clifford_a-_pickover_surfing_through_hyperspacebookfi-org

218 notes
Chapter 1
1. I asked Professor Michio Kaku, aurhor of Hyperspace, if the gravitational curvature
of space implies the existence of a fourth dimension. He responded:
We do not need a fourth spatial dimension in which to describe the curvature
of space. From one point of view, the fourth spatial dimension is fictitious.
This is because we can use "intrinsic" 3-D coordinates in which the
only coordinates are three bent spatial dimensions and one time dimension.
Thus, an ant on an ordinary balloon can only see two dimensions,
and says that the third dimension in unnecessary, because the ant cannot
travel in the third dimension, which is fictitious from his point of view.
However, we can also use "extrinsic" coordinates in which to visualize
the bending of space, by embedding spacetime within a higher dimension.
All the fancy graphical representations—of black holes as holes and funnels
in space, inflating balloons representing the Big Bang, and 99.99% of
all the pictures found in general relativity books—are done in extrinsic
coordinates. We see the 3-D balloon from the vantage point of a fictitious
fourth dimension, which has no physical reality. (After all, if the balloon is
the entire universe, then where are you standing when you look at the balloon?
You are standing in a fictitious fourth dimension.)
That being said, let me now say that current thinking in theoretical
physics postulates the existence of not just four spatial dimensions (one
being fictitious), but ten physical dimensions of space and time.
It is confusing that people use the word hyperspace to refer to both: the
fictitious fourth spatial dimension used in extrinsic coordinates (essentially
a gimmick in which to "see" balloons and holes in space) found in
ordinary general relativity, and also higher physical dimensions in which
superstrings live.
2. Kaluza-Klein theory (named after two European scientists) suggests the existence
of additional dimensions that are rolled up or "compactified" in such a way that they
are undetectable at macroscopic levels.
3. On the other hand, Joe Lykken of the Fermi National Accelerator Laboratory in
Batavia, Illinois, believes physicists may be able to find experimental evidence for
string theory. Although the extra dimensions of strings are compactified—that is,
curled up on scales of just 10~ 33 centimeters, which would be out of the reach of any
conceivable experiment—Lykken and several other groups are considering the possibility
that a few of those dimensions could unravel slightly, opening up onto scales that
precision measurements in accelerators or even on a benchtop might actually probe.
[For more information on practical tests of string theory, see Kestenbaum, D. (1998)
Practical tests for an 'untestable' theory of everything? Science. 281(5378): 758—59.]