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

[marcus]

I haven't had time yet to go through all the posts in this thread to catch up, but
did see the Balloon Analogy simulation. I get it,...
...

The thread is very long. I'm glad you watched the short movie. The thread has some useful stuff but it is rather repetitive. Eg we make the point repeatedly that to understand the analogy you have to concentrate. Imagine that 3D space inside and outside the 2D surface does not exist.

All existence is concentrated on the 2D spherical surface.

If any creatures exist they are 2D creatures in that 2D world. They cannot point in any direction not in that world. No point outside it (i.e. inside or outside the balloon) exists for them.

It takes concentration to use the analogy. If you think of the balloon as existing in a surrounding 3D space then it won't work for you as well---you won't "get it."

Hi Marcus,
But the balloon and the space inside it is 3D, right? ...

No. At least that is not the way it has been presented in this thread. Try to think of all existence concentrated on the balloon surface. You are a biologist? Maybe think of the creatures as amoebas slithering in the 2D world between two plates of (miccroscope slide) glass. They can't point their "fingers" or pseudopods in any direction that is not in today's space. No point outside today's 2D space exists for them.

Just as for us there is no point in today's 3D space that is "where expansion began."

How analogies work depends on how you use them. There is no one "right" way to see an analogy so I am just telling you one way to see/use/think about this one.

 

[megacal]

Thanks Marcus & Dave for your replies. I'll concentrate on them, and go through more of this thread and try to grok the concept of a 2D universe, at least until I need some Advil.

The Balloon Analogy isn't as straight forward as I thought looking at the video or
envisioning us as being on or inside the wave front or surface of the balloon.

I just bought a copy of Hawking's illustrated Universe in a Nutshell...it's from 1996, so may be badly out of date, and it doesn't have a ref in the index to the BA, but hope it will give me some understanding of these very mind-bending theories.

In the mean time, I'm going out to the desert tonight to wonder at it all..."My God! It's full of stars!"

Or more accurately..."My God! It's full of galaxies! No, universes!"

 

[megacal]

Hi Marcus,

I've started going through this thread methodically, and am only stumbling over this
part of the BA as you describe how to visualize it mentally:

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.

Ok, no inside or outside...is there the other side? i.e. is the curve continuous
to form a sphere? (balloons are so asymmetrical). Is the surface of the BA convex?
Would a disk would be a better analogy(?)

BTW, looked up the ΛCDM (Wiki), and that was very helpful.

 

[megacal]

Marcus,
came to realize I'm way out classed here...like a penguin trying to fly with eagles.

But more importantly, found I really don't need an answer now..."It is what it is"...
infinitely academic and all answers are uncertain and speculative, e.g. like the shape & size of the universe(s), what was before, and what's next billions of years from now.

But I appreciate your time, consideration, & trying to help me understand, and wish you
good speed as you & your group of fellow cosmologists wrestle with Dark Energy, Dark Matter, Quantum Gravity, strings, foam & fuzzballs.

I'll watch from afar and take more Advil.

 

[marcus]

Hi Marcus,

I've started going through this thread methodically, and am only stumbling over this
part of the BA as you describe how to visualize it mentally:
Ok, no inside or outside...is there the other side? i.e. is the curve continuous
to form a sphere? (balloons are so asymmetrical). Is the surface of the BA convex?
Would a disk would be a better analogy(?)

BTW, looked up the ΛCDM (Wiki), and that was very helpful.

Thanks for going back and reading more of the thread. I might be able to concentrate it into two or three current posts but a loose informal format has some plus sides too. Cosmology forum has a good FAQ compiled largely by Ben Crowell (prof at a college in Calif. and author of several online books if I'm not mistaken). It's my fault not yours that this thread is all spread out so that a newcomer can miss important details!

Like yes, the balloon model space is a closed edge-less 2D space. It is not like a disk. It is in all respects like the zero-thickness 2D surface of a ball or balloon EXCEPT WITHOUT THE INSIDE OR OUTSIDE 3D SPACE.

In math that is possible. You can have, and work with, and calculate with, a 2D object that does not "LIVE" in any surrounding 3D space. We say the 2D objected is not embedded in a larger 3D space. Although in some cases it COULD be embedded, but that might involve unnecessary complication.

It's not something to get a headache about, it is just people simplifying their lives by not assuming or worrying about a higher dimensional surround. Because back in 1820-1850 some guys figured out how to work within a curved space and do all the geometry and calculus they wanted without reference to points outside. It turns out that once you are equipped with the techniques, and if you have no evidence of there being an external higher dimensional space, it can be a lot simpler to just work within the given geometry and not "make up" something surrounding it.

So in that little movie of the expanding balloon surface, it really is a 2D sphere. You can probably see some photons of light going around to the other side and disappearing at your horizon, and some others coming from the other side and appearing on the horizon and moving in.

And although the balloon could obviously be embedded in a larger 3D room, and have existence inside and outside of the surface, you are encouraged to imagine it as a pure 2D thing with zero-thickness creatures and galaxies, and no inside or outside. That is encouraged because it is good practice for going mentally up one higher dimension and imagining our 3D world in an analogous way. We can't point our fingers out of it and we have no evidence of a larger surround. So we accept our limitations and don't make things up. There is no center point (in our 3D world) of the expansion. At least that is how people have over the years found it works best to think about it.

