On the infinity of the Universe

In summary, the conversation discusses the concept of the universe being infinite and the implications it has on energy and matter. There is mention of the possibility of multiple causally disconnected universes and the struggle with understanding the conservation of energy in an infinite universe. The origin of the universe is also questioned, with some suggesting that the Big Bang was only the origin of the observable universe, while others believe it to be the origin of the entire spatially infinite universe. The idea of the total energy of the universe being exactly zero and the balancing of positive and negative energy is also brought up. The conversation ends with the mention of a book by Lawrence Krauss that delves into these concepts.
  • #1
JamesOrland
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Okay, now this question has been asked over and over, and all that stuff, so I am not going to ask whether the universe is infinite or not. Actually, my physical intuition says that it probably is, and so do two very intelligent people I admire, namely Eliezer Yudkowsky (a mere AI programmer, just look him up) and the physicist Max Tegmark.

Actually, Tegmark starts his paper called 'Parallel Universes' assuming that the universe is flat (the WMAP experiment seems to point in that general direction), that distribution of matter is ergodic and so that it is spatially infinite. And while they could likely be wrong, it still appeals to me to imagine an infinite universe, so bear with me.

My question is not 'whether,' it's 'how.' Let's assume for a second that the Universe is spatially infinite, with all its far reaching consequences (including the multiple copies of yourself who are at most 10^10^115 metres away from you). How could that be so?

I mean, there's this place here which states that the Big Bang was not the origin of The Universe, but rather the origin of the Observable Universe, and as such The Universe actually is infinite. Then the forum's FAQ seems to corroborate, and that's just fine by me.

Now I have also read that the Big Bang's Singularity actually held an infinite amount of energy.

That's my problem, really. Where does all that energy come from? I was under the impression that the amount of energy was constant and finite in The Universe, not merely in the observable one. And let me reiterate that I'm okay with the idea that there is infinite energy in the universe, really. I just want to know.

Okay, I'm repeating myself, but I just want to be very clear: does the property 'spatially infinite' not imply 'energetically infinite'? How is that? Is the Big Bang not the origin of The Universe (capital T and U), but merely of the observable universe (lower-case o and u)?

Also, from what I understood of Tegmark's paper, the Big Bang was in fact the origin of The Universe, which is but one stable bubble of the inflationary bubbles that are created all the time, each infinite in volume. If each bubble is infinite in volume, should they not also have infinite energy? This is the problem I have, really, the relationship between energy and volume.

I know I'm not being clear, it's past midnight as I'm posting here, but this has been annoying me for the past few weeks, because I'd never given it too much thought before.

Thank you for your patience :)
 
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  • #2
In a spatially infinite and homogenous universe you are forced to concede it includes an infinite amount of energy/matter. One spatially infinite universe, however, appears to be enough. An infinite number of other spatially infinite universes that are causally disconnected does not make much sense to me.
 
  • #3
Not making sense is not the same as not being true, one should be reminded. We have Savannah-optimised brains that are not even supposed to deal with the actual fabric of reality, so that sort of intuition isn't very reliable.

And the model of chaotic cosmic inflation (which appears to be backed up by some considerable amount of evidence plus it's quite elegant) does seem to suggest the existence of causally disconnected bubbles outside the universe. Also, of course, since the actual universe is bigger than the observable one, one should expect that we are causally disconnected from a number of events (infinite number, maybe?) within our own universe, so it should come as no surprise to have other causally disconnected universes.

Another struggle I have with infinite energy is its conservation. If ∞ + 1 = ∞, what's to prevent energy from being created out of nowhere? If the amount of energy in the universe is infinite, it shouldn't matter. I'd thought Conservation laws only applied fully to isolated systems, which is exactly what our Universe is, but if it is an isolated system with infinite energy... you can see where I'm going with this, I suppose.
 
  • #4
If the universe is infinite and homogenous then it has an infinite mount of energy and an infinite amount of matter.

If the universe is finite and homogenous then it has a finite mount of energy and a finite amount of matter.
 
  • #5
Not necessarily. One possibility is that the total energy content of the universe is exactly zero, and that the large positive energy content associated with matter and radiation is balanced by the large negative energy content of the gravitational fields See, for example, the following book by Lawrence Krauss:

https://www.amazon.com/dp/145162445X/?tag=pfamazon01-20
 
  • #6
ImaLooser said:
If the universe is infinite and homogenous then it has an infinite mount of energy and an infinite amount of matter.

If the universe is finite and homogenous then it has a finite mount of energy and a finite amount of matter.

