Alexander A. Friedmann II, cosmos genius

1888-1925, born in St. Petersburg, Russia.

Atmospheric scientist and astronomer, mathematician of St. Petersburg.

Alexander A. Friedmann II became friends for his life with Yakov D. Tamarkin of the Ukraine at the Second Gymnasium at St. Petersburg. They were considered brilliant students. In 1905 they submitted a paper to Hilbert and next year had published the paper on Bernoulli numbers in Crelle's Journal, and on then new intergral mathematics. He was also a student for a while and befriended Paul Ehrenfest in 1907, who preserved some of Friedmann's works.

Friedmann graduated University of St. Petersburg in 1910.

Friedmann strove for position in the Department of Pure and Applied Mathematics.

Friedmann became Director of the Main Geophysical Observatory.

He was among the first to pursue dynamical atmospheric science, and later dynamic cosmology.

i) The universe expands:

Friedmann worked on solutions in the early 1920's to general relativity equations. He came up with several solutions. Some Russians are said to exclaim, ' We will soon understand these questions-Friedmann has set out to master the theory of relativity!' It has also been commented, 'Alexander Alexandrovich was among the first people at the University to understand the theoretical and practical value of integral equations, which did not enjoy much respect among the older generation of mathematicians.' A later authority, Issak Kikoin wrote, "We heard that he had made a very significant contribution to the general theory of relativity, having corrected Einstein himself." It is also widely known that Einstein was always wary of mathematicians.

Friedmann pointed out, "In the new mechanics, the principle of inertia is defined in the same way as in the old mechanics; it is only necessary to abandon the requirement (in fact, arbitrary) for the world to be Euclidean. Thus, the new mechanics establishes the following principle of inertia: Particles whose worldlines are straight worldlines of our world move by inertia. All other particles move under the action of forces." "In the Euclidean physical world only the particles, whose worldlines are straight lines, move by inertia. The motion of all other particles, whose worldlines are not straight lines, is caused by the action of forces."...in fact, it is easy to prove that these 'straight lines' in the Euclidean world are the ordinary straight lines..." 

"The geometrical world presupposes not Euclidean but a wider geometry-Riemannian. The existence of gravitating masses causes only motion by inertia, and therefore the force of universal gravitation is only an apparent force."

Friedmann is credited with creating an expanding cosmos upon which A. Einstein readjusted his static world theory of general relativity from ca. 1915,1917. In 1921, European science papers deliveries to St. Petersburg were resumed following WWI. Letter to Einstein December 6, 1922 based from Friedmann's paper :"On the Curvature of Space", "it will follow from the world equations derived by you that the radius of curvature of the world is a quantity independent of time." Shown in a letter to Einstein, "showed by direct calculations that the necessary condition for the disappearance of divergence of the matter tensor, which was pointed out by Einstein in his note, by no means implies that the radius of the curvature of the world is constant in time." "But it turns out that world equations (or gravitational field equations, as Einstein called them) do not allow of a static Universe. All that we read in the article shows that to Einstein this was unexpected." Also, "with the help of a corresponding change of the space coordinates:..where R  is a function only of X4: R is proportional to the radius of the curvature of space and therefore the radius of the curvature of space may change with time." Resulting in expansion, or an oscillating universe. Not a static one. An Einstein response, "The conclusion I shall arrive at is that the field equations of gravitation which I have championed hitherto still need a slight modification..."

Physicist Vsevelod K. Frederiks was detained in Gottingen, Germany during WWI. He worked next to David Hilbert and other scientists and when he returned to Russia around 1921 he had valuable information of European science to share and update with Friedmann and others. He co-authored a book with Friedmann "Fundamentals of the Theory of Relativity, part 1", published by Academia Publishers in 1924, and shared seminars with him.

Friedmann published specific manuscripts in 1922 and 1924. He made a case for a nonstationary universe. He is the first to postulate an expanding uinverse before any observational reports were confirmed on that, which addressed the science community on orientation of the universe, much like Copernicus did on the orientation of cosmic body positions. It may be recalled that Einstein did not favor infinities. They made for awkward calculations. So Einstein banished infinities from his calculations to make them more manageable.

