 God's equation by Amir de D'Axel chapter 5 page 61 Grossman's notebooks quote He on good terms with the teachers and understanding everything I a pariah discounted and little loved and quote Einstein and a letter to Marcel Grossman Grossman's widow Einstein a willful and impatient student nonetheless needed a solid grounding in mathematics for his revolutionary theories much of this he got by Cribbing from the notebooks of a better beloved behaved student Marcel Grossman Marcel Grossman 1878 to 1936 was born in Budapest or Budapest to a family with a long Swiss lineage when he was 15 Grossman returned to Switzerland finished high school and from 19 from 1896 to 1900 studied at the ETH in Zürich Grossman studied mathematics at the University of Zürich specializing in geometry and learn the doctorate in this field he later wrote Papers and textbooks on non Euclidean geometry in contrast to Einstein his fellow student at the ETH at the turn of the century Grossman was very Conscious always attending classes and taking meticulous notes a teacher's dream of a student Grossman attended the lectures of Mink Mikwalski and Of other mathematicians and physicists at the ETH his notebooks, which are now preserved and displayed At the archives of the ETH were later a later of crucial importance to Einstein in developing the mathematics He badly needed in order to produce his general theory of relativity Einstein's key equation was based on this and other more Advanced mathematics, but Einstein was indebted to his friend Grossman for more than mathematics Grossman's father helped Einstein obtain his position by the Swiss patent office in Bern when the young graduate could not find a job in 1905 the year Einstein published his first paper on Special relativity and the equation e equals mc squared. He also submitted his doctoral dissertation to the University of Zurich the thesis quote on a new Determination of molecular dimensions and quote was dedicated to his friends friend Marcel Grossman It was Grossman who in late? 1911 contacted Einstein in Prague to find out whether he would be Interested in returning to Switzerland to take up a position at the ETH in Zurich where he had been a student Einstein who by then had off Offers from a number of other universities in Europe was thrilled to accept the offer from the ETH and returned to Swiss soil where while he had to take up astro Austro-Hungarian citizenship in order to be able to accept this appointment in Prague earlier this year He had also kept his Swiss citizenship in early 1912 Einstein returned to his beloved Switzerland Having concluded that space is non Euclidean Einstein needed help He came for this help to his old friend now recognized Expert in exactly the area Einstein needed to understand Some Einstein biographers and writers of books on relativity Claimed that Einstein was not good in mathematics. There's nothing further from the truth The scientists who gave the world the theories of relativity was a superb mathematician The problem was that in his early days as a student at the ETH Einstein didn't care much about sitting in lecture halls to listen to mathematics He understood enough mathematics to devise special relativity and he was able to pick up Whatever else he needed on his own Einstein's relationship with the mathematician Hermann Mikowalski served as a case in point Einstein did not take seriously Mikowalski's lectures at the ETH Years later when special relativity was accepted by scientific community Mikowalski wrote about the mathematics of Einstein's relativity whose four-dimensional space is often referred to as Mikowalski space Unlike Einstein Grossman was a serious student of mathematics His notes hold a special place in the development of Einstein's general theory of relativity Now back at the ETH, Einstein realized that he needed help, very urgent help If space is non-euclidean then he would have to understand its Geometry well before he could do anything further with his ideas about gravitation and relativity For Einstein knew for Einstein knew next to nothing about the actual geometries of space Grossman pulled out his yellowing lecture notes from the turn of the century and look for hints as to where Einstein should start in his model of the universe and its forces of gravity The notes and Grossman's subsequent work on geometry told him that the specific methods His good friend would need were those developed in the late 1800s by two Italian mathematicians Giorgio Ritchie and his gifted student Tolino Levi Sevita Ironically back in Prague the mathematician Greg Pick had also told Einstein That the work of these two scholars could help him develop the mathematics mathematics he needed for pursuing his theory But apparently Einstein was not impressed at the time now with Grossman and his and his Guide to the world of geometry. He was eager to listen Non-euclidean geometry itself could not give answers to Einstein's equations Such geometries describe space in terms of Lines angles parallel circles and so on Einstein needed a needed a lot more. He needed most of all equality of invariance Good physics physical laws are invariant They do not change as the frame of reference in the units of measurements measurement change It should take two hours to drive a distance of 120 to drive a distance of 120 miles at 60 miles an hour and the answer should not change if you denote distance in Kilometers and the speed in kilometers per hour Einstein was looking for a mathematical tool to allow him to transcend the curvature of space It's non-euclidean nature so that the variables of the theory would be valid in any kind of space curvature Grossman was generous with his notes and references But this wasn't enough to solve Einstein's riddle of gravitation After working hard on the problem for several months in 1912 Einstein issued a plea to his old friend quote Grossman Do must do do must me help in sauce weird it's Vrock vrock Translated into English Grossman you must help me or else. I'll go crazy gross Grossman He did the plea and began collaborating in earnest with Einstein The result was a number of papers the two wrote in the problem of gravitation These papers were another step in the direction of a general theory of relativity But they fell short of what was needed for a complete understanding of the complicated phenomena the purported describe It was then that Einstein turned his attention to the concept of a tensor This concept also helps demonstrate the increasingly complex mathematics needed to solve the problem of relativity first the special theory and then more complicated general theory of relativity Simple systems can be described by equations whose elements are single number variables Align for example is given by the equation y equals ax plus b where x and y are Single numbers and a and b are coefficients Which are also single numbers in a line in a line with slope a equals two and Intercept b equals three one can solve the value of y when x equals five as y equals two Times five plus three equals thirteen as the problem becomes more complicated more one may Require several several equations or an equation whose variable Variables