Kaluza in a sentence

Kaluza–Klein geometry To build the Kaluza–Klein theory, one picks an invariant metric on the circle S 1 that is the fiber of the U(1)-bundle of electromagnetism.

The full Kaluza field equations are generally attributed to Thiry, who most famously obtained vacuum field equations, although Kaluza originally provided a stress-energy tensor for his theory and Thiry included a stress-energy tensor in his thesis.

Computing the scalar curvature of this bundle metric, one finds that it is constant on each fiber: this is the "Kaluza miracle".

History and development Kaluza–Klein theory main In the early 20th century, physicists and mathematicians including Albert Einstein and Hermann Minkowski pioneered the use of four-dimensional geometry for describing the physical world.

If the base manifold is four-dimensional, the Kaluza–Klein manifold P is five-dimensional.

In 1919, work by Theodor Kaluza showed that by passing to five-dimensional spacetime, one can unify gravity and electromagnetism into a single force.

Indeed, Kaluza did not assume it.

In part this was because Kaluza–Klein theory predicted a particle that has never been shown to exist, and in part because it was unable to correctly predict the ratio of an electron's mass to its charge.

In the Kaluza theory, the gravitational constant can be understood as an electromagnetic coupling constant in the metric.

It has been an objection to the original Kaluza hypothesis to invoke the fifth dimension only to negate its dynamics.

Kaluza also introduced the hypothesis known as the "cylinder condition", that no component of the five-dimensional metric depends on the fifth dimension.

Kaluza also set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.

Paul Wesson and colleagues have pursued relaxation of the cylinder condition to gain extra terms that can be identified with the matter fields, citation for which Kaluza otherwise inserted a stress-energy tensor by hand.

Quantum interpretation of Klein Kaluza's original hypothesis was purely classical and extended discoveries of general relativity.

The fact that the Lorentz force law could be understood as a geodesic in 5 dimensions was to Kaluza a primary motivation for considering the 5-dimensional hypothesis, even in the presence of the aesthetically-unpleasing cylinder condition.

The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews as well as the English translations of Thiry contain some errors.

They reintroduced Kaluza–Klein theory as a way of making sense of the extra dimensions.

Thiry is perhaps best known only because an English translation was provided by Applequist, Chodos, & Freund in their review book. citation Applequist et al. also provided an English translation of Kaluza's paper.

This set of possible mass values is often called the Kaluza–Klein tower.

This was the main shortfall of the 5-dimensional theory as Kaluza saw it, and he gives it some discussion in his original article.