It's what it seems, but I am not discussing whether it's infinite or not, I am using the assumption that it is in fact infinite and flat a priori, and speculating about its energetic contents. More than that, though, I am speculating about how Conservation Laws apply in a Universe with infinite energy/matter, and how infinite energy/matter could be contained in a singularity such as the one at t=0 and yet expand enough to create finite Hubble volumes in a finite time.

And actually one of my questions was whether the singularity at t=0 is the origin of our spatially infinite Universe or just the observable Universe. I understood it was the latter, and as I said, Tegmark seems to agree with that, and I respect his opinion a lot, even though I still haven't even started my physics major to understand enough (I'm waiting until after I finish Engineering for that).

phyzguy said:
Not necessarily. One possibility is that the total energy content of the universe is exactly zero, and that the large positive energy content associated with matter and radiation is balanced by the large negative energy content of the gravitational fields See, for example, the following book by Lawrence Krauss:

https://www.amazon.com/dp/145162445X/?tag=pfamazon01-20

Hm, that is interesting. And that would justify infinite energy in a spatially infinite universe, if it was canceled out by the negative energy of gravitational fields. I'm still stumped on the topics I mentioned above, though...
 
  • #7
JamesOrland said:
If ∞ + 1 = ∞, what's to prevent energy from being created out of nowhere? If the amount of energy in the universe is infinite, it shouldn't matter. I'd thought Conservation laws only applied fully to isolated systems, which is exactly what our Universe is, but if it is an isolated system with infinite energy... you can see where I'm going with this, I suppose.
Energy conservation is a local constraint, it does not hold globally and is in fact not a requirement in general relativity. This is a well-known issue that is related to the lack of uniquely defined sense of time translation that holds globally. I can't think of a good reference now, but googling "energy conservation in general relativity" should return some good results.

EDIT: Here's an article I came across a while back that I believe should address some of your issues: http://astronomy.case.edu/heather/151/davis.pdf [Broken]
 
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  • #8
bapowell said:
Energy conservation is a local constraint, it does not hold globally and is in fact not a requirement in general relativity. This is a well-known issue that is related to the lack of uniquely defined sense of time translation that holds globally. I can't think of a good reference now, but googling "energy conservation in general relativity" should return some good results.

EDIT: Here's an article I came across a while back that I believe should address some of your issues: http://astronomy.case.edu/heather/151/davis.pdf [Broken]

Okay, that makes sense. It all adds up to normality, I suppose.

So, from these answers, I gather that yes, indeed, The Universe, assuming it is infinite, ergodic and flat, has infinite positive energy - which may or may not be canceled out by the total gravitational energy, which would be in fact a very elegant solution, in my opinion.

Now... what about the Big Bang, then? Is it the origin of The Universe or the Observable Universe? Did it have infinite energy stored in the singularity, or just zero energy that, because of quantum fluctuations, happened to inflate into its own zero-energy Universe?
 
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  • #9
JamesOrland said:
Now... what about the Big Bang, then? Is it the origin of The Universe or the Observable Universe?

Well if the BB is the origin of the Universe then by default it is the origin of the OU.

We cannot assume the Big Bang as a "beginning" of anything, remember when we talk about the Big Bang we are talking about T>plancke time and not t=0.

I think isotropy has a large role to play here, but when we start discussing homogeneity with respect to an infinite Universe then isotropy meaning becomes less important. Maybe 1 in a trillion, trillion Hubble volumes is completely void of any mass - this would not invalidate homogeneity on the extremely large scales.

Personally I think all BB's were the same Bang and that time/space are infinite and flat in all directions - even though we are causally disconnected from anything outside our own OU.

All very interesting!
 
  • #10
It's important to point out that what we refer to as the "hot big bang" within the context of chaotic inflation is very different from the moment related to the origin and subsequent evolution of THE universe. While chaotic eternal inflation does not obviate the initial singularity (it's not "past eternal"), what us observers perceive as the hot big bang is really the reheating phase occurring in our local Hubble patch at the end of inflation. In this sense, there are necessarily many hot big bangs occurring in the chaotic inflationary universe, each one corresponding to the reheating of individual, causally disconnected "observable universes". The proposition that we live in an eternally inflating universe renders questions regarding the initial singularity essentially unverifiable.
 
  • #11
Cosmo Novice said:
Well if the BB is the origin of the Universe then by default it is the origin of the OU.

We cannot assume the Big Bang as a "beginning" of anything, remember when we talk about the Big Bang we are talking about T>plancke time and not t=0.

