Could there be an edge to the Universe?

[Futobingoro]

such, when we go back to t=0, the physical size of the universe (space included) approaches zero...

Why must it?

A balloon has the same amount of rubber whether it is inflated or fully deflated.

Why must there have been less space in the initial universe than there is today?

All we hypothesize is that matter/energy was more densely distributed within space, not how much space there was.

 

[SpaceTiger]

I understand that the assumption of isotropy means that there is no boundary. But isotropy is not empirical evidence--it is an assumption.

The CMB is pretty strong evidence for isotropy, at least within the observable universe. However, the cosmological principle could break down well outside the observable universe and there would be no way for us to know.

 

[Contrapositive]

A balloon has the same amount of rubber whether it is inflated or fully deflated.

You're taking an analogy too literally. The surface area of the balloon is simply analogous to the volume of universe.

 

[SpaceTiger]

Why must it?

A balloon has the same amount of rubber whether it is inflated or fully deflated.

Why must there have been less space in the initial universe than there is today?

All we hypothesize is that matter/energy was more densely distributed within space, not how much space there was.

You're right in the sense that an infinite universe could still be infinite in extent as t -> 0 (my statement only holds true for a finite universe). I don't think this is what you mean, however. The balloon analogy is only a crude analogy and we shouldn't consider the "amount of rubber" as equivalent to the "amount of space" or the physical size of the universe. In a finite universe obeying the cosmological principle, the universe does approach zero size as t -> 0. In the analogy, the size of the universe that we measure is analogous to the distance around the surface of the balloon.

 

[KingOrdo]

The CMB is pretty strong evidence for isotropy, at least within the observable universe. However, the cosmological principle could break down well outside the observable universe and there would be no way for us to know.

Actually, the CMB is just empirical evidence in support of isotropy in the Solar System. It does not weigh in in favor of isotropy elsewhere in the observable universe. It's like a Bedouin concluding that since he sees sand in all directions, all human beings see sand in all directions. That's both (1) false, and (2) a corruption of the Copernican principle.

In the case I'm curious about (R^3), the universe is almost everywhere isotropic (everywhere but near the boundary). Therefore, it is no surprise that appears isotropic to us, and moreover the Copernican principle is upheld because we inhabit the 99.999 . . .% of the 'normal' universe.

 

[Garth]

There's been a lot of very interesting commentary on this thread, and I thank everyone for that. However, my fundamental question has not been addressed; let me put it another way that might be clearer:

Assuming Omega=1 and the Universe is spatially R^3--therefore one day reaching a maximum volume (or asymptotically approaching a maximum volume), what empirical evidence is there that the Universe is not bounded?

Point 1 - In a plain GR expanding universe, where the scale factor in the Robertson-Walker metric is determined by the GR field equation (Friedmann equation), without a Cosmological Constant or Dark Energy (DE) (with negative pressure), and if "\Omega=1 and the Universe is spatially R^3" then the universe will expand forever and not reach a maximum volume.

The present standard \LambdaCDM mainstream model has \Omega=1, or thereabouts and added 73% DE so it accelerates in its expansion and so it will also not reach a maximum volume.

Point 2 - By the nature of the question there can be no empirical evidence to prove that the universe is not bounded, except that as far as we can see no boundary in encountered, which is indeed the case.

I certainly understand that this scenario (R^3) is compatible with an infinite universe--but it also seems compatible with a universe that has a boundary. Imagine, again, a sheet of rubber, with pennies stuck to it representing (e.g) galaxies: You stretch the paper out, fast at first, but slowing asymptotically to some maximum area. Little spaceships leaving the galaxies and going in one direction would, eventually, run into a 'brick wall' which they could not penetrate.

Why would they "run into a 'brick wall' which they could not penetrate"? They might just go on forever...

As far as I know, all our observations are totally compatible with this picture: But am I wrong about this? That's really what I want to know.

Observations are also totally compatible with the hypothesis that there are timid fairies at the bottom of my garden that are so scared they always hide when somebody comes near, because I never see them. But that does not mean they are actually there, the simpler hypothesis is that my garden is uninhabited by fairies.

I understand that the assumption of isotropy means that there is no boundary. But isotropy is not empirical evidence--it is an assumption.

No, isotropy on the largest scales is more than an assumption, it is an observation - at these scales the sky in one part of the sky looks like the sky in any other part, as far as the CMB is concerned it is isotropic to about one part in 10⁵.