One reason it's simpler is that when uneven curvature develops, and maybe even forms an extreme case of a black hole, you don't have to worry about where it "goes"---did the black hole go inside, or outside?---no. there isn't any inside or outside, I don't have to worry. and an infinite uncurved 3D space doesn't have any inside or outside, it just has itself, so it is very much like the limit of a curved 3D space where you just let the sphere get bigger and bigger and the curvature peter out to zero. So the flat 3D case is "of a piece" with the curved 3D case, neither are embedded.

 

[megacal]

Hi Marcus,

thank you for that explanation, although it went in one neuron and out the other.
Higher math concepts are just beyond me...I think if I meditated on it long enough
it may congeal, but feeling a bit dizzy at the moment.

It is in all respects like the zero-thickness 2D surface of a ball or balloon EXCEPT WITHOUT THE INSIDE OR OUTSIDE 3D SPACE.

...do you literally mean zero thickness? Do you mean very very thin compared to the other axes?

Is the BA just a mental excercise or supposed to describe another possible model of the universe? Maybe I don't understand the object of the thread.

I'm probably hampered in that I think left-brained & most of my concentration is on 3D programs...creating fluid simulations, other worlds, and now 3D fractals. (I wonder if fractal geometry shows up in the largest structures?)

Seriously, I do appreciate your reply and will read it (and meditate on it) to see if
the fog lifts & I can say, "Aha! So that's what he meant!"

And I really did have a throbbing headache when I posted last, though not sure if
trying to grok the BA was the source.

 

[marcus]

Hi Marcus,

thank you for that explanation, although it went in one neuron and out the other.
Higher math concepts are just beyond me...I think if I meditated on it long enough
it may congeal, but feeling a bit dizzy at the moment.

...do you literally mean zero thickness? Do you mean very very thin compared to the other axes?

Is the BA just a mental excercise or supposed to describe another possible model of the universe? Maybe I don't understand the object of the thread.

I'm probably hampered in that I think left-brained & most of my concentration is on 3D programs...creating fluid simulations, other worlds, and now 3D fractals. (I wonder if fractal geometry shows up in the largest structures?)

Seriously, I do appreciate your reply and will read it (and meditate on it) to see if
the fog lifts & I can say, "Aha! So that's what he meant!"

And I really did have a throbbing headache when I posted last, though not sure if
trying to grok the BA was the source.

Take care of yourself! Avoiding throbbing headaches and enjoying the life are ultimately more important than understanding the universe. The universe does not want you to have a painful headache and it wants to be enjoyed even more than understood. It's a beautiful day here, by the way. cold air blue sky bright sunlight.

I actually meant zero thickness. A truly 2D world. And the balloon analogy (BA as you say) is really meant as an ANALOGY not a possible model of real cosmos. You can think of it as a "toy" model dumbed down from 3D (which we see) to 2D (where zero thickness amoebas live in zero thickness houses in zero thickness galaxies.)

But if thinking about that 2D expanding balloon analogy does not make you happy and relaxed you should not feel you have to!

Another avenue is to think about our own familiar 3D space as very large but curving very gently so that you could actually circumnavigate it (if you had enough time and fast enough motor scooter and it wasn't expanding). The main thing is to be able to imagine space as EDGELESS or boundaryless, and approximately evenly scattered with matter. The largescale picture looks kind of like cobweb-filled attic where the galaxies and irregular clusters of galaxies and wispy clouds of dark matter form the cobwebs that fill ALL of space.

The edgelessness and approximate on average even distribution of matter are the important things, basic to the picture that cosmologists have. They haven't seen any convincing evidence of an edge or some major largescale unevenness. So they keep it simple and don't make up stuff they haven't seen like that.

Maybe if you take a break from it and come back later it will seem natural to you. I think if it is stressful for you it could be because I have explained it the wrong way.

 

[megacal]

Maybe if you take a break from it and come back later it will seem natural to you.

...Ok...will get back asap if I have a sudden epiphany.

I think if it is stressful for you it could be because I have explained it the wrong way.

No, not at all...the failure to comprehend it is only due to my lack of background and possibly how my brain is wired. The BA just doesn't correlate with anything I can relate to...it's something I have to imagine.

But am hoping it will come into focus all of a sudden. I'm sure your explanation is perfectly
sound...it just sounds impossible. , no offense.

 

[marcus]

Jorrie calculator

Jorrie (fellow PF member) has an online cosmology calculator that embodies the standard model of the U, just as Morgan's and Ned Wright's do
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc.htm

It has some extra features and some advantages that make it easier to use, in certain respects. May also have additional precision at high redshifts. So it is definitely worth checking out.

If you want to use it and don't have the URL handy, you can (I find) get it by googling
"cosmological calculator 2010"

i know you can get Ned Wright's cosmo calculator simply by googling "Wright calculator" (or you could the last time I tried) so I am also going to try getting Jorrie's by googling: "Jorrie calculator".

