The balloon model of the universe

[big314mp]

For the sake of argument, let's say that the universe is a balloon; the surface of the balloon being our universe.

 

Now if the radius of the balloon increases at a constant rate, then the surface area of the balloon will increase at an accelerating rate. Beings on the surface of the balloon would see their universe as having an accelerating expansion.

 

So my question is, could the growth of the universe be constant in some higher dimension that we can't observe? In other words, we can see the balloon as expanding by a linear increase of r, but the 2d beings on the surface of the balloon can't.

[aguy2]

For the sake of argument, let's say that the universe is a balloon; the surface of the balloon being our universe.

 

Now if the radius of the balloon increases at a constant rate, then the surface area of the balloon will increase at an accelerating rate. Beings on the surface of the balloon would see their universe as having an accelerating expansion.

 

So my question is, could the growth of the universe be constant in some higher dimension that we can't observe?

 

I would speculate, "Yes." We can't directly observe the 'arrow of time' (well, maybe we are, but are but intrepreting it as the 'spatual' velocity C), other than in our minds, and here, either by convention or some sort a psychological survival mechanism, we normally 'see' time as accumulating.

 

I am speculating that time and space could very well be 'equivalent' forms of one another, and that if our universe consists of a single cycle of a BB/BC situation, then it is easy to see that our universe is, "running out of time", and, of course, space would be expanding.

 

Ps. If there is a reasonable possibility that our context 'changed' from a 0 dimensional singularity to the multiple dimensions we currently observe, why isn't 'time' as expressed as 'change' known as the 1st dimension and not the 4th?

 

 

In other words, we can see the balloon as expanding by a linear increase of r, but the 2d beings on the surface of the balloon can't.

 

The models that assume isometric expansion (the balloon analogy) have real problems. see Is the Universe Collapsing?-2008 in this forum.

aguy2

[Sisyphus]

This doesn't invalidate your general idea, but the people on the surface of the balloon would see linear expansion, as measured by distances between objects. Per the question, it seems like if the omega constant is constant, you could probably find some linear derivative or something, but I'm not even remotely qualified to assess the significance of that.

[big314mp]

This doesn't invalidate your general idea, but the people on the surface of the balloon would see linear expansion, as measured by distances between objects. Per the question, it seems like if the omega constant is constant, you could probably find some linear derivative or something, but I'm not even remotely qualified to assess the significance of that.

 

Maybe my geometry is off here, but I thought the "universe" would expand at a rate of 4pi(r^2), and thereby accelerate as r gets larger.

 

EDIT: Actually, what needs to be calculated is arc length (for the distance between points), so I'm going to chew on that one for a while.

 

As to the omega constant, what is that used for? I'm guessing that it is some constant that defines the expansion of the universe. From what I'm reading, though, it looks like a mathematics constant, rather than a cosmological one.

[Sisyphus]

It depends on how you're measuring expansion. That is the rate at which the area of the universe would expand. However, distances between objects (i.e. arc length, or circumeference) expand proportionally to radius. In the analogy to our universe, it would be distances between objects (which I believe is the context expansion is usually talked about) vs. "volume of the universe," which presumably would expand with the cube of the former. (Again, though, I'm no cosmologist.)

 

Oh, and when I said "omega constant," I meant Hubble constant. Sorry.

[big314mp]

It depends on how you're measuring expansion. That is the rate at which the area of the universe would expand. However, distances between objects (i.e. arc length, or circumeference) expand proportionally to radius. In the analogy to our universe, it would be distances between objects (which I believe is the context expansion is usually talked about) vs. "volume of the universe," which presumably would expand with the cube of the former. (Again, though, I'm no cosmologist.)

 

Oh, and when I said "omega constant," I meant Hubble constant. Sorry.

 

I checked my geometry, and did eventually find my mistake.

 

So I suppose what this boils down to, is if you take the function that describes the expansion of the universe, and take the derivative enough times, do you get a linear function?

[Bignose]

I checked my geometry, and did eventually find my mistake.

 

So I suppose what this boils down to, is if you take the function that describes the expansion of the universe, and take the derivative enough times, do you get a linear function?

 

Not necessarily. What is the expansion is governed by a function proportional to [math]r^{2.5}[/math]? Or something like [math]r^3 + e^{0.001r}[/math]. You only get linear functions as the result of one or multiple differentiations if the function is a polynomial with integer exponents. There are many, many other functions out there.

[big314mp]

That's an interesting point. I'd forgotten that all of the functions that have an infinite series of derivatives.

 

So I guess the math end of the question has been answered. On the physics end of it, is there any way to tell which it is? Is there even any way to describe the expansion of the universe as a mathematical function?