Dealing with Infinity

Tanelorn

My teacher told me that parallel lines meet at infinity, however I am pretty sure that they dont, and even if they did it is so far away that it doesnt matter much to me all the way back here. Im not sure if that helps :)

bapowell

They don't. (In Euclidean space, that is.)

ImaLooser

The wavelength TENDS to infinity, but it never gets there.

If the universe is infinitely large and homogenous, then it has infinite mass and energy. It can still have a definite temperature. Temperature is (very roughly) heat energy divided
by volume. If they are both infinite then one may not divide to get the ratio. But a physicist may measure the temperature and get the ratio that way, so this isn't a problem.

Whovian

Parallel lines, by definition, never meet. Parallel lines meeting at infinity is correct in one sense, in that, for instance, for a right triangle, as a leg and the hypotenuse approach being parallel, the point of intersection approaches being infinitely far off. This, however, doesn't mean they meet at infinity, saying so would be as correct as saying 1/0=∞.

Absolutely correct. And I'd like to clarify this to everyone by saying that this doesn't mean that there's a point we can go out to which is an infinite distance away from our starting point, but it means that we can get however far away we want from our starting point.

Chronos

Division by zero yields illogical results.

Whovian

Precisely, saying parallel lines meet at infinity also yields illogical results.

WannabeNewton

http://en.wikipedia.org/wiki/Projective_space

bapowell

I suppose Whovian should have stipulated that he was referring to Euclidean space with trivial topology.

martinbn

I suppose you mean standard not trivial topology, and it is not really the topology but the geometry that he means.

Whovian

True, should've clarified that, I assumed most teachers would be talking about euclidian space.

To martinbn, I was talking about the geometry, but the topology should be quite relevant.

osxraider

Well, I see there has been an intense debate.

Well, I'll start my addressing the first replies since my last post.

I haven't reviewed Cantor but does it have to do with claiming 1 infinity is bigger than the other? This would seem like a contradiction and most likely is. Even if there is a work around mathematically, I'm not sure how that would translate into anything physical.

"Are there not an infinite number of real numbers in the interval [0,1]?"

I think this is a cheat. Math allows the creation of all sorts of numbers but they might not have any physical significance. The minimum distance that we could ever move physically is the planck length. Of course, we could move 0 distance but that would correspond to not moving at all. You can specify a distance that is less than the planck length but that could never be realized in the real world. Of course you could say the same thing about time and other such things.

As for parallel lines meeting at infinity, this seems like a contradiction. Again, if they ever meet at any point 1.) they are not parallel 2.) the subtle implication is that infinity is a definite point in space where something happens.

As for an infinite Universe having a definite temperature, I don't think this is possible. An infinite Universe can have infinite volume and things like that but I think the temperature would be zero then. The temperature would tend to zero as it is diluted into an infinite volume.

I'm sure I could be wrong but even given my blunt reasoning, what happens if you just keep traveling out into space. Assuming you can beat the rate of expansion and have A LOT of time, you should be able to overtake it? So what happens, do you hit a wall? the Universe's wall/bounds?

or that fact that you are suddenly farther out and technically part of the Universe, then the Universe is bigger now because you're out there?

Which also begs the question, what is the nature of space. Some say that space itself was created in the big bang. But with definite creation and in definite time, the Universe could have not have already become infinity? I know that some will say that the big bang happened everywhere but the Universe essentially came out of a singularity. We know singularities, they are at the centers of black holes. We can mark a definite point in space as a singularity yet the Big Bang singularity was everywhere or is it because we are inside this singularity which then became bigger and so from our perspective, it happened everywhere except that it didn't really happen everywhere but that everywhere was once the same place? correct?

But still, we can imagine an observer from outside this Universe and wonder's about his/her perspective? or can such an observer not even exist because there is nothing to exist in? After all, all these documentaries start of with a tiny little light that explodes into everything.

Can someone shed more light on singularities in the context of this discussion. Saying a little more about their nature mathematically and physically than just saying, point of infinite density and gravity and 0 volume would be helpful.

Also, I'm very well aware of my "amateurish-ness" with my questions and reasoning but I really am trying very hard to wrap my head around this. I understand we don't have all the answers yet but its always comforting to know that other people think about this and so many are trying to figure this out.

Also, one question: There is definitely a mechanism that enables the Universe/universes to form. We can agree on that. My question would then be what enables the mechanism that enables? so you see, we could keep on asking this question. Is there an ultimate? because even if these processes were circular, how would they even begin to exist? what mechanism enables circular mechanisms? if these processes are linear, the they tend to infinity in either direction?

so my question is, should I accept at this point that certain things might just be infinite but because of their infinite nature (that they will always be out of reach), it will never really matter "what's out there at infinity"?

[I'm all over the place but I hope you are able to consolidate all my questions and thoughts]

ImaLooser

Yes it does. Read it, it is a simple argument. You seem to be interested in such things.

If the amount of energy were finite then your argument would be correct. But there is no reason to think that. If the Universe is infinite and homogenous, then the amount of energy is infinite.

This has got to be in numerous FAQs somewhere, so maybe you should go read that. The basic answer is that space itself is expanding in the same way everywhere. Every part looks more or less like every other part.

