dealt a lethal blow to Weyl’s unified theory by arguing that Weyl’s theory was
at the very best—beautiful, and at the very least,
un-physical, because its concept of variation of the length of a vector from
one point of space to the other meant that certain absolute quantities, such as
the “fixed” spacing of atomic spectral lines and the Compton wavelength of an
Electron for example, would change arbitrarily as they would have to depend on
their prehistories. This venomous criticism of Einstein to Weyl’s theory
remains much alive today as it was on the first day Einstein pronounced it. We
demonstrate herein that one can overcome Einstein’s criticism by recasting Weyl’s
theory into a new Weyl-kind of theory were the length of vectors are preserved
as is the case in Riemann geometry. In this New Weyl Theory, the Weyl
gauge transformation of the Riemann metric gμν and the Maxwellian
electromagnetic field Aμ are preserved.
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