It helps to have tags that are easy to remember, saves time and fumble.

 

[megacal]

Hi Marcus,

thanks for those links.

BTW, did you get my pm?

 

[marcus]

I remember that pacific coast sunset you have a picture of at your website (that you pm'd about). Our relatives had a family reunion one year at Carlsbad CA. Our motel was right on the beach and it looked just like that. I'll pass on the Blender idea, though. Right now, when I remember to do it, I stash links in the Astro/Cosmo forum "AC Reference Library" thread.

 

[megacal]

re: Carlsbad...camping there 3 nights starting tomorrow...hope to get more sunsets.

Sent you another pm.

 

[Zygsterz]

As I understand it, the further we look out into the universe, the faster objects are accelerating. Expansion of gases in a vacuum has a delta V term, but wouldn't there be a jerk term to our observations? It would seem to me only if space was collapsing in dense areas and expanding in thin areas while objects are accelerating through collapsing or expanding space would we see objects have different accelerations the further out they are.

 

[marcus]

As I understand it, the further we look out into the universe, the faster objects are accelerating. Expansion of gases in a vacuum...

You seem to have a definite physical model in mind. I don't think this thread is the right place to discuss it. Please start your own discussion thread, you could even use the same post.

I'd be happy to reply, if you start a separate thread, and quite possibly others would want to reply also. But it doesn't fit in here, which is about the standard cosmo picture often illustrated using the balloon analogy.

 

[3112100000]

i have this understanding please correct me if I am wrong I am taking the mental freedom

expansion of universe is causing the galaxies to move away so universe has to be expanding from a given "dense source" which is loosely held,not stretched to its maximum like blowing a baloon which make sense why galaxies are moving away

(not like rolling out a carpet like stuff just rolling out from both end which does not stretch laid out part ie the expansion is not caused by creation of new substance(emptiness or whatever))

and as universe stretches further the inward bend or the concave curve made by matter (gravity) will eventually become flatten,flattening starts out from the outer realms of gravity, like if we take solarsystem for example as all the matter in universe then pluto will be the first to be free and it just drift off in the direction of kinectic energy and then neptune uranus as universe expands...an observer from Earth see farther planets moving away faster than nearer planets..

if we follow the life of pluto as representative of all matter after some time it will lose its kinectic energy and come to a still it will not orbit anything then pluto enters into another epoch where it just sit idly for gazillion million billion trillion years waiting for all protons to decay and ultimately dissolves in vacuum

 

[Drakkith]

expansion of universe is causing the galaxies to move away so universe has to be expanding from a given "dense source" which is loosely held,not stretched to its maximum like blowing a baloon which make sense why galaxies are moving away

What do you mean by "expanding from a given dense source"? I don't understand your analogies.

 

[3112100000]

What do you mean by "expanding from a given dense source"? I don't understand your analogies.

im too confused now i actually meant it like explosion of a bomb or fireworks but i now doubt it

if universe is just full of vacuum or space with no particles that is how universe is supposed to be i mean space doesn't need to be created anything created will be finite if space does not existed then we need space to put in space so only paradox in my view which need to be solved is matter particles and life/consciousness

bigbang i think is only created matter and matter life how could space expand if its expanding then it must be finite that doesn't make sense i can't digest expansion of space

 

[Drakkith]

The universe isn't "supposed" to be like anything, it exists as it is. The rest of your post can be answered by looking at the FAQs in the cosmology section. Your view on it is not anything like the current scientific model.

 

[3112100000]

The universe isn't "supposed" to be like anything, it exists as it is. The rest of your post can be answered by looking at the FAQs in the cosmology section. Your view on it is not anything like the current scientific model.

universe is supposed to be vacuum with no matter or energy or nothing but perfect nothing i can't take universe as it is like now how did all these stuff come into existence out of nothing

i had read quantum fluctuations proton is made of 90% nothing ?and bigbang it says star burns for abt 10 billion years but bigbang is predicted to be happened only 13 billion years ago ?

these theories and explanations is still building up and people with basic understanding can make assumptions
i have doubts which cannot be cleared with current understsnding of universe i don't think any significant breakthrough in cosmology will be made in my lifetime

 

[Drakkith]

universe is supposed to be vacuum with no matter or energy or nothing but perfect nothing i can't take universe as it is like now how did all these stuff come into existence out of nothing

No one anywhere who knows what they are talking about will tell you that they are sure that the universe came from nothing. That isn't even possible to verify. The truth is that we simply don't know. And please, don't try to tell me the universe is supposed to be vacuum with no matter or energy. You have absolutely no way of knowing that.

i had read quantum fluctuations proton is made of 90% nothing ?and bigbang it says star burns for abt 10 billion years but bigbang is predicted to be happened only 13 billion years ago ?

Attempting to ask what a proton is made up is inherently complicated unless you understand quantum mechanics. At that scale things are NOT like they are for us in our everyday life. Saying that is 90% empty space is a very limited way of looking at it and probably isn't correct.