I think isotropy has a large role to play here, but when we start discussing homogeneity with respect to an infinite Universe then isotropy meaning becomes less important. Maybe 1 in a trillion, trillion Hubble volumes is completely void of any mass - this would not invalidate homogeneity on the extremely large scales.

Personally I think all BB's were the same Bang and that time/space are infinite and flat in all directions - even though we are causally disconnected from anything outside our own OU.

All very interesting!

Yes, yes, of course, we're talking about extremely large scales.

bapowell said:
It's important to point out that what we refer to as the "hot big bang" within the context of chaotic inflation is very different from the moment related to the origin and subsequent evolution of THE universe. While chaotic eternal inflation does not obviate the initial singularity (it's not "past eternal"), what us observers perceive as the hot big bang is really the reheating phase occurring in our local Hubble patch at the end of inflation. In this sense, there are necessarily many hot big bangs occurring in the chaotic inflationary universe, each one corresponding to the reheating of individual, causally disconnected "observable universes". The proposition that we live in an eternally inflating universe renders questions regarding the initial singularity essentially unverifiable.

Let's be clearer when we talk about universe.
When I say The Universe, I mean the inflationary, spatially infinite, flat, ergodic bubble within which our Observable Universe/Hubble Volume (for the purpose of this discussion let's assume they're the same thing) lies. And then there's the other Universes with possibly different physical constants and dimensionality that are inflating elsewhere (other possible ground states, true vacuum, not sure of the terms here).

With that in mind... the 'hot big bang' you mention would be the end of the inflation period of our Universe (inflationary bubble, ground state)... or just Observable Universe/Hubble Volume?

And once again, where does all that energy come from? I mean, how can an infinite amount of energy expand to an infinite volume in a finite inflation epoch in our own Universe?
 
  • #12
JamesOrland said:
When I say The Universe, I mean the inflationary, spatially infinite, flat, ergodic bubble within which our Observable Universe/Hubble Volume (for the purpose of this discussion let's assume they're the same thing) lies. And then there's the other Universes with possibly different physical constants and dimensionality that are inflating elsewhere (other possible ground states, true vacuum, not sure of the terms here).
OK. Within the context of chaotic eternal inflation that I was referring to above, there is one Universe (infinite or not) according to your definition, comprised of a large number of separate "pocket" universes (Hubble volumes) that have stopped inflating and have undergone reheating (had separate hot big bangs). There could of course be entirely separate other Universes undergoing eternal inflation as well, but I am not referring to these, since we don't need them to set up an effective multiverse of the kind I just described. However, you mention the possibility of different Universes with different physical constants; this can happen even within a single Universe, where instead each pocket universe has a different vacuum and with different physical parameters.

With that in mind... the 'hot big bang' you mention would be the end of the inflation period of our Universe (inflationary bubble, ground state)... or just Observable Universe/Hubble Volume?
In chaotic internal inflation, you have a Universe that is undergoing inflation. Assume it is infinite for the sake of argument. Different regions of this Universe will stop inflating at different times, leading to the percolation of non-inflationary Hubble patches (what I called pocket universes above). So the picture is of an infinite inflationary universe with non-inflationary bubbles being constantly percolated -- it's called eternal inflation because there are always regions of the Universe that are inflating, despite the fact that non-inflationary patches are percolating out (in fact, the fractional volume of the Universe that is inflating is increasing into the future). These non-inflationary patches reheat and begin to evolve according to the standard hot big bang model. So...to clarify, the hot big bang to which I refer is the end of inflation in one of the Hubble volumes.

And once again, where does all that energy come from? I mean, how can an infinite amount of energy expand to an infinite volume in a finite inflation epoch in our own Universe?
I'm not sure I follow this. If the universe is infinite, it was always infinite. Our observable universe is finite and inflated for a finite period of time.
 
  • #13
bapowell said:
OK. Within the context of chaotic eternal inflation that I was referring to above, there is one Universe (infinite or not) according to your definition, comprised of a large number of separate "pocket" universes (Hubble volumes) that have stopped inflating and have undergone reheating (had separate hot big bangs). There could of course be entirely separate other Universes undergoing eternal inflation as well, but I am not referring to these, since we don't need them to set up an effective multiverse of the kind I just described. However, you mention the possibility of different Universes with different physical constants; this can happen even within a single Universe, where instead each pocket universe has a different vacuum and with different physical parameters.


