Size of the universe and the boundary problem

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STT said:
Here we discuss the fact that the size of universe is infinite otherwise we face a problem. Lets define the volume of the universe to be V, its boundary to be B and its shape to be S. Whatever the V, B and S are we need to embed the universe inside another thing. Lets call this as anther universe with volume of V’, boundary of B’ and shape of S’. It is obvious that we have the same problem with the second universe as we had with the first one, namely we have to embed it in another universe. This process has to be continued until there is no need for embedding any longer which means that the size of final universe must be infinite. It is obvious that we get ride boundary problem by sending the boundary to infinity.
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Matter is finite. Space cannot exist without matter. So the universe is finite.

Infinity only exists as an abstract concept.
 
yppop said:
TaM
Thank you for the unusual (for this forum) request for more information instead of the usual disputatious response, but could you be more specific?
Yppop
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🙂 Why is physical space discrete? Zero plus zero is zero. Or is it? “discrete space is defined by the rational numbers and continuous space defined by the real numbers.” Why?

Cool stuff
 
yppop said:
TaM
Thank you for the unusual (for this forum) request for more information instead of the usual disputatious response, but could you be more specific?
Yppop
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Here is a quote of some of what you wrote:
yppop said:
SST
It doesn’t take much imagination to figure this out.
… The “physical” space that defines the dimensions of the universe is discrete; the “abstract” space that defines the before/beyond is continuous.
Yppop
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How do you know that the space of this universe is discrete but that the space beyond is continuous? How do you reconcile General Relativity with a quantized view of space time?
 
I haven’t read all of the other responses, but regarding the OP:

Why is it assumed that the universe must be embedded in a larger setting? I understand that this would make the universe easier to visualize, but the inability to visualize a model doesn’t discredit the model.
 
edwest2 said:
E) Assuming a boundary, it may be reflective. Take the air inside a balloon and replace it with galaxies and energy. Like atoms of air, the galaxies reach the boundary and rebound back into the universe. Not because the boundary is made of a flexible material like a balloon but because the galaxies are deflected by the edge since it contains enough energy to cause the deflection. Perhaps like a charge difference or polarity difference. The alternative would be the boundary has accumulated so much energy that complete disintegration occurs, perhaps leaving behind some energy.
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I like to think of our universe being more like the surface of a balloon, not the air inside. Just like a balloon, the surface expands. If you put dots on a balloon, then expand it further, the dots get further apart. That is because space is expanding, not because they’re moving. Now certainly the objects in the galaxy do have local motion, but when people say the universe is expanding they don’t just mean the limit is growing, or that things are just drifting apart, they mean that the space between points is actually stretching like the surface of a balloon.

Now, I think the model that best fits the evidence is a universe with a curvature of 0, but that statement can be misleading, as you can have a closed surface that has a curvature of 0, even if it’s not 0 at all oval points. I believe a higher dimensional sphere does not fit this model, but that’s not the only closed, bounded manifold out there.

I did some very basic research into manifolds and topology a few years ago. Things are a little fuzzy now. Still, there are some great ways to project something as simple as a 3-sphere (3D surface bounding a 4D space) into 3D to make it comprehensible, without getting a weird rotation “slice” of a shape that makes the eyes hurt.

But I think STT’s point is that if the universe is a surface in any way then what type of space does it bound or exist in? Isn’t that some higher universe? Conceptually, trying to visualize it, it’s easy to come to that conclusion, but I’m not sure it’s necessary to hold that there is anything (even space) being bounded here, or space outside.
 
twf said:
There are various models. Some assume an infinite universe and others a finite universe. To understand either would, I think, require a PhD in astrophysics or equivalent knowledge / study. I won’t pretend that I can contribute to such a discussion.
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👍 Me either, but isn’t it interesting to think about it???
 
edwest2 said:
D) Infinity means infinity. Infinity times infinity does not yield a greater number or distance.
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Infinity to the infinity yields a greater number. The infinity of the reals is greater than that of the natural numbers.
 
edwest2 said:
A) The size of the universe is unknown. Even the last Hubble deep space image showed faint galaxies in the background.

B) Nothing cannot exist. The absence of all the things we recognize in the universe cannot exist and as far as anyone knows, cannot be known.

C) Our galaxy could be in the middle of the universe or near an edge, but what lies beyond that edge is unknown.

D) Infinity means infinity. Infinity times infinity does not yield a greater number or distance.

E) Assuming a boundary, it may be reflective. Take the air inside a balloon and replace it with galaxies and energy. Like atoms of air, the galaxies reach the boundary and rebound back into the universe. Not because the boundary is made of a flexible material like a balloon but because the galaxies are deflected by the edge since it contains enough energy to cause the deflection. Perhaps like a charge difference or polarity difference. The alternative would be the boundary has accumulated so much energy that complete disintegration occurs, perhaps leaving behind some energy.

Ed
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A boundary is something which separate two geometrical shapes from each other. If that is true then you have something inside the balloon and something outside the balloon. All I am saying is that the size of out side of the balloon should be infinite in order to get rid of boundary otherwise the balloon should be inside something else.
 
Oreoracle said:
I haven’t read all of the other responses, but regarding the OP:

Why is it assumed that the universe must be embedded in a larger setting? I understand that this would make the universe easier to visualize, but the inability to visualize a model doesn’t discredit the model.
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Visualization is part of reality. Isn’t it?
 
Wesrock said:
I like to think of our universe being more like the surface of a balloon, not the air inside. Just like a balloon, the surface expands. If you put dots on a balloon, then expand it further, the dots get further apart. That is because space is expanding, not because they’re moving. Now certainly the objects in the galaxy do have local motion, but when people say the universe is expanding they don’t just mean the limit is growing, or that things are just drifting apart, they mean that the space between points is actually stretching like the surface of a balloon.

Now, I think the model that best fits the evidence is a universe with a curvature of 0, but that statement can be misleading, as you can have a closed surface that has a curvature of 0, even if it’s not 0 at all oval points. I believe a higher dimensional sphere does not fit this model, but that’s not the only closed, bounded manifold out there.

I did some very basic research into manifolds and topology a few years ago. Things are a little fuzzy now. Still, there are some great ways to project something as simple as a 3-sphere (3D surface bounding a 4D space) into 3D to make it comprehensible, without getting a weird rotation “slice” of a shape that makes the eyes hurt.

But I think STT’s point is that if the universe is a surface in any way then what type of space does it bound or exist in? Isn’t that some higher universe? Conceptually, trying to visualize it, it’s easy to come to that conclusion, but I’m not sure it’s necessary to hold that there is anything (even space) being bounded here, or space outside.
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Can you in most simplistic case define the tangent of a curve on a given point without embedding the curve inside a 2D surface? tan(x)=dy(x)/dx.
 
I read a physicist/mathematician who said it is possible to have something approaching a point forever but never reaching it. Maybe we can weed this into the conversation?
 
thinkandmull said:
I read a physicist/mathematician who said it is possible to have something approaching a point forever but never reaching it. Maybe we can weed this into the conversation?
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Nooooo! I am being pulled into a black hole!
Are you really? You just froze near the event horizon.
 
STT said:
That is interesting. What do you think of post #33?
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The blind have a view of reality even though they lack sight. Those of us with sight do tend to
visualize things, but it becomes difficult when more dimensions are needed, say for example, with the Klein bottle, the clifford torus, exotic spheres, etc.
 
Can anyone explain what it means to be physically finite. Every object has an infinity if points
 
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