Re: Thoughts on why space must have three dimensions

Timothy Golden BandTechnology.com wrote:
Sue... wrote:
<< The major issue we have left to address is the origin
of four-dimensional gravity. We now suggest several rea-
sons that four-dimensional gravity can exist, leaving the
details for a forthcoming publication. Perhaps the least
interesting possibility is that dimensions are in fact com-
pact. One way our analysis could apply in that case is if
nine spatial dimensions expand to a large size in the early
evolution of the universe, and only afterwards stabilize at
a small size. Or the universe gets e ectively compacti-
fied without moduli fields due to the presence of the 7-
branes, which can effectively compactify dimensions as
in Ref. [13]. 7-branes are codimension 2 branes in 10d
and as such they change the metric not just in their local
neighborhood, but also affect the global geometry. >>
"Relaxing to Three Dimensions"
http://arxiv.org/abs/hep-th/0506053

There is a philosophical problem with this argument.
If we pose the question

'why three-dimensional space?'

The structural rigidity of a triangle. The inverse square distance law
Maxwell's equations... I could go on.


And we answer with nine-dimensional space we are then left with the
question

'why nine-dimensional space?'

Because you prefer three closets to a yard sale?


I once emailed Lisa Randall to this effect but never heard back.
I believe the answer is that there is no upper bound. The polysign
construction of spacetime supports this conclusion:

http://bandtechnology.com/PolySigned/PolySigned.html

Under polysign whether higher dimensions are supported or not there is
still a natural basis for spacetime. That the progression should just
stop is doubtful. Rather than curled up higher dimensions perhaps the
context of misbehaved higher dimensions will eventually take hold. If
they misbehave by curling up that would be a nice consistency. Nicer
yet would be that they just vanish.

Your polysign is a space-time (as opposed to a space) so I
don't get that knee jerk skepticism that Lisa's ruminations
evoke. Still... the mathmatical properties are, to me at least
in the category of a magic square until something testable
is described.
I remember you didn't feel confident expressing Maxwell's
equations in your construction (they *are* daunting in 3+1)
and I have been trying to come up with something simpler.
To no avail. Anything you could come up with to illustrate
the superposition of moving charges in your space-time
might spark some insight where someone else can help
to connect a few dots to a physical application.

Sue...





-Tim

.

Relevant Pages

  • Re: Thoughts on why space must have three dimensions
    ... of four-dimensional gravity. ... interesting possibility is that dimensions are in fact com- ... Under polysign whether higher dimensions are supported or not there is ... If in that way one-signed charge were to ...
    (sci.physics)
  • Re: Thoughts on why space must have three dimensions
    ... of four-dimensional gravity. ... interesting possibility is that dimensions are in fact com- ... Under polysign whether higher dimensions are supported or not there is ... If in that way one-signed charge were to ...
    (sci.physics)
  • Re: Thoughts on why space must have three dimensions
    ... of four-dimensional gravity. ... interesting possibility is that dimensions are in fact com- ... Under polysign whether higher dimensions are supported or not there is ... context of misbehaved higher dimensions will eventually take hold. ...
    (sci.physics)
  • Re: Thoughts on why space must have three dimensions
    ... Neil wrote: ... natural to have three dimensions of space and one of time, ... convenient for mathematicians that there is a cross product in 3-space, ... of four-dimensional gravity. ...
    (sci.physics)
  • Re: crank crank crank
    ... and that calculus can be done, just like the complex can be done by 'real' math. ... i already gave you links to papers about complex in n dimensions. ... in fact the polysign are a universal system for associative and commutative arithmetic. ... only downsides are zero-divisors and the loss of a simple rotation. ...
    (sci.math)