Mass Space & Infinity

This morning a neighbor and I had an interesting conversation about mass and space. We both agreed an infinite amount of mass could not occupy a finite amount of space. But we disagree whether a finite amount of mass could (or would) occupy an infinite area of space.

My position is the amount of mass and distance between objects (stars, planets, galaxies, etc) is what determines the size of the universe. His position is an infinite universe is able to hold any amount of finite mass.

Both of our ideas have merit and seem to be true.

@kilroy70 said
This morning a neighbor and I had an interesting conversation about mass and space. We both agreed an infinite amount of mass could not occupy a finite amount of space. But we disagree whether a finite amount of mass could (or would) occupy an infinite area of space.

My position is the amount of mass and distance between objects (stars, planets, galaxies, etc) is what det ...[text shortened]... erse is able to hold any amount of finite mass.

Both of our ideas have merit and seem to be true.

Don't forget you can't have matter (mass) less than the Planck scale. At that point, matter doesn't exist so "infinity" can't exist either...

@mlb62 said
Don't forget you can't have matter (mass) less than the Planck scale. At that point, matter doesn't exist so "infinity" can't exist either...

Infinitely small and infinitely large are imo impractical concepts. An infinitely large universe could not expand because (by definition) it's already as big as it can possibly be. It can't be or get any larger than infinitely large, so expansion would be out of the question.

I think my neighbor was approaching the idea of finite matter in an infinite universe from a different angle. From his pov a 3lb blob of mud can easily fit into an infinitely large bucket. From my pov there is no bucket, and that finite blob of mud is all there is.

@kilroy70 said
An infinitely large universe could not expand because (by definition) it's already as big as it can possibly be. It can't be or get any larger than infinitely large

That is not actually true, not all inifinities are the same size. It is a difficult concept
but this a excellent video explaining the concept:

YouTube

@trekkie said
That is not actually true, not all inifinities are the same size. It is a difficult concept
but this a excellent video explaining the concept:

https://www.youtube.com/watch?v=Vp570S6Plt8

"Infinity is used in a lot of different ways in mathematics"

Although this is true I don't believe mathematics is absolutely necessary for understanding the concept of infinity.

This is my second time here in a discussion about infinity. The first time rebuttal of my take on it revolved exclusively around math. I'm not here to argue the merits of mathematical applications (finite vs infinite), because the concept alone is imo adequate for examining how it can (or can't) be practically applied.

@kilroy70 the concept alone is imo adequate for examining how it can (or can't) be practically applied.

Do not remember the previous thread. Can you explain your concept of infinity ?

From your perspective, if i start counting 1, 2, 3, 4, .... can I keep going ? Wll there always be a higher number ?

@trekkie said

From your perspective, if i start counting 1, 2, 3, 4, .... can I keep going ? Wll there always be a higher number ?

Yes. And there can be no highest number.
A highest number would be the last number.

But the concept of infinity is not limited to counting or math constructs. If some endpoint or last number can be proven mathematically, that alone would not invalidate or alter the basic concept of infinity. It's an idea that can't be proven or disproven.

The Fish Tank.

The fish tank has life and stuff.

It also has that picture in the back that convinces the fish that their is space out there. Weeds...and stuff.

We live in a system like that.

@EndLame
I wonder if the idea of multiple universes has any evidence? Like if our universe is expanding exponentially, it sounds like it is expanding into a space of higher dimensions which would lead to the question if there are other universes, like bubbles of foam where each bubble is a separate universe with its expansions and such going on, will there be or is there already evidence we have 'bumped' into another universe?

@trekkie said
That is not actually true, not all inifinities are the same size. It is a difficult concept
but this a excellent video explaining the concept:

https://www.youtube.com/watch?v=Vp570S6Plt8

Great video, thanks for sharing, although I got lost in the terminology about halfway through. Beautiful explanation of the idea that infinity can be different sizes (e.g. 1+infinity=infinity)

@sonhouse said
@EndLame
I wonder if the idea of multiple universes has any evidence? Like if our universe is expanding exponentially, it sounds like it is expanding into a space of higher dimensions which would lead to the question if there are other universes, like bubbles of foam where each bubble is a separate universe with its expansions and such going on, will there be or is there already evidence we have 'bumped' into another universe?

Anytime I thought like that was when I would suggest we might be inside cells or a neural network or something.

It's not as crazy as it sounds.
Our bodies have cells with life inside them and I doubt they know much of what goes on outside their respective cells.

If that makes sense 🤔

@trekkie said
Do not remember the previous thread. Can you explain your concept of infinity ?

From your perspective, if i start counting 1, 2, 3, 4, .... can I keep going ? Wll there always be a higher number ?

Some discussion about infinity occurred here:

https://www.redhotpawn.com/forum/science/thought-experiment.194582

Without mathematics, conversations about infinity quickly gets muddled, and there is nothing more dull than trying to craft arguments without rigorous definitions of the terms being used. The fact is, some infinities are bigger than others, and that is what gives rise to much of the confusion and fuzzy thinking concerning the concept.

@sonhouse said
@EndLame
I wonder if the idea of multiple universes has any evidence? Like if our universe is expanding exponentially, it sounds like it is expanding into a space of higher dimensions which would lead to the question if there are other universes, like bubbles of foam where each bubble is a separate universe with its expansions and such going on, will there be or is there already evidence we have 'bumped' into another universe?

The Many-Worlds Interpretation of quantum mechanics certainly is consistent with known physics, so there is nothing against the existence of other universes. I find it more satisfying than the Copenhagen Interpretation, which basically amounts to: "The math works, so let's not worry about what it means."

@trekkie said
Do not remember the previous thread. Can you explain your concept of infinity ?

This was the previous thread. Thread 193157

@kilroy70 said
Infinitely small and infinitely large are imo impractical concepts. An infinitely large universe could not expand because (by definition) it's already as big as it can possibly be. It can't be or get any larger than infinitely large, so expansion would be out of the question.

I think my neighbor was approaching the idea of finite matter in an infinite universe from a diff ...[text shortened]... nfinitely large bucket. From my pov there is no bucket, and that finite blob of mud is all there is.

A universe is a cylinder one parsec in radius and infinitely long. This is an "infinitely large" universe insofar as it has infinite volume.

Now...start increasing the radius...2 parsecs...3...4...and so on... The "infinitely large" universe is expanding.

Your definition of "infinitely large" is hinted at but not explicated. If it's "Anything so large that it cannot get larger," you're just saying that an infinitely large universe occupies every point in some "space" that, I must presume, has been arbitrarily chosen to be three-dimensional. But just as a plane (an "infinitely large area"​) can be expanded into three-dimensional space, the latter can be expanded into a fourth spatial dimension.

And we haven't even gotten to the issue of mass. How concerned are you with physics? Do we play by Queensbury rules and assume a quantized universe, or thumb our noses at luminaries from Heisenberg back to Democritus and assume that matter is infinitely divisible?

Forgetting quantization, gravity, and other physical considerations, we could conceive of a ball of matter with density equal to 1 at a point P in space, and let the density drop off according to an inverse-square rule: at a distance r from P the density will be 1/r^2. It's a simple calculus problem to show that such a ball of matter has finite total mass, despite its radius being infinite. So in this way we can see that a finite amount of mass could, subject to our (lack of) physical constraints, occupy an infinite volume of space.