Effort to get us all on the same page (balloon analogy)

[StandardsGuy]

Getting me on the same page may take some doing if it means that I will have the same opinons as everyone else.

"To move on to the main course, here is Ned Wright's page with the balloon analogy animation"

The thing that bothers me about this site is that he says the galaxies are not expanding. I have a problem with that as there is a lot of space inside of one. What evidence is there that they are "bound"? Is that opinion part of the "Standard model" that I am supposed to accept?

 

[marcus]

What evidence is there that they are "bound"? Is that opinion part of the "Standard model" that I am supposed to accept?

Read the first 10 or 20 posts on this thread. I never say that space expands. Distances between widely separated observers each at rest relative to the Background do increase. That is Hubble law. It's about geometry, not about some substance called "space".

The solar system planets are in stable orbit around sun, no reason they should get farther.

The stars in Milky are in orbit around milky center. No reason for them to get farther.

Just because Milky has space in it is no reason for it to expand. Where do you get this idea? Could it maybe be popular science journalism ?

"Bound" which you put quotes around is a simple basic physics idea, it just means gravitationally bound, like in stable orbits, like planets and stars. Likw ir would take a big effort to drag them apart. It is not an opinion Guy. It is obvious from looking at these structures that they have gathered together into some semipermanent collective form.

Getting me on the same page may take some doing if it means that I will have the same opinons as everyone else.

"To move on to the main course, here is Ned Wright's page with the balloon analogy animation"

The thing that bothers me about this site is that he says the galaxies are not expanding. I have a problem with that as there is a lot of space inside of one.

Ned Wright is telling you straight. There is no reason connected with Big Bang cosmology that the galaxies should expand. They don't expand. If you have the notion that they should then you are confused and need to dump that idea.

You don't have to adopt OPINIONS, Guy. We are talking fairly simple straightforward stuff. Once you dump some misconceptions you will be fine. Please to go watch Ned's animation. He is giving the straight dope and it's real helpful.

 

[StandardsGuy]

The basic purpose of a thread like this would be achievable if new arrivals at the forum would read it (or a few posts containing a condensed version) before posting and would get free of some common misconceptions about the standard cosmology model. The standard should be like a home base point of reference. If you are going to explore alternatives at least first understand the common home ground from which you consciously deviate...

We don't know whether universe is spatial finite or infinite but the balloon analogy is a good teacher in either case. Infinite means think of a much bigger balloon. Or of zooming in so close that the balloon you have looks flat, as it would to a very tiny observer. All the analogy is supposed to be is an approximation to help with visualizing, so the balloon's finiteness shouldn't be a problem...
.

I am familiar with the LCDM model (standard model?), having made a 4-part summary of it on another forum. I must disagree with the second paragraph above. If the universe is infinite, then the balloon analogy fails, because then (as I see it) all points in the universe would not be equal to each other like the surface of a balloon, in fact it would be flat. The philosophical differences are huge.

 

[TalonD]

Well that brings up an interesting thought experiment and a question or three.
Suppose there is no gravity, well let's allow just enough to bind the gas of stars together to continue fusion, but no gravity to bind stars into galaxies, would galaxies then begin to expand and dissipate? or does expansion not operate on that small a scale?
I asked the question once before, what is it that is expanding? And the answer seems to be that all we can say is that there is a pattern of increasing distances.
Another question I have is.. if space can curve (GR) then why can't it's linear dimensions expand or lengthen? How do you know that's not what's happening? Obviously something is happening... Isn't it all just geometry?

 

[marcus]

...If the universe is infinite, then (as I see it) all points in the universe would not be equal to each other ...The philosophical differences are huge.

Why in Heaven's name, Guy? Why in a spatial flat infinite universe with matter more or less evenly distributed throughout, why in that picture is any point special?

You amaze me. I have never heard anybody draw that conclusion from the given assumptions. Why would the points all be more or less equal? Like on the balloon. Tell me what point would be distinguished or special in some way!

If you can not point to a special point, then I would say that the philosophical ridiculousness is huge.

 

[StandardsGuy]

You essentially called me an idiot here. What a way to welcome a "newbie"! I thought about reporting you, but decided to debate the issues instead.

Read the first 10 or 20 posts on this thread. I never say that space expands. Distances between widely separated observers each at rest relative to the Background do increase. That is Hubble law. It's about geometry, not about some substance called "space".

The solar system planets are in stable orbit around sun, no reason they should get farther.

The stars in Milky are in orbit around milky center. No reason for them to get farther.

Just because Milky has space in it is no reason for it to expand. Where do you get this idea? Could it maybe be popular science journalism ?

"Bound" which you put quotes around is a simple basic physics idea, it just means gravitationally bound, like in stable orbits, like planets and stars. Likw ir would take a big effort to drag them apart. It is not an opinion Guy. It is obvious from looking at these structures that they have gathered together into some semipermanent collective form.

Ned Wright is telling you straight. There is no reason connected with Big Bang cosmology that the galaxies should expand. They don't expand. If you have the notion that they should then you are confused and need to dump that idea.

You don't have to adopt OPINIONS, Guy. We are talking fairly simple straightforward stuff. Once you dump some misconceptions you will be fine. Please to go watch Ned's animation. He is giving the straight dope and it's real helpful.

I don't give a crap that you never said space expands. It's been a fundamental part of the Big Bang theory for over 40 years. I have a book Larousse Encyclopedia of Astronomy published in 1967 with a chapter called "...expansion of the universe". On the assumption that you are not impressed by that, see this modern link:

http://en.wikipedia.org/wiki/Metric_expansion_of_space

It says "While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such theoretical constraint when space itself is expanding."

Emphasis is mine. If you think that objects without relative motion can get farther apart without space expanding then you are nuts. No concept can get simpler than that. You haven't been reading Prof. Peacock have you?