In chaotic internal inflation, you have a Universe that is undergoing inflation. Assume it is infinite for the sake of argument. Different regions of this Universe will stop inflating at different times, leading to the percolation of non-inflationary Hubble patches (what I called pocket universes above). So the picture is of an infinite inflationary universe with non-inflationary bubbles being constantly percolated -- it's called eternal inflation because there are always regions of the Universe that are inflating, despite the fact that non-inflationary patches are percolating out (in fact, the fractional volume of the Universe that is inflating is increasing into the future). These non-inflationary patches reheat and begin to evolve according to the standard hot big bang model. So...to clarify, the hot big bang to which I refer is the end of inflation in one of the Hubble volumes.


I'm not sure I follow this. If the universe is infinite, it was always infinite. Our observable universe is finite and inflated for a finite period of time.

Okay, what you are saying is fundamentally different from what I am saying. From what I read (more specifically from Tegmark, here, who was the guy that made my thinking on this subject restart), these 'pockets' you mentioned are what I call the Universe, are themselves spatially infinite, and our Hubble Volume is but a fraction of a single pocket. So what I call 'The Universe' is one of those pockets.

When I say different universes I mean different pockets. I'm saying that out pocket is much larger than our Hubble Volume, and is what we should call our Universe because it comprises everything that behaves in the same way as our own Hubble Volume, and in principle everywhere inside it reachable (if it stops expanding acceleratedly), whereas different Pockets are in principle unreachable.

Hmmm... in short: the impression I got from Tegmark's paper was that the Pocket Universe you mentioned is not our Hubble Volume, it is much bigger than our Hubble Volume, it is in fact infinite, and within it there are infinite other Hubble Volumes, with one Hubble Volume exactly equal to ours down to the last photon at most 10^10^115 metres away.

In his paper, he calls these other Hubble Volumes that are within our own Pocket Universe 'Level I Parallel Universes.' Then, he calls the other Pocket Universes (with different physical constants but probably the same laws) caused by inflation 'Level II Parallel Universes,' which are the 'in principle unreachable' ones I mentioned above.
 
  • #14
Perhaps I was not careful with the term "pocket universe." What I mean is Hubble volume.
 
  • #15
Okay, let's be more specific here, then, with our names. What Tegmark calls Level IV and Level III Parallel Universes are irrelevant to this discussion, so we have three levels I'm concerned about:
  • There's the big, infinite, continually inflating universe, within which there are many pocket universes, each with its constants and dimensionality. We shall call that universe the Fractal Universe.
  • There's then our bubble within that universe, which is flat and infinite (that was my a priori assumption), and which we will call Universe, or the patch, or the pocket.
  • Finally, there's the Hubble Volume within which we reside, which consists of only the parts of the Universe that we can see. I will use Hubble Volume or Observable Universe to refer to that, never mind the subtle differences between both.

So, I'm okay with the Fractal Universe undergoing eternal inflation, with patches of it that stop inflating. Now, what I want to understand is, if the Big Bang is the end of the inflationary epoch of our patch, how can the patch be infinite and possesses infinite energy?

...although, looking at this, I'm thinking that maybe I understand. Let me get my facts straight.

According to chaotic inflation theory, the end of the inflationary period of the Universe coincides with that moment that, in previous Big Bang models, was at t = 10^-43s after the singularity. Is that correct?

If that is so, then was there no singularity at all?
 
  • #16
JamesOrland said:
According to chaotic inflation theory, the end of the inflationary period of the Universe coincides with that moment that, in previous Big Bang models, was at t = 10^-43s after the singularity. Is that correct?
It could be. There are inflation models that reheat at much lower temperatures too, though. For example, I've seen models constructed that reheat just above the scale of electroweak symmetry breaking. So, as far as our observable universe is concerned, our "hot big bang" might never have emerged through a Planck era at all, or really been all that "hot".

If that is so, then was there no singularity at all?
In the chaotic inflation scenario, no, not a singularity in the past of our Hubble volume. But, since even eternal inflation has an initial singularity, the Universe must still contend with it (or "bounce" around it, or what have you).

I also apologize if I'm telling you things you already know as if you're hearing them here for the first time -- that's not my intent. It's sometimes difficult to gauge people's levels of knowledge here.
 
  • #17
bapowell said:
It could be. There are inflation models that reheat at much lower temperatures too, though. For example, I've seen models constructed that reheat just above the scale of electroweak symmetry breaking. So, as far as our observable universe is concerned, our "hot big bang" might never have emerged through a Planck era at all, or really been all that "hot".


In the chaotic inflation scenario, no, not a singularity in the past of our Hubble volume. But, since even eternal inflation has an initial singularity, the Universe must still contend with it (or "bounce" around it, or what have you).

