1.- What is an S3 shape?

 - An S1 Shape:

A straight line is a one dimension space. If we were living in a space like this, we could only go forward or backward, but could travel in one of these ways as much as we wanted, because we wouldn't find a limit.

Now, suppose we cut this straight line in such a way we got a finite segment. and we join the two edges. Then, we will have obtain a circumference.

If we regard this circumference as a space, it will have similar properties to the straight line. The only difference will be that when we had travel for a while, we will have arrived to the starting point. This is call an S1 shape, in Mathematics.

 - An S2 Shape:

To imagine an S2 space, we have to regard a sphere surface as a space in which we can move. We live in the World, and this is just a big S2 space. We know that in short distances the world is like a plane surface: we can move forward, backward, left and right. So we have 2 dimensions, hence this shape is called S2 in Mathematics. We can observe an important detail in this S2 world: if we walk enough distance in a given way, we will return to the starting point. We will have gone round the World.

 - An S3 Shape:

Our (or at least mine) space feeling doesn't let us to imagine an S3 space seen from the outside, like in the S1 and S2 spaces. As we live in a 3 dimensional space we can see and imagine infinite objects of 2 and 1 dimensions, because our space can contain them. This doesn't happens with infinite 3 dimensions shapes.

So, the only way for our mind to understand what is a S3 shape is to go inside it (with our imagination) and study its properties:

• We can move in three different ways (up and down, left and right, forward and backwards), so it is a 3 dimensions space.
• We will return to the starting point if we walk enough, and doesn't matter the way we took.

2.- What does an S3 Universe involve?

Let imagine a star located at some place inside this S3 space. This star will through light radially, all around itself. If I take my attention to a particular ray of light of this star, I will realize that some time later this ray will arrive to the same point it had started this way round the S3 Universe.

This will happen to every ray emitted by the star, in every direction. So absolutely all the light emitted at the beginning from the star will return to this same star, some time ago.

There is another important fact: The light of the star, before arriving to the starting point (to be exact, at the middle of the way), will concentrate in a point due to the "sphereness" of the S3 Universe. Look at Picture 1.

On the other hand, the star light concentrates again on the other edge of the S3 Universe (You may see this light ray convergence in the Picture 1. This drawing represents an S2 Universe, but an S3 is very similar). So, what will I observe?

The observer will see a star throwing light and later (this depends upon the Universe scale) he will see a mirror image of this star where it was located before (supposing it is moving).

So, he will observe two stars (one of them is merely a mirror of the first one). If we wait enough, there will appear more mirrors of this star, forming a straight line, and at distances that depend on the Universe scale and the velocity of the star. Of course there will be another mirror (or if you wait enough, mirrors) in the opposite edge of the S3 Universe. This is this way because the star light is traveling constantly round the Universe

Hence, we already have the first result: There will be multiple images of the illuminated objects of the Universe.

On the other hand, I may consider if this phenomena, we have studied with the light rays, could be experienced with the interactions (the forces). If we regard gravitation like an interchange of particles (you know, gravitons), these particles will run through their trajectories in the Universe, starting from the star that threw them like the light rays. This is due to the mass of the star, that is gravitationally interacting.

So, gravitons, as everything that travels through the Universe, will have to run over closed trajectories, that is, coming to the starting point, like light rays do. The conclusion is that we will sense the gravity of the star image (not the real star), in the same way that we will see the star image. Hence, if the generated image of the star would be perfect (that involves a symmetric universe with no fluctuations, and that may not be the case), we will sense all the star light and interactions like if it were a real star. We couldn't difference it from a real star.

So, the second conclusion is: The image star will interact like if it were a real star..

Why do I think this model is correct?

The most important reasons to think that a theoretical model is correct are the confrontation between theory and empirical data. In this case, the empirical data are the Universe observations. Let's talk about that:

• Filamentary Structures:

Let's have a look to three graphics of the filamentary structures in the Universe (Pictures 2, 3, and 4). If we look graphics from other sources, we will find the same main features, that I will describe later. These graphics have been obtained from many observations of the extra galactic space. They are plane sections of the Universe and we are located in the middle of the pictures 2 and 3, meanwhile in the picture number 4 we are located in the lower edge (the sector vertice). The quality of the pictures 2 and 3 is much lower than picture 4, so in these figures you can't resolve every galaxy as a point in the sector, meanwhile in picture 4 you can do it. The advantage of pictures 2 and 3 is that they show the complete sector, but picture 4 shows only the upper extra galactic visible zone.
 