When talking about gravitationally bound, you said it wasn't opinion. Do you think you are God? Speaking of God, even though you intentionally misspelled the Lord's name, you still used it in vain in my opinion. I find that disgusting.

You say it is straightforward that space won't expand just because it is inside or a galaxy. I beg to differ! Show me any proof of that, I dare you.

BTW I had watched Ned's animation. I saw space expanding. What do you see?

 

[StandardsGuy]

Why in Heaven's name, Guy? Why in a spatial flat infinite universe with matter more or less evenly distributed throughout, why in that picture is any point special?

You amaze me. I have never heard anybody draw that conclusion from the given assumptions. Why would the points all be more or less equal? Like on the balloon. Tell me what point would be distinguished or special in some way!

If you can not point to a special point, then I would say that the philosophical ridiculousness is huge.

I didn't say anything of the kind. Did you leave you brain in bed? All I am saying is that in a flat universe the 4D hypersphere doesn't apply. Light can't go around and around anymore. There a lot more philosophical differences than that example. I think even you can see that. Are we on the same page yet?

 

[marcus]

...If the universe is infinite, then (as I see it) all points in the universe would not be equal to each other ...The philosophical differences are huge.

I didn't say anything of the kind. Did you leave you brain in bed? All I am saying is that in a flat universe the 4D hypersphere doesn't apply. Light can't go around and around anymore...

In the LCDM standard model's expanding hypersphere case, light can't go around and around. So that does not constitute a difference at all, and certainly not a philosophically huge one.
You seem to be changing what you are claiming. Earlier you said in infinite case all points "would not be equal to each other". Now you are saying that you meant something different but it is not clear what.

 

[StandardsGuy]

Hi Marcus,
I like the balloon analogy. I'm not a newbie to cosmology - it's has been my interest for many years. However, I don't claim to be an expert or to be up to date on terms and definitions. I agree with others that we could use a glossary or a list of definitions on this site which could include abbreviations like FLW and LCDM and maybe things like the Friedman formulas. I was going to do that for myself, but haven't yet.

In the LCDM standard model's expanding hypersphere case, light can't go around and around. So that does not constitute a difference at all, and certainly not a philosophically huge one.
You seem to be changing what you are claiming. Earlier you said in infinite case all points "would not be equal to each other". Now you are saying that you meant something different but it is not clear what.

You are correct that in an expanding hypersphere light can't go around and around, but it can in a constant one. It can't do that in flat space, or can it? I haven't changed my position. In a hypersphere two points can only get so far apart. Every point is "equal" to every other point because there is no edge. I think I know what you are going to say: "In flat space there is no edge either." Am I right? Maybe that is the problem with analogies. When I think of flat space, I think of a piece of paper which has an edge. This seems to be a continual problem for me. Let's make sure flat space is defined in the list.

-S

 

[blackfork]

This thread is extremely helpful! Thank you!

Here are a couple of questions I have been trying to figure out.. I hope it's not too off topic as far as trying to get everyone on the same page:

1) Isn't it equally valid to assume, using the balloon analogy, not that space is expanding or that the coins are moving apart, but that the coins are simply shrinking? That is, that space isn't expanding, but matter is contracting?

2) This one is a bit more awkward.. If we imagine the balloon is actually an expanding cube, how can we tell the difference between the cube simply growing into a larger and larger cube versus turning into a new shape, such as a truncated octahedron or rhombicuboctahedron, where the six square faces remain the same, but that the space between them is growing? (This can be thought of as shrinking rather than growing, too.)

 

[marcus]

1) Isn't it equally valid to assume, using the balloon analogy, not that space is expanding or that the coins are moving apart, but that the coins are simply shrinking? That is, that space isn't expanding, but matter is contracting?
...

Hi blackfork, have you watched the wright balloon animation carefully?
An important thing to watch is the photons. They always move the same speed across the balloon surface, no matter how little or big the balloon is.

I picture it as 1 millimeter per second. It depends on the size of your computer screen.

What you are asking about is not physics. you are asking about mathematical and measurement conventions. Convenience.

We tend to believe our clocks are satisfactory, it is convenient to think of them as running steadily. This gives us a standard of distance. As years go by there get to be more lightyears of distance between galaxies. It takes more and more years for light to travel between. We already have a geometry theory which says that this must happen, distances must increase on a certain schedule, slowing and then speeding up in a pre-determined way (and influenced by the matter that happens to be around.)

If you want to force galaxies to stay at the same "distance" then you need to change the definition of a year so that the same number of years pass (though in reality more do). So you have to adopt a phoney "time" which goes slower and slower compared to biological and physical rhythms. Let's call your new idea of time "fubar" time. Fubar years take more and more of our clock time (so that the galaxies can stay the same number of fubar lightyears apart.

For comparison, the theory of increasing distances we have now is based on a theory of geometry called General Rel. According to GR distances don't all increase at the same rate. Overall yes or nearly so, but if you look at detail, the law of GR makes there be a lot of variation in the way geometry changes. It is effected by matter. The single average rate is a simplification. So if one was trying to compensate, and force distance to stay the same, one would never know how much to compensate, to slow time, or to shrink matter by, in your system.

I think it would be clumsy maddening and painful to try what you suggest. And wouldn't change reality. Among other things we would need a new theory to replace General Relativity. It would be terribly complex. One could not keep all the distances between all the galaxies the same because the way things really work the expansion of distance is not uniform. It would be hideously complicated to try to compensate. A lot of trouble to say clock time is not the "real" time. "Real" time is fubar time which is running slower and slower compared with our clocks. So that the distance between galaxies officially stay the same fubar lightyears. But fubar time would not be running slower everywhere in a uniform way, because in the real world expansion is not uniform. So there would be a huge number of different fubar times each going slower than the local observers' clocks, but by different amounts.

The bitter thing is that going to all that trouble would not change physical reality. It would just change some mathematical and measurement conventions. In other words what you suggest would not be interesting, but would make the mathematics impossibly complicated.

