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Structure of space-time
at the microscopic scale.
...We
know nothing about the structure of space-time at the microscopic
scale. We simply assume that it is a continuum
(in learned terms, a differentiable manifold).
We also assume that at every point the topology of space
is hyperspherical. Yet, when we push this space-time
into its last recesses, we come up against two barriers
: the Planck length, 10-33 cm and the Planck time : 10-43
second. Beyond that, nothing makes sense anymore.
...One
can imagine all possible micro-textures. Take for example a
3d space. One can divide it into two disjoint domains using
the surface described below.
...You
will be able to build it using strips of flexible Bristol board 10 cm by
one cm, and a stapler. With this material you can make a
"recta-hexagon" :
...With
these strange facets, with negative curvature (since the
sum of the angles of this hexagon exceeds the Euclidean sum) one can
make the following object :
A sort of element
of an original central heating system, with six openings, thanks to which one
can make the (infinite) surface :
...It
will be noted in passing that the strips of Bristol board used are geodesics
(circular) of this surface. This one divides the 3d volume in two. The
two "3d half-universes" have identical geometries and volumes.
One passes from one to the other by a translation :
...For
those who have trouble seeing in space, there exists a "polyhedral"
version of this surface. It suffices to build elements that look
like the green cross of pharmacists, and to assemble them.
...One
thus obtains a surface that divides 3d space into two equal volumes,
which are also deduced from one another by translation.
...This
image allows us to imagine what two 3d universes could look like
that "cohabit within one another". One could travel there, but the
particles "living" in these two universes would never meet.
...The 2d image
of such a structure is simply the game of checkers. We know that one plays it
by moving pieces on the black squares.
...This
leaves half of the space unused. In a rather crowded club
one could therefore have two games played simultaneously by putting
the pieces of a second pair of players on the white squares.
The pieces of the
two games could not capture one another. .
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