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The higher the number of equations and consequently also the number of identities among them , the more precise and stronger than mere determinism is the content; accordingly, the theory is the more valuable, if it is also consistent with the empirical facts. In linear approximation, i. Cartan has already worked with it. I myself work with a mathematician S. Mayer from Vienna , a marvelous chap […]. He does not, however, regard this as sufficient, though those laws may come out. He still wants to have the motions of ordinary particles to come out quite naturally. The remaining two types are denoted in the paper by […].

It seems that this structure has nothing to do with the true character of space […]. But this aim seems to be in reach only if a direct physical interpretation of the operation of transport, even of the immediate field quantities, is given up. From the geometrical point of view, such a path [of approach] must seem very unsatisfactory; its justifications will only be reached if the mentioned link does encompass more physical facts than have been brought into it for building it up.

First, my mathematical intuition a priori resists to accept such an artificial geometry; I have difficulties to understand the might who has frozen into rigid togetherness the local frames in different events in their twisted positions. Two weighty physical arguments join in […] only by this loosening [of the relationship between the local frames] the existing gauge-invariance becomes intelligible. Second, the possibility to rotate the frames independently, in the different events, […] is equivalent to the s y m m e t r y o f t h e e n e r g y - m o m e n t u m t e n s o r, or to the validity of the conservation law for angular momentum.

Now the hour of revenge has come for you, now Einstein has made the blunder of distant parallelism which is nothing but mathematics unrelated to physics, now you may scold [him]. During the Easter holidays I have visited Einstein in Berlin and found his opinion on modern quantum theory reactionary. Unlike what I told you in spring, from the point of view of quantum theory, now an argument in favour of distant parallelism can no longer be put forward […].

It just remains […] to congratulate you or should I rather say condole you? Also, I am not so naive as to believe that you would change your opinion because of whatever criticism. But I would bet with you that, at the latest after one year, you will have given up the entire distant parallelism in the same way as you have given up the affine theory earlier.

And, I do not wish to provoke you to contradict me by continuing this letter, because I do not want to delay the approach of this natural end of the theory of distant parallelism. Only someone who is certain of seeing through the unity of natural forces in the right way ought to write in this way. Before the mathematical consequences have not been thought through properly, is not at all justified to make a negative judgement. With such rubbish he may impress only American journalists, not even American physicists, not to speak of European physicists.

The question of the compatibility of the field equations played a very important role because Einstein hoped to gain, eventually, the quantum laws from the extra equations cf. That Pauli had been right except for the time span envisaged by him was expressly admitted by Einstein when he had given up his unified field theory based on distant parallelism in see letter of Einstein to Pauli on 22 January ; cf.

Not as a criticism but only as an impression do we point out why the new field theory does not house the same degree of conviction, nor the amount of inner consistency and suggestive necessity in which the former theory excelled. His never-ending gift for invention, his persistent energy in the pursuit of a fixed aim in recent years surprise us with, on the average, one such theory per year. He varied g ik and R ik independently [ ]. For Lanczos see J. Einstein built a plane world which is no longer waste like the Euclidean space-time-world of H.

Minkowski, but, on the contrary, contains in it all that we usually call physical reality. In order to ease a comparison between both theories, we may bring together here the notations of R i c c i and L e v i - C i v i t a […] with those of Einstein. Einstein had sent him the corrected proof sheets of his fourth paper [ 85 ]. The basic idea was to consider the points of M 4 as equivalent to the ensemble of congruences with tangent vector X 5 i in M 5 with cylindricity condition werden.

We may look at this paper also as a forerunner of some sort to the Einstein. Mayer 5-vector formalism cf. Section 6. Some were more interested in the geometrical foundations, in exact solutions to the field equations, or in the variational principle. It is shown that the new equations are satisfied to the first order but not exactly. They found that these field equations did not have a spherically symmetric solution corresponding to a charged point particle at rest The corresponding solution for the uncharged particle was the same as in general relativity, i.

Tamm and Leontowitch therefore guessed that a charged point particle at rest would lead to an axially-symmetric solution and pointed to the spin for support of this hypothesis [ , ]. In this case he has been able to obtain results checking the observed perihelion of mercury. The purpose of this paper is to investigate, for the same case, the nature of the gravitational field obtained from the field equations suggested by Einstein in his first paper [ 88 ]. From the point of view of our previous notes this fact has its interpretation in the statement that the world will be pseudo-Euclidean only in the absence of electric and magnetic forces.

This means that gravitational and electromagnetic phenomena must be intimately related since the existence of gravitation becomes dependent on the electromagnetic field. Thus we secure a real physical unification of gravitation and electricity in the sense that these concepts become but different manifestations of the same fundamental entity — provided, of course, that the theory shows itself to be tenable as a theory in agreement with experience. At first, the possibility of gaining hold on the paths of elementary particles — described as singular worldlines of point particles — was central.

