| 12 |
(151)
A parenthesis : Space-time
orientation.
**...**In
2d's world we assimilated geometrical objects to letters. In 3d's world they
were assimilated to "right hand" and "left hand".
Four-dimensional structures
were assimilated to animated holograms.
**...**What
the hell could be a five-dimensional structure, or a ten dimensional one ?
Sometimes Ienvy God, don't you?
**...**He
must laugh, looking at our miserable four dimensional structures.
**...**But
a theoretical physicist, and even a mathematician, are nothing but oriented
four dimensional structures. If they were not, they could not distinguish
past from future, and the right from the left.
**...**The
universe, as a whole, is a four dimensional structure. Let us think about
it as a closed object, with locally spherical topology. Call t the time. At
a given time we can make a cut, which is a 3d hypersurface.If this last is
a hypersphere S3, time makes sens. The vector time crosses this hypersurface
and we get no paradoxical situation.
**...**Let
us reduce the number of dimensions. Imagine a closed two dimensional world,
some sort of space time (x,y,t).
**...**We
can cut it at t = constant, then we get a geometrical object whose dimension
is 3 - 1 = 2 : a 2d surface. At any point the oriented normal vector figures
the arrow of time.
If this space-time can
be oriented in time ( we suppose it is closed ) at given time, space is a
S2 sphere :
(152)
**...**But
suppose the surface representing space is single-sided. Take a Boy surface,
for an example ( which is a closed single-sided surface. See the section "Mathematics"
of the site ).
(153)
You can build a one just
gluying M�bius strips together. Ishow a one :
(154)
You know that you cannot
define an oriented normal vector :
(155)
**...**The
two folds cover of a Boy's surface is a sphere S2. If we assimilate our three
dimensional space-time to a sets of spheres S2, arranged like russian dolls,
each corresponding to a given value of a cosmic time t, we can think (hardly
) to some sort of space-time where antipodal points could be put together.
That was the topological structure suggested in the paper :
Jean-Pierre Petit : "The missing mass problem". Il nuovo Cimento B, vol.
109, july 1994, pp. 697-710.
**...**Then we know that antipodal points,
located on an "equator" of a sphere can be arranged as the two-folds cover
of a M�bius strip :
(156)
We see how this conjugates
space-antipodal regions with opposite time's arrows.
(157)
**...**By
the way, we see how it would conjugate enantiomorphic objects.
**...**Space
is a four dimensional hypersurface. If we can define a cosmic time t, we can
make cuts at t = constant and these cuts are 3d spaces. If space is closed,
we could assimilate it to a S3 sphere, which can be shaped as the two folds
cover of a projective space P3 ( the equivalent of a Boy's surface, in 3d
). This operation would put opposite time's arrow regions into interaction.
Index Dynamic Groups Theory