Friedmann utilized the Ricci scalar (R) to scale the curvature of the universe. He preferred  to gauge  with R for the expansion of the universe over others who relied on the energy density factor rho (p). Thereby depicting a dynamic universe, in contrast with the static, closed models of Einstein and de Sitter.

The Ricci scalar:, "represents the amount by which the volume of a geodesic ball in a curved Riemannian metric might differ from that of ordinary Euclidean n-space."

Friedmann used the non zero approach for speed and evolvement of the universe. A dust universe may best match with this model.

"Having studied the world of three-dimensional space of positive curvature, Friedmann extends the concept of dynamics to the world with a three-dimensional space with negative curvature."

ii) Negative Constant Curvature and the infinite:

Worked out an analysis of negative constant curvature of the morphology of the universe after suggestion by Yakov D. Tamarkin, among three options, and entered a manuscript of the work 1924. He reasoned that if the X and Y axis can extend forever, then why not also the universe. "We saw that the Einstein cosmological equations have solutions describing a world with negative constant curvature of space. This fact shows that the cosmological equations alone are not sufficient to answer the question of finiteness of our world. Knowledge of the curvature of space does not yet give us direct indications about its finiteness or infiniteness." "It is clear from here that before discussing the finiteness of the world, it should be clarified what points should be regarded as coincident and what as different." He introduced the term "hypersurface" in reference to being in a embedded universe. This may be the first time that the negative curvature constant has been computed.

"Friedmann was the first to state clearly and definitely the basic limitations of the cosmological theory based only on general relativity. Solving the 'eternal' question of the finiteness or infiniteness of the Universe is beyond its power." Friedmann equations, as they are known, could be applied to a general metric for General Relativity for the universe's evolution.

Friedmann relocated emphasis for computing the universe by saying that concentrating on locality was insufficient rather it should be approached globally with appropriate equations. "the geometrical argument which Einstein had for asserting the finiteness of space now disappears, the new geometrical  picture disproves finiteness of volume for space with negative constant curvature."

Friedmann has wrote: "In Einstein's theory, electromagnetic phenomena are expressed by special quantities, which do not represent any property of the geometrical world."

Friedmann, pursuing deeper meaning, mentions cosmology for the first time, he says, "I consider it particularly necessary to treat this question about the Universe in due detail, because...distorted ideas have spread about the finiteness, closedness, curvature and other properties of our space, which are supposedly established by the relativity principle." Later in a book he enters, "but in the more serious and specialists works on the relativity principle. I mean the notorious question of the finiteness of the Universe, i.e. of the finiteness of our physical space filled with shining stars." (In those days, what was seen in the firmament were vaguely described as nebulae or gas clouds, as was then supported by Harlow Shapley, and not the more distinct stars and galaxies we know today. He goes on to critique finiteness and reason of having a straight line in a world with finite length, "These by no means follow from the metric of the world, but the metric can only be derived from the world equations."

'The sea that I am entering has never been crossed', a line that Friedmann liked to use.

Friedmann derived concepts, from Einstein's speculations, on the status of the universe which could involve a repulsive energy or anti-gravity or cosmological term playing a role. Einstein wrote, "we need a generalizing modification of the field of equations of gravitation."

"The first cosmological paper by Friedmann deals with this equation under various conditions relating to the vacuum density. And this is precisely where Friedmann's conclusions on the nature of expansion follow....Recall that the vacuum density is a constant value that depends on neither time nor coordinates." From Friedmann's works it can follow: "This is how the antigravity of the vacuum appears: if the effective density is negative, the corresponding gravitational mass Mefv is negative as well, and therefore this mass will repel particles rather than attract them."

Posed material upon which it could be examined that the universe expansion could occur without the cosmological constant, aka dark energy. Friedmann was one of the first to work on several models of the state of the universe with various outcomes, instead of trying to derive only one solution. including rebounding universes which may do so every 10 billion years, and more from the data of general relativity. He was not shy about resorting to Reimannian curvature or Weyl. "We will call a straight line the curve, the direction of whose tangent is parallel transported along the curve." "The link of gravity with the properties of our world is one of the greatest ideas of Einstein, although the origin of the idea comes from earlier times, namely from the time when the famous work of Riemann appeared."  Friedmann also took exception to be dependent on flat, Euclidean planar depictions, "If one makes measurements on the Earth as described above, and with an accuracy much higher than in ancient Egypt, the result, as we understand it, will reveal that real geometry does not conform to Euclidean geometry. We live not on a plane, but on a curved surface which is fairly close to a spherical surface. A sphere is an example of a non-Euclidean two-dimensional space."  William K. Clifford translated some of Riemann's  works into English. He was also interested in non-Euclidean curvature and space. In 1990, Ruth Farwell concluded, 'it was Clifford, not Riemann, who anticipated some of the conceptual ideas of General Relativity.'