I also apologize if I'm telling you things you already know as if you're hearing them here for the first time -- that's not my intent. It's sometimes difficult to gauge people's levels of knowledge here.

No need to apologise, I can imagine that :)

And one thing you said is really new for me, which is the fact that even eternal inflation had an initial singularity, and that... sort of goes back to my original point. How can that be so? I mean, I can picture a finite amount of energy trapped in an infinitesimal point, but how could an infinite amount of energy such as the one contained within the Fractal Universe be enclosed in an infinitesimal singularity? I mean, if that was the case shouldn't this singularity sort of "create" energy eternally, since it would take literally forever for all the energy trapped inside it to be "released into the wild"?

One of my original problems had been infinite energy in a singularity, and so... it's back :P
 
  • #18
JamesOrland said:
One of my original problems had been infinite energy in a singularity, and so... it's back :P
That's just about the definition of a sticky problem. Of course, it's likely that there is no singularity to speak of, and that quantum gravitational effects smooth things out at a finite energy scale. Would this avert the conceptual difficulty that you see?
 
  • #19
Erm... not really. What quantum gravitational effects would do anything there? I'd thought quantum gravity was still in the limbo of unfinished theories...
 
  • #20
Chronos said:
An infinite number of other spatially infinite universes that are causally disconnected does not make much sense to me.

It seems counter-intuitive, but is very much possible.

Here's a video of Alan Guth explaining that a "bubble" universe arising from inflation can still appears to be infinite:

 
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  • #21
JamesOrland said:
Erm... not really. What quantum gravitational effects would do anything there? I'd thought quantum gravity was still in the limbo of unfinished theories...
Seriously? Are you familiar with the understanding that singularities signal a breakdown of the classical theory? Singularities correspong to unphysical infinities that indicate that the theory is ill-behaved in the corresonding energy regime. I'm guessing you know all that and you mean something else. But whether we have an accepted theory of quantum gravity yet or not, it is evident that a UV-complete theory of gravity is needed, and that resolving singularities -- i.e. giving sensible physical results at the Planck scale -- is a generic property of whatever that final theory is.
 
  • #22
bapowell said:
Seriously? Are you familiar with the understanding that singularities signal a breakdown of the classical theory? Singularities correspong to unphysical infinities that indicate that the theory is ill-behaved in the corresonding energy regime. I'm guessing you know all that and you mean something else. But whether we have an accepted theory of quantum gravity yet or not, it is evident that a UV-complete theory of gravity is needed, and that resolving singularities -- i.e. giving sensible physical results at the Planck scale -- is a generic property of whatever that final theory is.

Hm, I am in fact familiar with that, but I'd never thought of it quite that way. To be honest, now that you mention it and now that I analyse my previous thought processes, I'd up until right now always thought of an original singularity as sort of a property of the universe (as if spacetime really did break down in it) instead of a property of a theory (or the lack thereof). Mind Projection Fallacy all the way there.

Yes, I did know both that singularities are a breakdown in the description of a particular physical event, and that a final theory should explain that sort of thing, but I'd never really connected the two pieces of knowledge together.

That is... great. Thank you :)
 
  • #23
Cool. In fact, while admittedly not complete, loop quantum cosmology (based on -- you guessed it -- loop quantum gravity) predicts a bounce at the Planck scale. I'm not an expert (I'm hoping Marcus drops by at some point...he can shed much more light on this), but I think the bounce solution is quite generic in lqc.
 
  • #24
bapowell said:
Cool. In fact, while admittedly not complete, loop quantum cosmology (based on -- you guessed it -- loop quantum gravity) predicts a bounce at the Planck scale. I'm not an expert (I'm hoping Marcus drops by at some point...he can shed much more light on this), but I think the bounce solution is quite generic in lqc.

A similar thing occurs in string theory. If a particular curled up dimension collapsed to the Planck Length, unwound strings (that is, strings that are not wrapped around that dimension) become very heavy, and are too large to measure distance. So, instead, winding mode strings, strings that are wrapped around a dimension, must be used to measure distance. Since WM strings measure distance as the inverse of the unwound strings, this will create the perception that the universe is huge and expanding after hitting the Planck Length.
 
  • #25
Mark M said:
A similar thing occurs in string theory. If a particular curled up dimension collapsed to the Planck Length, unwound strings (that is, strings that are not wrapped around that dimension) become very heavy, and are too large to measure distance. So, instead, winding mode strings, strings that are wrapped around a dimension, must be used to measure distance. Since WM strings measure distance as the inverse of the unwound strings, this will create the perception that the universe is huge and expanding after hitting the Planck Length.

