Some spatial diagrams related to Fig 1 and 2

[Also65]

Hi Maya. Let me some comments:

I think the diagrams of figure 1 and 2 on your paper may be related to this spatial configuration:

The diagram represents a multiverse formed by two intersecting fields varying with opposite phase, forming two transverse and two vertical subspaces. Your diagrams would be representing the expansion or contraction states of the transverse subspaces.

I'm considering the left and right transverse subspaces follow an opposite phase. Half of the system follows a real time coordinate and the other half follows a purely imaginary time coordinate that is delayed (or advanced) with respect to the other.

However, I think you're not considering the case when the transverse subspaces are the simultaneous reflection of each other. That would occur when the phases of fluctuation of the intersecting fields synchronize:

Here the left and right subspaces follow the same phase, which is opposite with respect to the phase of the intersecting spaces.

With respect to the vertical subspaces, with opposite phases they will move left or right toward the side of the intersecting fiels that contract. With equal phases, the top vertical subspace will move upward while contracting when both intersecting spaces contract, and it will move dowward while expanding when both intersecting fields expand. When the vertical subspace decays in the concave side of the system, there will be an inverted subspace in the convex side that will receive and equivalent force of pressure causing a negative (as it will be below the zero pointy in the spacial coordinates) mass and energy which will be directly undetectable (and so considered dark) from the concave side. This inverted subspace with positive curvature and negative energy would be a de Sitter vacuum, while the decaying vertical subspace with negative curvature in the concave side would be an anti de Sitter vacuum.

In that context it can be inferred that there are two different types of multiverses, one antisymmetric whose mirror subsattes cannot be equal at the same time, and one symmetric whose transverse mirror substates are equal at the same time but their vertical substates are not.

We can also supose that those types of systems are the same system that synchronizes and desynchronizes periodically. Let's supose the symmetric system can be described by the Schrodinger complex equation and, independently, the antisymmetric system can be described by its conjugate solution.

However, if it comes to a rotational system a discontinuity is introduced, and the Schrodinger equation only will be able to describe half of the system:

So, in a classical wave type, when the two intersecting spaces (or longitudinal waves) simultaneously contract, the next situation we can expect is that they both expand; however, in the rotational framework, the expected symmetry is broken because rotating 90 degrees the right field still contracts and the left field already expands. That introduces a non linearity in the transformation of the system that is interpreted as quantum.

This behaviour can be visually seen observing the direction of the eigenvectors on the above diagrams. They can also be expressed with a 2x2 complex matrix of eigenvectors with a 90º rotational operator, where matrices A1 and A3 correspond to the two moments of the symmetric system (A1 when both fields are contracting, and A4 when they both are expanding), and A2 and A4 correspond to the two moments of the antisymmetric system.

I think to consider the universe wave function it's necessary to take account of the interpolation of both the symmetric and the antisymmetric systems, which may be interpreted as a sobolev space function interpolation, a convolution that adds the complex function and its harmonic conjugate, or a type of fourier transform.

The inner orbits of the transverse subfields would be elliptic fibrations.
The two intersecting spaces may be interpreted as a double torus or a two genus geometyry in a esterographic projection, where the inner circle corresponds to the contracting field causing an inward force of pressure with its negative curvature, and the outer circle corresponds to the expanding field causing an outward force of pressure with its positive curvature, while contracting or expanding respectively. (A single torus also allows represent simultaneously both states when it comes to the antisymmetric system.)