a113

Space at microscopic scale.

We ignore the microscopic scale space-time structure. We just assume space
time is a continuum . In technical terms, we assume the 4d structure
is a manifold, than can be differentiated. We also assume that local topology
is hyperspheric. But, when we look closer and closer, we find two characteristic
quantities :

The Planck's length : 10-33 cm

The Planck's time : 10-43 second

We cannot cut such intervals. On quantum mechanics grounds it does not make
any sens.

Various other space textures can be imagined. Take for
example a 3d space, an euclidean 3d space, like we imagine ours looks like.
You can split it into two disjoint sub-spaces. Take cartboard strips, both
firm and flexible. Size : half an inch x
three inches. You can join such elements with a
stapler.

Then you can build a hexagon whose angles are all
equal to 90�;.
(78)

With such strange "recta-hexagons" you can build the following object
(79)

The you connect similar "bottles with six entries" :
(80)

Remark : Your strips form circular geodesics of the surface. This latter
is a frontier between two worlds. These two "half 3d universes" are identical.
They have the same (infinite) volume. You can transform those by a simple
translation.
(81)

On figure (82) a simpler system to build, using a polyhedric representation.
Next, left, one element. Right, two elements connected.
(82)

These images show that two universes could be overlapped together.

These two 3d worlds are separate. At my home, we have an aquarium whose single
red inhabitant is a fish called by my wife : "Jonas". If Icould, Iwould
build a complex aquarium in which two liquid 3d volumes would be separated
by the above plexiglass surface. If two fishes would be put, each in one of
these "worlds" they could go "almost everywhere" but they could not meet together,
for they should be separated by this transparent surface, everywhere they
went.

This offers an interesting solution to make buildings in which two populations
can live "together", whilst never meeting.

About Jonas, Ihave a story to tell you. This poor fish was living in the
enterprise where my wife Claire works. Deadly boring people, by the way :
lawyers.

One day Claire found the poor Jonas alone in a pan. The boss of my wife had
decided to clean Jonas'aquarium with bleach !

Thinking Jonas was in danger, due to the behaviour of this woman, Claire
put the fish in a bottle and brought it at our flat. Then we bought an aquarium.
But Imade a mistake : Ichose one where one of the walls is a mirror. Then,
instead of one red fish, we have two. But Jonas was immediatly conviced that
his image in the mirror corresponded to another real red fish. He started
to patrol along the mirror-wall, his eyes fixed on his companion, all day
long (we supposed he stopped during the night but we cannot be assaured of
that). Jonas had no possibility to realize that this fish was his own image.
A fish sends sonic waves and records the waves sent by other creatures living
in water. The sonic signature of Jonas companion was surely identical to his
own one (that's why we think Jonas was patrolling nights too. Exhausting).
Jonas could also see, during the day, the "other fish". He was deeply convinced
that this image corresponded to some brother or living clone. Immediate terrirorial
problem.

We were sad, because Jonas was so busy, watching the "other fish" that he
did not pay attention to anything else. Finally, after three monthes we bought
another aquarium, without the mirror-wall and Jonas became friendly again.
It was cheeper than calling in an analyst specializing in red fishes.

Another remark : can a fish suffer sea-sick ?

What is sea-sick ? It comes from the opposition of two messages coming from
two distinct perception systems. We are inside a boat, in your cabin. The
walls do not move, but you feel the movement through your internal ear system.
Then you get sick.

If you take a fish, swiming in an aquarium, this is a very strange. In effect
the walls of the box, even if they are transparent, behave like flat mirrors,
with respect to soundwaves. By night, when the lights are switched off, Jonas
"see" an infinite number of brothers, due to the multiple reflexions of soundwaves
on orthogonal plane walls. In a pond, flat walls do not exist. The nocturnal
world of a red fish must be very strange, full of "ghosts".

During the day one could imbed the glass box into another one, composed by
five mirrors. If one moves the second box with respect to the transparent
one (which gives soundwaves mirror images), the fish will receive two contradictory
messages and get sick.

Remember this story. In the future we will widely talk about two interacting
universes (not about sea sick). But are there really two ? Could the "second
universe" be some sort of image in a "space-time mirror" ?

Remark we use mirrors. We have mirrors in our homes, toilets. They are usefull.
Thanks to the bath-room mirror, when Iam thinking about some complex mathematical
problem Idreamt about that night, Idon't put my tooth brush in my nostril.

All mathematicians mainly practice oniric work. Souriau, me , and many others.....
Few confess it.

Now, focuss on 2d mixed worlds.

The two-dimensional image of a didactic model where matter and ghost-matter
mix is simply checkers. You know that this game is played by moving pieces
on the black squares.
(83)

But could'nt we use the unused withe squares to play a second game, independent
from the first? Just put a second set of pieces like this. Then this gameboard
could be used by two teams of players.
(84)

The two games would be in these circumstances totally independent. In the
ghost matter model, we suppose that the first elements "communicate" with
second exclusively through the intermediary of gravitation. We could simulate
this by imagining the game to be played on a "soft gameboard." When a piece
is on a square, it would sink into the material and deform the surface. The
second game's pieces would thus be "informed of its presence," without being
able to interact with it, take it or be taken by it.

The solar neutrino deficit puzzle.

In classical general relativity, one assumes implicitly that there is a single
universe. People say :

• Apply Occam's principle : there is no need to change this vision
  !

In the center of stars, and sun, fusion reactions occur
and produce energy, which is carried by :

• Photons

• Neutrinos.

Neutrinos very weakly interact with matter. They easily can cross the sun,
for example. Then, they leave the central solar boiler in one second. The
energy carried by photons takes more time to reach the surface of the star,
its chromosphere. Emitted photons are absorbed by atoms, then emitted again,
an so on. Moreover, convective phenomena brings energy from the center of
the star to the surface, like in boiling watter.

On Earth, we measure photons' and neutrinos' fluxes (since the last few years).
This revealed a 50 % neutrino deficit. We must build a convincing explanation,
someday. If we cannot do that, a conclusion will assert itself :

We don't understand how a star works...

Solar dynamics : back to the starting box.

Some theoreticians are very disappointed. Some others
are very glad and say :
.

- Hourrah ! Quantum mechanics fails, at least. We will be
obliged to create something really new.