Wait, what? Correct me if I'm wrong, but... I understood that at the Planck Scales the other spatial dimensions become relevant and it's actually our spatial dimensions that get curled up, is that it? Or something like that.
 
  • #26
JamesOrland said:
Wait, what? Correct me if I'm wrong, but... I understood that at the Planck Scales the other spatial dimensions become relevant and it's actually our spatial dimensions that get curled up, is that it? Or something like that.

James,

You are making a small mistake in confusing a dimension being "small" and a dimension being curled up. In string theory (or more precisely, now M-Theory) the other 7 spatial dimensions are curled up into tiny Calabi-Yau manifolds. When you talk about the length of a dimension, you are talking about how much distance must be covered to traverse the entire dimension. Saying that a dimension is curled up is essentially saying you can return to your starting position after traversing that dimension.

So you are correct that when the 3 large dimensions shrink down to a Planck length, the other dimensions become noticeable. It is not known if our dimensions are curled up or not, but if the universe if unbounded it would suggest that they are curled up.

But if a dimension is curled up, it is curled up - period. Even if it changes size, it still retains it's shape. (Though the string theorist Brian Greene showed in the 90's that Calabi-Yau shapes can tear and recombine, changing dimensional arrangement. But that's getting off topic.)
 
  • #27
Mark M said:
James,

You are making a small mistake in confusing a dimension being "small" and a dimension being curled up. In string theory (or more precisely, now M-Theory) the other 7 spatial dimensions are curled up into tiny Calabi-Yau manifolds. When you talk about the length of a dimension, you are talking about how much distance must be covered to traverse the entire dimension. Saying that a dimension is curled up is essentially saying you can return to your starting position after traversing that dimension.

So you are correct that when the 3 large dimensions shrink down to a Planck length, the other dimensions become noticeable. It is not known if our dimensions are curled up or not, but if the universe if unbounded it would suggest that they are curled up.

But if a dimension is curled up, it is curled up - period. Even if it changes size, it still retains it's shape. (Though the string theorist Brian Greene showed in the 90's that Calabi-Yau shapes can tear and recombine, changing dimensional arrangement. But that's getting off topic.)

Um, I think I understand as well as I can right now given my current (lack of) understanding of M-Theory. But I think the WMAP had shown evidence that the Universe might after all be flat and (therefore?) unbounded.

I'm sorry, I have a... strong enough grasp of physics up until basic Quantum Mechanics, but once we get to the point of discussing M-Theory or other potential TOEs, I have no idea what I'm talking about.
 
  • #28
JamesOrland said:
Um, I think I understand as well as I can right now given my current (lack of) understanding of M-Theory. But I think the WMAP had shown evidence that the Universe might after all be flat and (therefore?) unbounded.

I'm sorry, I have a... strong enough grasp of physics up until basic Quantum Mechanics, but once we get to the point of discussing M-Theory or other potential TOEs, I have no idea what I'm talking about.

Oh, OK. If you are interested in a non-technical introduction to String Theory, I'd suggest The Elegant Universe by Brian Greene. It is probably the most well known book on the topic.
 
  • #29
Mark M said:
Oh, OK. If you are interested in a non-technical introduction to String Theory, I'd suggest The Elegant Universe by Brian Greene. It is probably the most well known book on the topic.

Noted. And if I want a technical one?
 
  • #30
JamesOrland said:
It's what it seems, but I am not discussing whether it's infinite or not, I am using the assumption that it is in fact infinite and flat a priori, and speculating about its energetic contents. More than that, though, I am speculating about how Conservation Laws apply in a Universe with infinite energy/matter,

Easy. The conservation laws apply in every finite subvolume. Extend to infinity by having an infinity of such finite subvolumes.


JamesOrland said:
and how infinite energy/matter could be contained in a singularity such as the one at t=0 and yet expand enough to create finite Hubble volumes in a finite time.

Since essentially nothing is known of the nature of the singularity it is hard to say. Nothing is known about why it expanded at all. Why wasn't it content to remain as it was? No one knows. We are left with guessing.

I think that perhaps you are assuming the singularity was finite. It could have been infinite. If the Universe is infinite now then I would think the singularity was infinite as well. But now I too am guilty of guessing.


JamesOrland said:
And actually one of my questions was whether the singularity at t=0 is the origin of our spatially infinite Universe or just the observable Universe.

Both. The visible universe is a subset of the universe as a whole.
 