And I'm not sure what your problem with stars burning for 10 billion years is. If the universe is 13 billion years old it is possible to have stars which have already burned that length of time.

i have doubts which cannot be cleared with current understsnding of universe i don't think any significant breakthrough in cosmology will be made in my lifetime

It sounds to me like you simply don't have a good grasp of the basics and are getting confused. I suggest you just keep learning the basic concepts.

 

[3112100000]

No one anywhere who knows what they are talking about will tell you that they are sure that the universe came from nothing. That isn't even possible to verify. The truth is that we simply don't know. And please, don't try to tell me the universe is supposed to be vacuum with no matter or energy. You have absolutely no way of knowing that.

matter has to be created it is the product of some process like life which is a product of matter that we can say for sure .so matter has to be churned out i know you don't agree I am also not sure of this, I am talking probablities

there got to be something incredible that we don't know yet
if physicist can tell what causing strong nuclear force & gravity rather than how these force works

 

[Drakkith]

matter has to be created it is the product of some process like life which is a product of matter that we can say for sure .so matter has to be churned out i know you don't agree I am also not sure of this, I am talking probablities

there got to be something incredible that we don't know yet
if physicist can tell what causing strong nuclear force & gravity rather than how these force works

Our current knowledge can only get us so far. Instead of saying "this MUST be true" you would be much better off learning about what we currently know and how we know it.

 

[alphachapmtl]

i have this understanding please correct me if I am wrong I am taking the mental freedom

expansion of universe is causing the galaxies to move away...

Maybe galaxies are not moving away but shrinking.
The end result would be the same (redshift , etc...)

 

[alphachapmtl]

As I understand it, the further we look out into the universe, the faster objects are accelerating...

Moving away, not accelerating.

 

[Drakkith]

Maybe galaxies are not moving away but shrinking.
The end result would be the same (redshift , etc...)

This is not an accepted view.

 

[salvestrom]

This is not an accepted view.

Doesn't it actually require the complete opposite of the bing bang: a large space with diffuse matter that slowly coalleces overtime and shrinks into a denser and denser state?

 

[zbe]

Hi everyone.

I have a question. As already mentioned the measurments tell us the universe is flat or nearly flat. It was also stated that only closed universe would be spatialy finite and both the open and flat one would be infinite. My question is: How can universe have a beginning and is spatialy infinite? It is widely accepted that our universe has a beginning so wouldn't that suggest that our universe is either closed or that flat/open universe doesn't have to be infinite, somehow? =)

Please, tell me if I am missing something.

Regards.

 

[marcus]

... It was also stated that only closed universe would be spatialy finite and both the open and flat one would be infinite.

There are so many concepts here it makes for confusion. I'm not sure what you mean by "open" and "closed".
Let's talk about the meaning of words another time. I understand you when you say spatially finite and spatially infinite. Either could be the case. We don't know yet which is more supported by the evidence. I don't believe either. I am waiting to see more evidence.

It is widely accepted that our universe has a beginning

I don't think there is any scientific evidence that our universe had a beginning. The "big bang" is not necessarily the beginning of time. It could have been preceded by a contraction. All that the evidence suggests is that the expansion that we see apparently had a beginning. We can follow time back to a very dense state. I am waiting for the models/theories to be tested, that go back further.

My question is: How can universe have a beginning and is spatialy infinite?

I don't see any contradiction. Personally I do not believe the U had a beginning because I do not see any observational evidence to support that belief. It is always possible that what we can understand and explain will go back farther in time as our science gets better. There is no fixed limit on how far back in time we can discover explanations and causes.

Understanding is a gradual step-by-step process. Perhaps it never ends. Right now our job is to understand what caused the start of expansion (the "big bang").

But maybe you know somebody who believes the U had a beginning! There are people who believe this! Let's say this person is named Bob. If Bob is able to imagine that the U had a beginning, then why can't he also imagine that the U is spatially infinite? What is the problem? Both things are hard to imagine, I admit. (And I prefer not to believe either, since there is no hard evidence for either.) But I don't see any contradiction.

If someone is able to believe that the U had a beginning, and wants to believe that, then why can't they also believe that it is spatially infinite, if they want? We should just let them think what they want.

 

[cepheid]

But I don't see any contradiction.

The contradiction would seem to be that the scale factor goes to 0 as t → 0. That seems to suggest that as you go back in time, everything collapses down to a singular point. For any finite spatial volume, that sort of almost even works, because it means that the universe contracts to zero size as you go back in time to the beginning of the expansion. I suppose you could view this as the expansion of spacetime from some "initial singularity" of infinite density, but that sounds like nonsense -- what does it even mean? So what it really seems to mean is that our current physics breaks down and is incapable of describing what happens at t = 0. This is my view, actually. For me a singularity is just a mathematical problem having no physical significance other than, "your equations don't work here."

For an infinite spatial volume, even if the scale factor goes to zero, it doesn't mean that the universe goes to zero size. It just means that what happens as t → 0 is undefined. (Even more undefined than in the finite case). So the point is, since the universe having a beginning (or at least a beginning of the expansion) seems to require the scale factor going to zero, and since it's undefined what happens to a infinite spatial volume under these circumstances, it seems that (spatially infinite universe + beginning of expansion) doesn't make sense conceptually. (Then again, neither does "initial singularity.")

