Unified field theory

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In physics, a unified field theory (UFT), occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field.


  • There was a period when cosmology got started. There were some important works in the 30s—the Einstein-Infeld-Hoffman ideas [equations]. ...Unified Field theories were the bane of GR in those days. Einstein... was convinced that physics should be primarily geometry... about 10 years later, maybe 15, Steven Weinberg was convinced that geometry was irrelevant... the important stuff is just field theory. ...Weinberg, later... collaborated in proving that physics really is geometry. Except not the geometry of space-time... it's the geometry of the graph paper on which the properties of space-time are conceptually plotted... the idea of a curved connection. If you want to plot... any physical quantity... like a magnetic field, quarks, gluons, etc. you need to plot it on curved graph paper. But Einstein... didn't have that broad an idea of geometry...
    • Ignazio Ciufolini, Richard A. Matzner, General Relativity and John Archibald Wheeler (2010) p. 23.
  • Regarding the study of the universe on scales of less than... 108 lt-yr... [T]he "top-down"... or "pancake" theory of Zel'dovich et al... [predicts that] pancakes of gas comparable to a supercluster were formed first... then galaxies... formed by fragmentation... [into] high-density regions... along lines, filaments and points... The problem of the missing mass, or dark matter... and... of the agreement with the observed level of isotropy of the blackbody radiation... are explained in this top-down model by massive neutrinos... which formed early condensations in the homogeneous plasma... [were] originally moving with relativistic speeds... [and] are usually called Hot Dark Matter. [Another] theory is the "bottom-up" scenario discussed by Lemaître and supported by... Peebles et al... [in which] galaxies were first formed by gravitational interaction... [and] only afterwards... a heirarchy of clusters formed. Some versions of [this] theory explain the missing mass problem... by... exotic particles such as "axions," "photinos," "selectrons," and "gravitinos," predicted by some unified field theories. This exotic form of dark matter, moving... much slower than the massive neutrinos, is... called Cold Dark Matter. Mixed models, hot plus cold dark matter, have also been proposed...
  • You could not imagine the sum-over-histories picture being true for a part of nature and untrue for another part. You could not imagine it being true for electrons and untrue for gravity. It was a unifying principle that would either explain everything or explain nothing. And this made me profoundly skeptical. I knew how many great scientists had chased this will-o’-the-wisp of a unified theory. The ground of science was littered with the corpses of dead unified theories. Even Einstein had spent twenty years searching for a unified theory and had found nothing that satisfied him. I admired Dick tremendously, but I did not believe he could beat Einstein at his own game.
  • Until the end of the thirties, the only accepted fundamental interactions were the electromagnetic and the gravitational, plus, tentatively, something like the “mesonic” or “nuclear” interaction. The physical fields considered in the framework of “unified field theory” including, after the advent of quantum (wave-) mechanics, the wave function satisfying either Schrödinger’s or Dirac’s equation, were all assumed to be classical fields. The quantum mechanical wave function was taken to represent the field of the electron, i.e., a matter field. In spite of this, the construction of quantum field theory had begun already around 1927. ...Nowadays, it seems mandatory to approach unification in the framework of quantum field theory.
  • [B]y quantum field theory the dichotomy between matter and fields in the sense of a dualism is minimised as every field carries its particle-like quanta. Today’s unified field theories appear in the form of gauge theories; matter is represented by operator valued spin-half quantum fields (fermions) while the “forces” mediated by “exchange particles” are embodied in gauge fields, i.e., quantum fields of integer spin (bosons). The space-time geometry used is rigidly fixed, and usually taken to be Minkowski space or, within string and membrane theory, some higher-dimensional manifold also loosely called “space-time”, although its signature might not be Lorentzian and its dimension might be 10, 11, 26, or some other number larger than four. A satisfactory inclusion of gravitation into the scheme of quantum field theory still remains to be achieved.
  • No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. ...because any unified field theory first must absorb the Riemannian geometry of Einstein's theory and the Lie groups coming from quantum field theory... The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity.
    • Michio Kaku, Hyperspace (1995) Ch.15 Conclusion, p.326.
  • If the possibilities anticipated here prove to be viable, quantum mechanics would cease to be an independent discipline. It would melt into a deepened ‘theory of matter’ which would have to be built up from regular solutions of non-linear differential equations, – in an ultimate relationship it would dissolve in the ‘world equations’ of the Universe. Then, the dualism ‘matter-field’ would have been overcome as well as the dualism ‘corpuscle-wave’.
    • Cornelius Lanczos, “Die Erhaltungssätze in der feldmässigen Darstellung der Diracschen Theorie” [The Laws of Conservation in the field representation of Dirac's Theory], Z. Phys., 57, 484–493, (1929) a paper attempting to combine Maxwell’s and Dirac’s equations; as translated by F. M. Goenner, On the History of Unified Field Theories (2004)
  • Einstein’s dissent from quantum mechanics and immersion in the search for a unified field theory were not failures but anticipations. After all, even if many string theorists would disagree with Einstein about the incompleteness of quantum mechanics, much of what goes on in string theory these days looks a lot like what Einstein was doing in his Princeton years, which was trying to find new mathematics that might extend general relativity to a unification of all the forces and particles in nature.
  • [A unified field theory is] a theory joining the gravitational and the electromagnetic field into one single hyperfield whose equations represent the conditions imposed on the geometrical structure of the universe.
    • Marie-Antoinette Tonnelat, La théorie du champ unifié d’Einstein et quelques-uns de ses développements (1955) as translated by Hubert F. M. Goenner, On the History of Unified Field Theories (2004)
  • A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory.
    • Hermann Weyl, Space—Time—Matter (1952) 1st American Printing of the 4th Edition (1922), Tr. Henry L. Brose (orig. title: Raum, Zeit, Materie (1918) from the Author's Preface to 3rd Edition (1919)
  • With Mie's view of matter there is contrasted another, according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter.
    • Hermann Weyl, Space—Time—Matter (1952) 1st American Printing of the 4th Edition (1922), Tr. Henry L. Brose (orig. title: Raum, Zeit, Materie (1918) from the Author's Preface to 4th Edition (1920)
  • Although the Special Theory of Relativity does not account for electromagnetic phenomena, it explains many of their properties. General Relativity, however, tells us nothing about electromagnetism. In Einstein's space-time continuum gravitational forces are absorbed in the geometry, but the electromagnetic forces are quite unaffected. Various attempts have been made to generate the geometry of space-time so as to produce a unified field theory incorporating both gravitational and electromagnetic forces.
  • The resemblance between the Coulomb force and Newton's gravitational force is very impressive. ...[T]he similarity between a planetary system and the electromagnetic structure of an atom... is due to the resemblance between their laws of interaction. ...After the creation of GTR, there followed attempts to reformulate electromagnetic theory in a similar way, attempts to construct a geometric theory of the electromagnetic field, and attempts to create a unified field theory which would combine gravitation and electromagnetism. All... failed. The gravitational field acts universally; it imparts equal accelerations to all objects. This... permits one to describe gravity by a change in the properties of... spacetime... The electromagnetic field does not have such a universality; various bodies... have different ratios of charge to mass and experience different accelerations. ...Roughly speaking, the electromagnetic field has energy; and this energy has weight... [T]he equations of GTR for a spacetime which contains an electromagnetic field necessarily force the field to satisfy Maxwell's equations. ...The idea of defining all fields by varying the spacetime curvatures that they create is... geometrodynamics Its most articulate exponent is... John Archibald Wheeler.

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