  • #31
ImaLooser said:
Easy. The conservation laws apply in every finite subvolume. Extend to infinity by having an infinity of such finite subvolumes.




Since essentially nothing is known of the nature of the singularity it is hard to say. Nothing is known about why it expanded at all. Why wasn't it content to remain as it was? No one knows. We are left with guessing.

I think that perhaps you are assuming the singularity was finite. It could have been infinite. If the Universe is infinite now then I would think the singularity was infinite as well. But now I too am guilty of guessing.




Both. The visible universe is a subset of the universe as a whole.

1. Yes, I understood the part that the Conservation Laws apply locally :)
2. Also yes, as I said in my last post, I realized I was committing the Mind Projection Fallacy with singularities, assuming they were a property of the world instead of a property of the theory. My mindset is adjusted now, so that problem was also dissolved.
3. And yeah, when I said that I meant 'The Universe or only the Observable Universe', that is, I was asking whether it was the origin of our whole bubble or exclusively the part we can see of it.
 
  • #32
A few things I thinks its worth mentioning.
1) Eternal inflation and chaotic inflation are not the same.
read here:
http://arxiv.org/pdf/gr-qc/0409055.pdf
2) Inflation has good evidence for it but its not a done deal yet, we still need to see the B mode polarisation for it to passs its final hurdle. Well nothing is ever final, but this is a key test, see here:
http://www.nature.com/news/2009/090415/full/458820a.html
3)Borde , Guth and Vilenkin have argued that eternal inflaiton has an initial singualrity, but that has been disputed by Aguirre and Gratton. see here:
http://arxiv.org/abs/0712.0571
If anyone knows of any way to observationally resolve this dispute, I'd love to hear it but I suspsect there is not.
4) Guth claims most inflationary models are eternal , but I note he doesn't say all.So if ifnaltion is shown beyond reaosnable doubt, there is stil a chance its not eternal. see here http://arxiv.org/abs/hep-th/0702178:[/URL]

5 LQC resolves singualrities inlcuding the one proposed at the beginning of eternal inflation by Borde Guth and Vilkenkin , see here:
[url]http://arxiv.org/abs/0812.4703[/url]
 
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  • #33
skydivephil said:
A few things I thinks its worth mentioning.
1) Eternal inflation and chaotic inflation are not the same.
read here:
http://arxiv.org/pdf/gr-qc/0409055.pdf
2) Inflation has good evidence for it but its not a done deal yet, we still need to see the B mode polarisation for it to passs its final hurdle. Well nothing is ever final, but this is a key test, see here:
http://www.nature.com/news/2009/090415/full/458820a.html
3)Borde , Guth and Vilenkin have argued that eternal inflaiton has an initial singualrity, but that has been disputed by Aguirre and Gratton. see here:
http://arxiv.org/abs/0712.0571
If anyone knows of any way to observationally resolve this dispute, I'd love to hear it but I suspsect there is not.
4) Guth claims most inflationary models are eternal , but I note he doesn't say all.So if ifnaltion is shown beyond reaosnable doubt, there is stil a chance its not eternal. see here http://arxiv.org/abs/hep-th/0702178:[/URL]

5 LQC resolves singualrities inlcuding the one proposed at the beginning of eternal inflation by Borde Guth and Vilkenkin , see here:
[url]http://arxiv.org/abs/0812.4703[/url][/QUOTE]

1) Is that so? Wikipedia does redirect to Eternal Inflation when you type in Chaotic Inflation :P
2) I didn't think it was a done deal, but I kinda like the idea. Plus it kind of appeals to my physical sense.
3 & 5) I'm pretty sure bapowell addressed this with a pretty good point: singularities state the breakdown of a theory, not the breakdown of physics. If a theoretical model possesses a singularity, that's evidence for its incompleteness, so saying that 'Eternal Inflation has an initial singularity' is pretty much the same as saying 'Eternal Inflation is [I]still[/I] not a good enough theory.' So even if LQC doesn't turn out to be true, the final theory should have as a property the ability to dissolve singularities.
4) Yes, I understand that, too, although I really like the idea of an Eternal Inflation. Of course, me liking it and it being true are not correspondent, and I haven't studied science for long enough to know whether my scientific hunches are anywhere on spot. I'm just going to follow them where science doesn't know what it's doing.
 