Am I thinking of this along the right lines? I really could use your insight here.

 

[marcus]

I think along similar lines. GR develops a singularity. A singularity means the theory is breaking down and you have to stop trusting it. Any manmade theory will have a limited "domain of applicability" and will give a worse and worse approximation to nature as you approach where it breaks down.

I'd say you are thinking along the right lines, but I'm not an authority on this or anything really. All I can do is observe that what you say makes perfectly good sense to me. (You may know more than I do about this in fact.)

I think we are in a transitional situation where everybody realizes that classical GR has limited applicability and we need a quantum theory of the U's changing geometry. So various theories are being developed and replacements and no one stands out as favorite.
GR is a non-quantum vintage 1915 theory of dynamic geometry (how it changes and interacts with matter). It's beautiful and exquisitely accurate over its vast range of applicability. Only a few flaws and blemishes at the extreme limits.

So people are now proposing quantum geometry theories that attempt to extend the domain of applicability. Cover for classical everywhere that classical is good PLUS push the bounds of what we understand just a little bit further, to understand better around the start of expansion and the pits of black holes.

It would be nice if a quantum geometry could also explain the cosmological constant too (maybe it arises in some natural way from the quantum theory, a natural tendency for expansion to accelerate? well...) It would be nice if a quantum geometry would tell us that tiny microscopic primordial black holes don't evaporate quickly (classically or semiclassically they do so we wouldn't expect to see any, but what is "dark matter"?)

Lots of things would be nice. But the main thing is to resolve the "initial" singularity and get a testable model of what was happening around the time expansion started.
A testable model that also reproduces the beautiful classical picture, with the same fine accuracy.

We're talking attitudes/opinions at this point. I told you mine. it's similar to what you said, I think.

 

[marcus]

Wow! I just looked at your "about me". You picked really interesting things to get a PhD in!
That stuff has the potential to really open up and get increasingly significant over the next 20 years IMHO. I'm just a retired mathematician who loves cosmology. I should be listening to you, not the other way around Good career and life choices!

 

[zbe]

There are so many concepts here it makes for confusion. I'm not sure what you mean by "open" and "closed".

By "open" and "closed" (or flat) I mean the curvature of the universe. And (on page 3 or 4) it was said that only closed universe would "guarantee" finite space --- but it looks like it is infinite since we most likely live in a flat universe.

I don't think there is any scientific evidence that our universe had a beginning. The "big bang" is not necessarily the beginning of time. It could have been preceded by a contraction.

I think that all our knowledge ATM goes towards notion that the beginning of our universe (big bang) is the most acceptable truth unless I am missing something here. It could have been preceded by a contraction indeed but that would not change the contradiction.

All that the evidence suggests is that the expansion that we see apparently had a beginning. We can follow time back to a very dense state. I am waiting for the models/theories to be tested, that go back further.

Exactly. That is my point. How could you follow - in a finite amount of time - infinitely big universe to a finite (or infinitely small, it doesn't matter) universe.

Understanding is a gradual step-by-step process. Perhaps it never ends. Right now our job is to understand what caused the start of expansion (the "big bang").

I couldn't agree more. The only thing that bothers me is why could there even be a possibility that universe is infinitely large since it has a start - of expansion.

But maybe you know somebody who believes the U had a beginning! There are people who believe this! Let's say this person is named Bob. If Bob is able to imagine that the U had a beginning, then why can't he also imagine that the U is spatially infinite? What is the problem? Both things are hard to imagine, I admit.

IMHO both things aren't hard to imagine unless they are both true for the same thing. =) Look at it that way: A 1x1x1 (cm, doesn't matter) cube is born.=) It grows. In what time does it reach infinity? Never! Or better - in infinite time. I say F*** infinity since it has nothing to do in physics.=)

Also, I would guess my point is somehow the other way around of the cepheid's one.

I strongly agree with everything known in cosmology, this is just one of the rare questions that popped in my mind while reading this thread. =)

Regards.

 

[cepheid]

Wow! I just looked at your "about me". You picked really interesting things to get a PhD in!
That stuff has the potential to really open up and get increasingly significant over the next 20 years IMHO. I'm just a retired mathematician who loves cosmology. I should be listening to you, not the other way around Good career and life choices!

Thanks for the kind words. I'm not a theorist and don't have really in-depth knowledge of General Relativity, just the basics and certain things that are applicable to cosmology. But I'm trying to learn it, over and above "building stuff" to collect more data via observations which is my main pastime, as you probably gathered.

 

[mysearch]

The contradiction would seem to be that the scale factor goes to 0 as t → 0. That seems to suggest that as you go back in time, everything collapses down to a singular point...It just means that what happens as t → 0 is undefined.

I don't think there is any scientific evidence that our universe had a beginning.

I say **** infinity since it has nothing to do in physics.

Hi,
I hope the extracts above and the highlighted words from previous posts do not misrepresent the original context, as they seem to capture some key issues, which I would like to raise. In the first quote, the key word appears to be whether ‘everything’ in the totality of the universe expanded from some conceptual singularity? In my own personal review of the various cosmology models, there seems to be plenty of scope to, at least, speculate that the expansion of what we often describe as the universe is only part of some larger process/universe.