But somehow, for Einstein, discretisation and quantisation must have been too close to bother about a fundamental constant. There are other possibilities giving rise to richer geometrical schemes while remaining deterministic. First, one can take a system of 15 equations […].

Finally, maybe there are also solutions with 16 equations; but the study of this case leads to calculations as complicated as in the case of 22 equations, and I was not fortunate enough to come across a possible system […]. I beg you to send me those of your papers from which I can properly study the theory. Now, everything is clear to me. Previously, my assistant Prof. This probably will restrict the free choice of solutions in a region in a far-reaching way — more strongly than the restrictions corresponding to your degrees of determination.

In this section, we loosely collect some of these approaches. The object of the present paper is to find these equations […]. By the work of Dirac, wavemechanics has reached an independent status; the only attempt to bring together this new group of phenomena with the other two is J. These are grouped together to form two four-vectors and satisfy wave equations of the second order. It is contended here that therefore his theory cannot be upheld without abandoning the theory of relativity.

While this story about geometrizing wave mechanics might not be a genuine part of unified field theory at the time, it seems interesting to follow it as a last attempt for binding together classical field theory and quantum physics. Electrons and protons cannot be distinguished from quanta of light, gas pressure not from radiation pressure.

One of the German theorists trying to keep up with wave mechanics was Gustav Mie. In the same year in which Einstein published his theory of distant parallelism, Dirac presented his relativistic, spinorial wave equation for the electron with spin. This event gave new hope to those trying to include the electron field into a unified field theory; it induced a flood of papers in such that this year became the zenith for publications on unified field theory. Although, as we noted in Section 6. This is a very sketchy outline with a focus on the relationship to unified field theories.

An interesting study into the details of the introduction of local spinor structures by Weyl and Fock and of the early history of the general relativistic Dirac equation was given recently by Scholz [ ]. There are several ways of embodying this invariant theory in a formal calculus. The one which is here employed has its antecedents chiefly in the work ofWeyl, van derWaerden, Fock, and Schouten.

It differs from the calculus arrived at by Schouten chiefly in the treatment of gauge invariance, Schouten in collaboration with van Dantzig having preferred to rewrite the projective relativity in a formalism obtainable from the original one by a sort of coordinate transformation, whereas I think the original form fits in better with the classical notations of relativity theory. These spinors have been recognised by several students Pauli and Solomon, Fock of the subject but their role has probably not been fully understood since it has quite recently been thought necessary to give special proofs of invariance.

The transformation given above carries the system of lines into the other. Up to now, quantum mechanics has not found its place in this geometrical picture; attempts in this direction Klein, Fock were unsuccessful. Only after Dirac had constructed his equations for the electron, the ground seems to have been prepared for further work in this direction. In this point, our theory, developed independently, agrees with the new theory by H. Nevertheless, it seems to us that the theory suggested by Weyl for solving this problem is open to grave objections; a criticism of this theory is given in our article.

His mass term contained a square root, i. As he remarked, the chances for this were minimal, however [ , ]. In two papers, Zaycoff of Sofia presented a unified field theory of gravitation, electromagnetism and the Dirac field for which he left behind the framework of a theory with distant parallelism used by him in other papers. By varying his Lagrangian with respect to the 4-beins, the electromagnetic potential, the Dirac wave function and its complex-conjugate, he obtained the 20 field equations for gravitation of second order in the 4-bein variables, assuming the role of the gravitational potentials and the electromagnetic field of second order in the 4-potential , and 8 equations of first order in the Dirac wave function and the electromagnetic 4-potential, corresponding to the generalised Dirac equation and its complex conjugate [ , ].

Mandel, G.


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Rumer, the author et al. No doubt, there are weighty reasons for such a seemingly paradoxical view. A multi-dimensional causality cannot be understood as long as we are unable to give the extra dimensions an intuitive meaning. Most authors introduce an orthogonal frame of axes at every event, and, relative to it, numerically specialised Dirac-matrices. To be sure, it is much too small by many powers of ten in order to replace, say, the term on the r. Yet it appears important that in the generalised theory a term is encountered at all which is equivalent to the enigmatic mass term.

Everybody should be kept from reading this paper, or from even trying to understand it. Moreover, all articles referred to on p. Will appear soon in Sitz. That the micro-mechanical world of the electron is Minkowskian is shown by the theory of Dirac, in which the electron spin appears as a consequence of the fact that the world of the electron is not Euclidean, but Minkowskian. Thus, we will have a frame in which to take the gravitational and electromagnetic laws, and in which it will be possible also for quantum theory to be included.

