Ballon expansion vs raisin bread expansion

[enotstrebor]

Cosmological expansion is volumetric. How does a space volume expand without expanding like the raisin bread model (non-isotropic redshift). Or how do you make a space volume "naturally" behave like a balloon surface.

 

[mrspeedybob]

Ok, I just looked up the raisin bread analogy on wikipedia. I'm not sure how it differd from the baloon analogy. It looks to me like the same thing. What differences are you asking about?

 

[enotstrebor]

What differences are you asking about?

Some of the raisins in the expanding raisin bread see a non-isotropic redshift. Only the raisin in the center will see an isotropic redshift on expansion.

All raisins on the balloon surface will see an isotropic redshift. We see and isotropic redshift.

But how can a 3-D space volume expand in the same way as a 2-d surface.

 

[marcus]

Neither analogy is perfect. You have to use your imagination to move beyond the analogy in either case.

In the raisinbread dough picture, you have to think of the dough as infinite. So there is no center. Anywhere in the dough you see approximately the same picture. There is no boundary or edge of the dough. Otherwise the analogy fails and misleads you.

In the balloon model you also have to do some work. You have to imagine that reality is collapsed down to 2D. All existence is concentrated on the 2D surface. Galaxies are 2d and planets and beings living on the planets are flat 2D. They cannot point their "fingers" in any direction that is not in the 2D surface.

For them also as you pointed out there is no boundary, it is the same in all directions, from any point. (isotropic and homog.)

But once you understand a 2D expanding universe, using the balloon model, you have to work your imagination to jack the picture up to 3D.
Instead of the 2D surface of a familiar usual sphere, you have to imagine the 3D surface of a "hypersphere" the higher dim. analogy. So you think of us living in a 3D space, not able to point our fingers in any other direction. And this space is very very slightly curved so that it somehow curves back on itself, and lightray paths going off in any direction eventually circle round and return.

 

[enotstrebor]

Instead of the 2D surface of a familiar usual sphere, you have to imagine the 3D surface of a "hypersphere" the higher dim. analogy. So you think of us living in a 3D space, not able to point our fingers in any other direction. .

I will allow you to have an n-sphere (or any other geometry you chose) but the n-sphere must contain three dimensionally positioned galaxies (associated inter-galactic distance ?0-spheres?) which emit light in all three dimensional directions. Now expand your n-sphere (or whatever is equivalent) and show that for any and all galaxies the expansion results in an isotropic redshift.

Has it been done? Reference please.

 

[marcus]

I will allow you to have an n-sphere (or any other geometry you chose) but the n-sphere must contain three dimensionally positioned galaxies (associated inter-galactic distance ?0-spheres?) which emit light in all three dimensional directions. Now expand your n-sphere (or whatever is equivalent) and show that for any and all galaxies the expansion results in an isotropic redshift.

Has it been done? Reference please.

There must be some misunderstanding. As I understand it, the balloon surface is the 2-sphere and we simply raise the model up one dimension, to a 3-sphere. Lightrays follow the curved 3D surface, distances are measured along the 3D surface...

There is nothing to show. It's obvious that the expansion results in an isotropic redshift. From the standpoint of any galaxy it is obvious that the distances to neighbors in ALL directions are increasing at the same percentage rate.

It is just a simple scale-up of the figure, that proceeds continuously.

I don't understand how you have a question and think something should be "shown". Perhaps you misunderstand what we mean by a 2-sphere or a 3-sphere? The sphere is not the solid ball. We are not talking about the "inside" of the balloon. Existence is imagined to be concentrated on its 2D surface.

And we are not talking about n-spheres. Just a simple 3-sphere model. (one step up analog of the balloon.)

 

[enotstrebor]

There must be some misunderstanding. As I understand it, the balloon surface is the 2-sphere and we simply raise the model up one dimension, to a 3-sphere.

It is clear that light traveling along the original balloon dimensions results in an isotopic redshift. But light must also travels along the new (raised) dimension. This dimension must be orthogonal to the other two as it is in the real world (even if not physically but only mathematically).

Now think how this new dimension behaves. As one example: Even if this model creates balloon "2-d" surfaces as combination of any two dimensions, i.e. three balloons, the expansion of all balloons would not result in isotropic behavior.