The way it is now we have a beautifully simple equation---the GR main equation---that says how distances will change. And any observer can have the steadiest available clock and consider time to go according to that. He doesn't have to substitute a phoney fubar time which doesn't correspond to his experience and ordinary physics in our local environment.

GR is the underlying law of why geometry is the way it is. Why for instance the angles of the triangle add up to very close to 180 degrees under familiar circumstances (and do not in certain other circumstances as Eddington discovered in 1919.) In order to change our definitions so as to make galaxies stay at the same "distance" we would have to do violence to GR and geometry as we know it. We'd need a new law of gravity, among other things. But the sheer impracticality kind of rules it out.

 

[marcus]

Probably nearly everyone here realizes that the quantum geometry people are working on revising GR, and revising cosmology (as one application of geometry.)
That is a major project now.
If you are interested in how the fundamental theories of science can evolve and get to be different, you might like to learn what is going on. We are in the midst of a revolution. Rovelli has a wide-audience essay on this that is free online.
http://arxiv.org/abs/gr-qc/0604045

That means that there is a premium on understanding the changes which are in progress with professionals working on them---and not on making up one's own personal replacement notions. There is too much going on for that. IMHO. It might make more sense if the situation were static.

If you are curious about where and how things are going in quantum cosmology, here is a keyword search for recent papers, ranked by number of citations to them in other research (a measure of impact or importance). Browse around.
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29

 

[blackfork]

Thanks, Marcus. I don't intend to replace Einstein, I was just wondering how something like that would work out. You're right that I am thinking of a different way to handle the data, not necessarily to replace what is actually happening in reality.
I did find your explanation helpful.. It makes sense.. I guess naively I thought perhaps it would make things a bit simpler, but it seems that it would instead just make things much more complicated and weird.

I have checked out the animation. .. I'm still wrapping my mind around it. I will just say, though, that this thread and your few links have helped me tremendously in getting a better understanding of the whole thing!

 

[marcus]

Thanks for the friendly feedback! It's encouraging to know when someone is getting something out of this thread. I'll keep an eye out for blackfork question threads in case you start some.

 

[Mihael@@/&]

NiceSiteEasy To FindThanks

 

[Mihael@@/&]

So, -x&+x can't see each other, and -y&+y can't see each other?
btw this balloon analogy sounds nice, only if our universe is not the surrounding (inside and outside) air but the balloon itself.

 

[bakalis]

the now of the universe-as we speak

To have an enjoyable cosmo forum we needed a balance between mental freedom on the one hand and a shared knowledge base on the other.
People should be free to imagine the universe the way they want, but everybody should try to understand the standard LCDM (Lambda-cold-dark-matter) model as a starting point.

I'm going to try to avoid mathematical equations in this thread because they put many people off and also to avoid using too many abbreviations like LCDM. This thread should be at the entry-level for the Cosmo forum. You are welcome to contribute ideas and comments.

The LCDM is based on a more general mathematical model called FRW or FLRW (Friedmann, Lemaître, Robertson, Walker) which is built into Ned Wrights calculator
Everybody who comes in and posts here should have played some with that calculator or one like it because in practical terms that is what a mathematical model is. Cosmology is mathematical (not verbal) and observational---it fits a mathematical model to data.
The galaxy counts, redshift surveys, supernova brightness, microwave background data and so on are all supposed to check out and match what the model says they should be.

When you use Wright's calculator you have specified three parameters (the default values are 0.73 for dark energy fraction, 0.27 for matter fraction, 71 for Hubble).
If you don't change the default settings, you get the standard LCDM. If you change them you get some other version of FLRW.

You can think of the LCDM as the fine-tuned version of the general FLRW where the parameters are chosen to get the best possible fit to our universe--to match the observational data.

So the existence of these models is always in the background but what we need to focus on here in this thread is the INTUITION. How to picture it so that if you were playing around with one of the calculators, changing the parameters and finding how far away various things were when they emitted the light we are getting etc, you would kind of know what to expect. Intuition about how the parameters effect things, and how redshifts relate to distance and recession speed.

So what I hope for is that those of us asking questions and discussing here at Cosmo forum all have a shared basic intuition---which is a kind of home base---and probably the most convenient way to get that is to properly understand the balloon analogy.

In my experience many of the misconceptions people have when they first come to this forum stem from misunderstanding what that analogy is intended to teach us. And a lot of the confusion we occasionally experience comes from getting that analogy somehow crossed up. So in this thread what I propose we do is, at least for starters, simply discuss the balloon analogy. Get clear on it. Find out any problems people have with it, if there are some.

We can do that without having to use a lot of math formulas, I think, and a minimum of technical jargon. Don't get me wrong---I'm all in favor of jargon, we simply won't need much of it here.

For people who want to get some hands-on experience with Wright's cosmo calculator it is here
http://www.astro.ucla.edu/~wright/CosmoCalc.html
the homepage for his other cosmo resources is
http://www.astro.ucla.edu/~wright/cosmolog.htm
you can always get these links just by googling "ned wright"
In my sig I have a link to MORGAN's cosmo calculator which has some valuable features and is harder to get by googling.
You might want to try that one too, it gives recession speeds.

