

String theory
Name: murphy
Status: N/a
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993
Question:
If string theories require us to have more than 4D space time, and
these other dimensions are "folded" over each other somehow, how can they meet
the criterion of being literally perpendicular to all previous dimensions and
still be topographically curved? And how does the number of dimensions affect
the number of proposed electron types (muon taon etc)?
Replies:
Imagining strange higherdimensional objects is one of the big
joys and frustrations of many mathematicians and physicists who do this sort
of thing. But it is usually a little difficult to put what they have imagined
into ordinary language, since these objects usually just cannot exist in our
space  and nothing like them really can, at least at the level of our normal
perceptions. One of the simplest analogies that does not really work is
simply the circle. What mathematicians and physicists discovered is that you
can separate out the "closedinonitself" property of the circle from the
"curved" property  you kind of imagine a straight line segment with ends
labeled A and B, and then declare that "A = B"! Such a circle of course
cannot exist in the ordinary space we know, but as a mathematical object there
is nothing wrong with it. Anyway, those extra dimensions you talked about all
look sort of like this circle  they are straight line segments closed in on
themselves without curving at all. You can also imagine a cylinder as an
example  the axis of the cylinder is one dimension that extends to infinity
both ways, while the circumference of the cylinder is a circle that is
perpendicular to this axis. However, That is embedding the 2dimensional
cylinder into 3 dimensional space, and it turns out you do not actually need
to even imagine embedding these higher dimensional spaces to work with them,
although usually it is possible.
Arthur Smith
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Update: June 2012