If you don't like three balloons, you can do it with two balloons, or a balloon and a line hoop (curved space) but when you add a third dimension, universe expansion comes out non-isotropic.

Give me your own example with a third dimension added or better yet a proof reference.

 

[alt]

It is clear that light traveling along the original balloon dimensions results in an isotopic redshift. But light must also travels along the new (raised) dimension. This dimension must be orthogonal to the other two as it is in the real world (even if not physically but only mathematically).

Now think how this new dimension behaves. As one example: Even if this model creates balloon "2-d" surfaces as combination of any two dimensions, i.e. three balloons, the expansion of all balloons would not result in isotropic behavior.

If you don't like three balloons, you can do it with two balloons, or a balloon and a line hoop (curved space) but when you add a third dimension, universe expansion comes out non-isotropic.

Give me your own example with a third dimension added or better yet a proof reference.

.. the expansion of all balloons would not result in isotropic behavior..

Indeed, this is just a beautiful way to express this, what appears to be absurdity. I've often pondered this in similar ways myself.

I've been checking back here for a response and further dialogue to your above, but alas - none so far ..

 

[enotstrebor]

.. the expansion of all balloons would not result in isotropic behavior..

Indeed, this is just a beautiful way to express this, what appears to be absurdity. I've often pondered this in similar ways myself.

I've been checking back here for a response and further dialogue to your above, but alas - none so far ..

Well, maybe that says something about some people's understanding of the mathematics because you don't raise the 2-D balloon up one dimension, you raise it two dimensions, one of which is time.

After much reflection, I believe the answer is in the time aspect. Distance being measured by c, one can always vary (distort) the time line ("shape") by construction, i.e

$$ds^2 = (dt^2 - dx^2 - dy^2 - dz^2)$$
such that expansion as measured is isotropic.

Let me know if you find anything wrong with what I have said, as the people "in the know" probably no longer look at this thread.

 

[marcus]

I've been checking back here for a response and further dialogue to your above, but alas - none so far ..

... as the people "in the know" probably no longer look at this thread.

I was distracted with other stuff and missed your comments until now. Sorry for the lapse of attention. As I understand it, you like the raisin bread analogy and do not like the balloon analogy---which to me indicates that you encounter some difficulty in raising the dimension.

I'm not especially "in the know" nor am I always able to explain what I have in mind and make myself understood. I can try, but you may have to wait until someone else, here or in some other forum, responds.

For me a 1-d ring is topologically the same as an infinite straight line compactified by adjoining one point at infinity. I was taught that as undergrad in beginning topology class that all the math majors had to take.

A 2-d sphere is the same as a flat plane with point at infinity adjoined. One can even describe the mapping with a picture. Place a sphere on the plane resting with its south pole on the origin and draw a straight line from the north pole thru any given point of the sphere, onwards to the point on the plane where that point gets mapped.

I can imagine being a 2d creature living in what seems to me to be an infinite flat plane, but discovering eventually that it is a 2d sphere. A lightray sent out in any direction eventually passes thru the point at infinity and returns, having circumnavigated.

And I just carry that experience over to being a 3d creature in what seems to me to be an infinite not-curved 3d space.
And I imagine that I have discovered that the 3d flat space is actually compactified by adjoining a point at infinity. Because I send out a light ray and after a long time it comes back to me from the opposite direction.

Precisely as would happen in the 1d case or the 2d case. They give you the conceptual tools to make all that precise, define neighborhoods, continuous functions etc etc.

So this what the imaginary 3d balloon teaches me. And for me the raisin bread analogy is exactly the same as the 3d balloon analogy, if you compactify it. Locally it gives an observer the same experience of his surroundings---both are homog. and iso.

That is what I mean by "jacking up the dimension" of the analogy. I do not mean some how tacking on another dimension by hand, sticking something "orthogonal" into the balloon picture. That would be very awkward. I mean carrying over the experience of the 2d creature exploring his 2d world and imagining the same analogous experience of a 3d creature exploring a 3d world.

