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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, that 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 sense.
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 carton 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)
Then 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 I could, I would 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, I have 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 I made a mistake : I chose one where one of the walls is a mirror. Then, instead of one red fish, we have two. But Jonas was immediately convinced 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 assured 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 territorial 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 months we bought another aquarium, without the mirror-wall and Jonas became friendly again. It was cheaper 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, swimming 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 "sees" an infinite number of brothers, due to the multiple reflections 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 embed 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 useful. Thanks to the bathroom mirror, when I am thinking about some complex mathematical problem I dreamt about that night, I don't put my tooth brush in my nostril.
All mathematicians mainly practice oniric work. Souriau, me, and many others..... Few confess it.
Now, focus 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 couldn't we use the unused white 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, and so on. Moreover, convective phenomena brings energy from the center of the star to the surface, like in boiling water.
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 :
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** - Hourrah ! Quantum mechanics fails, at least. We will be obliged to create something really new.
**