The Observable Universe and a Spinning 3 Torus

[Gibsense]

After checking out Jim Franklin's link - https://www.researchgate.net/publication/357328983_Big_Bang_A_Critical_Review - which talked about the issues with the Big Bang theory, I felt a bit deflated and thought that a lot of my posts were Naff. But after sleeping on it, I woke up with fresh ideas!

My last Thread "Joining the Dots: Speculation of Continuous Creation" with a spinning Torus seemed worth a deeper exploration that might compete with or adjust the BB theory to cope with some of the apparent issues. One obvious fault with my ideas that the universe was a hypersphere was how the observable universe fitted in with its age acting as the radius of a sphere. Slapped on the side of a hypersphere the maths do not work.

However, it seemed possible that matching the Observable Universe to the small circle of a Torus might work. In the case of a 3 Torus ( Like a Hypersphere but Hypertorroid - a higher dimension Torus), it seemed that a whole load of spheres could exist tucked into the Torus. With some help, I have developed this into a feasible theory (lol, says me). For once an idea has very many predictions capable of checking but the key is the spin

I am gonna take a break but will continue by using an edit so be sure to check back sometime if you are interested

1. The idea that the Observable Universe has a Radius that matches the radius of the Small Circle of a 3 Torus

So far as I have been able to check it seems that if a 3-torus is cut across the small diameter with a spherical knife then characteristics of both Spheres and Torroids are entwined. This may improve the feasibility that the age of the universe determines the size of the Observable universe via C=2pie x r

This might suggest that the entwined characteristics mentioned above would give different results depending on which way we looked

2. The Surface of a 3 Torus is 3 D and the interior is 4D

The question is which to regard as our universe. The Universe as the surface would be finite, unbounded and flat. The observable part then (the small circle of the torus) might be curved but globally flat.

Alternatively, could we exist in the 4D interior space of a 3 Torus? In this case, we could be a 3D Brane and possibly interact with other branes. A string theory subject. It would also support the idea of multiple universes.

How could we tell the difference?

3. Residual Torus Spin

Potentially this could be detectable by;

• CMB Anisotropies. We might detect patterns or directional bias in the Cosmic Microwave Background that indicate residual spin
• Galaxy formation and rotation might be consistent with residual spin and a preferred pattern or arrangement also
• Polarisation of light from distant galaxies or quasars through careful analysis
• I am told that Gravitational Waves as a spatial background may show a specific signature possibly detectable in the future.
• Galactic flow: If the universe is embedded in the surface of the toroid the galactic flow would indicate preference for this over the internal 4D space and possibly arise from residual spin

A Closer Look at the idea of a spinning 3-Torus

Structured Flows: Galaxies moving along specific paths might reflect the underlying geometry from the patterns of their movement A 3 Torus is finite and unbounded allowing galaxies to move in complex ways which just might align with known flows

The preserved angular momentum might be consistent with the observed large-scale flows and patterns

Mathematical models and simulations might help understand better the properties and effects of a Spinning 3 Torus

 

[Jim Franklin]

The universe is flat, with a margin of error of only 0.4%. This is based on measurements from experiments like WMAP, Boomerang, and Planck, as well as the Atacama Cosmology Telescope.

The shape of the universe is important because it determines the fate of the cosmos. For example, the shape of the universe can tell us if it will expand forever or collapse, and if it's finite or infinite.

The three possible shapes of the universe are: See the WMAP Page on this

• Flat: Like a sheet of paper
• Closed: Like a sphere
• Open: Like a saddle

The shape of the universe is determined by two factors: its density and its rate of expansion. For a better overview than I have time to type here, see this ARTICLE in Astronomy Magazine

 

[Gibsense]

A better Summary:

1. Observable Universe and 3-Torus Radius: The idea is that the Observable Universe could be matched to the small circle of a 3-torus. If we cut a 3-torus across its small diameter with a spherical "knife," we could see the characteristics of both spheres and tori. This might suggest that the size of the Observable Universe is determined by its age, with the formula C = 2 pi r playing a role.
2. 3-Torus Surface and Interior: The 3-torus surface being 3-dimensional and the interior being 4-dimensional poses an interesting question about the nature of our universe. If we consider the universe as the surface, it would be finite, unbounded, and flat, while the observable part might be curved but globally flat. Alternatively, if we exist in the 4D interior space, we could be a 3D brane interacting with other branes, aligning with string theory and the idea of multiple universes.
3. Residual Torus Spin: Detecting the residual spin of a torus could be possible through various observations:
   • CMB Anisotropies: Patterns or directional bias in the Cosmic Microwave Background.
   • Galaxy Formation and Rotation: Consistency with residual spin and preferred patterns.
   • Polarization of Light: Analyzing light from distant galaxies or quasars.
   • Gravitational Waves: Detecting specific signatures in the spatial background.
   • Galactic Flow: Indicating a preference for the torus surface over the 4D interior.

