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Effort to get us all on the same page (balloon analogy) 
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#235
Feb2812, 09:40 AM

Astronomy
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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. 


#236
Feb2912, 04:41 AM

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#237
Feb2912, 04:43 PM

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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. 


#238
Mar1212, 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 xt 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 1D analog rather than the 2D 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 spacetime diagram can go on far beyond our past lightcone". That can also be extended to illustrate nonovelapping Hubble volumes as in Figure 2 in this paper: http://arxiv.org/abs/grqc/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. 


#239
Apr212, 08:30 PM

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#240
Apr2512, 06:49 PM

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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 (comoving 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? 


#241
Apr2512, 07:38 PM

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#242
Apr2512, 08:53 PM

P: 10

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. 


#243
Apr2512, 09:02 PM

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#244
Apr2512, 09:59 PM

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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. 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. 


#245
Apr2512, 10:20 PM

P: 10

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? 


#246
Apr2512, 10:30 PM

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. 


#247
Apr2612, 04:42 AM

P: 10

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. 


#248
Apr2612, 07:59 AM

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#249
Apr2612, 08:11 AM

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#250
Apr2612, 08:47 AM

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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. 


#251
Apr2612, 08:59 AM

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#252
Apr2612, 09:01 AM

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