are set of numbers Here x would be a vector or an ordered set of numbers and the same would be true of y and any other variables in Physics velocity acceleration and force or all vectors Hence all of them have both a magnitude and a direction and thus each of them is Described as a set of numbers But what Einstein needed now was a generalization of vector to yet another level of complexity He needed a tensor a variable that is an extension of the concept of a vector a very a Vector in three-dimensional space has three components a second order Tenser in three-dimensional space has three to the nine three squared equals nine components a tensor maintains the invariance Principle required by Einstein and it accounts for the variable in a complex situation general relativity needed needed Posed very complex problems Einstein had to take into consideration ten quantities denoted G UV D G Mu V Which accounted for the curvature of the space of four dimensions three for space one for time the animal that accounted for The the animal that accounted for the curvature G mu V was a tensor called the metric tensor hence Since it was a measure of distance in curved space Curved space But the mathematics needed to yield meaningful results was not yet at hand Something else was needed something more general than the Ricci and levy Savita results Einstein had to have a way of manipulating the metric tensor so that the invariance principle would hold under any Transformation of his equation he needed a way of transcending the curvature of space Whatever form that curvature might take his work with Grossman allowed him in variants Allowed him invariance only under linear transformations a Situation which was too restrictive for what he Had to achieve But Einstein only became fully aware of the shortcomings of his work with Grossman in the summer of 1913 Einstein enjoyed very much his new life in Zurich. He was at a Place he knew and loved and he was with his family his wife Milva and their two sons were very attached to Switzerland and this contributed to his sense of well-being and Einstein was among friends. It was here that he began this Discussing the problems of universe with students and colleagues Einstein's developing equations of gravitation already had some Implications about the universe as a whole and he was enthusiastically trying to explore these Implications about the universe in which we live Friends and colleagues often described a carefree Einstein Leaving the lecture halls of the university Surrounded by a group of students and heading to his favorite cafe the Teresa cafe at the bottom of The Zurichburg They would spend hours there discussing the philosophical implications of the theories about the context Shape past and future of the vastness of space in which we live But in the spring of 1913 Einstein has a had a visit that would change his life and again cause him to Uproot himself and his family and move to another country. It was a visit to Zurich by Max Planck 1858 to 1947 and Hermann Ness 1864 to 1941 Max Planck was the greatest physicist of the time He was a key figure in the development of the of the quantum theory and according to a later Admission by Einstein Planck was the only scientist. He truly admired He knew that the Adminished Admiration and respect were mutual Planck and the physicist Herman Nurse had lobbied hard in Berlin for invitation to Einstein to join the faculty of the University of Berlin Planck and nurse arrived in Zurich and met Einstein at his apartment By that time he had he had other offers among them one for a professorship in Lieden The Netherlands the two worked hard at convincing Einstein to take the position in Berlin But he did not want to make a quick decision While he was making up his mind Planck and nurse went on a mountain climbing trip in the Swiss Alps Einstein promised them that by the time they returned he would have an answer for them Quote there will be a sign so you will know my answer as soon as you see me and quote he said when Their train rolled into Zurich railway station. They saw Einstein standing on the platform He was holding a red rose in his hand Einstein moved from Zurich to Zurich he loved to a Berlin where anti-semitism was already rising has been a topic of great speculation It seems that Einstein had several reasons for making such an unexpected decision first Berlin Was a far more important scientific center than was Zurich Giants such as Planck lived there Second Einstein's position required no teaching. This was an important consideration Since Einstein often complained that teaching responsibilities took too much time and energy away from his research activities And a third reason was that Einstein wanted to be near a major observatory So he could interact with astronomers more than ever he strongly desired an astronomical astronomical proof of the bending of light principle of his Evolving theory of general relativity in Berlin. There was at least one Astronomer with whom he had been corresponding regularly regularly Irwin Finley Froedlich Einstein did not immediately perceive a problem with the equations. He had developed with Grossman in early 1913 He wrote a letter to his friend Paul Ephraim Hest 1880 to 1933 in which he summed up his achievements quote the gravitational affair has been Classified to my full satisfaction one can specifically prove that generally Co-variant equations that completely determine the field from the matter tensor cannot exist end quote But within two years Einstein recognized his mistake and in fact developed generally Co-variant equations his field equations of gravitation This happened in Berlin at the height of World War one But Einstein felt a left behind World War one But Einstein left behind him in Zurich a curious little notebook containing his dirt derivations of equations and attempts at arriving at the desired field equations of gravitation This notebook would be discovered by researchers 80 years later and led to unexpected findings about Einstein's work Einstein and Grossman parted ways when Einstein left Zurich Grossman and spent the following years dealing with special and Political issues social and political issues He became deeply involved with charitable aid to students of all nationalities Who had become prisoners of war in 1920? He began to show signs of multiple multiple sclerosis From which he would eventually die in 1936 in 1931 long after Einstein's general theory of relativity had been accepted by the world Grossman wrote a bitter Treatise against aspects of the theory Apparently in anger after having heard that Einstein had given a lecture on these topics Einstein seems to have Forgiven the betrayal of their friendship and research Association and in 1955 wrote about Grossman and his Collaboration in a moving and affectionate tone He wrote that he had later discovered that the mathematical difficulty with which he and Grossman had struggled for many months in their work had been solved Almost a century earlier by the German mathematician Bernard Riemann and that's chapter 5 of God's equation Einstein relativity with relativity and the expanding universe by Amir Di as Excel