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Albert Einstein - general relativity and classical unification
Albert Einstein, building on, and including the work of others, including; Hermann Minkowski, was able to piece together a theoretical picture of gravity and the geometry of 4-dimensional spacetime.
Bernhard Riemann, a German mathematician, it should be noted, was perhaps the first to consider geometries in higher dimensional space. Riemann felt that the flat 3-dimensional geometry of Euclid was based more on common sense and human experience than on actual mathematical logic. To Euclid, nothing can be 4-dimensional. There is no such thing. A point has 0 dimensions, a line has 1 dimension, a sheet or membrane would have 2 dimensions (x, y) and a solid construction would have 3 dimensions (x, y, z). That's it in the world of Euclid's geometry. Aristotle and Ptolemy also proposed that the 4th spatial dimension was not possible. Riemann was challenged by Carl Friedrich Gauss, whom he had met at the University of Gottingen, to re-propose the foundations of geometry. Sadly, this led to Riemann's nervous breakdown in 1854. It was Riemann's lecture at the University of Gottingen and his essay: "On the Hypothesis Which Lie at the Foundation of Geometry." The lecture was eventually given and the work was published 12 years later in 1868. Riemann's idea was a metric. This metric was a collection of numbers at every point in space: a tensor. These numbers would describe how bent or curved that space was. Riemann proposed that 10 numbers at each point were necessary to describe the curvature of some 4-dimensional manifold. This worked, no matter how curved the manifold was. It seemed to work for any arbitrary kind of curvature. The greater the number on the tensor, the greater the curvature.
This will give birth to Riemannian geometry and to the mysterious 4th dimension used by Einstein in his theories of relativity. This is the birth of a new idea that will shock the world of physics: physical laws are simplified in higher dimensional space. Furthermore, Einstien's general theory of relativity will prove to be very successful at describing how gravitation is a consequence of the curvature of spacetime.
General relativity was so successful, in fact, that Einstein continued to work, in isolation, to incorporate electromagnetism into his theory of general relativity. This unified field theory would unite his theory of gravity with Maxwell's theory of electromagnetism. This was his quest for a classical unified field theory of fundamental interactions. This is a theory that would be able to explain all of the laws of nature, from atomic to cosmic scales. This theory of everything would have been the crowning achievement of Einstein's life. Einstein termed this sought after idea: the unified field theory. Einstein once summarized his quest for unification with the analogy of wood and marble. Marble was the beautiful world of geometry. Wood was the chaotic world of matter. Wood determined the structure of the marble. This was a problem for Einstein. The geometry of spacetime was determined by the presence of matter. Einstein wanted to create a universe of pure geometry. Sadly, after about 30 years of searching: Einstein was ultimately unsuccessful in his pursuit of unification, as he passed away in 1955.
Euclid
Albert Einstein
Herman Minkowski
Bernhard Riemann
Gunnar Nordstrom
Gunnar Nordstrom - 1914
Gunnar Nordstrom was a Finnish theoretical physicist. Nordstrom was the first to formulate a theory of gravity in 5 dimensions, to describe both electromagnetism and gravity in 4 dimensions. The theory, however, is not well known, as it had to compete with general relativity. Nordstrom's theory was too primitive to include both Einstein's and Maxwell's field equations. Despite this, he is considered by many writers as the "Einstein of Finland". He is also considered to have been an early rival of Einstein.
Believe it or not, Nordstrom's theory of gravity was put forth before general relativity was even published. His idea was to produce a 5-dimensional Maxwell theory to unify electromagnetism with gravity. Nordstrom's theory correctly described Maxwell's field in 4 dimensions. However, the theory was a scalar theory of gravity, which is known to be incorrect. It was too primitive to describe both the Einstein and Maxwell fields. Nordstrom's ideas were largely forgotten. He may have been before his time, as he published his theory 1 year before Einstein published general relativity. That being said, he couldn't properly produce a 5-dimensional theory of gravity, as it was described by Albert Einstein.
Hermann Weyl - 1918
Hermann Weyl
In 1918, Hermann Weyl, made a serious attempt at a unified theory.
Weyl expanded Einstein's theory of gravity by embedding the Maxwell field directly into the equations. There were other symmetries that the equations remained covariant under, such as scale transformations.
Sadly, Einstein, although he was initially impressed, found some anomalies in the theory. For example, lengths were not preserved in the way that was hoped and time would shift in closed path in a way that didn't make sense. You could say that the theory had too much symmetry and did not fit the data.
Arthur Eddington - 1923
Arthur Eddington
Another attempt at unified theory was by Arthur Eddington in 1923.
Eddington created a theory based on Ricci curvature to explain the emergence of electromagnetism. However, "distance" as we know it was not present in the equations (except in the last step). The theory was "pre-geometrical" in the sense that we could not define meters or seconds.
Wolfgang Pauli said the theory had "no significance for physics".
Even Einstein thought there was no physical content.
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