But certainly it is not always possible to communicate what one has in mind! It would be easier if we were in the same room together with a blackboard and I could gesture and draw pictures. Being able to draw sketches/diagrams in immediate response would be a big help. Without that, this is probably the best I can do in response. If I still don't get it across then someone else may step in and have a different more successful way of explaining.

 

[enotstrebor]

As I understand it, you like the raisin bread analogy and do not like the balloon analogy---.

In the raisin bread analogy as I know understand it was referencing the surface of the raisin bread, i.e. the same as the balloon analogy.

You can raisin some dimension or raisin some bread, but its all a Kline bottle to me.

On the serious side, I'm glad it makes sense to you and I get the gist, but I'll stick with my discovered answer until someone can give me another answer that makes sense to me.

I'm signing off this thread.

Thanks for your input.

 

[marcus]

In the raisin bread analogy as I know understand it was referencing the surface of the raisin bread, i.e. the same as the balloon analogy.
...

In the raisin bread analogy there is no surface. The dough is 3D and extends indefinitely in all directions. That is why it has no center.

It illustrates the homogeneity isotropy ideas: the same in all directions, seen from any point.

Yeast makes the dough expand and the raisins (standing for galaxies) get farther apart.

It is not the same as the balloon analogy because the latter is 2D.

 

[DavidMcC]

The problem with the raisin bread analogy is that it requires that the universe be infinite, as a previous poster mentioned. This is icompatible with its formation in a "big bang", which is big, but not infinite (IMO).
The only problem with the balloon analogy is that it is a reduced dimensionality analogy. The real universe has three dimensions, so is essentially a 3-shell in a 4-space, whereas the balloons we know are 2-shells in a 3-space. That is one reason I hold with a cosmology in which there is a 4D hyperspace supporting a 3D quantized "real space" which is finite yet unbounded, being closed, and with edges and a centre, but only in the 4D hyperspace continuum of a kind originally proposed by Ashtekar and Smolin, but then "messed up" (in diffferent ways) by both! (Ashtekar removed the hyperspace continuum and Smolin subjected the cosmology to an unrealistic analogy to biological natural selection.)
Incidentally, Ashtekar predicted the "big bounce" on the basis of a time-reversed model. This has a big flaw, and obviously misses out the rest of the initial universe - what was actually the collapse of one massive body within the earlier universe spuriously becomes the entire universe.

EDIT: I've just noticed that enotstrebor has already mentioned the 3-shell point I made above.

 

[marcus]

...Ashtekar predicted the "big bounce" on the basis of a time-reversed model. This has a big flaw, and obviously misses out the rest of the initial universe - what was actually the collapse of one massive body within the earlier universe spuriously becomes the entire universe.
...

?
I don't understand your objection.

As I recall the original result (Bojowald 2001) was not based on "time-reversal" but on numerical calculation---computer runs using a quantization of the standard Friedmann model that's basic in cosmology. It just turned out that there was a bounce, of the whole universe, not involving just "one massive body."

Is it possible that you are confusing what Ashtekar has been working on mostly since 2006, bounce cosmology, with what Smolin proposed back in 1992-1993? Smolin's CNS scenario, which he later put into a popular book circa 2000 (I think it was called Lives of the Cosmos) and which does indeed involve the collapse of a massive body, to a black hole. Loop cosmology typically does not.

Bounce cosmology as worked on by Ashtekar's group at Penn State and many others is entirely different. It has no mathematical connection with Smolin's scenario of black hole --> big bang.
Ashtekar's group revised Bojowald's 2001 model in 2006. Major improvement, almost like a complete makeover. Model has been studied in many different variations---with/without inflation, spatial finite/infinite, various types of matter, simulated numerically in computer and also formulated in solvable equations.

The bounce turns out to be rather robust. They try all these different variations (curved/flat, finite infinite, etc ) and they always get a bounce.

So it is something that can be either right or wrong, and has to be tested, which seems inherently rooted in the way they quantize the classical cosmo model. No matter what they do they do not get a singularity. When they work back into the past they get, instead, a bounce and a contracting prior classical universe.

They don't get a black hole --> big bang as in Smolin CNS. They get a whole classical U that collapses, very much like the "big crunch" we used to hear about, but at the last minute due to quantum corrections to gravity, gravity becomes repellent and it it bounces. Incidentally causing a brief "super-inflation" episode, that sets the stage for a regular inflation if the right matter field is present.

