedman's work caused a lot of unrest among physicists.
The idea that time once had a beginning did not appeal to many, wrote American astrophysicist Hawking. But I didn’t like this idea precisely because there was some, albeit vague, hint of interference in it divine powers. It is no coincidence that the Big Bang model was grasped by Catholic Church. In 1951, the Pope officially declared that the Big Bang model was fully consistent with the Bible.
Cosmologist W. Bonnor commented on this fact:
“Some scientists identified the singularity with God and thought that at that moment the universe was born. It seems to me that highest degree It is inappropriate to force God to solve our scientific problems. There is no place for such supernatural intervention in science. And the one who believes in God and associates the singularity with him in differential equations, risks losing the need for it when mathematics improves.”
“The view I take is that the Universe has an unlimited past and future. This may seem as puzzling as the assumption that her story is finite. However, in scientific terms, this point of view is a methodological foundation, and nothing else. Science should not arbitrarily accept hypotheses that limit the scope of its research.”
“Sometimes they say,” wrote Academician Kapitsa, “that Friedman did not really believe in his own theory and treated it only as a mathematical curiosity. He allegedly said that his job was to solve equations, and that other specialists—physicists—should understand the physical meaning of the solutions. This ironic statement about his work by a witty man cannot change our highly appreciated his discoveries. Even if Friedman was not sure that the expansion of the Universe, resulting from his mathematical calculations, exists in nature, this in no way detracts from his scientific merit. Let us recall, for example, Dirac's theoretical prediction of the positron. Dirac also did not believe in real existence positron and treated his calculations as a purely mathematical achievement, convenient for describing certain processes. But the positron was discovered, and Dirac, without even realizing it, turned out to be a prophet. No one is trying to diminish his contribution to science because he himself did not believe in his prophecy.”
An obituary written by Friedman's widow said:
“Excelsior (above) was the motto of his life.
He was tormented by a thirst for knowledge.
Having chosen mechanics, this paradise of mathematical sciences (according to Leonardo da Vinci), he could not limit himself to it and sought and found new branches, studied deeply, in detail and was forever tormented by the insufficiency of his knowledge. “No, I’m ignorant, I don’t know anything, I need to sleep even less, not do anything extraneous, since this whole so-called life is a complete waste of time.” He tormented himself deliberately, because he saw that he did not have enough time to embrace with his gaze the wide horizons that opened up to him while studying new science. Always ready to modestly learn from anyone who knew more than him, he was aware that in his work he was following new paths, difficult, unexplored by anyone, and he loved to quote the words of Dante: “The waters that I am entering have never been crossed by anyone.”
In 1931, posthumously, Friedman's research was awarded the. V.I. Lenin.
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FRIEDMAN, ALEXANDER ALEKSANDROVICH(1888–1925), Russian and Soviet mathematician and geophysicist, creator of the theory of the non-stationary Universe. Born June 16, 1888 in St. Petersburg. In school and student years was interested in astronomy. In 1906 he published his first mathematical work in one of the leading scientific journals in Germany, Mathematische Annalen. In 1906 he entered the mathematical department of the Faculty of Physics and Mathematics of St. Petersburg University, from which he graduated in 1910. He was retained at the department of pure and applied mathematics to prepare for a professorship. Until the spring of 1913, Friedman studied mathematics - he led practical classes at the Institute of Railway Engineers, and lectured at the Mining Institute. In 1913 he entered the Aerological Observatory in Pavlovsk near St. Petersburg and began to study dynamic meteorology (now this field of science is called geophysical hydrodynamics). In the spring of 1914, he was sent on a business trip to Leipzig, where at that time the famous Norwegian meteorologist Wilhelm Freeman Koren Bjerknes (1862–1951), the creator of the theory of fronts in the atmosphere, lived. In the summer of the same year, Friedman flew on airships, taking part in preparations for the observation solar eclipse in August 1914.
With the outbreak of World War I, Friedman volunteered to join an aviation detachment. In 1914–1917 he participated in the organization of air navigation and aerological services on the Northern and other fronts. Participated as an observer in combat missions.
In 1918–1920 – professor at Perm University. From 1920 he worked at the Main Physical Observatory (from 1924 the Main Geophysical Observatory named after A.I. Voeikov), and at the same time from 1920 he taught at various educational institutions in Petrograd. From 1923 – Chief Editor"Journal of Geophysics and Meteorology". Shortly before his death, he was appointed director of the Main Geophysical Observatory.
Friedman's main works are devoted to the problems of dynamic meteorology (theory atmospheric vortices and wind gustiness, theory of discontinuities in the atmosphere, atmospheric turbulence), hydrodynamics of compressible fluid, atmospheric physics and relativistic cosmology. In July 1925, for scientific purposes, he flew in a balloon together with the pilot P.F. Fedoseenko, reaching a record altitude of 7400 m at that time. Friedman was one of the first to master the mathematical apparatus of Einstein’s theory of gravity and began teaching a course in tensor calculus at the university as introductory part to the course of general theory of relativity. His book was published in 1923 The world as space and time(republished in 1965), which introduced the general public to new physics.
Friedman predicted the expansion of the Universe. The first non-static solutions of Einstein's equations obtained by him in 1922–1924 while studying relativistic models of the Universe laid the foundation for the development of the theory of the non-stationary Universe. The scientist studied non-stationary homogeneous isotropic models with a space of positive curvature filled with dust-like matter (with zero pressure). The nonstationarity of the considered models is described by the dependence of the radius of curvature and density on time, and the density varies in inverse proportion to the cube of the radius of curvature. Friedman identified the types of behavior of such models allowed by the gravitational equations, and Einstein's model of a stationary Universe turned out to be a special case. Refuted the opinion that the general theory of relativity requires the assumption of the finiteness of space. Friedman's results demonstrated that Einstein's equations do not lead to a single model of the Universe, no matter what the cosmological constant is. From the model of a homogeneous isotropic Universe it follows that as it expands, a red shift proportional to the distance should be observed. This was confirmed in 1929 by E.P. Hubb based on astronomical observations: the spectral lines in the spectra of galaxies turned out to be shifted towards the red end of the spectrum.
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