Flatlander 3D: Hypersphere to Flat Space

[Atlan0001]

Ok I get you there! Very relevant - thanks for that.
I think we can address this issue you raise. At the moment I can only make an assertion without references but I will check and return. My assertion would be that time is always positive and although it can reverse direction it is never negative.

Look one light second away, more and/or less, from anywhere at all and see time reversed!

 

[Catastrophe]

Gibsense, my "like" excludes:

My assertion would be that time is always positive and although it can reverse direction it is never negative.

Time is one of many items which can be measued.
The result is a number of units (e.g., hours) which do not carry a + or - sign.
These units can be applied before or after a defined point.

Cat

 

[Atlan0001]

Gibsense, my "like" excludes:


Time is one of many items which can be measued.
The result is a number of units (e.g., hours) which do not carry a + or - sign.
These units can be applied before or after a defined point.

Cat

There is SPACETIME (+|-), then there is REALTIME (0).

((+1) (-1)) = 1/0.
((+n) (-n)) = n/0.

 

[Catastrophe]

There is SPACETIME (+|-), then there is REALTIME (0).

((+1) (-1)) = 1/0.
((+n) (-n)) = n/0.

Atlan, sorry, I do not understand this.

Does it mean that you disagree with:

Time is one of many items which can be measured.
The result is a number of units (e.g., hours) which do not carry a + or - sign.
These units can be applied before or after a defined point.

Cat

 

[Atlan0001]

Atlan, sorry, I do not understand this.

Does it mean that you disagree with:


Cat

That which is immeasurable = ((t=0) instant). That which is possible of supposition, but not grasping = (T=1, G=1, c=1....).

 

[Catastrophe]

I suddenly realised I had often mistakenly described 'the surface of a hypersphere' as 3d'. My bad. The Hypersphere IS a surface!! Sorry about that. Hope that clears it up.

But of course that surface has 3 Dimensions (drawn and imagined as 2d but in the case of a hypersphere the surface is 3d)

Gibsense,

Hypersphere and sphere are NOT the same.

A hypersphere is the four-dimensional analogue of a sphere. Although a sphere exists in 3D-space, its surface is two-dimensional. Similarly, a hypersphere has a three-dimensional surface which curves into 4-space. Our universe could be the hypersurface of a hypersphere.

 

[Atlan0001]

Gibsense,

Hypersphere and sphere are NOT the same.

A hypersphere is the four-dimensional analogue of a sphere. Although a sphere exists in 3D-space, its surface is two-dimensional. Similarly, a hypersphere has a three-dimensional surface which curves into 4-space. Our universe could be the hypersurface of a hypersphere.

Cat, you are seeing that the magnetic spokes of a magnetic field, such as the Earth's, curving to the center point electroweak monopole moment, curving lines into the center point of a flat wheel or disk (galaxy, black hole.... what have you) , , is 3-d 2-dimensional in the latter case . . . and 4-d 3-dimensional in the former case.

 

[Atlan0001]

So, I sense that you, Gibsense, have grave difficulty turning Special Relativity....

Mass–energy equivalence - Wikipedia

en.wikipedia.org

....inside-out (outside-in)!

That you cannot turn the light cones' illustrations above on their heads while keeping the (universe traveler) observer (now a man-figure, or stick figure} larger than the universe (u) centered in the open endedness of the flipped cones with two opposite poled arrow lines, running each side of it out to the pointy-ended cone points of the Planck (BB) Horizon outside.

Inverse-square law - Wikipedia

en.wikipedia.org

'S' = Planck (BB) Horizon point in its two outer places.
'3r', just short of the figure larger than the universe . . . on both sides of it.

 

[Gibsense]

Gibsense,

Hypersphere and sphere are NOT the same.

A hypersphere is the four-dimensional analogue of a sphere. Although a sphere exists in 3D-space, its surface is two-dimensional. Similarly, a hypersphere has a three-dimensional surface which curves into 4-space. Our universe could be the hypersurface of a hypersphere.

I said "a sphere" n- spheres are surfaces. All are surfaces of 'n-balls' so to speak. Of course, a hypersphere is an analogue of a sphere - it is defined as such. A hypersphere Is a type of sphere. These points are not an issue for me Please see my post on Hyperspheres suggesting that is our ( white hole) universe. Also, the diagram regarding 3D Flatlanders.

So in summary: I have never pretended a 2-sphere and a 3-sphere are the same thing but they are both types of sphere. I hope that clears up misunderstandings

Another issue we seem to be having a problem with is what we mean by "Observable Universe". I think it is important to agree on something. It doesn't matter too much which provided the right one is used in context. I prefer that which exists within an event horizon. That is where the boundary is extending at the speed of light.
Although perhaps valid in various contexts I do not think that one that depends on the type and power of a variety of telescopes will serve our purpose; I prefer Hawking's ideas. Do we agree on this?

