Flatlander 3D: Hypersphere to Flat Space

[CryptoCraig]

CryptoCraig, welcome to the forum.




In the expansion, or in a possible contraction?

Gravity is suggested as the excuse for Hubble's "law" not working close up.

A weight on a spring appears to increase its expansion on the "way out", but who knows whether there is any "elasticity" in a universe (observable or otherwise)?
These are only words. The map is not the territory.

Cat

Cat, thanks for the welcome.

In both, expansion and a possible contraction in the future. The expansion is macro. Locally, sub-galaxy clusters, there is no evidence of expansion.

Very simplified, but say, for instance...

...Nearly all matter is located at the "edge" of a sphere, with some amount of matter residing within, and currently very little matter outside of said sphere. The matter within the sphere could be gravitationally pulled toward the edge, and "flung" out beyond the edge. This would mean that gravity plays a factor in the Universe's accelerating expansion as well as it's eventual contraction.

All of this is assuming the force on most matter created by the BB explosion, is still moving away from a central point in the Cosmos.

 

[Catastrophe]

Cat, thanks for the welcome.

In both, expansion and a possible contraction in the future. The expansion is macro. Locally, sub-galaxy clusters, there is no evidence of expansion.

Very simplified, but say, for instance...

...Nearly all matter is located at the "edge" of a sphere, with some amount of matter residing within, and currently very little matter outside of said sphere. The matter within the sphere could be gravitationally pulled toward the edge, and "flung" out beyond the edge. This would mean that gravity plays a factor in the Universe's accelerating expansion as well as it's eventual contraction.

All of this is assuming the force on most matter created by the BB explosion, is still moving away from a central point in the Cosmos.

I have difficulty understanding this.

A sphere has no edge. It is a 2 dimensional figure but curved in 3D.

Regardless of the choice of convention for indexing the number of dimensions of a sphere, the term "sphere" refers to the surface only, so the usual sphere is a two-dimensional surface.

There is nothing inside or outside which relates to a sphere.
A 'flatlander' living on a spherical surface, for example, would be oblivious to anything not confined to that spherical 2D surface.
We can visualise an 'inside' but a flatlander could not.

There is no central point in the cosmos, any more than there is a central point on the surface of a sphere. If you wish to pursue that thought, use a bubble instead of a sphere.
A bubble is not a sphere.

Universe and universes - some conformity please.

Many of us are familiar on when it is appropriate to use a capital U or small u. Korzybski (Science and Sanity) clearly teaches that "the map is not the territory". Some find it easier to understand "the menu is not the meal". The words are not the reality they may purport to describe. :)...

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Cat

 

[Atlan0001]

I'm irritated at myself. I know I've seen it before, maybe even pointed to it in one of my posts, but I can't find the greater dimensional asymptotic flatland plane sitting atop the hypersphere and where the straight-line of the flat touches the curve of the sphere, a 0-point portal. Altogether, 0-d, 1-d, 2-d, 3-d, and if the flatland plane penetrates down into and through through the sphere, both holding to their own dimensionality, a 4-d result at all points of contact . . . or probably, where centering.

How many flatland planes can touch the surface of the sphere at a point?! An infinity of flatland planes . . . altogether in their transitions through one another, flat plane and plane, and plane, and curving sphere, forming an "Infinite MULTIVERSE Universe"!

 

[CryptoCraig]

I have difficulty understanding this.

A sphere has no edge. It is a 2 dimensional figure but curved in 3D.



There is nothing inside or outside which relates to a sphere.
A 'flatlander' living on a spherical surface, for example, would be oblivious to anything not confined to that spherical 2D surface.
We can visualise an 'inside' but a flatlander could not.

There is no central point in the cosmos, any more than there is a central point on the surface of a sphere. If you wish to pursue that thought, use a bubble instead of a sphere.
A bubble is not a sphere.





Cat

I'm sorry you have difficulty understanding this. When discussing complex predictions on what could be what we are observing is nearly impossible. You know, obviously more than I know, but we both have a different set of knowledge. Me not knowing the terminology that you know, has definitely hindered what I am attempting to describe.

So, if I were to use a bubble instead of a sphere, could you picture what I described?

By, "central point", I was referring to gravitational center. Where there is equilibrium. Like the gravitational center of the Earth Moon system is located somewhere within the Earth, but on the side where the Moon is located.

 

[Catastrophe]

I'm sorry you have difficulty understanding this. When discussing complex predictions on what could be what we are observing is nearly impossible. You know, obviously more than I know, but we both have a different set of knowledge. Me not knowing the terminology that you know, has definitely hindered what I am attempting to describe.

So, if I were to use a bubble instead of a sphere, could you picture what I described?

By, "central point", I was referring to gravitational center. Where there is equilibrium. Like the gravitational center of the Earth Moon system is located somewhere within the Earth, but on the side where the Moon is located.

Hi CryptoCraig, Thanks for your reply.

