### Gauge Theories In The Twentieth Century

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Furthermore, these two theories happen to be incompatible.

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In other words, either theory loses its predictive power whenever it becomes impossible to ignore the other. Therefore besides the purely aesthetic need to have a single fundamental physical theory, there is a very real need for a theory which explains what happens at those tiny length scales at which neither quantum mechanics nor gravity can be ignored.

String theory emerged in the mid-eighties as a likely candidate for such a theory. The fundamental premise of string theory is that the basic objects in nature are not point-like, but rather string-like. Remarkably, out of this deceptively simple generalisation, one obtains a theory which does not just incorporate gauge theory, supersymmetry and gravitation in a natural and elegant way, but actually needs all three of them for its very consistency.

It is precisely this fact which makes string theory such a compelling candidate for a unified theory. Or that the symmetry of the moving magnet and conductor problem is due to the screw nature of electromagnetism. Gross says this was the first instance of the geometrization of symmetry. The trouble with that is that the principle of equivalence only applies to a region of infinitesimal extent. To no region at all. As John Synge said , the principle of equivalence performed the essential office of midwife at the birth of general relativity, but the midwife now needed to be buried.

He says momentum is conserved due to the invariance of the laws of physics under spatial transformations. But the laws of physics have no real existence. They merely describe the things that do. And those things that do, do what they do because of the way they are, not because of mathematics. In extremis this creates a gamma-ray burster issue for conservation of charge, which is said to be due to gauge invariance. Hermann Weyl was responsible for that. He invented gauge theory. Weyl wrote a paper on gravitation and electricity in He talked about parallel transport and said the final direction of a vector depends on the path taken.

## Gauge Theories In The Twentieth Century

I think he was spot on. He was saying Einstein was wrong. He says Weyl saw this regauging of the metric as a new beautiful type of symmetry which would hopefully show that electrodynamics like gravitation was a geometrical construct. Straub asks Did Weyl screw up? But only because he was critical of general relativity and Einstein. David Delphenich has again provided a translation. The title is a new extension of the theory of relativity. But the foundation is lacking, which is perhaps why Weyl proposed a path-dependent length rather than a position-dependent length.

It would seem that Paul Dirac and other physicists thought so too. Nobody pursued the idea, least of all Einstein. Even though with his purely geometrical physics Weyl was definitely barking up the right tree.

The geometry of the world is surely there because of rescaling. In simple terms, if all your lattice elements are the same length, there is no curvature in your lattice:. They say Planck and Sommerfeld reacted positively, but that Planck then changed his mind. But Einstein was still critical in , which is when Weyl gave up on his idea. However all was not lost. Vladimir Fock wrote a paper in on the invariant form of the wave and motion equations for a charged point mass. Helge Kragh gives the history in his essay Equation with the many fathers.

## Gauge Symmetry for Boneheads – a brief explanation of the fundamentals.

The Klein Gordon equation in A variety of physicists came up with the Klein-Gordon equation in an attempt to model the electron, including Oskar Klein in a 5D unification paper, and Walther Gordon in a paper on the Compton effect. See their figure 2. The lines depict electron plane waves where the phase is advanced on one side of a solenoid and retarded on the other:.

See page It would seem Fock was something of a realist.

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Gauge symmetries characterize a class of physical theories, so-called gauge theories or gauge field theories , based on the requirement of the invariance under a group of transformations, so-called gauge transformations , which occur in a theory's framework if the theory comprises more variables than there are physically independent degrees of freedom.

Since all three fundamental quantum field theoretic interactions as well as gravity can be reconstructed within a gauge theoretic framework, gauge field theories represent the backbone of modern physics today, that is, the physics of the Standard Model and beyond. Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide.

## Hermann Weyl | Biographical Memoirs: Volume 82 | The National Academies Press

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### HERMANN WEYL

The British Journal for the Philosophy of Science. Brading, H. Brown: Aspects of Objectivity in Quantum Mechanics. Butterfield, Pagonis, C. From Physics to Philosophy. Cambridge University Press, Cambridge Physical Review. D 14 10 : — Earman: Gauge Matters. Philosophy of Science. In: K.

Brading, E. Castellani, editors.

Symmetries in Physics: Philosophical Reflections. In: E.