Garth

 

[SpaceTiger]

Actually, the CMB is just empirical evidence in support of isotropy in the Solar System. It does not weigh in in favor of isotropy elsewhere in the observable universe. It's like a Bedouin concluding that since he sees sand in all directions, all human beings see sand in all directions. That's both (1) false, and (2) a corruption of the Copernican principle

Note the caveat "within the observable universe". An observer a great distance away would have a different observable universe, seeing things that we could not see, even if they were within our observable universe. All we can say is that the parts of our observable universe that they can see will be isotropic.

So yes, the CMB is only evidence for homogeneity/isotropy within our observable universe, but it is near the limits of the evidence we can ever expect to have. Asking for further empirical evidence is unrealistic with what we currently know about the universe.

 

[KingOrdo]

Point 1 - In a plain GR expanding universe, where the scale factor in the Robertson-Walker metric is determined by the GR field equation (Friedmann equation), without a Cosmological Constant or Dark Energy (DE) (with negative pressure), and if "\Omega=1 and the Universe is spatially R^3" then the universe will expand forever and not reach a maximum volume.

So this is false: "If the universe were flat, it would also expand forever, but the expansion rate would slow to zero after an infinite amount of time."? (http://skyserver.sdss.org/dr1/en/astro/universe/universe.asp)

Why would they "run into a 'brick wall' which they could not penetrate"? They might just go on forever...

No, ex hypothesi the ants cannot go on forever (it is a truly 2D piece of paper--not a normal piece of paper).

Observations are also totally compatible with the hypothesis that there are timid fairies at the bottom of my garden that are so scared they always hide when somebody comes near, because I never see them. But that does not mean they are actually there, the simpler hypothesis is that my garden is uninhabited by fairies.

No. You are the one making the extraordinary claim here. You are positing something that we have no empirical evidence of. We have only your intuition--an intuition not shared by everyone (viz. me). That's precisely why my central question is, 'What is the empirical evidence in support of a boundaryless Universe?' The burden of proof is on you to prove such a thing. That's the entire problem with this issue: You're taking a physical issue on faith because, I suspect, it satisfies some other prejudicial notions. But these are physical decisions that should be made on empirical evidence. Einstein made a similar mistake when he added Lambda to the equations of GR. He said: 'Whoa! My equations imply the Universe had a beginning. That's too much like what those nutty religious folks say. How can I get it to be steady-state?' Einstein, unwittingly, let his physics be perverted by religion (albeit in an somewhat inverted way). And I cannot help but get the sense that all this opposition to a boundary is due to similar reasons. Remember, good physics is about ignoring religion/faith/etc. totally and looking objectively at the evidence.

No, isotropy on the largest scales is more than an assumption, it is an observation - at these scales the sky in one part of the sky looks like the sky in any other part, as far as the CMB is concerned it is isotropic to about one part in 10⁵.

No. The Universe is isotropic from the Solar System. But it is an assumption to say that measurements taken elsewhere (say, outside the Virgo Supercluster) would be the same.

 

[marcus]

...
(1) I'm talking about a standard FRW model in which Omega=1. To answer Contrapositive's question, it's vital that the Universe be flat because if, say, the geometry were S^3, then there's obviously no edge...

KingOrdo, I'm curious to know if you reject picturing space as S^3 for some reason.

You are the one who first mentioned it, in this thread and you mention the fact that it has no boundary. Since you know that shape, and it is consistent with the data, do you ever consider that as a possibility.

In case other people who don't know the background on this are following, S^3 would be favored if we got a high-confidence errorbar for Omega like [1.005, 1.015]
That is, if we could EXCLUDE the case that Omega is exactly 1.00 with high confidence.
If we could say confidently that Omega is something > 1 somewhere around 1.01, then we'd say the universe is spatially nearly flat and might look like a slightly banged-up S^3.

roughly spherical but locally dented and bumpy by local above and below average concentrations of matter-----spherical on average.

with such a large radius of curvature that it looks almost flat (the way the surface of the Earth does, only moreso)

I see errorbars approximately like that with 65 percent confidence, from time to time, but that is not enough. We would need them to be 95 percent or better, in order to start talking. But I think it MIGHT be and it looks like an interesting possibility.

So do you take account of that, KingOrdo? Or do you exclude that one for some reason?

 

[SpaceTiger]

No. You are the one making the extraordinary claim here. You are positing something that we have no empirical evidence of. We have only your intuition--an intuition not shared by everyone (viz. me). That's precisely why my central question is, 'What is the empirical evidence in support of a boundaryless Universe?'