Obviously, this artifice will be needed if some phenomenon would force the physicists to believe in a variability of the [electric] charge. Flint has drawn my attention to a recent paper by O. Klein [ ] in which an extension to five dimensions similar to that given in the present paper is described. It leads also to a wave equation which we can identify as relating to a system containing electrons with opposite spin.

The domain of either electron alone might be rotated in a fifth dimension and we could not observe any difference. He proceeded from the special relativistic homogeneous wave equation in fivedimensional space and, after dimensional reduction, compared it to the Klein-Gordon equation for a charged particle. Our efforts have lead to a derivation corresponding, according to our opinion, to all demands for clarity and naturalness and avoiding completely any not so transparent artifice.

Mayer on the theory of spinors. We already could clear up the mathematical relations. A grasp on the physics is far away, farther than one thinks at present. In particular, I still am convinced that the attempt at an essentially statistical theory will fail. In the first paper in the reports of the Berlin Academy, the mathematical foundations of the semi-vector formalism are developed [ ]. The basic idea of Einstein and Mayer is the possibility of a decomposition of any proper Lorentz transformation described by a real matrix D into a product BC of a pair of complex-conjugate , commuting matrices B and C.

The transformations represented by B or C form a group isomorphic to the Lorentz group. With the spinors, Dirac found novel field quantities whose simplest equations permitted the derivation of the properties of the electron to a great extent. With my collaborator, Dr. The simplest equations to be satisfied by such semi-vectors provide a key for the understanding of the existence of two elementary particles with different ponderable mass and like, but opposite, charge.

These semivectors are, besides the usual vectors, the simplest mathematical field-objects possible in a four-dimensional metrical continuum; it appears that they naturally describe essential properties of the electrical elementary particles. As soon as an electromagnetic field is present, in the projective theory, calculation with spinvectors is simpler than calculation with semivectors. In his letter to Einstein, Pauli had also mentioned his papers to be published in Annalen der Physik and discussed here in Section 7. Two more papers were written by Einstein and Mayer before Einstein quietly dropped the subject.

However, geometry shows that every V 3 is a subspace of a particular F 6 , i. This shows us that transition to F 6 is the final step. As I already felt frightened by the various 5-dimensional theories, and had little confidence that something beautiful would result in this way, I was very skeptical.

A most interesting task far beyond this review would be to reconstruct, in detail , the mutual influences among researchers in the development of the various strands of unified field theory. An interesting in-depth-study for the case of Weyl has already been made [ ]. Noether, Weyl. Berwald in Prague, with whom I had an intensive exchange of ideas from September , and who was so friendly as to give me his manuscripts before they went into print.

Schouten during his visit to America as a possible geometrical interpretation of the theory of spin-quantities which he was then developing. Pauli was so friendly as to permit me to quote this theorem from an unpublished manuscript. Pauli induced me to investigate this invariance. On the one hand, Einstein must have been best informed by receiving papers, books, and the latest news, or even visits from many of his active colleagues. On the other, he rarely referred to these papers and books; as far as I am aware his extended correspondence included Eisenhart, Eddington, Kaluza, Mandel, Pauli, Veblen, A.

Wenzl, Weyl, and Zaycoff, but not Schouten, J. Thomas, T. Thomas, O. From that point on, the American press played Einstein to the maximum. Even a superficial survey such as the one made here shows clearly the dense net of mathematicians and theoretical physicists involved in the building of unified field theory and of the geometric structures underlying it. But Mr. Einstein is not one of those afraid of difficulties; even if his attempt does not succeed, it will have forced us to think about the great questions at the foundation of science.

It has been discovered by exclusively formal considerations, and its mathematical consequences have not yet been developed sufficiently for allowing a comparison with experiment. Nevertheless, to me this attempt seems very interesting in itself; it mainly offers splendid possibilities for the [further] development, and it is with the hope that the mathematicians get interested in it that I permit myself to expose and analyse [the theory] here.

Yet in the meantime one thing may be said in defence of the theory. Advances in scientific knowledge must bring about the result that an increase in formal simplicity can only be won at the cost of an increased distance or gap between the fundamental hypotheses of the theory on the one hand, and the directly observed facts on the other.

Theory is compelled more and more from the inductive to the deductive method, even though the most important demand to be made of every scientific theory will always remain that it must fit the facts. But if the limit is clearly reached of what the statistical fad can achieve they will again return full of repentance to the space-time picture, and then these equations will form a starting point.

Seen precisely from this angle, it is regrettable that after these broad designs, such as the ones available in gauge theory and distant parallelism, no further attempts in the classical direction can be noticed. It might be an interesting task to confront the methodology that helped Einstein to arrive at general relativity with the one used by him within unified field theory. See the contributions of J. Renn, J. Norton, M. Janssen, T. Sauer, M. Schemmel, et al. If it is the same, then it might become harder to draw general conclusions as to its importance for the gain in and development of knowledge in physics.

