# Hypergeometrical Universe

## First Peer Review -2

continuation of First Peer Review:

I must admit that I am very confused by what the author proposes. It appears to me that, at least initially, the HU does not change any of the standard laws of physics but only changes the geometry in which the Universe is embedded. He proposes that the observed universe is the surface of a 3-sphere expanding into a new non-compact spatial direction. If this indeed the fundamental proposition, then it does not work:

Answer: The reviewer is honestly confused. That is not his fault. He is trying to understand something without reading the full article on HU (some 77 pages long - it is mentioned in the references). In addition, the reviewer fails to understand the proposed topology and states that

“I propose the observed Universe to be the surface of a 3-sphere expanding into a new non-compact spatial direction.”

That is not correct. If you replace 3-sphere by 4-sphere then it starts making sense or work.

It is important to notice that the Universe is not the volume inside a sphere but the ‘area’ on the hypersurface of the lightspeed expanding hypersphere!

The other very important missing part is that this hypersphere is expanding at speed of light c. Since the reviewer had such a limited understanding of the model, it is surprising that he reached any conclusion. I should remind you again that this article is not presenting HU, instead the article is presenting an analysis based on HU (two assumptions from HU) of the Supernova Survey data.

The idea behind this article was to mention the theory and to provide the assumptions derived/supported by HU theory:

1. Epoch-dependent Gravitation
2. The Ligthspeed Expanding Hyperspherical Universe topology

Here is the article:

Hypergeometrical Universe Theory Supernova High Z Predictions

These are assumptions that are not required to be supported by anything. They could had been taken as hypothesis without any support. Because of that, I didn’t expect that editors would speculate on my theory without reading it nor understanding it nor asking me any questions. That said, here is a brief explanation of HU theory.

The reviewer mentioned that HU doesn’t change any of the standard laws of physics. That is a naive view of the presentation of the theory. The theory recovers the laws of physics (electromagnetism and Gravitation) from first principles. It doesn’t simply recover them but instead it presents a different law of Gravitation (Gyrogravitation) which is consistent with what we know about Gravitation, Gravitational Lensing, Mercury Perihelion Precession. HU Gravitational Potential for a non-rotating Sun is equal to the Gerber’s potential. HU also discards Strong Force and Weak Force by introducing a new model for matter. HU GyroGravitation is a Velocity-Dependent Gravitation which is not amenable to General Relativity Geodesics methodology.

here you can see why G is epoch-dependent. ${R}_{0}$ is the 4D radius of the Universe and the Gravitational Constant is inversely proportional to it.

So it is incorrect to simply say that HU does not change the laws of physics.

HU replicates the standard laws of physics for the simple reason that HU has to comply with reality. That said, HU provides a different reason for that reality.

It changes the laws of physics (see attached article with the theory and derivations). It reduces all laws to a single law:

Dilators will dilate in phase with the surrounding dilaton field

This simple law (The Quantum Lagrangian Principle) is just stating that dilator do not do any work or conversely, that space dilation is quantized. This requirement makes dilators to shift sidewise (tangential motion) an amount x depicted below:

${R}_{0}$ is 13.58 billion light years (the current 4D radius of the Universe) and ${\lambda }_{1}$ is approximately the Compton wavelength of a hydrogen atom (femtometer). x is proportional to acceleration, if one considers motion as a deformation of the local metric (local fabric of space):

The Silver Surfer above is shown over a relaxed Fabric of Space (FS). Below is another one traveling left:

The FS is a preferential reference frame but it is not easily detectable from within our hypersphere. In the same way that the Cosmological Time ($\varphi$) which times the expansion of the Universe is also no easily detectable. Although we all know that there is an absolute time and an absolute time flow. We use it to tell that the Universe is 13.58 billion years old.

These Silver Surfers are presenting a paradigm shift on the way we see forces. In HU, there is no need for Force, Masses. The only thing one needs is to know where a dilator will be and when. Those two questions are answered by the Quantum Lagrangian Principle (QLP). That said, I used the QLP to derive Electromagnetism and Gravitational forces from first principles. QLP is fundamental and because of that it can be used to derive Laws we consider Natural (God Given or Natural Part of this Universe - no explanation required).

Newton’s laws have a Stress-Strain mapping on HU. This means that a Force exerts a torque onto the Fabric of Space, tilting ever so slightly it at each de Broglie step of the Universe expansion. Details are in reference 1 of the article.

I derived Natural Laws by considering the model for matter based on Dilators. The Fundamental Dilator is a coherence between “stationary” deformation states of the local metric. It represents electron, proton, positron and antiprotons depending upon which phase is in-phase with the Universe (they tunnel and spin within the 4D spatial manifold).

Stationary is between quotes because all dilators travel within the 3D locus of the lightspeed expanding hyperspherical hypersurface, so they are not stationary in the lato sensu. Below is the representation of the Fundamental Dilator for proton and antiproton:

As dilators change shape and spin within the 4D spatial manifold, they generate waves (dilaton field) and change their footprint within the 3D Universe.

They only interact at their largest footprints (quantized phases which generates intermittent interaction).

The times of these interactions are called within the theory de Broglie Steps (of expansion of the hyperspherical shockwave universe).

This view of matter differs from the current view. Matter within HU is made of space (deformed, changing, spinning space).

The only requirement is that dilators will position themselves at each de Broglie step at positions where they are in phase with the surround dilaton field. Electromagnetism and Gravitation are derived from this Law. Strong and Electro-Weak are replaced by elements of the HU Standard Model.

This means that HU is also proposing a replacement of the Standard Model. That said, this is not relevant for the reviewing of my application article. HU could be wrong on everything on its Standard Model and still the Universe could be an lightspeed expanding hypersphere and G could be epoch dependent.

I will refrain to include the whole theory here (77 pages long). I hope it will not be necessary to defend the whole Theory of Everything just to present an application (prediction) of the theory. If it is, I will be happy to do the best I can do at that time.

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