So, Marcus, let me join in. I'll just warm up here

We know telescopes provide a window to the past but the farther we go away (or back in time) the situation becomes pretty sticky. Consider "looking" (catching the light) from a space object (star, quazar, AGN, whatever) 47 billion years away (that's the farthest we've gazed so far, right?). The light actually left the object well before that time (has to be less than 13.7 billion years) and then it got stretched due to the expansion of space and reached us only today. Today, this object is not there anymore but its matter is somewhere in a different form or formation. So, where are today all those particles that took part in the reaction that produced the light that ultimately reached us? For as long as the object they were part of was alive, they should be moving farther away from us with it, so their light path received by us after all those years is the path of the object observed. Still, this path is 47 billion years away and less than 13.7 billion years back in time. On the other hand, the object (or its particles) could have moved away from us during all those years faster than light, so we we'll never catch a glimpse even if we wait forever. Whatever the case, everything we see today in the sky is not there anymore and they have moved away from us at some speed. Plus, almost everybody agree that there is no central point in the universe and all vantage points are equivalent. I suppose this holds if one takes for granted that any point in the universe has the same restrictions as we have, being able to see around it only the evolution of the universe but not the absolute present state of the universe, so this equivalence principle holds in somewhat different way for any given moment in time (like our absolute NOW or our absolute one hour later etc.). Equivalence of vantage points at any given moment still holds if indeed those points sit on the surface of the balloon, so anyone point is no different than the others. But if there is ”something” inside the balloon (unlikely) equivalence breaks
To make things simpler, I do not consider here the non-existence of absolute time and, of course, I don’t consider the possible implications of extra dimensions or other exotic stuff
So, is it that TODAY everything sits on the broader (almost) "two-dimensional" surface of a balloon universe (that can be considered to be flat, as far as the number of dimensions is concerned) and everything we look at is just snapshots of the earlier state of that very balloon while it was swelling with the help of space expansion? In other words, are we just seeing in the sky the evolution of the universe through time (which is the staple notion) and the reality of NOW is sitting around us on the same sphere we are sitting? If this is the case, is there anything between the surface of the balloon and its center TODAY, and, does a center even exist TODAY? I think it’s unlikely, and the inside the balloon (which has no meaning TODAY) is just the progression of time. The big bang was indeed the center (actually, the origin) when it all started, but all the light we see now coming from the past and ever closer to the center of space and time should not be there anymore. It should follow the same path as the sun and the Earth did, and it should sit on the sphere roughly at the same distance from the primordial center of it all. Sure enough, I stress that I know the balloon analogy has been out there for decades, my question is if the balloon is actually more than an analogy and it is the closest thing we got to reality

All the above are not conclusions of course, they are mere questions of a lay person that has read a few books in his spare time and wants to clear the mess in his head. I know I’m not alone

 

[marcus]

my question is if the balloon is actually more than an analogy and it is the closest thing we got to reality

Thanks for contributing a question to the thread, Bakalis. My answer to your question would no it is not more than an analogy.

The balloon is a mere 2D analog of the 3D hypersphere we are trying to talk about.

I say the balloon is 2D because it is the idealized surface we are talking about, not the rubber of a certain thickness, or the air inside or the space inside/outside. Just the pure infinitely thin 2D surface.

In the analogy all of space is depicted by that 2D surface and all existence is imagined to be concentrated there. Creatures and their planets are all 2D. Planets are disks. Creatures are amoeba shapes surrounding the disks. All thinner than paper. Zero thickness. The galaxies too are all 2D

That is totally unlike reality.

We use this 2D analogy because it the animated movies of the expanding balloon get across an idea efficiently. The whole point is, don't think about it. Watch the movie.

You will see little whirling white shapes which stay in the same latitude/longitude position on the balloon as it expands. These are galaxies and it teaches you not to think of the galaxies as moving. They do not move but they get farther apart.

And you will see little wigglers traveling across the face of the balloon starting from the vicinity of one galaxy and traveling to another. That is light. The light is actually traveling and it always goes the same speed.

After you have absorbed the 2D picture fairly thoroughly, try to picture how it is in the 3D analog of the balloon.

To a first approximation, the 3D galaxies are not moving either. Light is traveling from one to another, as before. The galaxies are getting farther apart, as before. But it is happening in the spatial context of a hypersphere.

A hypersphere is a 3D place where if you could freeze expansion you could eventually imagine circumnavigating. Head of in one direction (say at the speed of light) and eventually find yourself coming back home from the other direction. Such a 3D space can exist, but you could not put it in a standard 3D Euclidean space with cartesian coordinates. A hypersphere is slightly curved, which allows it to close back on itself.
It's no big deal. We may live in one.

But many people find the 3D closed hypersphere awkward to imagine. You don't try to picture it from the outside. You visualize the experience of exploring inside. Like a 2D amoeba exploring the 2D surface of his balloonworld. But many people let themselves be put off by that. So that is why we go down to a 2D analog and study the balloon model, as an introduction.

If you haven't watched the movie yet, google "wright balloon model".

The light wigglers change color as their wavelength gets stretched out. Longer wavelength means more reddish, so they get redder as the balloon expands. It's neat

 

[bakalis]

The balloon is a mere 2D analog of the 3D hypersphere we are trying to talk about.

I say the balloon is 2D because it is the idealized surface we are talking about, not the rubber of a certain thickness, or the air inside or the space inside/outside. Just the pure infinitely thin 2D surface.

Thanks for the reply Markus.

In my previous post I was saying "is it that TODAY everything sits on the broader (almost) "two-dimensional" surface of a balloon universe (that can be considered to be flat, as far as the number of dimensions is concerned) and everything we look at is just snapshots of the earlier state of that very balloon while it was swelling with the help of space expansion? The big bang was indeed the center (actually, the origin) when it all started, but all the light we see now coming from the past and ever closer to the center of space and time should not be there anymore. It should follow the same path as the sun and the Earth did, and it should sit on the sphere roughly at the same distance from the primordial center of it all.