A report on the rich further development of the field past will be given in Part II of this review. Albert Einstein — Nobel Prize for his work on the light-electric effect photon concept. Best known for his special and general relativity theories. Important results in Brownian motion and the statistical foundations of radiation as a quantum phenomenon. Worked for more than 30 years on Unified Field Theory. Wolfgang Ernst Pauli — Born in Vienna, Austria. Studied at the University of Munich with A. Sommerfeld who recognised his great gifts.

Received his doctorate in for a thesis on the quantum theory of ionised molecular hydrogen. After a year with Bohr, Pauli, became a lecturer at the University of Hamburg in From — guest professor at the Institute for Advanced Study, Princeton. Did important work in quantum mechanics, quantum field theory and elementary particle theory fourth quantum number spin , Pauli exclusion principle, prediction of neutrino. Fellow of the Royal Society. Nobel Prize winner in Fortunately, he has made accessible contributions in the Russian language by scientists in the Soviet Union.

Vizgin also presents and discusses attempts at unification prior to In present-day interpretation, the first two fields are fields mediating the interactions while the third, the electron field, really is a matter field. Theodor Franz Eduard Kaluza — Born in Ratibor, Germany now Raciborz, Poland. Aber das ist nicht der Fall. Die Konstruktion scheint am Problem der Materie und der Quanten zu scheitern. Jan Arnoldus Schouten — Born near Amsterdam in the Netherlands. Studied electrical engineering at the Technical University Hogeschool of Delft and then mathematics at the University of Leiden.

His doctoral thesis of was on tensor analysis, a topic he worked on during his entire academic career. From until he held a professorship in mathematics at the University of Delft, and from to he was director of the Mathematical Research Centre at the University of Amsterdam. He was a prolific writer, applying tensor analysis to Lie groups, general relativity, unified field theory, and differential equations. Received his doctorate in , became scientific assistant at the University of Freiburg Germany and lecturer at the University of Frankfurt am Main Germany.

Worked with Einstein in Berlin —, then returned to Frankurt. Became a visiting professor at Purdue University in and came back on a professorship in Worked mainly in mathematical physics and numerical analysis. After he held various posts in industry and in the National Bureau of Standards. Left the U. David van Dantzig — Born in Rotterdam, Netherlands.

Studied mathematics at the University of Amsterdam. Worked first on differential geometry, electrodynamics and unified field theory. Known as co-founder, in , of the Mathematical Centre in Amsterdam and by his role in establishing mathematical statistics as a subdiscipline in the Netherlands. His courses covered special and general relativity, the physics of fixed stars and galaxies with a touch on cosmology, and quantum mechanics. Hermann Klaus Hugo Weyl — Born in Elmshorn, Germany.

Then until retirement he worked at the Institute for Advanced Study in Princeton. Weyl made important contributions in mathematics integral equations, Riemannian surfaces, continuous groups, analytic number theory and theoretical physics differential geometry, unified field theory, gauge theory. For his papers, cf. Arthur Stanley Eddington — Born in Kendal, England. After some work in physics, moved into astronomy in and was appointed to the Royal Observatory at Greenwich.

From director of the Cambridge Observatory. As a Quaker he became a conscientious objector to military service during the First World War. Eddington made important contributions to general relativity and astrophysics internal structure of stars. Wrote also on epistemology and the philosophy of science.

Oskar Klein — After work with Arrhenius in physical chemistry, he met Kramers, then a student of Bohr, in His first research position was at the University of Michigan in Ann Arbor, where he worked on the Zeeman effect. His later work included quantum theory Klein-Nishina formula , superconductivity, and cosmology. Luther Pfahler Eisenhart — Born in York, Pennsylvania, U.

Studied mathematics at John Hopkins University, Baltimore and received his doctorate in Eisenhart taught at the University of Princeton from , was promoted to professor in and remained there as Dean of the mathematical Faculty and Dean of the Graduate School until his retirement in All his work is in differential geometry, including Riemannian and non-Riemannian geometry and in group theory.

Oswald Veblen — Born in Decorah, Iowa, U. Entered the University of Iowa in , receiving his B. He taught mathematics at Princeton — , at Oxford in —, and became a professor at the Institute for Advanced Study in Princeton in Veblen made important contribution to projective and differential geometry, and to topology.

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He gave a new treatment of spin. Elie Joseph Cartan — He lectured at Montpellier — , Lyon — , Nancy — , and Paris — His following work on the representation of semisimple Lie groups combines group theory, classical geometry, differential geometry, and topology. From he worked on differential equations and differential geometry, and developed a theory of moving frames calculus of differential forms. He also contributed to the geometry of symmetric spaces and published on general relativity and its geometric extensions as well as on the theory of spinors.

