World Geometry

All these multifarious activities took a lot of Einstein s energies but did not keep him from his physics research. In 1922 he published Ins first paper on unified field theoiy, an attempt at incorporating not only gravitation but also electromagnetism into a new world geometry, a subject that was his main concern until the end of his life. He tried many approaches none of them have worked out. In 1924 he published three papers on quantum statistical mechanics, which include his discoveiy of so-called Bose-Einstein condensation. This was his last contribution to physics that may be called seminal. He did continue to publish all through his later years, however. 

Although Weyl s conjecture could not be substantiated in its original form it was pointed out soon afterwards by Schrodinger [43] and London [44] that the classical quantum conditions could be deduced from Weyl s world geometry by choosing complex components for the gauge factor, i. e. 

An imperfect lower-dimensional analogue of the envisaged world geometry is the Mobius strip. It is considered imperfect in the sense of being a two-dimensional surface, closed in only one direction when curved into three-dimensional space. To represent a closed system it has to be described as either a one-dimensional surface (e.g. following the arrows of figure 7) curved in three, or a two-dimensional surface (projective plane) closed in four di-... 

This methodology inspired the chapter on world geometry, based on the assumption that the cosmos is best described by the most consistent version of geometry available at the time. It enables the study of subtleties that cannot be revealed by a more primitive version and anticipates better comprehension of the world through geometries of the future. In the same spirit the present chapter explores the theories of physics and the cosmic picture that they reveal. The next chapter will examine chemical theory in the same way. 

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