We currently do not know how to define the ‘outer edge’ of the cosmos, but I would say it’s where light goes and matter follows.
I should make it clear that the Universe being flat tells us nothing about the size of the Universe.
The Universe is infinite in the sense that it is not a closed ball, or more accurately, positively curved.
We know the Universe isn't infinitely old. Light from the Big Bang has had only 13.8 billion years to travel.
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All baffling stuff. The Torus or Donut is apparently one of 18 flat shapes that can exist in 4D according to mathematicians.
I know it doesn't look flat from the outside, but its different if you are on the surface of it.
We have discussed the mysteries of Gaussian Curvature before. Somehow if you look far enough with a lot of these flat shapes, you might see the back of your head.
Or come back to where you started from. So us ants can tell something about what we live on by crawling around and doing observations.
https://www.scientificamerican.com/article/how-many-holes-does-the-universe-have/
But it answered @Bonsai in his previous musings about the matter distribution within the +300,000 year Cosmic Microwave Background radius:
Matter all the way back to the CMB and beyond!
I downloaded the (old) Grisha Perelman 2008 paper, and it was totally beyond me.
I think cutting the grass will be a better use of my time today. I am assuming the back lawn is this shape:
Here goes. I will report any surprises. 🙂
Best, Steve.
I know it doesn't look flat from the outside, but its different if you are on the surface of it.
We have discussed the mysteries of Gaussian Curvature before. Somehow if you look far enough with a lot of these flat shapes, you might see the back of your head.
Or come back to where you started from. So us ants can tell something about what we live on by crawling around and doing observations.
https://www.scientificamerican.com/article/how-many-holes-does-the-universe-have/
But it answered @Bonsai in his previous musings about the matter distribution within the +300,000 year Cosmic Microwave Background radius:
Matter all the way back to the CMB and beyond!
I downloaded the (old) Grisha Perelman 2008 paper, and it was totally beyond me.
I think cutting the grass will be a better use of my time today. I am assuming the back lawn is this shape:
Here goes. I will report any surprises. 🙂
Best, Steve.
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I'm still none the wiser! 🙂
It reads to me as if you regard the Big Band as an explosion where radiation and matter spread out from a central point toward an 'outer edge'.
Instead, the Big Bang occurred everywhere in space at once, there is no 'outer edge'.
Light travels towards us from the space outside of our observable Universe, but it simply has not yet had enough time to reach us.
“It reads to me as if you regard the Big Band as an explosion where radiation and matter spread out from a central point toward an 'outer edge'.”
I am not saying that and since we have touched on this in previous exchanges, you know that is not my understanding.
If the cosmos has expanded, as the cosmologists tell us it has, then there must be an outer bound. Whether this is closed and takes one of the forms Steve alluded to, or some as yet unknown shape, we don’t know. We can never observe the universe from ‘outside’ but if it’s expanding the the difference between its previous size and some later, expanded size must have been the difference in the outer bounds.
I suspect as something approaches c, or moves at c (photon), time and space take on some strange properties per SR, so the shape of the universe will indeed be complex and dependent upon the observers POV and the velocity of what is being observed.
I am not saying that and since we have touched on this in previous exchanges, you know that is not my understanding.
If the cosmos has expanded, as the cosmologists tell us it has, then there must be an outer bound. Whether this is closed and takes one of the forms Steve alluded to, or some as yet unknown shape, we don’t know. We can never observe the universe from ‘outside’ but if it’s expanding the the difference between its previous size and some later, expanded size must have been the difference in the outer bounds.
I suspect as something approaches c, or moves at c (photon), time and space take on some strange properties per SR, so the shape of the universe will indeed be complex and dependent upon the observers POV and the velocity of what is being observed.
The inflation was "everywhere" but not the big bang - it had a centre... I'm mean, for sure... because all matter was in a ping pong ball - how could it not have a centre?
//
The mathematical description of the expansion of the Universe does not require it to have an edge or anything for it to expand into.
The mathematics is simple - the Universe gets bigger with time - and that's it.
It's a concept we may all have trouble wrapping our heads around.
https://www.space.com/33005-where-is-the-universes-edge-op-ed.html
We’re back to the time thing again Galu. And the fact it’s given short shrift in some people’s view of things only makes a description of what is going on more difficult. Is the universe getting bigger because distances are getting bigger, or is it time that’s getting bigger? For things moving at or near c, time and therefore distance have little or no meaning. So where does that leave us if whole galaxies are moving at c at what we perceive is the edge of the observable universe.
Jings, crivvens and help ma boab, more googling for me to do! 😉
In his doctrine of transcendental idealism, Kant argued that space and time are mere "forms of intuition" that structure all experience and that the objects of experience are mere "appearances". The nature of things as they are in themselves is unknowable to us.
People have been known to call me a Kant!
In his doctrine of transcendental idealism, Kant argued that space and time are mere "forms of intuition" that structure all experience and that the objects of experience are mere "appearances". The nature of things as they are in themselves is unknowable to us.
People have been known to call me a Kant!
This situation is described by general relativity, which allows the separation between two distant galaxies to increase faster than the speed of light.
I think I explained recently that the galaxies themselves are not moving at or beyond the speed of light in their local frame of reference and therefore time and distance continue to have the usual meaning for them.
OK, I obviously couldn't get my head round the concept of time getting bigger so concentrated on "if whole galaxies are moving at c" instead.
The distances between coordinate points in expanding space are getting bigger. That's all I know.
Oh yes it is!
But you have to make it yourself: https://www.bmstores.co.uk/recipes/giant-crunchie-bar
Time and distance [space] are intermingled. I suspect Einstein couldn’t untangle the two, so settled on space time. A bit like ‘energy time’ you can’t treat them as separate things beyond a certain point. Paradoxes they shall remain.
Back on Planet Earth, I got a good enough shot under clouds to say No Nova tonight:
The toroidal idea isn't bad at all. You just have to extend it to a 3D surface in your imagination:
https://evolvingsouls.com/blog/toroidal-universe/
What would that look like to us, living on it?
An illustration would be good, but I'm not making one, at least tonight.
Think of us living at the South Pole of a 2-sphere and looking toward the North pole, in any direction you like as it works out.
In the far distance you will see the Cosmic Microwave Background like the edge of the North Pole ice sheet.
As the sphere gets bigger, the CMB gets further away in time and distance, relatively smaller compared to the sphere, and more redshifted.
But the neat thing is it looks like the CMB is in every direction you look. Which is to say it would look exactly like our Universe!
But remember, we are talking a 2D analog of a 3D situation here.
Frankly, I amaze myself sometimes. 😆
Best, Steve.
The toroidal idea isn't bad at all. You just have to extend it to a 3D surface in your imagination:
https://evolvingsouls.com/blog/toroidal-universe/
What would that look like to us, living on it?
An illustration would be good, but I'm not making one, at least tonight.
Think of us living at the South Pole of a 2-sphere and looking toward the North pole, in any direction you like as it works out.
In the far distance you will see the Cosmic Microwave Background like the edge of the North Pole ice sheet.
As the sphere gets bigger, the CMB gets further away in time and distance, relatively smaller compared to the sphere, and more redshifted.
But the neat thing is it looks like the CMB is in every direction you look. Which is to say it would look exactly like our Universe!
But remember, we are talking a 2D analog of a 3D situation here.
Frankly, I amaze myself sometimes. 😆
Best, Steve.
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