I think the main difficulty is referencing sphere. Are you talking about out "Universe" being bounded by a sphere, or, if you like being akin to a bubble with the "Universe" inside?
Please quickly check Cosmology -

Universe and universes - some conformity please.

This will help us both if you understand what I mean.

The first difficulty I have, if you mean a "Universe" bounded by a sphere, is what is outside your sphere - if the "Universe" is "all there is"? Personally I do not believe that there is any such boundary. If we could see it from "one dimension up" I think it would look like the equivalent of a Moebius Strip, or Klein Bottle. OK, if we just forget any actual boundary and think of the matter in the U. being confined to a ball like shape, is there any reason why you think the matter would be mostly around the surface? Are you thinking of expansion leaving a "hole" in the middle?

If so, it is not necessary. Think of the flatlander. He is confined to the surface of the sphere (technically the surface is the sphere - there is no interior. That is the difference between a sphere (geometrical shape) and a bubble or ball (real world).

A flatlander would not understand a sphere expanding, which requires 3 space dimensions. He experiences expansion as the distance between points on the surface getting larger.
Mathematically, we would call a sphere as a two dimensional surface embedded in a third dimension. Not easy to understand, I appreciate.

You can see we have a problem here. I am using the analogy of a flatlander living on or in the surface. There is no above the surface or inside the sphere in his case.

If I understand you correctly, I would say that there is no need to try to give shape to the U. We don't understand anything here really. In this picture, I would just see matter existing in space, and mostly moving apart from other matter. There is an exception at small distances in that gravity overcomes expansion. Nearby galaxies, like Andromeda, are moving closer together because gravity overcomes the force causing expansion.

Don't forget that gravity falls off very quickly as distance increases. Although it does reach a long way, it weakens very rapidly, so I don't see this

The matter within the sphere could be gravitationally pulled toward the edge, and "flung" out beyond the edge.

happening at all. There is no sharp edge - just a gradual thinning - and gravity would still pull towards the centre - not towards any "edge". And the expansion is not leaving a "hole" in the middle. Everything (galaxies) is moving away from everything else (except the few very close to us). The moving apart is also weakening the gravity.

Does this help at all? Please come back and discuss

Cat

 

[CryptoCraig]

Hi CryptoCraig, Thanks for your reply.

I think the main difficulty is referencing sphere. Are you talking about out "Universe" being bounded by a sphere, or, if you like being akin to a bubble with the "Universe" inside?The first difficulty I have, if you mean a "Universe" bounded by a sphere, is what is outside your sphere - if the "Universe" is "all there is"? Personally I do not believe that there is any such boundary. If we could see it from "one dimension up" I think it would look like the equivalent of a Moebius Strip, or Klein Bottle. OK, if we just forget any actual boundary and think of the matter in the U. being confined to a ball like shape, is there any reason why you think the matter would be mostly around the surface? Are you thinking of expansion leaving a "hole" in the middle?

If so, it is not necessary. Think of the flatlander. He is confined to the surface of the sphere (technically the surface is the sphere - there is no interior. That is the difference between a sphere (geometrical shape) and a bubble or ball (real world).

I don't believe our Universe is "bound" by anything, other than the speed of light. I do believe that galaxies outside of our own appear much different than if we were outside of a galaxy. We are the flatlander when peering into the depths of space, beyond the Milky Way. We cannot observe "reality" outside of our own galaxy due to the bending of light and gravitational lensing.

Images of galaxies may be accurate, however, their location and distance in relation to the Milky Way will be skewed.

Imagine the path of the light coming from stars in a galaxy that is estimated to be 500 million LY away. Is it possible that the light, on its way to our planet, passes through a black hole in the center of our galaxy? If so, where is the galaxy actually located? Is that galaxy actually 500 million LY away? Did the light from that galaxy only really have to travel from the center of the Milky Way to planet Earth? If the light needs to pass through a black hole in our galaxy's center, is it possible that this very same light also passed through other black holes in the Milky Way's center causing duplicates of this galaxy? Is there a reason why planets are spherical in shape, solar systems are disk-shaped, galaxies are disk-shaped and our observable universe seems to be totally random?

A flatlander would not understand a sphere expanding, which requires 3 space dimensions. He experiences expansion as the distance between points on the surface getting larger.
Mathematically, we would call a sphere as a two dimensional surface embedded in a third dimension. Not easy to understand, I appreciate.

You can see we have a problem here. I am using the analogy of a flatlander living on or in the surface. There is no above the surface or inside the sphere in his case.

If I understand you correctly, I would say that there is no need to try to give shape to the U. We don't understand anything here really. In this picture, I would just see matter existing in space, and mostly moving apart from other matter. There is an exception at small distances in that gravity overcomes expansion. Nearby galaxies, like Andromeda, are moving closer together because gravity overcomes the force causing expansion.

Don't forget that gravity falls off very quickly as distance increases. Although it does reach a long way, it weakens very rapidly, so I don't see this



happening at all. There is no sharp edge - just a gradual thinning - and gravity would still pull towards the centre - not towards any "edge". And the expansion is not leaving a "hole" in the middle.