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  • #34
skydivephil said:
A few things I thinks its worth mentioning.
1) Eternal inflation and chaotic inflation are not the same.
read here:
http://arxiv.org/pdf/gr-qc/0409055.pdf
Yes, indeed. To be clear, above James and I were discussing chaotic inflation, which is necessarily eternal (hence my phrasing "chaotic eternal inflation"). There are models of eternal inflation that are not technically chaotic (which refers to the distribution of the initial field values.)
2) Inflation has good evidence for it but its not a done deal yet, we still need to see the B mode polarisation for it to passs its final hurdle. Well nothing is ever final, but this is a key test, see here:
http://www.nature.com/news/2009/090415/full/458820a.html
Yes, but if B-modes are not detected that doesn't falsify inflation (nor does it necessarily confirm it, see the quick note by Brandenberger on some other B-mode sources: http://arxiv.org/abs/1104.3581)
3)Borde , Guth and Vilenkin have argued that eternal inflaiton has an initial singualrity, but that has been disputed by Aguirre and Gratton. see here:
http://arxiv.org/abs/0712.0571
Interesting. I was not aware that it was under dispute. For completeness, here's a reference to the original paper by Borde and Vilenkin: http://arxiv.org/abs/gr-qc/9312022. The later paper with Guth was an extension.

And James, for a good technical introduction to string theory try Zwiebach. I've not read it myself but it seems highly praised by many in the field. More advanced standards are the texts by Polchinski and Green, Schwarz, and Witten. The latter is a now out-dated by has its unique strengths.
 
  • #35
And to be clearer, I'd thought the Chaotic Model was the only Eternal Inflation Model, I didn't know there were other Eternal Inflation theories. But I didn't really do enough research on the field as of yet so I'm just going with the flow for now until I obtain more knowledge on that and can actually participate more actively in such discussions.
 
<h2>1. What is the concept of the infinity of the Universe?</h2><p>The concept of the infinity of the Universe is the idea that the Universe has no end or boundary, and that it is constantly expanding and evolving. It suggests that the Universe is infinite in size and contains an infinite number of galaxies, stars, and planets.</p><h2>2. How do scientists measure the infinity of the Universe?</h2><p>Scientists use various methods to measure the infinity of the Universe, such as observing the redshift of distant galaxies, studying the cosmic microwave background radiation, and analyzing the distribution of matter in the Universe. These methods help scientists estimate the size and age of the Universe and support the idea of its infinite nature.</p><h2>3. Is it possible for humans to fully comprehend the concept of the infinity of the Universe?</h2><p>It is difficult for humans to fully comprehend the concept of the infinity of the Universe as it is beyond our everyday experience and perception. However, through scientific research and theories, we can gain a better understanding of the vastness and complexity of the Universe.</p><h2>4. What are some implications of the infinity of the Universe?</h2><p>The infinity of the Universe has significant implications for our understanding of the origins, evolution, and fate of the Universe. It also raises philosophical questions about the nature of existence and our place in the vastness of the cosmos.</p><h2>5. Are there any theories that challenge the idea of the infinity of the Universe?</h2><p>There are some theories, such as the cyclic model or the multiverse theory, that propose alternative explanations for the size and structure of the Universe. These theories suggest that the Universe may not be infinite, but rather part of a larger system or cycle. However, the concept of the infinity of the Universe remains widely accepted among scientists based on current evidence and observations.</p>

1. What is the concept of the infinity of the Universe?

The concept of the infinity of the Universe is the idea that the Universe has no end or boundary, and that it is constantly expanding and evolving. It suggests that the Universe is infinite in size and contains an infinite number of galaxies, stars, and planets.

2. How do scientists measure the infinity of the Universe?

Scientists use various methods to measure the infinity of the Universe, such as observing the redshift of distant galaxies, studying the cosmic microwave background radiation, and analyzing the distribution of matter in the Universe. These methods help scientists estimate the size and age of the Universe and support the idea of its infinite nature.

3. Is it possible for humans to fully comprehend the concept of the infinity of the Universe?

It is difficult for humans to fully comprehend the concept of the infinity of the Universe as it is beyond our everyday experience and perception. However, through scientific research and theories, we can gain a better understanding of the vastness and complexity of the Universe.

4. What are some implications of the infinity of the Universe?

The infinity of the Universe has significant implications for our understanding of the origins, evolution, and fate of the Universe. It also raises philosophical questions about the nature of existence and our place in the vastness of the cosmos.

5. Are there any theories that challenge the idea of the infinity of the Universe?

There are some theories, such as the cyclic model or the multiverse theory, that propose alternative explanations for the size and structure of the Universe. These theories suggest that the Universe may not be infinite, but rather part of a larger system or cycle. However, the concept of the infinity of the Universe remains widely accepted among scientists based on current evidence and observations.

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