This is why many observational cosmologists prefer to just use "universe" to describe the observable universe. We can't know for sure what lies beyond it. One of the main reasons that there is a prejudice towards the applicability of the cosmological principle on the largest scales (aside from Occam's Razor) is inflationary theory. This "early universe" theory posits that an early exponential expansion of space causally disconnected our observable universe from other regions of space and that the "real" universe is actually much, much larger than what we can see. If this theory is correct, then the exponential expansion would have naturally "smoothed" things out and the larger universe would obey the cosmological principle as well. Although this theory naturally solves the flatness, horizon, and monopole problems, subsequent evidence for it has been hard to come by. So far, the best evidence is in the spectrum of cosmological perturbations, which appears to be well described by a gaussian random field and has a power law slope consistent with the expectations of inflation.

 

[Garth]

So this is false: "If the universe were flat, it would also expand forever, but the expansion rate would slow to zero after an infinite amount of time."? (http://skyserver.sdss.org/dr1/en/astro/universe/universe.asp)

That statement is completely true, what is false is your statement "one day reaching a maximum volume (or asymptotically approaching a maximum volume)".

If the universe's expansion rate slows to zero after an infinite amount of time its maximum volume is infinite.

No, ex hypothesi the ants cannot go on forever (it is a truly 2D piece of paper--not a normal piece of paper).

But the sheet of paper, as a 2D representation of the 3D space, is infinite in your example - see my last comment.

No. You are the one making the extraordinary claim here. You are positing something that we have no empirical evidence of. We have only your intuition--an intuition not shared by everyone (viz. me). That's precisely why my central question is, 'What is the empirical evidence in support of a boundaryless Universe?' The burden of proof is on you to prove such a thing. That's the entire problem with this issue: You're taking a physical issue on faith because, I suspect, it satisfies some other prejudicial notions. But these are physical decisions that should be made on empirical evidence.

What evidence do you look for, a 'brick wall at the end of the universe? It is that that I find extraordinary - that is why I used a ridiculous example - to make a point.

It is possible that the galaxies etc. could just peter out at a certain distance from us, but there is no evidence of such a thing.

Now absence of evidence is not evidence of absence - but it does mean the thing proposed has no evidence (yet) on which to build our hypothesis.

Einstein made a similar mistake when he added Lambda to the equations of GR. He said: 'Whoa! My equations imply the Universe had a beginning. That's too much like what those nutty religious folks say. How can I get it to be steady-state?' Einstein, unwittingly, let his physics be perverted by religion (albeit in an somewhat inverted way). And I cannot help but get the sense that all this opposition to a boundary is due to similar reasons. Remember, good physics is about ignoring religion/faith/etc. totally and looking objectively at the evidence.

Agreed - religion has nothing to do with it, good science is about sticking to testable and falsifiable theory and evidence - what evidence do you have for the hypothesis of a boundary?

No. The Universe is isotropic from the Solar System. But it is an assumption to say that measurements taken elsewhere (say, outside the Virgo Supercluster) would be the same.

I never said anything about measurements/observations made elsewhere - all we have to build our theory on are the observations we make from our own little solar system.

We can make all kinds of speculations about what we might see if we were at the far side of the universe, but until we can go there that is all they would be - speculations.

Garth

 

[KingOrdo]

KingOrdo, I'm curious to know if you reject picturing space as S^3 for some reason.

You are the one who first mentioned it, in this thread and you mention the fact that it has no boundary. Since you know that shape, and it is consistent with the data, do you ever consider that as a possibility.

In case other people who don't know the background on this are following, S^3 would be favored if we got a high-confidence errorbar for Omega like [1.005, 1.015]
That is, if we could EXCLUDE the case that Omega is exactly 1.00 with high confidence.
If we could say confidently that Omega is something > 1 somewhere around 1.01, then we'd say the universe is spatially nearly flat and might look like a slightly banged-up S^3.

roughly spherical but locally dented and bumpy by local above and below average concentrations of matter-----spherical on average.

with such a large radius of curvature that it looks almost flat (the way the surface of the Earth does, only moreso)

I see errorbars approximately like that with 65 percent confidence, from time to time, but that is not enough. We would need them to be 95 percent or better, in order to start talking. But I think it MIGHT be and it looks like an interesting possibility.

So do you take account of that, KingOrdo? Or do you exclude that one for some reason?

Oh, I certainly accept that as a possibility. Like you said, if the evidence comes in for Omega > 1, then that's it: the Universe is S^3, no boundary, it makes perfect sense to me why, etc. Nice, elegant, and all tied up.