"Friedmann introduces, the notion of curvature through the procedure of a parallel vector transfer." "Friedmann explains in detail the procedure of a parallel transfer" "We shall only stress, together with Friedmann, that 'notion of parallelism plays an outstanding role in spaces differing in their metric properties from Euclidean space'" "But two 'straight lines' on a sphere always intersect, therefore, in this case the above-given propositions on parallelism and non-intersection do not mean the same thing. Thus, the curvature of the sphere's surface, its non-Euclidean character, is manifested."

"The measure of the sphere's curvature is the ratio of the spherical excess to the area of the triangle, which, in the view of what has been said, equals the reciprocal square of the sphere's radius."

"If one constructs a triangle on a sphere from arcs of great circles, the sum of its angles will exceed two right angles. The difference between the sum of the angles and two right angles is called the spherical excess" "Curvature is a proper, invariant property of space, therefore, its quantitative measure does not depend upon the system of coordinates chosen."

"Curvature can be measured if one knows the space metric tensor. Although the type of a metric tensor depends very strongly on what system of coordinates is used, the curvature calculated from it is free from such dependence. "

On world metric, he had noted, "the interval should be purely imaginary at all points of the world and for all events, having the same space coordinates." It is noted after his computations, "So, it does not follow from the constancy and positiveness of the curvature of the Universe at all that our Universe is finite." He also notes on computation for positioning, "we cannot say by using only the trajectory at what of its points at a given moment of time our material point will be." [This, years before the 1927 Heisenberg principle is posited.]

"Friedmann chooses a non-traditional approach which takes the reader right to the essence of the matter...The author helps the reader to overcome the mathematical barrier. What is remarkable is that he is leading the reader toward the goal not by avoiding his apparatus (as was done by Einstein and others after him), but with the help of mathematics." 

"The geometry necessary for general relativity is not the 'conventional' Euclidean geometry which we are all familiar with, but a broader mathematical theory which incorporates, of course, the 'usual' geometry, but only as a simplest particular case."

"Friedmann is a mathematician, but he applies his science to the real world and therefore acts as a physicist, as a natural scientist." "What is needed is the kind of geometry which generalizes the 'conventional' Euclidean geometry  and which, fortunately, mathematicians (Lobachevsky, Bolyai, Riemann) had already created by the end of the 19th century independently of physicists and their interests. The accepted name for this geometry is Riemannian geometry; it deals with a space whose properties, in the most general case, are different at different points."

"In the second work he takes a further step: he breaks away from the geometrical constraint adopted by Einstein and de Sitter. Previously, only worlds with three-dimensional space similar to a sphere had been considered. Friedmann introduces into cosmology a new three-dimensional space which also has homogeneity and isotropy, but is of another geometrical type, namely that of Lobachevsky's geometry."

"The analogy between the theory of relativity and the problems of the vertical temperature gradient may seem unjustified, yet, 'the search in the dark with its tense suspense' (Einstein) is involved in solving both basic and particular problems in the sciences. Besides, this comparison is justified by the fact that two years later it was Friedmann who managed to 'get rid' of notions which were hindering progress and were shared by Einstein himself."

"The new physics, however, brought an essentially different conception of the world. It led to a radical break with the tradition which had been dominant in the scientific community, to a drastic change in the previous system of views. This is what Friedmann accomplished in his investigations. He discovered dynamics and development in the Universe. His works created the evolutionary cosmology which became the genuine science of the Universe." "It is noted, from Friedmann's works, that there are 18 different varieties of topology in Euclidean space, and for curved spaces the number of allowable topological realizations could be infinite."