By that it's obvious I don't consider the two-dimensional balloon analogy to serve as the closest thing we got to reality, and you are right to sayt existence cannot be pictured there. Using the expressions "broader (almost) two-dimensional surface" and "roughly at the same distance from the center" clearly alludes to a third dimension. It's just that the balloon analogy was readily available and widely understood. What I'm talking about is actually something like the crust of the earth. This is a three-dimensional part of the Earth sphere that has the rest of the Earth underneath it and the rest of the universe outside it. Magnify this earth-crust-analogy (a term I just coined to distinguish it from the balloon analogy) to the universe at large and you got yourself a three-dimensional outer part of a sphere, with nothing beyond it (this "nothing beyond" is where the gutted sphere is expanding to, probably thinning all the while due to light-paths fluctuations but always keeping its shape) and nothing inside it (this "nothing inside" is where the earth-crust structure came from and going away from as time progresses. This is easier for me to picture than the 3-D hypershpere-but then those two approaches could be closer than they look

I stress again that I do not consider here the possible implications of extra dimensions or other exotic stuff, ot the non-absoluteness of time (all of which should play a role but let's leave this for later)

For the record, my first name is Stelios

 

[marsd]

I understand the pennies on the balloon and raisins in dough analogies, but they are different. With the balloon, everything is on an expanding spherical surface, but with the dough they are INSIDE an expanding sphere. Which is the better analogy?

If the universe is an expanding sphere, is it true to say that BB happened in the geometric centre of this sphere? If so where is this point in today's universe?

BB created the universe out of "nothing" (quantum fluctuations?), and it is now expanding into the "nothing" out of which it came. Is this correct? What does the border between our physical universe and the "nothing" beyond look like?

This my first ever post to any forum, so apologies if I have inadvertantly asked inappropriate questions.

 

[Pjpic]

4. to understand that something can be curved without there being an extra dimension---part of the mental exercise is to picture the balloon surface as all there is, there is no inside the balloon and there is no outside---only the balloon surface exists.
I haven't talked about this part yet.

How can there be a curve without there being one dimension more than that which is curving? ( it seems like a curved line implies a plane and a curved plane implies a volume)

 

[marcus]

...
How can there be a curve without there being one dimension more than that which is curving? ( it seems like a curved line implies a plane and a curved plane implies a volume)

I believe the answer to your question was worked out around 1850 by people like Bernhard Riemann and Carl Gauss. They showed that a curved geometry (of any dimension) can be defined mathematically without assuming that it is embedded in a space of some higher dimension. In particular a curved 2D space does not have to be embedded in a 3D. And a curved 3D space does not have to be embedded in a 4D or 5D or whatever.

2D animals in a 2D universe might measure the local curvature by studying triangles---measuring how much more or less than 180 degrees---summing the internal angles.
They would have no LOGICAL reason to imagine that their universe was embedded in some higher dimensional one, unless some further physical reason appeared (something mysterious that needed additional spatial dimensions to explain.)

When Einstein postulated Gen Rel in 1915, he used Riemann's 1850 geometry. He did not need to assume that our GR universe was embedded in some higher dimensional surrounding. Since he did not need to assume it, he did not assume it. (Good scientific practice!) Ever since then it has been traditional NOT to assume that because it violates Occam Razor---it adds unnecessary complication---"extra baggage".

On the other hand, there are some minority cosmologies (studied relatively less than the usual curved spatial 3D cosmology, fewer papers and books, but they exist) that DO assume our 3D space is embedded in higher dimensional space. The motivation for such ideas is to produce alternative explanations for other observed stuff. So there are these other conjectures but they are not forced by the mere fact of curvature.

They arise for other reasons than mere curvature. For example Steinhardt and Turok invented what they called "ekpyrotic" cosmology in an attempt to get rid of inflation. This was some 8 or 9 years ago and they liked superstring. They suspected inflation was incompatible with superstring models with their compactified "rolled-up" dimensions. Inflation would cause them to unroll. So they worked hard to get rid of the need to assume inflation. Inflation had become popular starting around 1980 because it explained certain observed characteristics of for instance the microwave background. Steinhardt and Turok came up with the idea that we might live in a membrane embedded in a higher dimensional surround, to explain some of the same things that inflation explains. But for the most part it didn't catch on. Their scenario did not come to replace the assumption of of an inflationary epoch, in most people's research.

Since (I would estimate) around 2005 that "ekpyrotic" idea is no longer researched so much---professional interest in it has been on the decline. But that's just one example. My point is there are always these minority cosmologies that use higher spatial dimensions---motivated by other considerations than mere curvature---motivated by attempts to explain stuff that the authors think is not satisfactorily explained.

 

[marcus]

...If the universe is an expanding sphere, is it true to say that BB happened in the geometric centre of this sphere? If so where is this point in today's universe?

In mathematics a 2D sphere can be defined without assuming that it is in 3D surroundings. Therefore a 2D sphere does not need to have a geometric center. A geometric center does not have to exist. Anywhere.

Modern geometry, called differential geometry, began around 1850. It is somewhat more powerful than the geometry of, say, Archimedes or Ptolemy, although those Greeks were certainly very capable!

Again, in a modern geometry context you can have a 3D hypersphere that is not embedded in any higher dimensional surroundings. To someone in it, it looks and feels like intuitive Greek 3D except it has a circumference----if you travel far enough in a straight line you get back home---you pass Go again. The 3D hypersphere has no need of a geometric center. A center does not have to exist.

So the answer to your question is no. It is not true to say the BB happened at the geometric center.

You can artificially make it look that way. You can arbitrarily set up coordinates so that time is radial and "t=0" is like a central point (not a point in "today's universe", but a point in your artificial construct.) It wouldn't fit the bumps and warts of reality very well. Radial time would not be convenient and as a rule people do not use those coordinates. Still, it's an option

I understand the pennies on the balloon and raisins in dough analogies, but they are different. With the balloon, everything is on an expanding spherical surface, but with the dough they are INSIDE an expanding sphere. Which is the better analogy?

With the balloon, a point is very much INSIDE the 2D patch of area that surrounds it. The answer to your question is that neither analogy is better in that sense. One is a 2D picture, and inside means inside a 2D patch of area. The other is a 3D picture and inside means inside a 3D blob of volume.

BB created the universe out of "nothing" (quantum fluctuations?), and it is now expanding into the "nothing" out of which it came. Is this correct? What does the border between our physical universe and the "nothing" beyond look like?

Who said "it is now expanding into the nothing out of which it came"? Who said there is a "border"?