Everything (galaxies) is moving away from everything else (except the few very close to us). The moving apart is also weakening the gravity.

Everything, "except"... This is exactly what I mean. Everything is moving apart and supposedly at an accelerated rate. The moving apart, or away from the gravitational center is weakening gravity? Where/how? From everything collapsing on itself? You just wrote that galaxies close to us are doing the opposite. Maybe Andromeda will not merge with the Milly Way, but will slingshot by and cause both galaxies to move away from an observer at an accelerated rate. Other galaxies may also be doing the same, or have done the same in the past.

You also say that gravity reaches a long way, but weakens rapidly... That's what I was thinking as well. Let's revisit the bubble which I am calling the Universe again. After the BB would you think matter would just hangout? No, it's going to spread apart. Spread out. Once it spreads out, looking at the left side of the "bubble", wouldn't matter on the left side of the bubble have more effect on the left side than matter that's on the right and vice versa. Gravity is stronger locally, therefore, on a cosmic scale, would be almost non-existent except for objects nearer to each other.

You must remember the flatlander... The flatlander's mind would explode in trying to understand how the Universe works while being within a galaxy, within a solar system which reside within the Universe.

It's like you are writing what I am thinking, but somehow coming to an alternate and almost opposite conclusion.

 

[Catastrophe]

Most interesting, but a few points really are incorrect. You seem to suggest that the "universe" (whichever?) is densely populated with mass, so light can barely travel without being diverted in its path by some mass or other.

This reminds me of Olber's Paradox:

Olbers' paradox, in cosmology, paradox relating to the problem of why the sky is dark at night. If the universe is endless and uniformly populated with luminous stars, then every line of sight must eventually terminate at the surface of a star.

As you will know, the night sky is not uniformly saturated by light, with no darkness between neverending stars.

You als write of light passing through black holes. The reason they are called "black" is that light cannot escape from them.

Also, galaxies do not slingshot each other. Stars are so distant from each other that that a galaxy might pass right through another without any stars actually colliding. This does not mean that stars will not be gravitationally influenced. But the results can be seen in many photos where a string of stars extends between galaxies which have thus interacted.

Hubble’s Dazzling Display of 2 Colliding Galaxies - NASA Science

Located in the constellation of Hercules, about 230 million light-years away, NGC 6052 is a pair of colliding galaxies. They were first discovered in 1784 by William Herschel and were originally classified as a single irregular galaxy because of their odd shape. However, we now know that NGC...

science.nasa.gov

colliding galaxies - Google Suche

I guess that will do for a start.

Cat

 

[Catastrophe]

Above, you posted the following:

Maybe Andromeda will not merge with the Milly Way, but will slingshot by and cause both galaxies to move away from an observer at an accelerated rate. Other galaxies may also be doing the same, or have done the same in the past.

I pointed out that galaxies are not individual compact units, and thus they do not slingshot each other as you suggest.

However, it is possible for individual stars in colliding galaxies to suffer this fate.

The following is quoted from "Andromeda", by Giles Sparrow, All About Space, Issue 154, March 2024, pages 16-22:

. . . . . . Andromeda and the Milky Way are approaching one another at a speed of about 110 km (68 miles) a second. 4 to 5 billion years from now, they are destined to meet in a spectacular event. Collisions between individual stars will be unlikely, but many will have their orbits disrupted as they are flung off into intergalactic space. Huge bursts of star formation will be triggered as gas clouds from the two galaxies are rammed together, while over hundreds of millions of years their central black holes will spiral around each other before merging. The ultimate form of the merged galaxy . . . will depend on how much star-forming gas survives the process.

I hope you will find this an excellent picture of galaxies colliding.

Cat

 

[Gibsense]

How many flatland planes can touch the surface of the sphere at a point?! An infinity of flatland planes . . . altogether in their transitions through one another, flat plane and plane, and plane, and curving sphere, forming an "Infinite MULTIVERSE Universe"!

At a tangent: one

 

[Gibsense]

It was recently pointed out that the approach of Andromeda would not necessarily involve a collision with the Milky Way. When the whole cluster of galaxies is included in calculations the chances become 50:50. Time will tell. I have no idea if a 'miss' would cause a slingshot.

 

[CryptoCraig]

A different approach to determining the Universe's rate of expansion using distances.

Is the expansion accelerating or is expansion slowing down? Or is the Universe expanding at all?

It is known that when observing a galaxy at a distance of 5 billion light years away, we are seeing that galaxy as it appeared 5 billion years ago. It is also known, because of the presence of red shift in our observations, galaxies further from us are moving away from us faster than more local galaxies.

If we are observing objects 10 billion light years away, moving from us faster than objects 100 million light years away, then the expansion of the Universe is slowing down, not accelerating.

Objects were moving away from us faster 10 billion years ago than they are today. Or at least faster than galaxies that we can observe closer to the present.