PS A hypersphere is a surface (by definition)

 

[Gibsense]

https://i.postimg.cc/JhK5sDxS/3-D-perception-of-4-D.jpg[/img][/url]

[/url][/IMG]
I posted this image again because the thread has become very complex. Anyway it should dispel any idea that I don't know - at least the basics - of what a hypersphere is.

• The red circle depicts the hypersphere i.e the surface of a 4D Ball
• Events are marked at various equally spaced positions on the hypersphere
• The red straight tangent Line represents Our 3D flat Euclidian space
• The 4D events are marked off on the 3D Flatlanders space (the straight tangental line)
• Note that the events on the tangent red line are no longer equally spaced.
• T=0 in the diagram exists on the red circle not at the origin of the circle (hypersphere)
• It is T=0 because time runs 90 degrees to space. To an observer at 'A' time for any object moving from event to event from A to t=0 has rotated (got time dilation)
• Therefore to the 3D flatlander T=0 appears to be the beginning of time whereas, to a 4D person, T=0 is just dilation (same as passing the event horizon to someone far away)

 

[Atlan0001]

Gibsense,
The above #85 is good hard thought! I see one wrong piece in it, though. It's (t=0), NOT (T=0).

(T=1)! If you were following up on my request of you with your own preferred idea, please don't get it confused it with either entangling concurrent REALTIME NOW instant (t=0) or light's coordinate points' past-future histories' SPACETIME ((t=+1) (t=-1)).

 

[Catastrophe]

Gibsense,

This is your thread and, in your introduction, you state:

There are previous posts regarding the Flatlander illustration: How a 2D flat person would perceive a 3d object passing through a 2D flatlander plain. This post applies the same principle to the interpretation of 3D Flatlanders viewing a 4D universe. The Hypersphere and its 3D space (the surface) are described in a previous post.

This has almost nothing to do with my interest in using a sphere (what almost everybody would understand as a sphere) in an analogy to explore the term 'universe' and some of its ramifications. Therefore, I apologise for wasting your time in posting here.

However, I would just like to ask you what prompted a thread, which seems rather esoteric, particularly when involving the flatlander concept. Whilst you have every right to post this matter here, it does unfortunately muddy the water in causing confusion in the question of my using the sphere (I think we all know what I intended here) in the universe analogy.

Cat

 

[Catastrophe]

BTW, in your "more friendly" discussion in post #2, you state:

It is worth noting (if you have bothered to draw it yourself) that at what appears to be t=0 (an origin of the BB) is in fact the event horizon of our observable universe

I thought that it is generally accepted that BBT is distinguished from t = 0 by an increasingly smaller time interval, possibly involving trillionths of a second. This distinction is the more important as t = 0 no longer only represents a singularity but can alternatively represent a nexus in a cyclic system.

Furthermore, the Universe did not become observable at t = 0. Vide:

Until roughly 380,000 years after the Big Bang, the entire universe was a thick opaque cloud of plasma of electrons and nuclei. As the universe expanded, it cooled off enough to let the plasma become atoms, and the cosmos became transparent. We observe the light from this time as the cosmic microwave background (CMB). (My emphasis).

Please understand that these suggestions are intended as friendly assistance.

Cat

 

[Catastrophe]

Re: observable universe, I think we agree on this:

Is The Big Bang just the observable universe?

Overview. The universe's size is unknown, and it may be infinite in extent. Some parts of the universe are too far away for the light emitted since the Big Bang to have had enough time to reach Earth or space-based instruments, and therefore lie outside the observable universe.

Of course, the observable universe is specific to the observer. If a manned "voyager" left the solar system with a human passenger, he would "carry his observable universe with him".

Cat

 

[Atlan0001]

Re: observable universe, I think we agree on this:



Of course, the observable universe is specific to the observer. If a manned "voyager" left the solar system with a human passenger, he would "carry his observable universe with him".

Cat

If there was a scale of 1-10 for likes of a post, I'd give you a 10 for this one, Cat! "Carry his observable universe with him". However many words and posts I've used over years, you said it more clearly and simply than I ever have in just six words, Cat!

 

[Atlan0001]

And the beat goes on!

The Case for a Small Universe

Astronomers don't know if the Universe is finite or infinite. Whatever the case, it's larger than the Observable Universe, which measures 93 billion light-years across. A new paper proposes that the actual Universe is comparatively tiny, not much bigger than its observed size - just a few orders...

www.universetoday.com

 

[externo]

The universe is a sphere of quaternion geometry associated with the algebra of physical space (APS)

Algebra of physical space - Wikipedia

en.wikipedia.org

This geometry was invented by Hamilton in 1843 and perfected by Clifford. Hamilton said that the scalar dimension was time. Minkowski's space-time is only a mathematical fiction but the space-time of quaternions is a reality, time is the scalar dimension of space, that is to say the one which controls its density. Length contraction in relativity is one example of changing density of space-time, general relativity is another.

