Question about Balloon Universe model

[coversation]

I've got a sorta weird question about the common "dots on a balloon" model for the expansion of space. The model works like this: Dots are marked across a balloon's surface and the balloon is then inflated partially. The distance between dots is measured, then the balloon is inflated further and the distance measured again. The demonstration shows that the further away each dot is from a reference point, the faster it is moving away. Great. My question goes a little bit farther. The "universe" of the balloon (let's call it a perfect sphere just for simplicity's sake) has three dimensions since the simulated galaxies are flat dots: length, width, and time. The distance between two "galaxies" can be measured in meters. The surface area of the balloon (the total area of the universe) can be measured in meters squared. What, then, does the volume of the balloon in meters cubed represent?

My very shaky guess:
Time can also be represented in meters in this model, but not meters on the balloon's surface--meters into the balloon. Given this, the volume of the universe is length * width * time, giving a unit of cubic meters which represents three dimensional spacetime.

[EdgarJPublius]

In this model, the universe being described is actually two-dimensional. The volume of the balloon is ignored.

That's just one reason why I prefer the 'raisin-bread' or 'chocolate-chip cookie' model where the dots (or 'chocolate chips') move away from each other in three dimensions as the dough rises and expands.

[eSOANEM]

It doesn't. The balloon universe is only an analogy so it has a couple of flaws when interpreted as the real thing, the most obvious being that it leads to the questions "what is inside/outside the universe" neither of which have answers, they're equivalent topologically to asking what is north of the north pole.

[Dr. Diaphanous]

It doesn't. The balloon universe is only an analogy so it has a couple of flaws when interpreted as the real thing, the most obvious being that it leads to the questions "what is inside/outside the universe" neither of which have answers, they're equivalent topologically to asking what is north of the north pole.

Surely in the balloon universe, the inside of the balloon is the past and the outside is the future, where the surface of the balloon is the present (assuming it is expanding).

And surely the volume of the balloon can be used as a meaningful measure (giving a volume in square-metre-seconds) or analogously for the universe (a four-dimensional measure in cubic-lightyear-seconds). My house is 315 Megalitre-years big/old.

[Aelfyre]

It doesn't. The balloon universe is only an analogy so it has a couple of flaws when interpreted as the real thing, the most obvious being that it leads to the questions "what is inside/outside the universe" neither of which have answers, they're equivalent topologically to asking what is north of the north pole.

Surely in the balloon universe, the inside of the balloon is the past and the outside is the future, where the surface of the balloon is the present (assuming it is expanding).

And surely the volume of the balloon can be used as a meaningful measure (giving a volume in square-metre-seconds) or analogously for the universe (a four-dimensional measure in cubic-lightyear-seconds). My house is 315 Megalitre-years big/old.

this would only hold if you take as given the assumption that the universe will always be expanding. If for whatever reason it were to reverse and begin to contract that would be in effect backwards time travel in your model.

[eSOANEM]

And surely the volume of the balloon can be used as a meaningful measure (giving a volume in square-metre-seconds) or analogously for the universe (a four-dimensional measure in cubic-lightyear-seconds). My house is 315 Megalitre-years big/old.

And how is that measure useful? Sure you can multiply the things together to get some sort of 4-volume, but unless it has some physical use, it's completely pointless.

this would only hold if you take as given the assumption that the universe will always be expanding. If for whatever reason it were to reverse and begin to contract that would be in effect backwards time travel in your model.

This is an important point, but even with the assumption that the universe will always be expanding, "into" the balloon is still not into the past because, if I move into the balloon I am no longer on its surface and have "left" the universe. In order to try and make "into" mean "in the past", you have to actually change your time co-ordinate (note, you don't have to worry about your position as that is taken care of if you work intrinsically).

Ultimately, the problems with the balloon model come from the fact that they teach you to think about the universe extrinsically by embedding it in some bulk space.

We cannot observe anything extrinsic about our universe being, as we are, inside it; as such, all observables are intrinsic properties of the universe.

Because there is no way to observe an extrinsic properties of the universe, we cannot know whether or not there is a bulk space that the universe is embedded in and so, by Occam's razor, it is not the most suitable explanation.

[PM 2Ring]

Surely in the balloon universe, the inside of the balloon is the past and the outside is the future, where the surface of the balloon is the present (assuming it is expanding).