ON TIME: Friedmann noted, "THUS, TIME IS OVERTHROWN FROM ITS PEDESTAL. ...

and the physical world appears before us in its true light, as a collection of things called events, ... This means that the physical world can serve as the interpretation of the space of four dimensions; an event of the physical world becomes the interpretation of a point of the four dimensional geometrical space. This new point of view of the physical world makes it possible to overcome the difficulties of its studies, which we pointed out at the end of the previous chapter: time ceases to interfere with our studies, on the contrary, having lost its privileged position and considered on equal footing with the spate [space?] coordinates, time becomes an active assistant in the study no longer of the physical time, which by themselves do not exist, but of the manifold spacetime-the physical world." Hence, time is downgraded from the former status of being eternal, immutable and untouchable of previous treatments. But he posits that time is a measurable.

" I would rather follow a different course and begin by considering physical time."

He argues that the time we follow is an arbitrary, old habit. It is not the only way to measure. " Time, like space, has properties which are not intrinsic."

Albert Einstein, clinging to postulates of Ernst Mach, held that space and time could not exist without having matter present to measure it. Unless the supply of mass was infinite, the extent of spacetime could not be infinite, unless there is no matter.

de Sitter in 1916 described a universe infinite in extent. Einstein had to drop Mach's idea from general relativity as incongruent. He had to accept that space is separate from matter. This latter is reinforced by Alexander Friedmann in a paper in 1922.

Friedmann's name is on his "Friedmann equations" and the theory tensor: FLRW or FRW in at least astrophysics. In Friedmann equations, are the calculations that show the expansion of the universe. This is before Edwin Hubble stated that observarion. Other notables are in his earlier fields of atmospheric science and hydrodynamics.

At times in his circle, he is reported to have said, "I know nothing. I should sleep less and should not do anything outside of science, because all this so-called 'life' is a mere waste of time."

It is found in some of his papers he has made couple of astonishing notations. Will not reproduce them here. And he was lucky, two Russian scientists that supported infinity, Dmitri F. Egorov and Pavel A. Florensky, later were hunted down by Soviet agents. In Sept. 1931, Egorov starved.  Florensky was ordered for execution Dec.1937 at Leningrad in a gulag for being perceived as antimaterialist.

Actually, the Russians now use the term Kosmos instead of astro.

Unfortunately, Friedmann did not live to reap or expand on the results of his works on the universe or live to see the birth of his son by his second wife, physicist Natalia Malinina, Alexander Friedmann III who in turn died childless in 1983. Even though Alexander A. Friedmann II held many positions, hard living conditions contributed to his death at the age of 37, September 16, 1925 from Typhus. Yakov D. Tamarkin (1888-1945) left St. Petersburg in 1925 and became a professor later at Dartmouth College with the name, Jacob David Tamarkin and finished his career at Brown University producing many papers.

Friedmann's notoriety did not last around Russia and scientific communities. Mostly in the 1930's, mention of his theories amongst Europeans diminished. Instead, Georges H. Lemaitre was given much credit then for being the first expander of the universe, even though in his own early work he acknowledges Friedmann as the first expander. Lemaitre's endeavors were met with success because also he was operating at the time that astronomers were measuring and calculating the speed of galaxies wending away from each other rather than approaching each other which had an impact on general relativity and cosmological directions. There is no record that Alexander  A. Friedmann II received a Nobel Prize in science, especially for making the universe nonstatic and with curvature. However, a few years later, confirmation of the physical expansion of space was being confirmed by the observations and calculations of Edwin Hubble.

Some seminal papers on Alexander A. Friedmann's II computations in English can be found:

"Papers On Curved Spaces and Cosmology" by the Minkowski Institute Press. Other translations are of course in German and Russian. Similar source, is a book, "The World as Space and Time"  There are few other publications. Friedmann's "Selected Works" from 1927 was reprinted in 1966 by the Academy of Sciences.

Much of the material on Alexander A. Friedmann here is derived from the 1993 biographical book, "Alexander A. Friedmann: the man who made the Universe Expand", written by E.A. Tropp, Frenkel and Chernin.

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Recommended reading: "Does the Inertia of a Body Depend Upon Its Energy Content?" Albert Einstein, 1905.