If traces of this bounce are not found in the ancient CMB light it will be a serious blow to Ashtekar's program. Essentially it would shoot down the Loop approach to cosmology, because the bounce result has been so thoroughly studied in that model for so long. At least since 2006, and with the earlier Bojowald version going back to 2001.

So what is the "flaw"?

 

[Chronos]

The 'raisan bread' analogy is merely a dumbed down [layman] explanation for expansion. It should not be construed as holding deeper meaning.

 

[DavidMcC]

Marcus, I think you'll find that Ashtekar's original simulation result that produced the "big bounce" was a time reversed one. I'll try to find the reference if you want.

 

[DavidMcC]

Marcus: "Bounce cosmology as worked on by Ashtekar's group at Penn State and many others is entirely different. It has no mathematical connection with Smolin's scenario of black hole --> big bang.
Ashtekar's group revised Bojowald's 2001 model in 2006. Major improvement, almost like a complete makeover. Model has been studied in many different variations---with/without inflation, spatial finite/infinite, various types of matter, simulated numerically in computer and also formulated in solvable equations.

The bounce turns out to be rather robust. They try all these different variations (curved/flat, finite infinite, etc ) and they always get a bounce.

So it is something that can be either right or wrong, and has to be tested, which seems inherently rooted in the way they quantize the classical cosmo model. No matter what they do they do not get a singularity. When they work back into the past they get, instead, a bounce and a contracting prior classical universe."

What I am saying, marcus, is that both Ashtekar ans Smolin created artifacts in their cosmologies by their different versions of LQG. Ashtekar dropped the hyperspace continuum, and consequently could not predict a multiverse, only a "big bounce". Smolin initially realized that LQG could predict a multiverse, but then dropped the whoe idea by introducing the spurious concept of "natural selection" of BHs.
The one thing they were both surely correct about was that they didn't get a mathematical singularity. But they could have gone further than that, IMO.
ASI said before, I'm also sure that the bounce was a spurious result, caused by working backwards from only a small part of the original universe - that is the part that formed ours, which is why it only seemed like a bounce of "everything".

 

[Chronos]

DavidMcC, your version of the universe is inconsistent with current mathematical and observational evidence.

 

[DavidMcC]

In what way, Chronos?

 

[DavidMcC]

Actually, Chronos, there is no such thing as "mathematical evidence". There is only observational evidence, and "my version of the universe" is the only one that I know of that is capable of describing the universe as we observe it. It allows for something akin to string theory for particles, except that it provides something to anchor the "strings" to. Other models have to be content with such assertions as "inflation must have happened, otherwise the universe wouldn't be uniform on a large scale", etc. Hardly an explanation.

 

[DavidMcC]

Marcus: "They don't get a black hole --> big bang as in Smolin CNS. They get a whole classical U that collapses, very much like the "big crunch" we used to hear about, but at the last minute due to quantum corrections to gravity, gravity becomes repellent and it it bounces. Incidentally causing a brief "super-inflation" episode, that sets the stage for a regular inflation if the right matter field is present.

If traces of this bounce are not found in the ancient CMB light it will be a serious blow to Ashtekar's program. Essentially it would shoot down the Loop approach to cosmology, because the bounce result has been so thoroughly studied in that model for so long. At least since 2006, and with the earlier Bojowald version going back to 2001.

So what is the "flaw"? "
I'm pretty sure that the fatal flaw in Ashtekar's cosmology is dropping the hyperspace continuum from the model. So near, yet so far, you might say! See some of my previous posts on the subject. (Unfortunately, they are rather spread out, among the large number of related threads on this site, each one starting with one specific issue that raises the big issue of what is space.)

 

[DavidMcC]

Another aspect of the "big bounce" is something I haven't been able to find: what was the minimum size of the universe? If it was less than its own Schwarzschild radius, then it must have become a black hole before re-expanding! If that had happened, it might also have been embarrassing for the author to mention the actuakl suize, even though he must have known it from the modelling results.

 

[marcus]

I'm pretty sure that the fatal flaw in Ashtekar's cosmology is dropping the hyperspace continuum from the model...