 

[Gibsense]

Gibsense,

This is your thread and, in your introduction, you state:



This has almost nothing to do with my interest in using a sphere (what almost everybody would understand as a sphere) in an analogy to explore the term 'universe' and some of its ramifications. Therefore, I apologise for wasting your time in posting here.

However, I would just like to ask you what prompted a thread, which seems rather esoteric, particularly when involving the flatlander concept. Whilst you have every right to post this matter here, unfortunately, it does muddy the water, causing confusion in the question of my using the sphere (I think we all know what I intended here) in the universe analogy.

Cat

I think this is a misquote or out of context. I do not recall having made the above comments. Rather, there is a missing statement i.e. something I posted, and then your subsequent response involving muddy water.
Just for the record 'esoteric' would have been appropriate for any significant advance in the last 100,000 years. Not that my suggestions are correct, but that any solution to Cosmology mysteries is likely to be considered 'esoteric' at first glance.
But thanks for the input which acts as a stimulant for thought

 

[Catastrophe]

I think this is a misquote or out of context. I do not recall having made the above comments. Rather, there is a missing statement i.e. something I posted, and then your subsequent response involving muddy water.
Just for the record 'esoteric' would have been appropriate for any significant advance in the last 100,000 years. Not that my suggestions are correct, but that any solution to Cosmology mysteries is likely to be considered 'esoteric' at first glance.
But thanks for the input which acts as a stimulant for thought

Gibsense, sorry about that. It seems my quote from your #2 (I think) got erased.
Hence the space.
All that remains is my comment, so obviously it is not recognisable.

I will see if I can find anything relevant.

Cat

 

[Gibsense]

Gibsense, sorry about that. It seems my quote from your #2 (I think) got erased.
Hence the space.
All that remains is my comment, so obviously it is not recognisable.

I will see if I can find anything relevant.

Cat

That's a relief I thought old age was catching me up faster than expected

 

[Catastrophe]

Gibsense, I think it might help if we pretended that I had not seen your posts about hyperspheres, and just wanted to explain use of my analogy, in the light of my having had it around in my head for a while now.

I mean no disrespect to your ideas. I just do not think they help in understanding what I am trying to convey. My analogy may differ slightly from your ideas - I think they are fine, but just tend to overcomplicate what I intend. In other words, I have no criticism at all regarding your 4D statements - they are just not helpful (IMHO) in my analogy.

Let us consider a mathematical sphere. Considering a bubble is not helpful, as a bubble has two surfaces containing a thin film of aqueous medium. (Water plus surfactant).

Let us, just for the sake of this analogy, consider that this sphere (surface) represents the universe for a flatlander. I have suggested elsewhere that expansion of the universe only makes sense to a being able to appreciate one more dimension than the flatlander.

Thus, considering a larger spherical surface represents the view of his universe expanding.
It is not a picture over time, per se, since time is included in the universe.
It supports my suggestion that expansion of 'our' universe can only be understood by appreciation of a higher dimension than is available to us.

There are organisms which live on water surfaces, so the idea is not so outlandish.

Floaters, sometimes called pleuston, are the organisms that live floating at the ocean surface. Numerous floating cnidarians (jellyfish) live at the ocean's surface, some famous (or infamous) and others rarely seen. Species like Velella sp.

If we use a bubble, the thickness starts causing problems which are not really relevant, but we can adjust to that if we just think there is a thickness wherein they live, if necessary.
The only point I want to make is that expansion of the universe can be better understood if we consider the abilities of a being with higher understanding of dimensions.

Is that OK?


Cat

 

[Gibsense]

Gibsense, I think it might help if we pretended that I had not seen your posts about hyperspheres, and just wanted to explain use of my analogy, in the light of my having had it around in my head for a while now.

I mean no disrespect to your ideas. I just do not think they help in understanding what I am trying to convey. My analogy may differ slightly from your ideas - I think they are fine, but just tend to overcomplicate what I intend. In other words, I have no criticism at all regarding your 4D statements - they are just not helpful (IMHO) in my analogy.

Let us consider a mathematical sphere. Considering a bubble is not helpful, as a bubble has two surfaces containing a thin film of aqueous medium. (Water plus surfactant).

Let us, just for the sake of this analogy, consider that this sphere (surface) represents the universe for a flatlander. I have suggested elsewhere that expansion of the universe only makes sense to a being able to appreciate one more dimension than the flatlander.