It sounds like something made up. I don't think a scientist would say that. But a professional might have and I would be curious to see the source where you got it. Do you have an online source that you could show us?

I've heard the idea that the BB arose from a quantum fluctuation in some previous circumstance. That is just one idea of several! It is not an official story. There are a number of ways that professional cosmologists have proposed the BB might have occurred---a book that collects all the various ideas is scheduled to appear next year.
But "nothing" is a rather confusing popularization. People hype their ideas by talking like that because it appeals to the popular imagination---sounds jazzy.
When you get down to the details there is usually something, something that the guy has in mind.

So a "quantum fluctuation" beginning has some plausibility---though it is not the only idea out there (probably not even the most credible or accepted idea, currently.)

But even with quantum fluctuation BB there is no need for a "border" with the universe expanding out into "nothing". That seems to be an embellishment, an intuitive elaboration.
So there is no need to ask "what would it look like?" It doesn't have to look like anything because in the standard cosmo picture there is no assumption of anything like that.

 

[Pjpic]

2D animals in a 2D universe might measure the local curvature by studying triangles---measuring how much more or less than 180 degrees---summing the internal angles.
They would have no LOGICAL reason to imagine that their universe was embedded in some higher dimensional one, unless some further physical reason appeared (something mysterious that needed additional spatial dimensions to explain.)


If these 2d animals didn't need a higher dimension to define a geometry where 180 degrees isn't the sum of internal angles of a triangle, are they using different definitions than Euclid?

 

[marcus]

You might be interested in reading the Wikipedia article about the Parallel Postulate.
The fifth postulate of Euclid.
http://en.wikipedia.org/wiki/Parallel_postulate

I'm told that even the Greeks considered doing without it. In any case Carl Gauss was doing that by 1820 or 1830. And others came to similar realizations as Gauss. One can use Euclid's definitions and axioms, but omit this one postulate, and do a version of geometry.

Gauss actually suspected that if he could arrange to measure a large triangle using surveying equipment it might turn out to have a detectable excess or deficit angle. That is, 3D space might itself turn out to have a geometry which deviates from Euclid's fifth postulate.
As I recall he applied for a government grant to do this. He did some other surveying work for the government but this particular thing did not go through, if I remember right.

Gauss was ahead of his time in this. Nowadays we accept that the angles of a triangle don;t add exactly to 180. Euclidean plane geometry is only a approximately right at best, and then only in low gravity. In intense gravity it is not even approximate. So his supicion was basically correct.

 

[Pjpic]

The balloon analogy seems to be an extrinsic way of looking at the big bang. It sounds, to me, like a contradiction to the intrinsic way of looking at the big bang used by science.
If so, is it because the intrinsic way has the advantage of ignoring (?) anything that may or may not exist beyond the surface of the balloon? Especially because those things have no effect (except in some brane theories?) on what happens on the surface of the balloon.
I do have a question on why Occam’s razor would say the balloon is not embedded in a higher dimension if the intrinsic measurements show the space is not flat. If I measured the internal angles on a triangle and they equaled anything but 180 degrees, I’d jump to the conclusion that the plane was imbedded in a higher dimension.

 

[bakalis]

It seems nobody, especially Marcus, was online for a couple of months until somehow the thread was back on track late December. So, let me repeat my last post hoping for a reply that could revive the talk. So, Marcus said:

The balloon is a mere 2D analog of the 3D hypersphere we are trying to talk about.

I say the balloon is 2D because it is the idealized surface we are talking about, not the rubber of a certain thickness, or the air inside or the space inside/outside. Just the pure infinitely thin 2D surface.

Thanks for the reply Markus.

In my previous post I was saying "is it that TODAY everything sits on the broader (almost) "two-dimensional" surface of a balloon universe (that can be considered to be flat, as far as the number of dimensions is concerned) and everything we look at is just snapshots of the earlier state of that very balloon while it was swelling with the help of space expansion? The big bang was indeed the center (actually, the origin) when it all started, but all the light we see now coming from the past and ever closer to the center of space and time should not be there anymore. It should follow the same path as the sun and the Earth did, and it should sit on the sphere roughly at the same distance from the primordial center of it all.

By that it's obvious I don't consider the two-dimensional balloon analogy to serve as the closest thing we got to reality, and you are right to sayt existence cannot be pictured there. Using the expressions "broader (almost) two-dimensional surface" and "roughly at the same distance from the center" clearly alludes to a third dimension. It's just that the balloon analogy was readily available and widely understood. What I'm talking about is actually something like the crust of the earth. This is a three-dimensional part of the Earth sphere that has the rest of the Earth underneath it and the rest of the universe outside it. Magnify this earth-crust-analogy (a term I just coined to distinguish it from the balloon analogy) to the universe at large and you got yourself a three-dimensional outer part of a sphere, with nothing beyond it (this "nothing beyond" is where the gutted sphere is expanding to, probably thinning all the while due to light-paths fluctuations but always keeping its shape) and nothing inside it (this "nothing inside" is where the earth-crust structure came from and going away from as time progresses. This is easier for me to picture than the 3-D hypershpere-but then those two approaches could be closer than they look

I stress again that I do not consider here the possible implications of extra dimensions or other exotic stuff, ot the non-absoluteness of time (all of which should play a role but let's leave this for later)

For the record, my first name is Stelios

 

[6nqpnw]

Hopefully I'm not outta line here (first post on any forum ... ever), but I feel the Balloon Analogy is a flawed model of the universe as it's based on the assumption of an expanding universe. Please be gentle with the flaming, as I'm at a loss for where to go or what to do with my recent realization, but do be brutal with the honesty. I'm in need of some direction / clarification / validation.

Here's what I know to be science fact:

1. Neighboring galaxies are moving away from one another as evidenced via analyzing the red shift.

2. Not only are they currently expanding, but also at an accelerating rate, which was determined by studying Type 1a supernova.

