Register to reply

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

by marcus
Tags: analogy, balloon, effort
Share this thread:
marcus
#235
Feb28-12, 09:40 AM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 23,125
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
#236
Feb29-12, 04:41 AM
PF Gold
mysearch's Avatar
P: 521
Quote Quote by marcus View Post
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
#237
Feb29-12, 04:43 PM
P: 226
Quote Quote by cepheid View Post
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
#238
Mar12-12, 04:21 PM
P: 255
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 ballon 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 ballon 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
#239
Apr2-12, 08:30 PM
Sci Advisor
P: 1,676
Quote Quote by GeorgeDishman View Post
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
#240
Apr25-12, 06:49 PM
P: 10
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
#241
Apr25-12, 07:38 PM
DaveC426913's Avatar
P: 15,319
Quote Quote by Perduta View Post
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.

Quote Quote by Perduta View Post
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
#242
Apr25-12, 08:53 PM
P: 10
Quote Quote by DaveC426913 View Post
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?

Quote Quote by DaveC426913 View Post
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
#243
Apr25-12, 09:02 PM
P: 10
Quote Quote by Perduta View Post
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
#244
Apr25-12, 09:59 PM
DaveC426913's Avatar
P: 15,319
Quote Quote by Perduta View Post
3 meters remain 3 meters and 3 billion light years remain 3 billion light years. They do not expand.
All true.
Quote Quote by Perduta View Post
Galaxies are just as "everyday" as anything else in the universe and I don't think anyone claims they are expanding.
Also true.
Quote Quote by Perduta View Post
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.


Quote Quote by Perduta View Post
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.

Quote Quote by Perduta View Post
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.

Quote Quote by Perduta View Post
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
#245
Apr25-12, 10:20 PM
P: 10
Quote Quote by DaveC426913 View Post
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
#246
Apr25-12, 10:30 PM
DaveC426913's Avatar
P: 15,319
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
#247
Apr26-12, 04:42 AM
P: 10
Quote Quote by DaveC426913 View Post
... 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
#248
Apr26-12, 07:59 AM
Mentor
Drakkith's Avatar
P: 11,619
Quote Quote by Perduta View Post
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
#249
Apr26-12, 08:11 AM
DaveC426913's Avatar
P: 15,319
Quote Quote by Perduta View Post
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
#250
Apr26-12, 08:47 AM
P: 10
Quote Quote by Drakkith View Post
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.
bapowell
#251
Apr26-12, 08:59 AM
Sci Advisor
P: 1,676
Quote Quote by Perduta View Post
=
while gravity decreases with R²
Oh goodness. Are you really thinking Newtonian gravity here?
Perduta
#252
Apr26-12, 09:01 AM
P: 10
Quote Quote by DaveC426913 View Post
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.
Except that I give an explanation for what makes the balloon expand.


Register to reply

Related Discussions
The balloon analogy (please critique) Cosmology 64
Update to the BALLOON ANALOGY web page Cosmology 2
Balloon Analogy Cosmology 1
Charge movement in a magnetic field along the z-axis (into page/out of page) Introductory Physics Homework 16