The balloon analogy is a 2D example of our 3D world. In the balloon analogy, we live on the surface -- there is no inside! The actual universe would be the surface of a 3-sphere.ThomasT said:So I guess I just don't get why such a strange analogy is necessary. If the universe is a 3D structure, and if it's expanding like an inflating balloon, then it's both bounded and finite. And we're not on its surface, we're inside it.
That makes no sense.bapowell said:The balloon analogy is a 2D example of our 3D world. In the balloon analogy, we live on the surface -- there is no inside!
No. You're not getting that the balloon is a 2D analogy of a 3D space.ThomasT said:That makes no sense.
If we're assuming that the universe is 3D and bounded and expanding isotropically, more or less like an inflating balloon, then we'd be part of all the stuff that's happening inside the balloon, not on its surface,
I get that. I just don't understand why it's necessary.DaveC426913 said:No. You're not getting that the balloon is a 2D analogy of a 3D space.
Yes, but if we're assuming that we live inside an expanding 3D volume, then I don't get why it's necessary to talk about it in terms of us living on the surface of a 2D sphere. Is it generally thought that this makes the expansion and what it entails easier to understand? Why isn't it understandable (or less understandable) describing it in 3D terms?DaveC426913 said:For an ant living on the surface of the balloon, it is not expanding from its centre - he knows nothing of a "centre" of a 3D balloon, he knows only the 2D surface he lives on - and the surface he lives on is simply getting larger in all directions equally.
That's what I'm asking. How is it known that the 3D volume that's our universe doesn't have a boundary? What does it mean, in 3D terms not a 2D analogy, to say that a volume is finite but not bounded? Is it actually known that traveling in a straight line will bring one back to the point of origin, or is this just a byproduct of the geometry that's used? Is it possible that our universe can be described in 3D Euclidian geometry? Because that's is how I'm thinking about it. I think of the curved space geometry as a simplification of the effects of wave mechanics happening in a 3D Euclidian space. Is it possible that the boundary of our universe is an expanding wave shell (maybe more or less spherical) in 3D Euclidian space, and that the material universe of our experience is the more or less persistent wave structures that have emerged in its wake?DaveC426913 said:In our 3D universe, the same thing happens - the volume expands without a boundary.
Because it's easier to visualize a 2-sphere expanding in 3-space than to visualize the actual universe, which would be the surface of a 3-sphere expanding in 4-space (although as DaveC pointed out -- you don't actually need this higher dimensional space). The surface of a 3-sphere is finite but unbounded.ThomasT said:Yes, but if we're assuming that we live inside an expanding 3D volume, then I don't get why it's necessary to talk about it in terms of us living on the surface of a 2D sphere.
How is it known that the 'actual universe' is in 4D Euclidian space? Why not just the regular, visualizable 3D Euclidian space of our experience, where we would be part of the interior volume bounded by a 2D shell?bapowell said:Because it's easier to visualize a 2-sphere expanding in 3-space than to visualize the actual universe, which would be the surface of a 3-sphere expanding in 4-space (although as DaveC pointed out -- you don't actually need this higher dimensional space).
But not 3 dimensional ones, right? So why can't we envision our universe as a 3 dimensional object expanding in the 3 dimensional space of our experience, while regarding the 4-space as a mathematical contrivance for the purpose of calculating and predicting gravitational behavior.bapowell said:I don't know about you, but I have a hard time visualizing 4 dimensional objects.
Thanks for your input/feedback, but this isn't addressing my questions. Please see my previous post (#43).bapowell said:Because *if* the universe is a sphere, then it does not have the topology of ordinary 3D Euclidean space. It has the topology of a sphere, a 3-sphere to be exact. Most people have a hard time visualizing the surface of a 3-sphere, since it is 3D space with nontrivial topology. Hence the balloon analogy -- it let's us visualize the correct topology of the universe by reducing the dimensionality to something the brain can digest.
Because the region you are proposing does not have spherical topology. A positively curved 3D universe has the shape of a 3-sphere, with the 3D universe corresponding to the surface of the sphere.ThomasT said:How is it known that the 'actual universe' is in 4D Euclidian space? Why not just the regular, visualizable 3D Euclidian space of our experience, where we would be part of the interior volume bounded by a 2D shell?
The 4-space is indeed mathematically superfluous, but it helps us visualize. Here's an example: a torus is readily visualized as the 2D surface of a donut. We can easily visualize the torus by picturing a donut in everyday 3D space. But we don't need the 3rd dimension -- we can define a torus using only 2 dimensions by starting with a 2D surface and assigning rules for how the edges are to be connected (think of the Asteroids Atari game -- that is an example of bona fide toroidal topology, and it is perfectly defined on just your 2D screen.) So, getting back to the universe. Supposing that the universe is positively curved and has 3 spatial dimensions, then we are dealing with a 3D volume that has spherical topology. Geometrically, this is the surface of a 3-sphere. Now, we don't need the 4th dimension to fully define the topology or geometry (just as we didn't need the 3rd for the torus), but it helps us visualize -- especially since the 4D space becomes the 3D ambient space when we consider the balloon analogy.But not 3 dimensional ones, right? So why can't we envision our universe as a 3 dimensional object expanding in the 3 dimensional space of our experience, while regarding the 4-space as a mathematical contrivance for the purpose of calculating and predicting gravitational behavior.