These structures are featured by:

• Great Wall: This is the name given to the arc shape structure round our position (Picture 5). If it has an arc shape and not a complete circumference shape it is due to (supposition of the author) there is a big area in the sky where we can't observe extra galactic objects (Great Wall is one of these) because our own galaxy is in the middle of the field of vision.

So, we may think that the Great Wall is not really an arc, but a complete circumference (Picture 9). If we make this assumption, we will realize that curiously the center of the circumference is exactly where we are, in our galaxy cluster, that is, the observer position (Picture 7).

We are studying sections of the Universe, but not this one as a whole. So, is normal to think that what is a circumference in a plane surface, will be an sphere in a cubic space (a 3D space). We know the space of our Universe has three dimensions, like the cubic space. Hence, the Great Wall might be a complete sphere around us (and our galaxy just in the center, What a curiosity!). Later, when we apply the S3 model of the Universe, we will realize that this effect doesn't mean that we are in the center of the Universe, but every observer will see the same effect everywhere he was located in the Universe.
 
 

1. We observe that crossing with the Great Wall there are filamentary structures (Picture 8) that curiously are pointing to us (the observers). We also see that Great Wall is really a wide band radially stratified. That means it is composed by a lot of fine structures pointing to us (Picture 10).

1. Great Voids (Picture 6) are distributed around the Great Wall (Picture 5) and the galaxy cluster where our galaxy is found (Picture 7).

When we make a stereo graphic projection, what we actually are making is represent an spherical space S2 as if it were a flat space. A World map is a stereo graphic projection of the World, and this makes the shape of the Antarctic to appear distorted. If this maps showed beyond Antarctic, you know, Australia and so on (respect Europe), we will observe those regions much more distorted than Antarctic. It will appear like a circular region rounding us, (I mean Europe). This is due to the fact that the other edge of the world is equally distant from us in every direction.
 
 

So, if we suppose our Universe to be an S3 space, we would have a clear explanation of the suspicious spherical shape of the Great Wall centered on us. It will be the result of our own image after taken a full round to the Universe. Look at Figure 11: On the left side, we find a galaxy cluster centered on image. We are supposed to be in the center of the cluster. On the right side, we have the stereo graphic projection of the left image, supposing an S3 Universe. On the right side output image two Great Walls are shown. Actually an infinite number of then should have been obtained. I'm drawing only the two firsts Great Walls. In the experimental observations we can only see the first one. This picture is a computer simulation of the S3 projection applied to a random cluster shape. As the Great Wall is about 400 million light years from us, this would be the S3 Universe perimeter.
 

Experimentally, we see that the Great Wall is an ellipsoid around us. This is explainable if we make the assumption that our Universe is an non-perfect S3 shape. We find the same case in the World Map. The Earth is not a perfect sphere, but an ellipsoid. So, the distance of a world round going to the Poles is less than going to the Equatorial zone. This effect is making that the circumference shape of the Great Wall turn to be an ellipse shape. So, the fact that the Great Wall is an ellipsoid is not difficult to explain.
 

 

The following fact to explain are the Great Voids. The images of the low density regions of our own Galaxy Cluster and close regions are the Great Voids. They exist just because there are long radial filamentary structures and a Great Wall.

To finish with the Filamentary Structures subject, I have made an stereo graphic projection of the image experimentally obtained of our galaxy cluster (Pictures 14a, 14b and 15). Besides the projection itself, I have considered a rotating movement of our galaxy cluster, so as to radial structures were aligned exactly like experimentally are observed. If we calculate the angular velocity considered for the structures to match, we will obtain that they would take 14400 millions of years to turn 360 degrees. This stereo graphic projection matches with the experimental maps of our surrounding galaxies (Pictures 15 vs 3, 4 and 5). Nevertheless the matching is not exact due to the next reasons:
 

• The stereo graphic projection we observe experimentally does not come from the shape of our galaxy cluster as we observe today, but its shape 400 million years ago. I am supposing that its shape has not deeply changed. However, it is natural to think this shape has changed, at least, a bit. This changes are contributing to the mismatch between the theoretical and the experimental galaxy patterns.