For his Collected Works, cf. Dirk J. Struik — Born in Rotterdam in the Netherlands. Studied mathematics and physics at the University of Leiden with Lorentz and de Sitter. Received his doctorate in He stayed on the MIT mathematics faculty until As a professed Marxist he was suspended from teaching duties during the McCarthy period but was reinstated in In , he became an honorary research associate in the History of Science Department of Harvard University. The second fundamental form comes into play when local isometric embedding is considered, i.

In the following, all geometrical objects are supposed to be differentiable as often as is needed. In an arbitrary basis for the differential forms cotangent space , the connection may be represented by a 1-form. In the literature, different notations and conventions are used. We will reserve the name geodesic for curves of extreme length; cf. Riemannian geometry.


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  • This scalar density was used by Einstein [ 77 ] cf. Tullio Levi-Civita — Born in Padua, Italy. Studied mathematics and received his doctorate at the University of Padua. Was given the Chair of Mechanics there and, in , went to the University of Rome in the same position. Together with Ricci, he developed tensor calculus and introduced covariant differentiation.

    He worked also in the mechanical many-body problem, in hydrodynamics, general relativity theory, and unified field theory. Strongly opposed to Fascism in Italy and dismissed from his professorship in See [ ]; his sign conventions are different, though. Joseph Miller Thomas — Studied mathematics in Philadelphia at the University of Pennsylvania.

    From assistant professor at the University of Pennsylvania, from assistant and in full professor of mathematics at the Duke University in Durham, North Carolina. His fields were differential geometry and partial differential equations. He was the principle founder of Duke Mathematical Journal. A representation of a group is defined as a map to the vectors of a linear space that is homomorphic in the group operation. The full Lorentz group contains as further elements the temporal and spatial reflections. For a contemporary exposition of the use of spinors in space-time, see the book of Penrose and Rindler [ ].

    For an arbitrary Riemannian manifold this no longer holds true. Aber leichter ist ahnen als finden. Elektromagnetismus zu kommen. In his textbook, M. Satzes erscheinen die elektrody. Folge der Gravitationsgl. Der Gedanke liegt nahe, dass diese es sind, die die auseinanderstrebenden elektrischen Ladungen zusammenhalten. Stachel [ ]. Denn man kann versuchen, denjenigen Feldbegriffen […] auch dann physikalische Bedeutung zuzuschreiben, wenn es sich um die Beschreibung der elektrischen Elementarteilchen handelt, die die Materie konstituieren.

    Studied mathematics at the University of Vienna where he obtained his doctoral degree in Became a professional officer during the First World War. He obtained professorships in Graz and Vienna and, in , at the University of Amsterdam. He specialised in the theory of invariants cf. See Section IV, pp. Im allgemeinsten Fall werden die Gleichungen allerdings 4. Es ist ein Genie-Streich ersten Ranges. Allerdings war ich nicht imstande, meinen Massstab-Einwand zu erledigen.

    Aber ich finde: Wenn das mit einer Uhr bzw. So wie Mie seiner konsequenten Elektrodynamik eine Gravitation angeklebt hatte, die nicht organisch mit jener zusammenhing, ebenso hat Einstein seiner konsequenten Gravitation eine Elektrodynamik d. Sie stellen eine wirkliche Einheit her. Wilhelm Wirtinger — Born in Ybbs, Austria. Studied mathematics at the University of Vienna. From a full professor at the University of Vienna, but accepted professorship at University of Innsbruck, returning to Vienna only in Wrote an important paper on the general theta function and had an exceptional range in mathematics function theory, algebra, number theory, plane geometry, theory of invariants.

    In the same year, Wirtinger sent in a paper on relativity theory published only in [ ]. Paul Dienes — Born in Tokaj, Hungary. Studied mathematics. A detailed investigation of this subject will appear soon, and will be included in the next update of this article [ ]. Some letters of Einstein to Kaluza are quoted by Pais [ ], p. Greek lettered indices run in M 5 , Latin ones in space time; x 4 is the time coordinate, x 5 the new spacelike coordinate. Weyl beschrittene.

    Wenn Sie wollen, lege ich Ihre Arbeit doch der Akademie vor […]. Jakob Grommer — Born near Brest, then in Russia. First a Talmud student with a keen interest in mathematics. Worked with Einstein for at least a decade — as his calculational assistant. He held a university position in Minsk from on and later became a member of the Belorussian Academy of Sciences. From his youth he was inflicted with elephantiasis. His notation representing the covariant derivative by a lower index is highly ambiguous, though, and will be avoided. In place of our K ik Einstein used R ik. Niemand kann empirisch einen affinen Zusammenhang zwischen Vektoren in benachbarten Punkten feststellen, wenn er nicht vorher bereits das Linienelement ermittelt hat.

