Dear Marco,

The idea that the universe has a hyperspherical shape is an idea that I like and use, since it solves the problems of its limits very easily.

Besides, I think I have been able to prove it, since I have deduced Einstein's field equations only based on that hyperspherical form.

Remember also that several thousand years ago the Earth was also considered flat..

Dear Sergio,

By the way, what you call a hypersphere is different from what I call a hypersphere. I call our Universe's 3D spatial coordinates to be the locus of a lightspeed expanding hyperspherical hypersurface. Time is there to time the expansion and it is not part of the topology, as it is in a 4D Spacetime.

That also means that the forces we know are perpendicular to the direction of motion and cannot influence expansion. Hence, you CANNOT derive Einstein's equation from the topology that is consistent with SDSS astronomical observations.

If you use it and used it only after 2006, please refer to my work as a precedent to your usage. You can get my timeline from here:

https://hypergeometricaluniverse.quora.com/Articles

I say that, not just to be protective of my own work, but also to ask you for your understanding since I have being censored since 2005.

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Here are the newest publications:

Main Article:

2017:

The Hypergeometrical Universe Theory: Cosmogenesis, Cosmology and Standard Model

http://www.worldscientificnews.com/wp-content/uploads/2017/07/WSN-82-2017-1-96-1.pdf

2018:

The Case for the 4th Spatial Dimension and the Hypergeometrical Force:

http://www.worldscientificnews.com/wp-content/uploads/2018/02/WSN-98-2018-127-139.pdf

The Coma Cluster, Bullet Cluster and Weak Gravitational Lensing

http://www.worldscientificnews.com/wp-content/uploads/2018/04/WSN-101-2018-222-228.pdf

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Using it as an "idea" is different from using it as the result of astronomical evidence. I provided that evidence by analysing correctly the Sloan Digital Sky Survey.

The Case for the 4th Spatial Dimension and the Hypergeometrical Force:

http://www.worldscientificnews.com/wp-content/uploads/2018/02/WSN-98-2018-127-139.pdf

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If you learned about the Universe being a hypersphere, you should also had learned that it travels radially at the speed of light. Most academicians don't thread there, and by doing so, that refutes General Relativity, L-CDM etc.

I provided falsification of all Dark Matter and Dark Energy. That is what I was referring to when I mentioned my correction to Newtonian Dynamics.

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So, I was suggesting,

You cannot model the influence of the deterministic recurrences of the hyperspherical mode if you don't use the information we already have about it.

If you want to replicate my discovery, you can do so,

https://hypergeometricaluniverse.quora.com/Universe-Trove

the scripts are in a github repository:

https://github.com/ny2292000/TheHypergeometricalUniverse

I strongly suggest you to do so, since the emotion of your first time seeing the Universe is overwhelming...:)

If you have trouble with the scripts, let me know.

Dear Marco,

There is only one definition of a hypersphere and embedding in a 4-dimensional Euclidean space must comply with the following relationships, if it is not, it be something else, but not a hypersphere:

http://mathworld.wolfram.com/Hypersphere.html

On its surface if you move in "straight" line in any of its 3 intrinsic dimensions in the end you will reach the same point, but from an extrinsic point of view, Euclidean of 4 dimensions you will see that its geodesic lines form circles

Yes, that was my first idea, using time as the hyper-radio dimension, but there is a problem, what happens if we go backwards in time? there is a time 0, and before? What existed before time? How was time created? with the energy? Tell me some energy process that can create time? it is evident that time can not be that 4 dimension because it gives many problems..

Yes, you can get Einstein's equations (look at my work and check it yourself ...) based on a very simple idea, if the universe is hyper-spheric and contains all the mass-energy of the universe, that mass-energy is what gives it its shape (obviously, less mass-energy will cause less curvature) (look at the part where I explain gravity, you'll see that it's so intuitive that it almost comes out alone), and showing before that E = mc^2 is a potential energy, knowing the how and why of that energy and doing a series of calculations

" If you learned about the Universe being a hypersphere, you should also had learned that it travels radially at the speed of light. Most academicians don't thread there, and by doing so, that refutes General Relativity, L-CDM etc. "

Yes and no, look at my way of deducting E = mc ^ 2 and the medium I use for the transmission of light to understand it better..