• I do not have enough information of our galaxy cluster shape. (Look at the differences between the image is going to be projected in the picture 15 and that of the pictures 14a and 14b).

• In the simulated projection has not been considered that our S3 Universe may not be a perfect S3 sphere. If it were not a symmetric S3, as the Earth is not an exact sphere, the projection would be different.

• Another limitation of this projection is that it has been supposed that the Universe is turning around the perpendicular axis and that is surely not true. In that case we have another reason to understand the mismatch previously commented.

All the previously exposed points lead us to a very important possibility to explain the nature of the Filamentary Structures, the Great Wall and the Great Voids.
 
 

• The Red-Shift Problem

If we think again in the S3 Universe model, we may realize that coming from a given galaxy, we receive not only its direct light, but we also receive the light of the image that has been generated on the other edge of the S3 Universe, and the light of the image generated on the initial position (when the light has turned one complete round to the S3 Universe), and so on. If we measured the distances between these images we would obtain the half perimeter of the S3 Universe and its multiples, because the light has turn around the Universe completing first half round, later one round and so on. It is important to understand that astronomers measures the galaxy distance with the Red-Shift method. This means, that they are not directly measuring the real distance, but the the time that the light coming from the galaxy has taken to arrive to the Earth.

If we suppose that the original galaxy is not moving, we will obtain images of this galaxy in the same position that the galaxy was originally located. If it were moving, the original galaxy would appear distant from its image. The conclusion is that we will observe in the general case (that is considering that all the galaxies are moving) a group of similar galaxies. Actually, they are the same, but with a 400 million years of evolution of difference.
 

In brief:

• There will appear groups of galaxies.
• Them all will be very similar (actually we will be seeing the original galaxy and its images 400 million years ago or more)
• They will be aligned (this will be true only if the galaxy is free to move on their own. If it was under a gravitation field, its trajectory wouldn't be linear)
• There will be great differences in the red-shift between them.
• There may be gravitational bridges between them (it is natural, considering that the image also interacts with other galaxies gravitationally)
• All them will be of similar size (the fact that the light that forms the image turns around the Universe one round doesn't mean it is going to be seen smaller due to the distance, because the image formed is like the original galaxy and is at the same distance).

There are many examples. For example we have the Stephans Quintet galaxies. All these groups of galaxies show anomalies, that were unexplainable, until now.

  

• The Quasar Phenomena

Remembering that with an S3 Universe galaxies produces several images of themselves, is logical to think that the very old images will have such a red shifted spectrums that almost their whole emission will be centered in the radio waves (these waves are under the red in the frequency scale). On the other hand, we must receive low radiation in the visible range from these images, because all this emission should become from the UltraViolet or X-Ray radiation from the original galaxy, and that uses to be of low intensity. Hence, the whole spectrum received must be as intense as the one emitted originally, but shifted to the red until become centered on the radio wave frequency.

Respect to the quasar problem of being too distant to be so bright, if we suppose an S3 Universe, we could say that all the light emitted originally by this quasar has not been lost in the deep space, because the trajectories of all these light rays converge in the quasar image every time they complete half round to the S3 Universe. If the light never loses they will conserve their light through the apparent big distance.

Another fact hard to explain now a days is the observation of fast movements in the quasars structure or between neighbors. So fast that they move over the light speed. Now, in the S3 Universe this phenomena is very easy to explain, just taken account of that the real distance to the galaxy image is not the distance measured with the red shift method (this last one would be the distance from the original quasar to the Earth considering a plane Universe), but it is a much shorter one. The scale would become much smaller, and the velocities would also be smaller.

Taking account of the multiple images generated by quasars in the S3 Universe, astronomers would have to experimentally observe very interesting relations and alignments between quasars and galaxies. Some examples are:

• The most bright quasar with visible spectrum is 3C273, in the Virgo constellation. It has got a very big jet. Near in the sky, around 10º to the North, we may find the M87 galaxy. This one is a special galaxy, because it emits high intensity in radio waves, and it has a jet, similar to the 3C273 jet, and they are oriented almost in the same direction. Near from these two objects, a very big intergalactic nebula was discovered several years ago. It has also a liner shape oriented in the same direction that the M87 and 3C273 jets.