3. Discovered in the 70's, CMB (Cosmic Microwave Background) was the final piece of evidence to support the 'big bang' theory, explained as the expanding outer shell of our universe, and solidified it into scientific and main-stream acceptance.

4. The repulsive properties of Dark Energy was ... uhmm ... discovered (maybe, but I don't think so) and further supports the accelerating expansion of the big bang universe, to help fill the lack-of-interstellar-mass gap.

5. Black Holes exist: small ones strewn about our galaxy and large ones at the center of galaxies.

6. Spaghettification: proximity effect of black hole gravity; the closer to the singularity, the faster the rate of acceleration (starting to see where I'm going with this?). Meaning that if one were to dive into a black hole, the pull of gravity on your head would be greater than that on your feet, causing you to be stretched out.

A couple weeks ago, I entertained the idea of a collapsing universe (based on the big bang theory, the big crunch, I believe it's been termed), which led to pondering the forces needed to initiate the big crunch process. That's when it occurred to me, what if there was no big bang; only a continual crunch?!

What if the driving force of our universe were nothing more than a gargantuan, galatic-gobbling black hole of undiscovered and unimaginable proportions, slowly devouring everything as far as the interstellar eye can see and ejecting the transmugraphticated molecules (atoms, elements, whatever the small, basic stuff is ) out its poles in a jet vortex that eventually succombs to the black hole's gravitational grip and gets sucked back in, starting the whole process of star systems and galaxies all over again.

With my limited knowledge, this model fits: explaining the accelerated expansion of galaxies based on the Theory of Relativity without conjuring up fantastic repelling properties of Dark Energy as there is no need for the universe to cool off and collapse. Thusly, our universe becomes a galactic terrarium, a self-sustaining environment, with no means of determining it's age, no loss or gain of matter, just a never-ending cycle of rearranging particulates.

As for the CMB, I dunno. What're your speculations? I think it's either from the black hole particle jets gradually falling inward, or maybe a byproduct of the black hole itself. As I mentioned, I'm no scholar or professional for that matter. I'm a farmer in Southern Louisiana with an intuition on cycles and patterns.

I can't answer the tough questions, or can't even ask the tough questions for that matter. All I know is that I can't stop obsessing ::: I can't sleep, my children make fun of my babbling, my wife tunes me out or leaves the room, friends nod in agreement then change the subject, and I can't find anything on the Internet where someone else has pondered this possibility.

More importantly, I can't find anything to debunk it. If I could find a flaw, I can move on. The closest I've came is Somedude-Hawkings Thermodynamics predicting black hole evaporation through energy loss ... but that's unproven, isn't it? Do they evaporate? Disappear? Explode? Anything? Or are they just there ... forever ... infinite ... Einstein's cosmilogical constant? Please help put my weary mind to rest before I, myself, implode.

 

[robertm]

6nqpnw:

The thread you have posted in is 9 page long attempt to inform and clarify, yet I can see no evidence from your post that you read anything but the title.

You don't have to worry about flaming here, but you would do well to read what has already been discussed before wasting all the effort to type up long incoherent musings on a subject you haven't rigorously studied.

If you haven't and/or don't want to commit to a serious long term exhaustive and exhausting study of physics and the related mathematics, then you must be content with partial analogies and popularizations.

Though, there is no reason that, by reading this thread and following the several quality links provided (I suggest starting with the links provided in marcus's comment signature), you can not soon come to understand the gist of the picture.

Remember; if your looking for a quick and easy road to knowledge, science has nothing to offer.

 

[Cuetek]

What I'd like to know is how or why specifically relativity dictates that space itself is expanding rather than matter translating "normally" away from all other matter? It seems to me that we would observe the same red shift galactic drift and homogeneity profile with the vis U being a very tiny cross section of a meta-scaled event. Using the analogy of a super nova, say the vis U is equivalent to a cubic meter of hot gasses at about the orbit of Mars with the total voume of the recent super nova having made it out to about the orbit of Pluto.

All the dust around us here at Mars orbit would be uniformly expanding by translation and could well be very very homogeneous. And there could be virtually undetectable assymetry in that expansion. So, I guess my question is, what led Einstein to presume the expansion of space in the first place rather than us being a tinty part of a bigger phenomenon?

 

[Cuetek]

6nqpnw:

The thread you have posted in is 9 page long attempt to inform and clarify, yet I can see no evidence from your post that you read anything but the title.

You don't have to worry about flaming here, but you would do well to read what has already been discussed before wasting all the effort to type up long incoherent musings on a subject you haven't rigorously studied.

Well, I thought that 6mqpmw said he only posted once and that was the only one I read and it's not like he was going totally spaghetti monster on us. I suppose he could have posted in a more appropriate forum, but his thesis of a meta-scale solution (big black hole jet stream) speaks to what I see as the biggest weakness in the Big Bang model. The BB will almost certainly be discovered to be a finite (if mind-numbingly immense) sub-feature in a larger hierarchical material arrangement just like every other physical phenomenon ever observed or discovered. Such progression is precisely the discovery of the next hierarchical structure.

The homogeneity of the Crystal Spheres gave way to the hierarchical truth of the Galaxy, which gave way to the greater hierarchy of the multi-Galactic steady state model, which gave way to the more accurate expanding Big Bang model. This ongoing hierarchy will almost certainly not stop at the Big Bang. Yet issues like curvature of space and the amount of matter that must exist both presume and rely mathematically on there being no further intrusions of forces or features from a greater scale.

6nqpnw's model has expansion potential, CMB potential and is not the whackiest version out there. But it does address what history shows to be the greatest weakness of all human cosmological presumption. We constantly make models that terminate the material hierarchy, every one of which was corrected by it's reinstatement. Seems to me we should formally, if conditionally, presume a material hierarchy.