The idea of structured flows and preserved angular momentum also suggests that galaxy movements might reflect the underlying geometry, with mathematical models and simulations helping to understand these properties.

 

[Gibsense]

The three possible shapes of the universe are: See the WMAP Page on this

• Flat: Like a sheet of paper
• Closed: Like a sphere
• Open: Like a saddle

Yes, but it could be all three in one structure: A Torus

• The torus has an open surface on the inside curve.
• The Torus is closed like a sphere
• A Torus is globally flat

The latter point needs further interrogation. A cylinder although curved is flat this being easily understood in that it can be cut and laid down flat. A Torus can be considered flat in the same way that a cube (if stretched and each end joined to the other) as per a video game - the object goes out one side and enters the other (the cube is flat.

These points I picked up from the Topology in Wikipedia. There are some amazing simulations there!

 

[Jim Franklin]

Yes, but it could be all three in one structure: A Torus

• The torus has an open surface on the inside curve.
• The Torus is closed like a sphere
• A Torus is globally flat

The latter point needs further interrogation. A cylinder although curved is flat this being easily understood in that it can be cut and laid down flat. A Torus can be considered flat in the same way that a cube (if stretched and each end joined to the other) as per a video game - the object goes out one side and enters the other (the cube is flat.

These points I picked up from the Topology in Wikipedia. There are some amazing simulations there!

I am not sure you are understanding geometry here, whilst it can be argued that a torus may represent all three possibilities, in practice, it is a torus and thus it is not all three in one, it is a torus. A pyramid is closed like a sphere, it does not make it a sphere though, the inside surface of a torus is not actually open because it is physically joined to a 3 dimensional structure and the idea a torus is globally flat is playing with words because that is purely dependent on scale and shape, a torus need not be globally flat.

 

[Gibsense]

I am not sure you are understanding geometry here, whilst it can be argued that a torus may represent all three possibilities, in practice, it is a torus and thus it is not all three in one, it is a torus. A pyramid is closed like a sphere, it does not make it a sphere though, the inside surface of a torus is not actually open because it is physically joined to a 3 dimensional structure and the idea a torus is globally flat is playing with words because that is purely dependent on scale and shape, a torus need not be globally flat.

Unless I misread it (in Wikipedia) explicitly said flat. I'll check. Also, a pyramid topologically is a sphere.
Also
Time as a Flattening Force: If time can be thought of as acting in multiple directions orthogonal to space, it can influence how we perceive the geometry of objects. This could effectively "spread out" the curvature over these multiple time dimensions, making shapes appear flat in this higher-dimensional context.

In mathematical terms, a torus can be regarded as "flat" because it has a property called zero Gaussian curvature. This means that, locally, the surface of a torus is similar to the flat plane—we can unfold or "unwrap" it to a plane without stretching. This is different from, say, a sphere, which has positive curvature and can't be unwrapped to a flat surface without distortion.

So, there we have it:
Flat
Closed
inside curvature negative
NB re negative curvature I refer to the surface adjacent to the hole

 

[Jim Franklin]

Unless I misread it (in Wikipedia) explicitly said flat. I'll check. Also, a pyramid topologically is a sphere.
Also
Time as a Flattening Force: If time can be thought of as acting in multiple directions orthogonal to space, it can influence how we perceive the geometry of objects. This could effectively "spread out" the curvature over these multiple time dimensions, making shapes appear flat in this higher-dimensional context.

In mathematical terms, a torus can be regarded as "flat" because it has a property called zero Gaussian curvature. This means that, locally, the surface of a torus is similar to the flat plane—we can unfold or "unwrap" it to a plane without stretching. This is different from, say, a sphere, which has positive curvature and can't be unwrapped to a flat surface without distortion.

So, there we have it:
Flat
Closed
inside curvature negative
NB re negative curvature I refer to the surface adjacent to the hole

Oh dear, I'm out of this conversation because if you will not listen to common sense and reason, assuming your incorrect statements are right, then there is no hope.

 

[Gibsense]

h dear, I'm out of this conversation because if you will not listen to common sense and reason, assuming your incorrect statements are right, then there is no hope.

Common sense is a not-so-useful tool in multidimensional discussion. Ignoring the mathematics of Topology is, for an engineer, not unusual. You clearly are more comfortable with the on-hand science of telescopes and the like. I would recommend you do explore Topology as there are plenty of surprises sitting there to open a new horizon of learning for you.
PS Your reference to problems with the BB theory article is a bit out of date.

 

[Gibsense]

the inside surface of a torus is not actually open because it is physically joined to a 3 dimensional structure

I was referring to the 'outside' shape adjacent to the hole. That shape is clearly negative curvature. It can be argued that as part of a larger object, in this case, a 3 Torus, this is irrelevant. That would be a good argument were it not important in the consideration of a 3 Torus which has a 3D surface that could be a contender for the shape of the universe. But we never got that far as Mr Franklin has declined to defend his case. Understandable.