" If you learned about the Universe being a hypersphere, you should also had learned that it travels radially at the speed of light. Most academicians don't thread there, and by doing so, that refutes General Relativity, L-CDM etc.I provided falsification of all Dark Matter and Dark Energy. That is what I was referring to when I mentioned my correction to Newtonian Dynamics. ####################################################So, I was suggesting,

1. you not using L-CDM, Dark Matter in your modeling of galaxy formation"

I do not treat dark matter in my work, although it can easily be seen that if the universe is hyperspherical and the light propagates Euclidly in a straight line, to the distant galaxies mass-energy should be added to obtain its real curvature (although that does not mean that that mass-energy exists, it can be an error of "perception")

" 3. using the Hypergeometrical Force and Loaded Matter to explain galaxy formation instead. "

I think, more or less we refer to the same, but I interpret it as the force that creates the matter (see my deduction of E = mc ^ 2 and you will understand ..)

And now that I think about it, if you use a signature - +++ or + ---, you can not use a hypersphere directly like I did, should you make the corresponding change to adapt the hypersphere to that metric, no?

We are speaking of the same hypersphere.

Yes, that was my first idea, using time as the hyper-radio dimension, but there is a problem, what happens if we go backwards in time? there is a time 0, and before? What existed before time? How was time created? with the energy? Tell me some energy process that can create time? it is evident that time can not be that 4 dimension because it gives many problems..

Why wouldn't time be essential? Why do you posit that it has to be created?

I chose to use The Simplest Model where time is always there and it times metric and dimensionality fluctuations that yield Universes. Fluctuations are governed by the Heisenberg Principle, which is supported by observations. So, that explains what was before and what will be after and that model is just fine with observations.

There is no need to create time with energy. That is a convoluted model which has no observational support of any kind and shouldn't be pursued.

Yes, you can get Einstein's equations (look at my work and check it yourself ...) based on a very simple idea, if the universe is hyper-spheric and contains all the mass-energy of the universe, that mass-energy is what gives it its shape (obviously, less mass-energy will cause less curvature) (look at the part where I explain gravity, you'll see that it's so intuitive that it almost comes out alone), and showing before that E = mc^2 is a potential energy, knowing the how and why of that energy and doing a series of calculations

To state that the intrinsic energy of a body in an Universe traveling at the speed of light is mc^2, is trivial, given that that energy was impacted in an impulse. That is no insight.

Insight is to understand that Gravitation is perpendicular to the direction of expansion and thus cannot have any work done or have any effect upon the expansion. That is what I concluded and that is what is consistent with observations.

Yes and no, look at my way of deducting E = mc ^ 2 and the medium I use for the transmission of light to understand it better..

I have to confess ignorance of your derivation. That said, it it that relevant since I agreed upon your conclusion E=mc^2 by considering that the Universe was accelerate to c impulsively. That is a very, very, very small part of the argument I created.

I do not treat dark matter in my work, although it can easily be seen that if the universe is hyperspherical and the light propagates Euclidly in a straight line, to the distant galaxies mass-energy should be added to obtain its real curvature (although that does not mean that that mass-energy exists, it can be an error of "perception")

That is the problem I am trying to explain to you. Since all forces, include gravitation have no influence on the expansion and the expansion is timed by a Cosmological Time. So the hypersphere is a circle also on the 4D spacetime and it does not care upon the Universe content.

What you use in the current spacetime curvature has to do with the twisting of the local time. Just look at the double cross-sections, representing the Current Universe.

This is all irrelevant since the constant expansion means that Einstein's equations are fundamentally incorrect.

I derived a velocity and epoch dependent law of gravitation that is Quantum Mechanical, Relativistic.

I also provided a new model for matter, which is used to derive the Natural Laws. I also corrected Newtonian Dynamics with the introduction of the Hypergeometrical Force and corrected Newton Laws of Dynamics with the introduction of the Fundamental Dilator and the Quantum Lagrangian Principle.

And now that I think about it, if you use a signature - +++ or + ---, you can not use a hypersphere directly like I did, should you make the corresponding change to adapt the hypersphere to that metric, no?

Don't use a metric at all. The refutal of Einstein's Equations by the my discovery using the SDSS data shows that the geodesics paradigm is not to be used.

If you have an Algebraic Addiction, you might need help..:)

That said, Merry Christmas.

Please, read this:

https://hypergeometricaluniverse.quora.com/Proof-of-an-Extra-Spatial-Dimension

Run the scripts here:

https://hypergeometricaluniverse.quora.com/Universe-Trove

to convince yourself that you cannot use, ever, the geodesics model. It is just wrong. Einstein's interpretations of Time are also incorrect, etc, etc.