Once you presume a larger diversity surrounding some locally pervasive homogeneity, you begin to see that we will, likely as not, always have issues (like dark energy, perhaps) that turn out to be more a result of meta effects from a greater scale than to be locally determinable properties. Like when the discovery that the homogeneous field of stars actually moved with respect to each other gave us the galactic view over the Copernican model, it probably took a while before people would allow that hierarchical presumption to trump the Crystal Sphere terminus of the hierarchy. Just because we can't yet find the moving stars doesn't mean that we shouldn't, at the very least, philosophically presume them. In our case it would be the detection of some deviation from the Cosmological Principle.

Unfortunately such philosophical presumption necessarily clashes with the prevailing model in a way that makes people angry. Beliefs are very dear to us and having them altered by anyone who is not highly versed in the prevailing wisdom is hard on everybody. I realize that an enormous amount of discipline is necessary to understand the elegance of how seamless the current theoretical models are structured. But so too was the Ptolemaic model very sophisticated in accurately describing the observations of what was later found to be much simpler arrangement.

So we are faced with an inherent dilemma. I mean, you have to know that some part of any human cosmology will be discovered to be flat out wrong, yet anyone deviating from that exact same wrong principle will be seen by those in the know as fools who just don't get how well that part fits in and how essential it is for the model to work at all (like retrograde equations in the Ptolemaic model).

What might be helpful in those forums that deal with the periphery of human knowledge is to identify which features of the prevailing model are most vulnerable to change based on how past models changed. The conditional presumption of a material hierarchy is one such feature. The presumption of our pursuit of overly complicated mechanisms to satisfy anomaly (inflation?) might be another.

-Mike

 

[pixchips]

... So, I guess my question is, what led Einstein to presume the expansion of space in the first place rather than us being a tinty part of a bigger phenomenon?

Answers.com (http://www.answers.com/topic/general-relativity) has a nice recapitulation of GR history. Einstein didn't presume the expansion of space, but rather assumed a static universe (his greatest blunder). Schwarzschild found the first black hole solution. Friedman found the first expanding universe solution, which Lemaitre used to formulate the first 'big bang' model, which rhymed with discoveries by Hubble. So Einstein came up with a formulation of classical physics that was self consistent in a way that Newtonian physics wasn't. He and others used (and continue to use) the solutions of that to predict and explain observations of our universe. There is nothing (as far as I know ... which is pretty limiting) in GR to preclude "us being a tiny part of a bigger phenomenon". In fact, studies of galactic clustering suggest that there definitely are bigger phenomenon out there: the universe is lumpy on pretty large scales ( http://en.wikipedia.org/wiki/Great_Attractor ). So far GR has held up incredibly well as far as we can test it, and we do keep testing it (http://en.wikipedia.org/wiki/Tests_of_general_relativity).
If you are looking for an interesting read on the history of discovery of CMB and the big bang, I really enjoyed "Wrinkles in Time" by George Smoot. He did some of the original experiments that teased out the CMB data. Reading it you get the sense that nobody just jumped to conclusions, or was allowed to engage in idle speculation. It shows the blood, sweat and tears that went into the models, explanations and equations we tend to take for granted.

 

[Cuetek]

If you are looking for an interesting read on the history of discovery of CMB and the big bang, I really enjoyed "Wrinkles in Time" by George Smoot.

Thanks for the reference, Pix. I'll order it from Amazon. Seems like it will clear a few things up for me.

-Mike

 

[pixchips]

No problem Mike. It never hurts to question things. I've been wondering for a while why folks were so convinced that the CMB data meant that we lived in a BB universe. (I asked on the forum once and nobody volunteered an answer) What if the average temperature of the rest of the universe was just 3 deg K, how could we tell the difference between that and the BB model? Here's a link that starts to get at this in a pretty detailed way:
http://zebu.uoregon.edu/2002/ph123/lec04.html

Answering my own question: From our current standpoint, if the universe was static and uniform, the average temperature would be that of the surface of a star (no matter where you pointed, you'd be pointing at the surface of a star that was not moving relative to you). So, if the universe is full of galaxies and stars, it is either expanding (far galaxies get red shifted), or light loses energy with distance, or there's enough dust to absorb the light (but then the dust would get hot and reradiate... so even that doesn't work). Only the expanding universe explains this without new physics. And on top of that, GR doesn't have a static solution (unless you include the cosmological constant).


Answering 6nqpnw's proposal: I was trying to dispassionately think this through. What if the whole universe was a gigantic black hole just sucking eveything in and squirting (some of) it out of its polar jets? I'm guessing that (in this scenario) we're in a galaxy outside of the black hole and accelerating toward it. If that were the case, the gigantic black hole would be radiating according to its size (bigger is colder). If it were the right size, it would be a few degrees K, so it could mimic the CMB. But not really. The CMB comes from all directions, that's one of it's primary characteristics. In the BH universe, the Hawking radiation would come from one direction and we would be heading toward it. So we would see a huge anisotropy in the CMB, which we don't. We see a little anisotropy which leads us to the conclusion that we are moving relative to the standard Hubble flow. And that leads us to the conclusion that the universe is a lot lumpier than we thought, and one of those lumps is accelerating us toward it. When that thought was first expressed, it was a big controversy. Now it's part of our model because it fits the data. Smoot relates the story in "Wrinkles in Time" and he had the same problem as 6nqpnw. He was suggesting something outside the status quo and got some grief for it. The difference is that Smoot had spent a great deal of effort to get the data to prove his point. In this forum I doubt if any of us is going to spend the time or money to 'prove' a new model of the universe. But we should be able to ask 'what if' and get a sensible answer from known data and known physics. Better yet, we should be able to use the available materials to explore our conjectures on our own. But I still think it's fun to report the results.

 

[HarryWertM]

This impressive thread answers many questions but I could not find the answer this:
What was the density of the universe [matter per unit of space] at the time of the BB? Seems like an interesting question. Inspires another question: Did the higher density cause time dilation, as higher gravitational fields do? If so, how much dilation?