twin universes
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...Below, a didactic model intended to illustrate the phenomenon of joint gravitational instabilities. Imagine a kind of swimming pool. At mid-height, underwater, we place a horizontal, flexible, weightless sheet. Above it, we place heavy balls, which will therefore press down on the sheet. Above that, we arrange an equal number of ping-pong balls, of the same volume. These, sensitive to Archimedes' buoyancy, will also exert pressure on the sheet, but in the opposite direction. We can also arrange things so that all the balls have the same diameter.
...If there is a uniform distribution of heavy balls and ping-pong balls on both sides, the net force exerted on the sheet will be zero everywhere, and the sheet will remain horizontal (curvature will be zero). But chance might cause heavy balls to gather in one spot. They will then sink into the sheet, pushing the ping-pong balls away. Schematically, taking a cross-section, the surface will take the following shape:
Heavy balls gather and sink the sheet.
They push the ping-pong balls outward, which then gather around the depression.
...Intuitively, one imagines that these two phenomena, rather than opposing each other, reinforce one another. The presence of this ring of excess ping-pong balls around the depression will deepen the hollow, thus enhancing the "confinement" of the dense balls.
...Gravitational instability could be illustrated with just one population by placing heavy balls on a sufficiently soft foam mattress. If a few of them happen to gather somewhere by chance, they will create a depression, into which their neighbors will tend to fall. This is known as an accretion phenomenon.
...If we had a sheet with only ping-pong balls placed beneath it, this system would also be unstable. If a few ping-pong balls gather at some point on the sheet, they will encourage their neighbors to join them. With this two-population model—heavy balls and ping-pong balls—we have two coupled effects, evoking the phenomenon of joint gravitational instabilities. This model also has the advantage of illustrating the symmetry existing between the two subsystems.
...Returning to the two-population system, this would look like:
Ping-pong balls gather and bulge the sheet upward.
They push the heavy balls outward.
...Thus, we sought to test this idea by starting from two distributions:
- Cold matter, density r
- Ghost matter, density r * @ 64 r, hotter: the average thermal motion velocity in the ghost universe V*th being four times higher than in our own, parameters derived from studies of the joint expansions of the two universes [see website: Geometrical Physics, 3, section 3 and figure 5].
...Calculations were performed via 2D numerical simulations with two sets of 5,000 point masses. These are only indicative. 3D calculations would be needed, requiring the handling of vastly more point masses than our system could manage. Therefore, these 2D results should not be taken literally.
...Qualitatively, ghost matter leads the process. It rapidly forms clumps (its accretion time, inversely proportional to the square root of density, is shorter). These clumps then push our own matter into the remaining space, giving it its lacunar configuration. See: J.P. Petit, P. Midy, and F. Landsheat: Matter and ghost matter astrophysics. 5: Results of numerical 2D simulations. VLS. About a possible schema for galaxy formation. [See website: Geometrical Physics A, 8, 1998.]
The two superimposed:
...The interest is that this distribution is then stable. The clumps of ghost matter stabilize the lacunar matter distribution, and conversely, the matter distribution traps these clumps within its "meshes." This would explain the high stability achieved (on the order of the age of the universe). The "meshes" of matter thus act as potential barriers against ghost matter elements originating from clumps and accelerated during collisions (in the Anglo-Saxon sense of "encounter," i.e., binary interaction between two ghost matter point masses).
Note (February 2000):
All these calculation results date back six years. Those who have read my books may know that these quite interesting and promising simulations were carried out in 1993–94, first by my colleague and friend Pierre Midy on an old Cray computer, then by "Fred," a young researcher who preferred to remain anonymous—a choice I fully respect. The calculations were performed "in disguise" on a powerful computer managing data from a European particle accelerator. Later, Fred moved labs, and such computations were no longer feasible in his new unit. Thus, the numerical simulation approach was abandoned for six long years. But recently, a new development occurred. First, computers have made such strides in six years (speed and especially memory capacity) that calculations previously possible only on powerful research-grade machines are now within reach of... ordinary individuals. Two men, specifically retired engineers passionate about astrophysics and cosmology, have therefore come forward. By programming their own machines, they achieved fairly impressive simulations, perturbing a 2D "digital galaxy" made of 3,000 point masses with a "passing companion" composed of 300 points. In short, the classic scenario leading to the spiral shape of the Whirlpool Galaxy, alias M51. When one sees these images, one immediately thinks, "This is exactly what we could do ten years ago in research environments with powerful computing resources." Of course, the spiral structure does not persist—it disappears once the perturbing companion moves away (an aspect long known). Our two engineers, encouraged by these promising results, approached six well-known astrophysicists for "guidance," but none had the courtesy to respond. I was thus the seventh astrophysicist they contacted. You can imagine how delighted I was to receive this unexpected support, and I immediately set these new collaborators on new simulations. Apparently, they are doing very well, and if all goes well, we will have "fresh results" in the coming months. An exciting prospect, as the goal is nothing less than simulating the birth of a galaxy. Stay tuned.
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