Not quite. To make things easier to visualize, let's drop another dimension and consider a universe with one spatial dimension wrapped around a circular "balloon" in the horizontal plane, with time increasing in the up direction normal to the horizontal. As time increases, a linearly expanding universe traces out the surface of a cone; points inside the cone do not actually exist in our 1+1 dimensional universe.

Ultimately, the problems with the balloon model come from the fact that they teach you to think about the universe extrinsically by embedding it in some bulk space.

We cannot observe anything extrinsic about our universe being, as we are, inside it; as such, all observables are intrinsic properties of the universe.

Because there is no way to observe an extrinsic properties of the universe, we cannot know whether or not there is a bulk space that the universe is embedded in and so, by Occam's razor, it is not the most suitable explanation.

+ eleventy billion.

Modern cosmology eschews "God's eye view" models of the universe. Extrinsic models tend to introduce artifacts that may not be actually real (like the interior of the balloon), and much progress has been made by adopting the approach that the cosmos has to be "self-supporting" and not rely on external support. The various multiverse and brane world theories don't change this, they're just working with a larger cosmos.

[EdgePenguin]

To quote Terry Pratchett (via Death), we are "Trying to understand the complexity of creation via a language that evolved in order to tell one another where the ripe fruit was" http://www.lspace.org/books/dawcn/dawcn-english.html

The balloon analogy is just an anology. If anything, the radial dimension of the balloon is time, but even that is inadequate. Our best understanding of the large scale nature of the Universe is expressed in the mathematics of general relativity, and there is no intellectual shortcut to understanding it.

[Dr. Diaphanous]

there is no intellectual shortcut to understanding it

Awwwww

Not quite. To make things easier to visualize, let's drop another dimension and consider a universe with one spatial dimension wrapped around a circular "balloon" in the horizontal plane, with time increasing in the up direction normal to the horizontal. As time increases, a linearly expanding universe traces out the surface of a cone; points inside the cone do not actually exist in our 1+1 dimensional universe.

OK, so if we put the dimensions back in, we have a five-dimensional universe model, with 3 dimensions of space, 1 of time, and 1 that doesn't exist except for this analogy.
I think I got it.

And surely the volume of the balloon can be used as a meaningful measure (giving a volume in square-metre-seconds) or analogously for the universe (a four-dimensional measure in cubic-lightyear-seconds). My house is 315 Megalitre-years big/old.

And how is that measure useful? Sure you can multiply the things together to get some sort of 4-volume, but unless it has some physical use, it's completely pointless.

There must be something...
What if you were selling fossils to a museum, and they pay more for something that is bigger or older, such that a small old fossil is worth (exactly) the same as one that is twice as big (by volume) but half as old? You could say, "how much will you pay for ten million litre-years of fossils?"
Maybe?

[eSOANEM]

There must be something...
What if you were selling fossils to a museum, and they pay more for something that is bigger or older, such that a small old fossil is worth (exactly) the same as one that is twice as big (by volume) but half as old? You could say, "how much will you pay for ten million litre-years of fossils?"
Maybe?

This is an artificial use. When I say what use is there for this measure, I don't mean what economic system can you construct which uses it, I mean, what physical process can you construct which features it.

[Soralin]

There must be something...
What if you were selling fossils to a museum, and they pay more for something that is bigger or older, such that a small old fossil is worth (exactly) the same as one that is twice as big (by volume) but half as old? You could say, "how much will you pay for ten million litre-years of fossils?"
Maybe?

This is an artificial use. When I say what use is there for this measure, I don't mean what economic system can you construct which uses it, I mean, what physical process can you construct which features it.

The total contents held by a leaky container?

[eSOANEM]

Well, the pressure depends on the depth rather than the volume and the flow rate will depend on pressure so you'll get an integral of depth*dt.

[Soralin]

Well, the pressure depends on the depth rather than the volume and the flow rate will depend on pressure so you'll get an integral of depth*dt.

Well I was going for something like the total 4-dimensional hypervolume held by the container, from the start point, to the point that it's empty, in Liter*Minutes or something. Still not sure what that would be useful for though.

You could sell storage space by the m³day. Which I suppose people do, although measuring it like that might not be very useful, you can't store up m³day and make use of them later, and having a small amount of storage for a long time won't allow you to store something really big for a short period of time, as much as the numbers might seem to match up.

[eSOANEM]

You could sell storage space by the m³day. Which I suppose people do,

Of course they do. Storage will be priced in £/m^3/day (or equivalent units) although I suspect given the design of storage units they'd formulate it in terms of floor area. Anyway, the point is, if this thing is a useful measure physically then there will be physical processes which use it.