That clarifies why we've been sort of 'talking past' each other.bapowell said:... keep in mind that this discussion assumes from the outset that the universe is globally positively curved ...
Ok, so can we assume that our universe is described by flat 3D Euclidian space -- the interior volume of an expanding wave shell?bapowell said:... it might not be.
If the curvature index is zero then you can assume the universe is described by Euclidean 4 - space but, even if it is the most likely, this is still an assumption as there are other 4 - manifolds that are flat but do not have the same topology as Euclidean 4 - space.ThomasT said:That clarifies why we've been sort of 'talking past' each other.
Ok, so can we assume that our universe is described by flat 3D Euclidian space -- the interior volume of an expanding wave shell?
If so, then it would seem to be visualizable with no need for spherical surface analogies.
Except you don't need the 4-space -- Euclidean 3-space is sufficient to describe a flat expanding cosmology (with trivial topology).WannabeNewton said:If the curvature index is zero then you can assume the universe is described by Euclidean 4 - space but, even if it is the most likely, this is still an assumption as there are other 4 - manifolds that are flat but do not have the same topology as Euclidean 4 - space.
bapowell said:Except you don't need the 4-space -- Euclidean 3-space is sufficient to describe a flat expanding cosmology (with trivial topology).
We've been discussing the spatial part of the geometry in this discussion! Sorry if that was not made clear. But yes, good catch!WannabeNewton said:That is what I don't get. The Friedmann metric with k = 0 involves Euclidean 4 - space and Euclidean 3 - space would be a space - like hypersurface of it so how is it sufficient to describe an expanding cosmology with nothing but that space - like hypersurface?
Chronos said:You need not know how big the universe is to realize it is expanding. Einstein deduced the universe could not be static, it had to either be expanding or contracting. Hubble confirmed it was indeed expanding, causing Einstein to commit his biggest blunder - withdrawing his cosmological constant idea.
GODISMYSHADOW said:Does that say anything about the Schwarzschild radius? If we observe the universe is expanding, does that mean we're not sitting in a black hole?
What does it mean for space-time to have density?Physics_Kid said:are there any consequences (in math or physics) for space-time to become infinitely less dense?
Physics_Kid said:are there any consequences (in math or physics) for space-time to become infinitely less dense?
is it possible that the uverse (however its mechanics are defined) has fixed density?
bapowell said:What does it mean for space-time to have density?
are we sure? i mean, if you lasso the uverse you are essentially lasso'ing what we know as space-time. perhaps time itself has no relationship to "density", but it is related to the universe as a whole? can time extend past the edges of the unverse?Chronos said:It means nothing.
Physics_Kid said:are we sure? i mean, if you lasso the uverse you are essentially lasso'ing what we know as space-time.
perhaps time itself has no relationship to "density", but it is related to the universe as a whole? can time extend past the edges of the unverse?
but, to my question, any implications for density to become infinitely small?
Chronos said:You need not know how big the universe is to realize it is expanding. Einstein deduced the universe could not be static, it had to either be expanding or contracting. Hubble confirmed it was indeed expanding, causing Einstein to commit his biggest blunder - withdrawing his cosmological constant idea.
The "constant" in the "cosmological constant" is not in reference to the expansion rate -- it refers to the fact that it appears as a constant (times the metric tensor) in the Einstein Equations. This means that it behaves as a constant energy density. A constant energy density results in an accelerating spacetime. Due to the recentish discovery that the universe is in fact presently accelerating, there is renewed interest in the potential presence of a cosmological constant.Akaisora said:So that idea has been debunked? The universe expands at a changing rate instead of a static constant? Could it be something related to the distribution of energy and mass?
dexterdev said:If something is expanding...what is there there outside of the expansion volume...
i think you have written a real catch-22/enigma. for anyone to say "its expanding" that implies you are able to measure the boundaries at least twice. but here you say there are no edges, so how is it possible to conclude expansion?Drakkith said:There are no edges to the universe as far as we know.
A balloon can expand, and this can be measured by assessing the growth in distance between points fixed to the balloon, and yet it has no edges.Physics_Kid said:i think you have written a real catch-22/enigma. for anyone to say "its expanding" that implies you are able to measure the boundaries at least twice. but here you say there are no edges, so how is it possible to conclude expansion?
Physics_Kid said:i think you have written a real catch-22/enigma. for anyone to say "its expanding" that implies you are able to measure the boundaries at least twice. but here you say there are no edges, so how is it possible to conclude expansion?
i know we have indirect measurements of very far away stuff seemingly moving away at very high speeds, but this alone cannot conclude expansion, because after-all, space itself may just be a really really big thing and we can only observe small pieces of things inside moving around...?
Drakkith said:No, it implies that we are able to make a measurement of objects within expanding space.
Science disagrees. Would you like to know why?
bapowell said:A balloon can expand, and this can be measured by assessing the growth in distance between points fixed to the balloon, and yet it has no edges.
bapowell said:The balloon analogy is a 2D example of our 3D world. In the balloon analogy, we live on the surface -- there is no inside! The actual universe would be the surface of a 3-sphere.