infinite universe

phinds

No, you have that exactly backwards. Look up Hilbert's Hotel.

Radrook

Adding guests doesn’t affect the hotel’s infinity in any way.
But if we add a room, or height, then the hotel wasn’t infinite to begin with because we cannot add to what is literally infinite. Perhaps you are confusing sequential infinity with literal infinity. They are completely different from each other.


Sequential infinity is represented by a number line with two arrows indicating that the number sequences go on forever. In short, that we can always add one more to the sequence.

Literal infinity doesn’t allow that. The fellow who wrote the article is confusing the two as well. In fact, he contradicts himself semantically by saying that a hotel’s infinite number of rooms are countable. Countability requires finiteness.

phinds

I don't know enough math to argue with you, but that doesn't seem right and consider that that a huge number of physicists seem to have no trouble with the idea that our universe may be infinite and I'm sure they are all aware that it is expanding. How do you explain that? What am I missing?

PatrickPowers

Yes and no.

You are right in a way, but not right in another way.

This stems from the problem of comparing two infinities. There are a number of ways to do it, which are not the same.

One way is Cantor's hierarchy of infinities. In this view the definition is that "you can make a bijection (one-to-one and onto mapping) from one set to another if and only if they are the same size." Then he defines any set that has a bijection with the integers is a countable infinity, and proves that the real numbers are not countable: they are a larger order of infinity than the integers.

The other way is measure theory. You have an infinite number of situations but somehow the probability sums to one. Each situation has the probability zero, so there seems to be a paradox. There are ways to get around this completely sensibly: usually you use calculus. But the upshot is that you CAN quite reasonably divide an infinity by an infinity if you are careful about it.

You seem to have heard of Cantor's ideas. But in physics the measure theory idea dominates. With good reason: it gives actual numbers.

Now in real life it is quite possible that we have an instance of an infinity divided by an infinity. The universe could be infinitely large and contain an infinite amount of mass. Nevertheless since we assume that that mass is evenly distributed, we can both define the ratio using measure theory, and actually measure that ratio in real life.

So while in the Cantor sense the Universe isn't getting any bigger, in the measure theory sense it is. We assume that the amount of mass is staying the same, then if that ratio is decreasing then the amount of space is getting larger.

shifty88

Would it be to much of a stretch to say that it would be impossible to ever determine the size and shape of our universe because we are naturally a part of the universe with a limited view.

If somehow we could detach ourselves from the universe (i.e an aerial view of the landscape reveals much more than being on the ground) then we would be able to determine the dimensions of the universe. Whilst we observe it as a whole

phinds

There IS no "outside" from which we can get such a vantage point, so your question is pretty much equivalent to asking if pigs had wings, could they fly?

Cosmo Novice

What phinds says is correct. If the Universe had an "outside" then it would not be the Universe. The Universe can be defined as: "the totality of everything that exists" therefore if something exists, by definition it is part of the Universe.

For their to be an "outside" would also require a "center" and an "edge" which would invalidate the cosmological principle of isotropy.

We can, however, measure curvature from within the metric to determine if space is euclidean or not - unfornutaley the degree of error is rather small and it is entirely possible that out little patch of the Universe we can see (The Observable Universe) is too small a piece of the whole (Whether finite or not) to determine curvature with any acceptable margin of error.

Global curvature is the key to the "shape" of the Universe in my opinion.

Hope this helps.

Cosmo

shifty88

Obviously. Therefore we can never know for sure what shape or size the universe it.
We can only use our best educated guess from what observations we can make.

Chronos

The observable universe is obviously finite, so it can expand to its heart's content without offending our logical sensibilities. It is also very close to being dead flat - according to WMAP and supernova studies. This suggests the universe is much larger than the part observationally accessible to us. In is, however, possible the universe could be both flat and finite.

PatrickPowers

To me it seems impossible for a finite being to observe an infinity.

It would be possible though to deduce an infinity, by showing that a contradiction occurs if the infinity is not there.

Detaching ourselves from the Universe is by definition impossible. But it could be that our current conception of the Universe is wrongly limited, and there is another view within our Universe that would look at our current conception from outside. Indeed the geometry of spacetime is hyperbolic, and a hyperbolic geometry is one way to fit an infinity inside of a finite space. If there are more than four physical dimensions in our Universe it is possible that there is a perspective in which 4D spacetime is a bounded subset within some other space.

PatrickPowers

What do you mean? Spatially infinite but inhomogeneous with a finite amount of matter? That could be.

Chronos

There are at least four possible topologies that are flat, finite and obey the cosmological principal.

vanvlizr

The universe is finite but like explain earlier with an ant on a beach ball to the eye it would seem infinite because the only dimensions we can see is the ones we are in. If you were born and lived on an island all your life you might think that the island is all there is. So if you cannot see an edge to the universe it doesnt make it infinite. To be able to prove non mathematically that our universe is finite we would have to go beyond our own universe but since we cannot detect past the 4th dimension we are stuck.

phinds

This is pure speculation on your part and should be stated as an unsupportable opinion, not a fact.

vanvlizr

that is my unsupportable postion atleast with current technology, but it is a fathamable and possible theory. as of now there is no way to be sure, everything about this topic is speculation.

Radrook

Can you specify exactly what is so nonsensical about what he just said.

Radrook

The question is why state opinion as if it were fact in the first place. If indeed the universe is finite then it is bounded. Which brings up the question as to what is outside those boundaries. If indeed there is nothing outside, then that answer itself becomes nonsensical because it is self contradictory. In short, it is identical to the "Who created God" paradox of infinite regression. The only way around it is to negate the existence of dimensionality and to declare its perception as a sensory illusion.