I agreed that what happens as t->0 is ‘undefined’ in terms of current science, i.e. both GR & QFT, although we might be allowed to speculate that our ‘universe’ could have been triggered by some sort of quantum process within some larger definition of the universe.

In this respect, the speculative larger universe might not have any obvious ‘beginning’, although it might still be correct to say that our ‘local’ universe came into existence some 13.7 billion years ago.

However, there still appears to be the troublesome issue of infinities, which I am not sure that physics or the maths can ultimately avoid. If the common description is taken at face value, then you have to explain a universe, which is 13.7 billion years old, created from a singularity of near ‘infinite’ density that would conceptually occupy a near infinitely small volume, outside of which ‘absolute’ nothing exists or has ever existed. In this context, the issue of ‘creation’ from absolute nothing always seemed a bit metaphysical for my taste. Of course, the speculative model suggested cannot really avoid infinities, as the idea of an extended universe suggests a possibly infinite size and infinite age. Maybe Marcus, as a mathematician, and Cephid, as an astrophysicists, might like to comment further on such issue. Thanks

 

[marcus]

To be honest, I'd appreciate it if anyone who wants to talk about these more philosophical matters would start a separate discussion thread. The original topic here is the most basic idea in cosmology: the pattern of expanding distances between observers at rest relative to the ancient light.
It's very much for beginners.
The idea is well conveyed by Ned Wright's short computer animation plus discussion of quantitative basics such as universe time, Hubble law, proper distance.

To get the brief movie diagramming expansion, google "wright balloon model". In a diagrammatic 2D analogy it shows photons moving at constant speed THRU space while the galaxies remain approximately at rest.

 

[mysearch]

To be honest, I'd appreciate it if anyone who wants to talk about these more philosophical matters would start a separate discussion thread. The original topic here is the most basic idea in cosmology: the pattern of expanding distances between observers at rest relative to the ancient light. It's very much for beginners.

Marcus, my apologises, I will happy comply with the original intention of this thread. However, it might be argued that the issues raised were not intended to be philosophical as they would seem to define the boundary conditions of any cosmological model. Equally, many of the questions within this thread appear to stem from certain assumptions about the implied ‘start’ of the Big Bang, the very name of which seems to be the source of much confusion. Again, my apologises.

 

[salvestrom]

The contradiction would seem to be that the scale factor goes to 0 as t → 0. That seems to suggest that as you go back in time, everything collapses down to a singular point. For any finite spatial volume, that sort of almost even works, because it means that the universe contracts to zero size as you go back in time to the beginning of the expansion. I suppose you could view this as the expansion of spacetime from some "initial singularity" of infinite density, but that sounds like nonsense -- what does it even mean? So what it really seems to mean is that our current physics breaks down and is incapable of describing what happens at t = 0. This is my view, actually. For me a singularity is just a mathematical problem having no physical significance other than, "your equations don't work here."

For an infinite spatial volume, even if the scale factor goes to zero, it doesn't mean that the universe goes to zero size. It just means that what happens as t → 0 is undefined. (Even more undefined than in the finite case). So the point is, since the universe having a beginning (or at least a beginning of the expansion) seems to require the scale factor going to zero, and since it's undefined what happens to a infinite spatial volume under these circumstances, it seems that (spatially infinite universe + beginning of expansion) doesn't make sense conceptually. (Then again, neither does "initial singularity.")

Am I thinking of this along the right lines? I really could use your insight here.

I see no reason, so far, not to ponder if t=0 implies the moment at which spacetime was "begun" or created. Just as matter was created via reheat, perhaps the very mechanism that causes space expansion today and since t=planck time, also created the first space. I know I'm not alone in suggesting that what we think of as t=0 may not be the beginning of time. I go further and suggest it may only be the beginning of the spatial universe.

I sometimes feel there's too big a push to "get rid of it" and dismiss the singularity as a breakdown. I understand why, but feel intriguing possibilities are being overlooked.

EDiT: Having said all that, and in reading Marcus's request to not discuss philosophy, I guess I just want to make sure that people understand there isn't a consensus on "the singularity". Only opinion.

 

[GeorgeDishman]

Returning to the original question, I think we have to be careful in pushing the balloon analogy too far. It is easy for beginners to get the impression that it represents the current model when it actually gives the wrong impression in a number of ways. One has already been mentioned, the surface of the balloon is a finite area and while that is good for explaining how a closed universe can be finite but unbounded, it is not applicable to an open universe. This page from the WMAP site gives a balanced view on this:

http://map.gsfc.nasa.gov/universe/uni_shape.html

The second problem is that it is easy in the balloon model to see time as the radius of the sphere with the big bang singularity at the centre. This raises complex questions of a preferred direction of time and the difference between GR in general and specific solutions. An alternative is to still use the spherical shape of the closed model on the WMAP page but treat the big bang as the "south pole" and the big crunch as the north pole. A small area at the equator can then be likened to an x-t spacetime diagram in SR, treating the path of a photon as always being at 45 degrees to a vertical line (of "longitude"). Space is then a horizontal slice, i.e. a circle so a 1-D analog rather than the 2-D usual interpretation of the balloon model. I've heard of this being described as the "American Football" model. Of course that still only applies to the closed solution so the first objection remains valid.