    Allgemein: nicht nur die zeitliche Fortsetzung, sondern auch der Anfangszustand unterliegt Gesetzen. Tracy Yerkes Thomas — Born in Alton, Illinois, U. Professor at Princeton, then from — at the University of California in Los Angeles, and since professor and chairman of the mathematics department at Indiana University in Bloomington, U. Henri Eyraud — Perhaps he considered his papers on the geometry of unified field theory as a sin of his youth: In Poggendorff , among the 33 papers listed, all are from his later main interest.

    The geometry of paths involves a change of connection that preserves the geodesics when vectors are displaced along themselves. Some extended discussion about the transformation of the field components with regard to time-reversal exist, in which two differing points of view are expressed cf. To me, this seems to be a case of whiggish historical hindsight. Im Makroskopischen zweifle ich nicht an ihrer Richtigkeit. Hierin unterscheidet sich die Elektrodynamik von der Gravitation; deshalb erscheint mir auch das Bestreben, die Elektrodynamik mit dem Gravitationsgesetz zu einer Einheit zu verschmelzen, nicht mehr gerechtfertigt.

    George Yuri Rainich — Of Russian origin. Leopold Infeld — Born in Cracow, Poland. Studied at the University of Cracow and received his doctorate in For the correspondence between Einstein and Infeld, cf. I have not yet been able to read the contributions from other Japanese authors [ , , ]. Damodar D. Kosambi — Of Indian origin; born in Goa he moved to America in with his learned father and graduated from Harvard University in in mathematics, history and languages. Mathematician, historian, and Sanskrit scholar.

    Walther Mayer — It seems that Mayer was appreciated much by Einstein and, despite being in his forties, did accept this role as a collaborator of Einstein. After coming to Princeton with Einstein in , he got a position at the Mathematical Institute of Princeton University and became an associate of the Institute for Advanced Study. Wrote a joint paper with T. Der ganze Inhalt findet sich in der Arbeit von O. Vladimir Aleksandrovich Fo c k — Born in St. Petersburg renamed later Petrograd and Leningrad. Studied at Petrograd University and spent his whole carrier at this University.

    Fundamental contributions to quantum theory Fock space, Hartree-Fock method ; also worked in and defended general relativity. The correspondence is taken from Pais [ ] who, in his book, expresses his lack of understanding as to why Einstein published these two papers at all. Heinrich Mandel From lecturer at the University of Leningrad, and from research work at the Physics Institute of this university.

    Enea Bortolotti — Born in Rome. After a break during the First World War, he received his Ph. After teaching at the medical school, he became professor of geometry at the Univerity of Cagliari in From there he moved on to the same position at the University of Florence in Despite his premature death, Bortolotti published about a hundred papers, notably in differential geometry.

    The curly bracket was introduced in Equation Mayer stammt. Auf diese Weise gelang es, das Gravitations - und das elektromagnetische Feldals logische Einheit zu erfassen. Banesh Hoffmann — Born in Richmond, England. Studied mathematics and theoretical physics at Oxford University and received his doctorate in Became an assistant at Princeton University and worked there with Einstein in — From professor at Queens College in New York.

    His scientific interests were in relativity theory, tensor analysis, and quantum theory. A similar picture is already given in [ ], p. Mathematische Annalen was a journal edited by David Hilbert with co-editors O. Blumenthal and G. Hecke which physicists usually would not read. Einstein had been co-editor for the volumes 81 to ; thus he had easy access. Thus, the inverse matrix must be calculated.

    Born in Brussels. Studied mathematics and physics at the University of Brussels and received his doctorate in Member of the Royal Belgian Academy. Research on variational calculus, general relativity, electromagnetism, thermodynamics, and wave mechanics. He writes the tensor density V with an upper coordinate and two lower bein-indices, i. If summation over indices is to be performed, it is irrelevant whether bein-indices or coordinate indices are written. As to the person of H. Hilbert in If it is the same person, then H.

    At the time, experienced teachers at Gymnasium could carry the title of professor. Sauer [ ], p. The quantity G ik defined here must be distinguished from the Einstein tensor in Section 2. Gawrilow Raschko Zaycoff — Born in Burgas, Bulgaria. Cartan hat schon darin gearbeitet. Ich selbst arbeite mit einem Mathematiker S. Sauer which I received 6 month after after having submitted this review [ ]. An evaluation of this correspondence has been given in [ 15 ].

