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The origin of "negative masses".
...In the chapter "Would the universe be a combination of two things?" let us cite the work of Souriau: Structure of Dynamical Systems, Dunod 1970, pp. 197-200 (recently translated into English: Structure of Dynamical Systems, Birkhauser Ed. 1997). Starting point: groups. By analyzing the action of the "complete" Poincaré group on its moment, Souriau shows that the universe could employ both particles of positive energy and of negative energy (hence of negative mass).
Group theory does not oppose this. But the possible encounter between two particles of opposite masses (nothing to do with antimatter, which has a positive mass, see above) raises a problem.
The result would be a complete annihilation. Not even photons. Nothingness in its pure state. A universe made up of an equal mixture of positive and negative masses would disappear purely and simply. Solutions suggested by Souriau:
- Either God, in his infinite wisdom and sagacity, deliberately omitted to create negative masses.
- Or, as a precaution, one amputates the Poincaré group of its two "antichronous" components, which not only reverse masses but also time, keeping only its two "orthochronous" components.
...Souriau does not, however, rule out the possibility of the existence of negative masses in the universe, and he then opts for the following dynamics:
- Positive masses attract one another according to Newton.
- Negative masses repel one another according to "anti-Newton".
- A positive mass and a negative mass repel one another according to "anti-Newton".
...By repelling one another, negative masses would not create structures, objects, stars, galaxies. They would flee one another and flee everything found in the universe. A panphobia, in a way (etymologically: horror of everything). This fundamentally isolationist behavior would then guarantee their existence.
What could a universe containing negative masses look like?
...These would fill every region of space deserted by matter. In these regions this negative matter would adopt the most uniform possible distribution. Thus, light, in crossing these no-matter's land, would undergo no gravitational lensing effect.
Therefore, as regards detection by observation: zero.
The inverse gravitational lens effect.
...We mentioned above the gravitational lens effect, the curvature of light rays, due to the presence of a concentration of matter. See figure 44. The 2d didactic model is then the good old model of the blunted posicone.
...Quid of the effect of the presence of a concentration of negative mass on the trajectory of photons. This corresponds to a zone of negative curvature, to a "blunted negacone", see figures 88 and 89. The geodesics diverge.
This geometry is also a solution of Einstein's equation.
See: "Jean-Pierre Petit and Pierre Midy: Matter ghost matter astrophysics. 2: Conjugated steady state metrics. Exact solutions. [See on site: Geometrical Physics A, 2-
5], 1998."
...It suffices to take up the Schwarzschild solutions (interior and exterior) and to reverse the sign of the mass.
Below is the 2d didactic image. Negative masses "repel" light rays.
But a uniform distribution of mass, positive or negative, produces no gravitational lens effect, positive or negative.
Confinement effect due to negative masses.
...Positive masses are self-attractive, sensitive to gravitational instability. They give birth to condensations, which drive out negative masses, whose distribution then becomes lacunary.
Galaxies, for example, could come to lodge in such a lacunary distribution.
...The gravitational counter-pressure exerted by negative masses on positive masses could then participate in their confinement.
...A word in passing on the 2d didactic model which could evoke the geometry of a universe populated by a mixture of positive masses and negative masses. Imagine a tent canvas, very vast, placed on pegs. If the pegs are very pointed, they will be point-like positive masses. If they are blunted, concentrations of positive masses.
...The portion of canvas that hugs the rounded shape of the peg has positive curvature. Beyond that, the curvature is negative. If the peg is pointed, the vicinity of the top of the peg evokes the shape of a cone (the envelope of the tangent plane). The point in question then represents concentrated curvature. If the canvas is stretched "over flat ground", the overall curvature is zero. Which means that there is as much positive curvature in the regions curved "plus" as there is negative curvature in the regions curved "minus".
On this canvas some geodesics have been drawn. If all this is projected onto the flat ground, one obtains:
But let us leave the didactic image. Quid of a "4d hypersurface"?
Einstein's equation was written:
S = c
T
where S is a geometric tensor and T the "energy-matter tensor". When one makes it explicit, under certain conditions, in a certain form, one sees explicitly appear the matter energy density r
and the pressure p (which is an energy density per unit volume: a pascal is also a joule per cubic meter).
...Let us call r+ and p+ the contributions to the density
and to the pressure due to positive masses. Let us call T+
the tensor constructed with these quantities. The contributions r-
and p-
, due to negative masses, would be negative. With these quantities
one would construct the tensor T-.
The corresponding field equation is then:
S = c (T +
- T-)
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