The third problem is that dark energy means expansion is accelerating. Taking the football model and opening the top to eliminate the big crunch and make an inverted bell solves that (although again a horizontal slice remains a circle hence it still models a finite universe) so the "timeline" graphic is IMHO a better representation:

http://map.gsfc.nasa.gov/media/060915/index.html

If the boundaries of the bell are identified with the observable portion, the idea of expansion with infinite extent might be more accessible. The best explanation I have seen of that though is perhaps in Ned Wright's tutorial near the bottom of this page just after the Mercator illustrations:

http://www.astro.ucla.edu/~wright/cosmo_03.htm

"Also remember that the Ωo = 1 spacetime is infinite in extent so the conformal space-time diagram can go on far beyond our past lightcone".

That can also be extended to illustrate non-ovelapping Hubble volumes as in Figure 2 in this paper:

http://arxiv.org/abs/gr-qc/0102010

Sorry if some of this has been covered before, I'm new here and it's long thread but the Balloon analogy was intended to illustrate a specific concept (finite but unbounded) and IMHO is quite misleading in terms of modern cosmology.

 

[bapowell]

Returning to the original question, I think we have to be careful in pushing the balloon analogy too far.

All good points. For me, the value of the balloon analogy is in showing that the big bang was not a localized explosion occurring in some pre-existing space. This is a common misconception, and despite the cited limitations of the balloon analogy, nicely shows how the big bang can be understood to have occurred everywhere at once, with the isotropic separation of galaxies (dots on the balloon) a result of the expansion of space (the balloon) itself. And yes, this does require that people understand that the singularity is not the center of the balloon, and that while the surface of the balloon exists in a higher-dimensional space, the universe need not, etc.

 

[Perduta]

Physically we observe an accelerated increase in distance between us and entities elsewhere in space. This has been experimentally determined as a function of the distance to said entities expressed in Hubble's law.

Space, however is just a mental concept. Increase brings with it the concept of time, making a 4D space time for which the metric is defined by theory of relativity. Measuring space and time and the permitted geometrical operations within it are formulated in terms of conceptual rigid measuring sticks and clocks and in "empty" space, the Lorentz transformation. These are our reference that defines geometry of reality.

Thus IMO we need to get on the same philosophical page of what is meant by "space is expanding". i.e. Evidently our rigid conceptual measuring sticks are not "expanding" and 3 meters in any direction remains 3 meters in that direction regardless.

So my question is to what extent the various cosmic distance definitions (co-moving radial distance, angular size distance, luminosity distance, redshift distance etc...) maintain geometrical correspondence with the established 4D time/space metric of relativity. Would it not be more appropriate to say there is an observed increase in distance to other entities in time space, for which the causal agent is not yet very well understood and would the equivalence principle not allow us to attribute it to a gravitational field that is "outward" bound?

 

[DaveC426913]

Evidently our rigid conceptual measuring sticks are not "expanding" and 3 meters in any direction remains 3 meters in that direction regardless.

Yes. Every day objects are not expanding. Even distances between every day objects are not expanding. It only is measurable on intergalactic scales.

Would it not be more appropriate to say there is an observed increase in distance to other entities in time space, for which the causal agent is not yet very well understood and would the equivalence principle not allow us to attribute it to a gravitational field that is "outward" bound?

Except there is no precedent - nor any reason - to believe gravity has a repulsive counterpart.

 

[Perduta]

Yes. Every day objects are not expanding. Even distances between every day objects are not expanding. It only is measurable on intergalactic scales.

3 meters remain 3 meters and 3 billion light years remain 3 billion light years. They do not expand. Galaxies are just as "everyday" as anything else in the universe and I don't think anyone claims they are expanding. So the philosophical question remains: Exactly what is the thing that science claims is expanding relative to the way we measure dimensions?

Except there is no precedent - nor any reason - to believe gravity has a repulsive counterpart.

Observed Hubble expansion is one reason. Einstein's equivalence theorem is another.

Returning to the balloon analogy we might consider it to be the effect of a gravitational field with it's centre of gravity diametrically opposite us on the balloon and a mass equal to everything in the universe.

 

[Perduta]

Returning to the balloon analogy we might consider it to be the effect of a gravitational field with it's centre of gravity diametrically opposite us on the balloon and a mass equal to everything in the universe.

In fact the more I think about it the more sense this makes: The gravitational field is proportional to the volume integral of all the mass inside the enclosing surface focussed on it's center of gravity... which on the balloon is the entire universe centred on the opposite side of the balloon and that centre of gravity is always relative to each observer... sucking everything away from us.

 

[DaveC426913]

3 meters remain 3 meters and 3 billion light years remain 3 billion light years. They do not expand.

All true.

Galaxies are just as "everyday" as anything else in the universe and I don't think anyone claims they are expanding.