    Hans Reichenbach — Philosopher of science, neo-positivist. Professor in Berlin, Istanbul, and Los Angeles. Wrote books on the foundations of relativity theory, probability, and quantum mechanics. In fact, this generalisation was to be worked out soon by V. Bargmann in [ 5 ] cf. Es lebe die neue Feldtheorie Einsteins! The paper extended a previous one within the framework of special relativity [ ]. There is no contradiction with the result of Einstein and Mayer [ ]; this paper proceeds from different field equations.

    Norbert Wiener — Born in Columbia, Missouri, U. Studied at Tufts College and Harvard University and received his doctorate with a dissertation on mathematical logic. From instructor at the Massachusetts Institute of Technology where he first studied Brownian motion. Wiener had a wide range of interests, from harmonic analysis to communications theory and cybernetics.

    Manuel Sandoval Vallarta — Born in Mexico City. He studied at the Massachusetts Institute of Technology MIT , where he received his degree in science and specialised in theoretical physics With a scholarship from the Guggenheim Foundation — , he studied physics in Berlin and Leipzig. His main contributions were in mathematic methods, quantum mechanics, general relativity and, from , cosmic rays.

    So far, I have not been able to find a publication by Dr. What should we conclude if none exists? That Einstein lost his interest in this particular version of unified field theory? That the calculations were erroneous, or just not reaching far enough? Further hypotheses are possible. Here, and in the sequel, I mostly take over the English translation by J. Leroy and J. Ritter used in the book. Nun ist mir alles klar. Whittaker [ ]. Die Elektronen und Protonen sind nicht zu unterscheiden von Lichtquanten, der Gasdruck nicht vom Strahlungsdruck.

    Unfortunately, in his paper, in contrast to his previous and our notation, Veblen now used N for the index and k for weight.

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    Fock referred to his paper of [ ]. Rumer, Verfasser u. Alle sollten abgehalten werden, diese Arbeit zu lesen oder gar zu versuchen, sie zu verstehen. Erscheint baldigst in den Sitz. For the alpha-matrices, cf. Ferdinand Gonseth — Born in Sonvilier, Switzerland. His interest were in the foundations of mathematics, geometry and in problems of space and time.

    With G. Bachelard and P. Bernays he founded the philosophical review journal Dialectica. Mayer an der Theorie der Spinoren. Ich fand nun mit meinem Mitarbeiter, Dr. Sobald in der projektiven Theorie ein elektromagnetisches Feld auftritt, ist die Rechnung mit Spinvektoren einfacher als die mit Semivektoren. Schouten referred to Pauli several times [ ], pp. In his letter to Einstein, Pauli had also mentioned his papers to be published in Annalen der Physik and discussed in Section 7. After all, Cartan had discovered spinors in in the context of his classification of simple Lie algebras [ ].

    Dirac had made an antiparticle to the electron appear in his theory as early as in [ 55 ]. Emission von elektromagnetischer Strahlung paarweise erzeugt bzw. Born tried to support Rumer in various ways, as can be seen from his correspondence with Einstein [ ]. Ludwig Berwald — Born in Prague. Studied mathematics in Munich and became a full professor at the German Charles University in Prague. His scientific work is mainly in differential geometry, notably on Finsler geometry and on spray geometry, i. He died in Poland after having been deported by the German authorities just because he was Jewish.

    For the historical development of gauge theory from the point of view of physics, cf. Straumann [ , ]. Mais M. Compare with the fate of contemporaneaous quantum- geometrodynamics [ ]. My reservations hold only if the toolbox does not also contain quantum field theory. The carefully worded and detailed comments of a referee have been helpful in improving on the original version.

    I would also like to thank the staff of Living Reviews , notably Mrs. Christina Weyher and Mr. Robert Forkel, for their friendly and generous assistance. Skip to main content Skip to sections. Advertisement Hide. Download PDF. Living Reviews in Relativity December , Cite as. On the History of Unified Field Theories. Open Access. First Online: 13 February In all the attempts at unification we encounter two distinct methodological approaches: a deductive-hypothetical and an empirical-inductive method.

    At the time, another road was impossible because of the lack of empirical basis due to the weakness of the gravitational interaction. A similar situation obtains even today within the attempts for reaching a common representation of all four fundamental interactions. Nevertheless, in terms of mathematical and physical concepts, a lot has been learned even from failed attempts at unification, vid.

    Even before the advent of quantum mechanics proper, in —26, Einstein raised his expectations with regard to unified field theory considerably; he wanted to bridge the gap between classical field theory and quantum theory, preferably by deriving quantum theory as a consequence of unified field theory. Sections 4. In the period considered, mutual reservations may have existed between the followers of the new quantum mechanics and those joining Einstein in the extension of his general relativity.