• If we observe NGC 300 we will appreciate that, near this galaxy there are hydrogen clouds with some type of alignment and very near we find a line of quasars. The direction of the line of quasars is not very different of the clouds (Picture 16).

• Near M33, we find hydrogen clouds, and another line of quasars (Picture 17).

 

Serious science needs experimental confrontation of the facts that the model or theory predicts. Until now, this is what we have been doing: to develop the model (finding out the consequences of supposing an S3 Universe) and confront it with experimental observations (similarities in the Universe map, red shift and quasar phenomena, ...).

Now, we may expose another kind of reasons to think that the Universe is an S3. These are philosophical reasons. When I developed this S3 model, I had only philosophical reasons to believe in it. After developing it, I found experimental data fixing with the model results. So, it may be interesting to study these philosophical reasons:
 

Why do I have to think the Universe is closed?
 
There is a very short answer: "So as the Universe not to be infinite". At first, we may not understand why it is necessary the Universe to be finite. If the Universe were infinite in space, we never would be able to know it completely, unless it were cyclic. In that case, we would have a closed Universe (such as the S3). Physics tell us that nature also doesn't like infinities in the description of nature: just think about quantification. Quantification is limiting infinitesimal values so as not to be as small as we want: quantum numbers uses to be natural numbers. These means quantification is limiting physical magnitudes by the lower side. An S3 Universe would be limiting magnitudes by a higher side. Another example of limitation is Relativity: the speed of light.
 

Why the Universe has to be an S3 and not another kind of closed shape in 3D?

There are two reasons:

First, our Universe has to be locally flat, because that is what we observe. S3 is not the only shape that is locally flat, but that reason is limiting the number of shapes to choose.

Second, in Nature is usual to find spherical symmetry in much more cases than any other symmetry. It is important to use a shape with symmetry, because the symmetry is giving us a theory with fewer parameters. If we had, for example, a cylindrical symmetry we would have to explain why the symmetry axis is pointing where it is and not to another direction.

I have always said that Physics is built over two principles: The Principle of "Finiteness" and The Principle of Simplicity.
The first one says that every magnitude never reach Infinite and is discrete (that is, it may only increase by multiples of an elementary unit). The second one says that Universe must be as simple as possible, because if it were not simple, that would mean that we would need extra parameters to describe it globally, and the value of these parameters never would be explained. The only way to explain the whole Universe in a complete way is to suppose it is as simpler as possible.

These two principles imply the two last philosophical reasons for the Universe to be an S3.
 

The End

To conclude the exposure of the Universe S3 model, I would like to remind the reader that it is almost sure that there are other important conclusion when you suppose the Universe is an S3. For example, if we think in Quantum Mechanics, a closed Universe is directly in relation with the existence of magnetic mono poles.

On the other hand, supposing the Universe is an S3 we may create interesting ideas, such as the next one: "The Andromeda Galaxy, that is very near from our, and very similar, could be the image of our own galaxy, the Milky Way, 400 million years ago. With a very powerful telescope or interferometric techniques we would be able to locate the Solar System in that galaxy and the Earth, and see our own past and evolution, or even go there. It's like a time machine."

My only hope is that this model will be studied seriously by the scientific community to conclude if it is correct or no.

Thank you for your attention.

Bibliography:

• Easy to read:
• "Historia del tiempo" by Stephen Hawking. Editorial Crítica.
• "El sueño de Einstein" by Barry Parker. Editorial Cátedra.

• Hard to read:
• "En el confín del Universo: Cuásares" by Jorge Ruiz Morales. Editorial Equipo Sirius.
• "Controversias sobre las distancias cósmicas y los cuásares" by Halton Arp. Editorial Tusquets.
• "Macroestructuras del Universo: Cúmulos y Supercúmulos de Galaxias" by Alberto Castro Tirado. Editorial Equipo Sirius.
• "The New Physics" Edited by Paul Davis. Cambridge.