AAWSAP DIRD, Warp Drive, Dark Energy, and the Manipulation of Extra Dimensions, April 2010

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(5.1)
where the Greek indices run from O to 3 (0 represents the time coordinate and 1...3 the
space coordinates), and where the higher dimension is expressed using y. The powers
of ¢ are selected for later convenience. Upon solving Einstein's equation in this higher
dimensional space using this metric, Kaluza was able to accurately reproduce both GR
and electromagnetic theory. However, the theory made an additional prediction which
was not consistent with observation and was somewhat of an embarrassment for
Kaluza.
The main failure of Kaluza's idea, and an
issue that caused Einstein to delay his
endorsement of the paper by two years,
was the very obvious fact that we clearly
exist in three spatial dimensions and not
four. This issue was tackled in 1926 by
Oskar Klein (Reference 28), who
suggested that the 5th dimension
compactifies, so as to have the geometry
of a circle of extremely small radius. One
way to envisage this additional dimension
is to imagine a garden hose. It is only
when one magnifies the image the
toroidal structure is visible. From a long
distance it looks like a 1-dimensional line,
but a closer inspection reveals that every
point on the line is, in fact, a circle (see
Figure 3. Internal Structure of a Seemingly One­
Figure 3 for an illustration).
Dimensional Object
While Kaluza-Klein (KK) theory is considered elegant in its simplicity, it is not without
problems. One obvious criticism is that the theory is non-predictive, in that it does not
extend Einstein's or Maxwell's theories, but merely synthesizes the formalism within a
new mathematical framework. A more serious criticism regards the introduction of the
5th dimension, which was, and still is, seen as an artificial construct since our universe
is apparently 4-dimensional. 8
KK theory remained largely ignored and was considered somewhat obscure for the first
half of the twentieth century, as were the speculations regarding additional spatial
dimensions. However, the birth of string theory generated a renewed interest in the
idea, largely due to string theory's promise of being a quantum theory of gravity. 9
Unification is one of the main themes in the history of science and is a guiding principle
in theoretical physics. Countless examples exist where diverse and seemingly unrelated
phenomena have been understood in terms of a small number of underlying principles.
In the 1940s, it was demonstrated that quantum mechanics and electromagnetism
could be accurately described by quantum field theory, and by the 1970s the weak and
8 Including time, of course.
9 Quantum gravity is considered somewhat of a "holy grail" within the theoretical physics community.
9
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