    Einstein belonged to those who regarded the idea of unification as more fundamental than the idea of field quantisation [ 95 ]. During the time span considered here, there also were those whose work did not help the idea of unification, e. As a rule, the point of departure for unified field theory was general relativity. We are used to g being a symmetric tensor field, i. The second structure to be introduced is a linear connection L with D 3 components L ij k ; it is a geometrical object but not a tensor field and its components change inhomogeneously under local coordinate transformations The connection is a device introduced for establishing a comparison of vectors in different points of the manifold.

    For each vector field and each tangent vector it provides another unique vector field. We have adopted the notational convention used by Schouten [ , , ]. For a vector density cf. Various subcases of affine spaces will occur, dependent on whether the connection is asymmetric or symmetric , i. In physical applications, a metric always seems to be needed; hence in affine geometry it must be derived solely by help of the connection or, rather, by tensorial objects constructed from it.

    This is in stark contrast to Riemannian geometry where, vice versa, the connection is derived from the metric. From both affine curvature tensors we may form two different tensorial traces each. Connections that are not metric-compatible have been used in unified field theory right from the beginning.

    Riemann-Cartan geometry is the subcase of a metric-affine geometry in which the metric-compatible connection contains torsion, i. Riemannian geometry is the further subcase with vanishing torsion of a metric-affine geometry with metric-compatible connection. The covariant derivative for tensor fields in the space of homogeneous coordinates is defined as before cf.

    Up to here, no definitions of a tensor and a tensor field were given: A tensor T p M D of type r , s at a point p on the manifold M D is a multi-linear function on the Cartesian product of r cotangent- and s tangent spaces in p. A tensor field is the assignment of a tensor to each point of M D.

    Spinors are representations of the Lorentz group only; as such they are related strictly to the tangent space of the space-time manifold. To see how spinor representations can be obtained, we must use the homomorphism of the group SL 2,C and the proper orthochronous Lorentz group, a subgroup of the full Lorentz group The group of coordinate transformations acts on the Latin indices.

    In Section 2. With its help we may formulate the concept of isometries of a manifold, i. Within a particular geometry, usually various options for the dynamics of the fields field equations, in particular as following from a Lagrangian exist as well as different possibilities for the identification of physical observables with the mathematical objects of the formalism. The components of the metrical tensor are identified with gravitational potentials.

    In his letter to Einstein of 11 November , he writes [ ], Doc. Ishiwara, and G. Naturforscherversammlung, 19—25 September [ ] showed that not everybody was a believer in it. He claimed that in bodies smaller than those carrying the elementary charge electrons , an electric field could not be measured. Thus, while lengths of vectors at different points can be compared without a connection, directions cannot. Let us now look at what happens to parallel transport of a length, e. Due to the additional group of gauge transformations, it is useful to introduce the new concept of gauge-weight within tensor calculus as in Section 2.

    Weyl did calculate the curvature tensor formed from his connection but did not get the correct result 82 ; it is given by Schouten [ ], p. Weyl had arranged that the page proofs be sent to Einstein. Einstein was impressed: In April , he wrote four letters and two postcards to Weyl on his new unified field theory — with a tone varying between praise and criticism. However, as long as measurements are made with infinitesimally small rigid rulers and clocks, there is no indeterminacy in the metric as Weyl would have it : Proper time can be measured.

    As a consequence follows: If in nature length and time would depend on the pre-history of the measuring instrument, then no uniquely defined frequencies of the spectral lines of a chemical element could exist, i. Einstein saw the problem, then unsolved within his general relativity, that Weyl alluded to, i. Presumably, such a theory would have to include microphysics. Einstein then suggested the affine group as the more general setting for a generalisation of Riemannian geometry [ ], Vol.

    The quadratic form Rg ik dx i dx k is an absolute invariant, i. Of course, as he noted, no progress had been made with regard to the explanation of the constituents of matter; on the one hand because the differential equations were too complicated to be solved, on the other because the observed mass difference between the elementary particles with positive and negative electrical charge remained unexplained.

    In his general remarks about this problem at the very end of his article, Pauli points to a link of the asymmetry with time-reflection symmetry see [ ], pp. Section 4. As he had abandoned the idea of describing matter as a classical field theory since , the linking of the electromagnetic field via the gauge idea could only be done through the matter variables.

    Honoring the Book

    Weyl himself continued to develop the dynamics of his theory. The changes, which Weyl had introduced in the 4th edition of his book [ ], and which, according to him, were of fundamental importance for the understanding of relativity theory, were discussed by him in a further paper [ ].

    His colleague in Vienna, Wirtinger 98 , had helped him in this They are able to motivate others, argue objectively and overcome conflicts in a goal oriented manner. They know how to inspire creative solutions based on their analyses, are able to learn and willing to put themselves and their decisions to work to produce the best possible product and therefore do what is best for the company.

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