Thus, considering a larger spherical surface represents the view of his universe expanding.
It is not a picture over time, per se, since time is included in the universe.
It supports my suggestion that expansion of 'our' universe can only be understood by appreciation of a higher dimension than is available to us.

There are organisms which live on water surfaces, so the idea is not so outlandish.



If we use a bubble, the thickness starts causing problems which are not really relevant, but we can adjust to that if we just think there is a thickness wherein they live, if necessary.
The only point I want to make is that expansion of the universe can be better understood if we consider the abilities of a being with higher understanding of dimensions.

Is that OK?


Cat

Cat, perfect!
It makes sense.

 

[E.B.E1]

To add a more friendly description -

We can not picture a 4D spatial environment but we can still understand the situation by use of mathematics or by drawing using one dimension less. For example, a cross-section of a hypersphere is an everyday sphere. A circle is a cross-section of a 3D sphere.

We can use a circle to illustrate a hypersphere (limited to circumference but still useful). As the 3D space of a hypersphere is its surface, any distance travelled in a hypersphere 3D space is along the circumference of our drawn circle. As our perception of 4D space is limited to its effect on our 3D perception we view events occurring in our hypersphere reality as a flat 3D space.

We can illustrate this 3D interpretation by projecting from the circle (hyperspherical 4D space) to a baseline representing the diameter of the hypersphere. This provides us with a 3D view of what is 'going on'. It is worth noting (if you have bothered to draw it yourself) that at what appears to be t=0 (an origin of the BB) is in fact the event horizon of our observable universe

As we look to the event horizon the curvature of the hypersphere appears to us as if distances were shorter between events. Similarly nearby, where the hypersphere curvature appears to us as flatter. the distance between events is interpreted (on our flat baseline) as larger. This might be interpreted by us as the universe expanding faster (when this is not the case).

In addition, the belief that when 'looking out into space' we are looking back in time to the Big Bang is an error - we are looking back to the event horizon of our observable universe. The BB occurred at the origin of the hypersphere which does not exist (even back in time) in our 3D space. However, because we think the universe is flat 3D we assume that the BB is expanded to 'everywhere' but in FLAT space and then it follows that if we could see t=0 it would show the original state (or nearly). This is wrong.

The explanation is that time expands the hypersphere. The increase in radius (of the hypersphere) is felt by us as time NB you can illustrate this yourself by calculating the Hubble constant which corresponds closely to the current value.

This hypothesis even if incorrect does illustrate the importance of considering the actual SHAPE of our universe before we make assumptions about reality and 'how things work'. Also, it shows that mathematics alone needs an 'everyday' interpretation to enable easy progress. I may well have it all wrong but it shows how 'Flatlander thinking' can clear away fog and once again that the world may not be as simple as we might hope.

I hope I have not appeared too arrogant but very many years ago on similar sites to this I was 'trolled' relentlessly and I gave in trying to get the idea across. I am so grateful for the tolerance here which lets me get most of it "off my chest". Thank you.

very interesting and not at all arrogant, it's people like you who are brave enough to put forward these educated theories and ideas that help advance our understanding of the universe by getting the conversation moving forward.
Even if you're right or wrong it gets people thinking about other possibilities and probabilities that can eventually prove the truth, either way we learn from our mistakes and advance with our successes and that is what it's all about

 

[CryptoCraig]

Of course, no one knows whether the Universe will continue expanding indefinitely, whether it will reverse, and, if so, any circumstances arising at and after expansion discontinues. It may be that expansion reaches a point where atoms are all separated, or some circumstance before or after that point. Anyway, no conscious material life would be there to boil eggs.

Do you think it's possible that mass / gravity could be the determining factor of universe expansion?

Currently the universe is expanding at an accelerated rate of expansion. We can assume that at the time of BB, matter was created and began moving away from the "center" slower than now. This could be due to all matter being bunched up together? Time dilation?

As we approach the present, objects (mostly galaxies, really), are moving away from each other, seemingly faster than before due to gravity being spread out across a larger distance.

Could the acceleration of the universe's expansion be due to the mass of the universe being spread across greater distances? If this were the case, imagine that BHs simply place matter that falls through their EH back to the location of the BB. This would mean that once enough matter "falls" into BHs, the universe's expansion would slow, eventually stop and then reverse.

This theory could potentially be observed by looking at differing sized galaxies and at their relative speed.

Creating a cyclical universe. Gravitational force upon matter will pull two objects together no matter how far away they are from each other, so long as they both have mass.

So, is the universe's age 13.7 billion years old considering the effects of time dilation?

 

[Catastrophe]

CryptoCraig, welcome to the forum.

Do you think it's possible that mass / gravity could be the determining factor of universe expansion?

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