Not every singularity is the same. The Big Band was very different from a black hole. There is no relation.

Yep. Well, it's just plain wrong so the first thing is to erase that from one's mind.

In general a singularity is where our math stops making sense. IMO singularity is a more elegant name than "WTF." We have very little idea of what was going on at the very beginning of the Big Bang. It could have been a quite complicated process about which we have no idea whatsoever.

We dunno. IMO people who speculate about this are wasting their time. It makes more sense to wait until there is some data. Now we have nothing at all.

As far as an infinite universe is concerned, the idea is that every part looks pretty much the same as every other part.

skydivephil

"In general a singularity is where our math stops making sense. IMO singularity is a more elegant name than "WTF.""
lol, brilliant,that really made me laugh. But now I am coming round to the idea of renaming the singualrity WTF is a good idea.
In all seriosuness there are attemtps to resolve the singualrity. To me the most devleoepd fo these is in loop quanutm cosmology.
You can read about it here:
http://arxiv.org/abs/0812.4703

There is work going to see what thsi means for the polarisation of the CMB . I dont think is a waste of time and we shoudl wait for more data. If they theory makess prediction for the next set fo data (hopefully the B mode polarisation) and it matches that people will be far mroe impressed if the theoy is developed after the data is already out, then some might say it was fitted to meet the data we already know.

julcab12

Odds are in favor(only way) with B mode due to some good features in such that we can deduced the confusion of radio signals, accuracy of weeping beam strategy and even with circular scan strategy and posses answers to uniformity of CMB, scale invariant of initial conditions and why Ω = 1? (cmb observations fit LCDM standard cosmological model) Which appears to be infinite?

One prediction is that gravity waves of all sizes might be apparent during the primordial universe.

Will the LCMD be consistent still?

I still find some interesting stuff in ekpyrotic prediction (cyclic universe) by Paul Steinhardt and Neil Turok. . Maybe the universe is infinite at all or Not but sure 'looks' that way for now.

bapowell

You know this? I wasn't aware there was a complete theory of quantum geometry. Do send it my way! ;)
But the big bang happened everywhere in the universe at once -- even if it is infinite. There should be no trouble in assigning an energy density to the resulting radiation that fills the universe, and questions about establishing thermal equilibrium notwithstanding, assigning a temperature to this radiation. The CMB is 2.7 K, whether or not the universe is infinite.

Nobody knows, but it's unlikely that the universe has a boundary (unlikely mostly in an aesthetic sense) A popular conception of a closed universe is a sphere, or more generally, a closed manifold without boundary. The universe could also be infinite (of course, it's important to distinguish between the observable universe, which is of finite volume and has a well-defined boundary, and *the* universe.)

The centers of black holes are examples of singularities -- singularities are a general feature in relativity. A gravitational singularity occurs whenever/wherever the gravitational field (metric) becomes infinite.
The big bang singularity is not something that should be interpreted physically -- it is sign that the theory is broken at that point. Infinite densities and their associated singularities are nonphysical, and so ultimately something must replace the big bang singularity.

Yes, and those producers should all be fired.


Yes. Until we have a scientific understanding of the physics behind the origin of the universe, we can only resort to philosophy. The infinite regress is a consequence of not knowing the physical bounds of the process.

osxraider

Why would the Universe expand at all if it is an infinite Universe? Seems like there would be no reason for any mechanism to operate to expand the Universe if it wasn't expanding it to an amount that was "balanced" so to say. This might sound like a bad question because it might imply purpose and regardless of anything, the Universe has been observed to be expanding but....

Anyway, I guess I am simplifying it to a great extend. For example, heat flows only when there is difference of temperature. What purpose does the expansion fulfill. I mean sure, we can say that if this was slightly different or that was slightly different, we wouldn't be here to observe it but regardless of whether we are here or not, why is the mechanism for expansion operating? if not to fulfill a certain role.

Also, I tried looking into Cantor's infinity theory but couldn't make sense of it. It involves cardinality and powerset (which I have trouble grasping.)

Could someone please shed some light on this? (in a simplistic manner using an appropriate analogy?)

Also, could someone shed some light on the black hole- white hole theory? to me it sounds very appealing that there are other Universes through black holes and what we see as a black hole in out universe is seen as a white hole/big bang in another Universe. There is just one problem. What is the first black hole in this branching universe set (again comes in infinity.) But is this recognized as a plausible theory or is the M-Theory with branes more appealing?

Bapowell:I was able to understand all your responses except for the one about planck length. Am I not right about that? the problem is we don't know what replaces the laws of physics below planck length (or whether any law even exists that governs such a distance scale) because as far as I have gathered from sources, it should be the minimum physical distance (given the the physics we know today.) In that sense, it is incomplete but correct me if I'm wrong.

bapowell

No, you are absolutely correct -- we don't know what happens to geometry on scales beyond the Planck length. You seemed to be suggesting a discrete spacetime in response to my earlier post regarding the fact that there are an infinite number of reals in the interval [0,1]. Now, I don't necessarily disagree with this view of a discrete spacetime, but we simply don't know yet what the nature of spacetime is at these scales: it could be discrete, or it coule be something else entirely.