Unfortunately I don't know what you mean by "dropping the hyperspace continuum". I don't see any paper by Ashtekar where he "drops the h. c." Do you know of such a paper?

Also I still have to ask the same question "what fatal flaw?". It has not yet been shown that Asht. cosmology is flawed. It makes testable predictions. These have not yet been shown wrong.

So far there is no scientific evidence for any of the various "multiverse" fantasies. No rational basis to assume any of them are right. So far they are just stuff that various people have dreamed up. As far as I can tell from looking at your posts you seem to take some "multiverse" idea seriously. This makes me dubious of your other statements, David. Maybe you should start a thread on the topic "scientific evidence of a multiverse" and let people comment both credulously and skeptically---both pro and con. It could be educational, might make an interesting thread.

 

[Chronos]

Actually, Chronos, there is no such thing as "mathematical evidence"...

Surely you jest, there is plenty of 'mathematical evidence' supporting LCDM. Are you saying FLRW is unsound? Mathematical vetting is as important as observational evidence in modern cosmology.

 

[DavidMcC]

Unfortunately I don't know what you mean by "dropping the hyperspace continuum". I don't see any paper by Ashtekar where he "drops the h. c." Do you know of such a paper?

Also I still have to ask the same question "what fatal flaw?".

It has not yet been shown that Asht. cosmology is flawed. It makes testable predictions. These have not yet been shown wrong.
So far there is no scientific evidence for any of the various "multiverse" fantasies. No rational basis to assume any of them are right. So far they are just stuff that various people have dreamed up. As far as I can tell from looking at your posts you seem to take some "multiverse" idea seriously. This makes me dubious of your other statements, David. Maybe you should start a thread on the topic "scientific evidence of a multiverse" and let people comment both credulously and skeptically---both pro and con. It could be educational, might make an interesting thread.

http://www.thefullwiki.org/Loop_quantum_gravity"
"In general relativity, the Einstein field equations assign a geometry (via a metric) to space-time. Before this, there is no physical notion of distance or time measurements. In this sense, general relativity is said to be background independent. An immediate conceptual issue that arises is that the usual framework of quantum mechanics, including quantum field theory, relies on a reference (background) space-time. Therefore, one approach to finding a quantum theory of gravity is to understand how to do quantum mechanics without relying on such a background; this is the approach of the canonical quantization/loop quantum gravity/spin foam approaches."

I take this to mean "no hyperspace continuum", which would be consistent with the "big bounce" instead of the generation of new space.
The real answer to that problem is that excitations of loops pass from one loop to another without energy input (just as the energy of, say, linked pendula passes from one to the next), so that the background disappears from measurements anyway.
All but one of the "various multiverse theories" are, indeed, fantasies. However, that leaves one, based on Smolin's "fecund universes", which may not have been linked to LQG in the the author's mind, but was in reality, IMO, because it provides a mechanism for the non-visibility of one universe from another. This makes it all the more convincing, as it meant that it wasn't contrived just for the purpose.
Another fantasy is that there was only one big bang, when this is a natural process. Insisting that there was only ever one is a bit like insisting that there is only one star in the universe, and all those points of light in the sky are just holes in the crystal spheres! Fortunately, as I've said on other threads, there are hints of other universes in just about all of the major results of astronomy and cosmology and even particle physics (slight lack of charge-parity symmetry), so it is out of date to dismiss them as "just a fantasy".

 

[DavidMcC]

PS, I still haven't found out to what size the universe was supposed to have collapsed before "bouncing back". This is crucial, because it determines whether it had become a black hole (ie was smaller than its own Swarzchild radius) during the bounce.

Also, I haven't started my own thread because most of the existing threads raise relevant issues in any case, even if not everyone realizes it.

 

[DavidMcC]

Surely you jest, there is plenty of 'mathematical evidence' supporting LCDM. Are you saying FLRW is unsound? Mathematical vetting is as important as observational evidence in modern cosmology.

Vetting isn't of itself evidence. Mathematics is only a tool with which to express a model to discover how well it fits the actual evidence. It's a point of principle, and nothing to do with specific models. Mixing up different concepts only leads to confusion, IMO.