Also true.

So the philosophical question remains: Exactly what is the thing that science claims is expanding relative to the way we measure dimensions?

The distances between things.

Galaxy A and galaxy B may be 10 billion light years apart today, but a billion years from now they might be 20 billion light years apart.

Observed Hubble expansion is one reason.

No, that's what you're trying to demonstrate. You can't use your premise as evidence that your premise is true.

Einstein's equivalence theorem is another.

I think you'll have to spell this out explicitly. I don't think it fits the way you think it does.

Returning to the balloon analogy we might consider it to be the effect of a gravitational field with it's centre of gravity diametrically opposite us on the balloon and a mass equal to everything in the universe.

So, there's a special place somewhere out in the universe that's compact and has the mass of the entire universe? This seems plausible to you?

And it is exactly opposite our location? If I went to a star 5 billion light years away, would it be exactly opposite that point too?

If yes, that's impossible - the attractor can't be in two places at once.
If no, then just like in your balloon analogy extension, the Earth holds a very special place in the universe, violating the principle of mediocrity.

 

[Perduta]

All true.
So, there's a special place somewhere out in the universe that's compact and has the mass of the entire universe? This seems plausible to you?...

And it is exactly opposite our location? If I went to a star 5 billion light years away, would it be exactly opposite that point too?

If yes, that's impossible - the attractor can't be in two places at once.
If no, then just like in your balloon analogy extension, the Earth holds a very special place in the universe, violating the principle of mediocrity.

No it is not impossible at all in fact it is nearly inevitable. It is quite simply the plain old concept of centre of gravity.

To understand this, reflect first on how we would calculate the Earth's gravitational force at a point inside the Earth. The answer comes from Gauss' law.

Then replace that with doing the equivalent for being inside the universe: First think of our balloon again. Pick any point you like to represent us. What would you say is going to be the centre of gravity of the entire 2D balloon for that point? How would you apply Gauss' law on the balloon? Which way does the gravity suck things?

 

[DaveC426913]

You said there's a special place on the balloon "diametrically opposite us". Which means it can't be diametrically opposite any other point. That means our spot on the balloon is special - unlike any other point on it.

Try reviewing your extension to the balloon analogy.

Where are we on the balloon? Call it point A
Where is this diametrically opposite point? Call it point A'.
How does A' behave such that it affects A? Does it contract ('suck' things)?

OK, now. Pick a point 90 degrees around the balloon from us. Call it point B.
Does it see our point (A')? Or its own (B')?
Does it see exactly the same phenomena there as we do here? (equal 'sucking' in all directions?)

If the former, then we see a unique view of the universe, shared by no other point,
If the latter, then you have two x' points. Indeed, you have infinite n' points, one for each x.

 

[Perduta]

... If the latter, then you have two x' points. Indeed, you have infinite n' points, one for each x.

Correct. Every point in the universe sees everything else falling away from them just like we do. That is because the centre of gravity of the universe is unique to every observer.

Observers at your point A will see point B falling towards your A'. Observers at B will see A falling towards B' ...and so on. Thus the explanation for accelerated expansion of the universe and redshift is amazingly simple and consistent with Einstein's equivalence principle. It also explains why the space/time each observer sees and the apparent relative movement is different too.

p.s. also it explains why the acceleration was greater in the past and will keep getting smaller in the future: In the past the balloon was smaller so the centre of gravity was closer and we all know that gravity decreases with distance.

 

[Drakkith]

p.s. also it explains why the acceleration was greater in the past and will keep getting smaller in the future: In the past the balloon was smaller so the centre of gravity was closer and we all know that gravity decreases with distance.

The expansion is accelerating and will become greater in the future. However this did not start to happen until recently. Prior to this point in time the expansion was slowing down because of gravity.

 

[DaveC426913]

Correct. Every point in the universe sees everything else falling away from them just like we do. That is because the centre of gravity of the universe is unique to every observer.

Observers at your point A will see point B falling towards your A'. Observers at B will see A falling towards B' ...and so on. Thus the explanation for accelerated expansion of the universe and redshift is amazingly simple and consistent with Einstein's equivalence principle. It also explains why the space/time each observer sees and the apparent relative movement is different too.

Then you have not described anything new at all. In order for each point to see every other point as receding, the balloon must be expanding consistently, at every point on its surface, which is exactly what the model shows in the first place.

 

[Perduta]

The expansion is accelerating and will become greater in the future. However this did not start to happen until recently. Prior to this point in time the expansion was slowing down because of gravity.

Meh - I read somewhere that the Hubble constant was decreasing. I.e in the future galaxies at a certain distance will be accelerating slower than the ones we can see currently at that same distance.

OTOH if it is true that the universe is breeding more and more dark matter/energy to fill it's expansion then the total mass will keep growing in proportion to the volume i.e R³ while gravity decreases with R², so that would make sense too as the acceleration would then be proportional to the Radius of the universe and eventually we would get to the point where evereything is just ripped apart. It all depends on this dark matter malarkey.

p.s. Note: In the 2D balloon model the radius of the universe woulod correspond to half the circumference of the balloon.