I will say that I think the fact that Omega appears to be so darned close to 1 might give some extra support to Omega=1. I mean, of all the possible values of Omega, it's right near the critical value? There might be some anthropic reasoning there, though, that I haven't taken account of; I haven't thought too much about that.

But again: If we got an errorbar like the one you mentioned, S^3 and no boundary it is.

-----

That statement is completely true, what is false is your statement "one day reaching a maximum volume (or asymptotically approaching a maximum volume)".

If the universe's expansion rate slows to zero after an infinite amount of time its maximum volume is infinite.

Okey, something’s not making sense to me. Why does (1) the Universe’s expansion rate slowing to zero after an infinite amount of time not imply (2) the Universe will asymptotically approach a maximum volume?

But the sheet of paper, as a 2D representation of the 3D space, is infinite in your example - see my last comment.

Again, no: in my example, it really is a 2D world. It is not an embedding. A 2D ant will reach a boundary which it cannot cross.

Agreed - religion has nothing to do with it, good science is about sticking to testable and falsifiable theory and evidence - what evidence do you have for the hypothesis of a boundary?

The principle of parsimony--Occam's razor. Since apparently there is no empirical evidence against the existence of a boundary, and no empirical evidence in favor of infinite space (instead, only talk of 'best fit', conceptual clarity, etc.), I will judge a theory based on its simplicity. I have never encountered the infinite except in the abstract (in mathematics). Everything I have ever encountered is finite. Everything else in physics is finite—masses, velocities, stars, galaxies, clusters, superclusters, black holes, supernovae, etc. Why should the Universe be any different? Unless there’s evidence to say it is, you’ve still got work to do--or so it seems to me.

 

[Futobingoro]

You're taking an analogy too literally. The surface area of the balloon is simply analogous to the volume of universe.

The thing I have a problem with is that the surface area expands only from the perspective of somebody watching the balloon inflate. One would need to leave our universe to gain that same perspective (which brings its own challenges and uncertainties assuming it is even possible or meaningful).

You must realize that the balloon is an analogy to the very fabric of our universe. Stretching, squeezing or deforming the balloon neither adds to nor subtracts from the amount of fabric in the balloon. This is important because an expanding universe needs an addition of fabric. The balloon model is therefore insufficient in visualizing a mechanism by which expansion takes place.

 

[andrewj]

The answer, I am told, is 'No'. But I do not understand why. Assume:

(1) The Universe is spatially flat. It will one day stop expanding.

(2) There is no weird dark energy.

These are, I think, plausible assumptions.

Then: What evidence is there to weigh against the conclusion that there is an edge to the Universe (and therefore a unique center)?

It is certainly compatible with the observed expansion, no? To use a rubber sheet example: Imagine the Universe is a standard 2D sheet of computer paper, but made of rubber. Stick coins to it to represent galaxies. Then stretch it apart to represent the expansion--fast at first, but slowing asymptotically to zero. Then we have (1) all galaxies receding from each other, (2) a unique center, but not one that would be easily (or perhaps even possibly) evident to the galaxies' inhabitants.

Thanks in advance.

do you assume that you could pass the edge of space as the universe is not only expanding but being created

 

[Contrapositive]

do you assume that you could pass the edge of space as the universe is not only expanding but being created

What do mean by 'being created'? The universe? Space?

 

[SpaceTiger]

The thing I have a problem with is that the surface area expands only from the perspective of somebody watching the balloon inflate. One would need to leave our universe to gain that same perspective (which brings its own challenges and uncertainties assuming it is even possible or meaningful).

As the balloon inflates, wouldn't an ant on its surface find that it took longer to get from point to the next as time went on? Similarly, would an immortal observer in our universe not find that it takes longer for light to reach them from a distant galaxy as the universe expands?

The "amount of rubber" between two objects on the balloon's surface is somewhat analogous to a comoving distance, but not to a physical one. As was already explained to you, we have "rulers" that allow us to place a scale on the expansion of the universe without having to leave the universe.

 

[Contrapositive]

The thing I have a problem with is that the surface area expands only from the perspective of somebody watching the balloon inflate. One would need to leave our universe to gain that same perspective (which brings its own challenges and uncertainties assuming it is even possible or meaningful).

Imagine two ants on the surface of a balloon. As it expands, the two ants see each other move away from each other. So you can be on the balloon (i.e. inside the universe) and see it expand.

You must realize that the balloon is an analogy to the very fabric of our universe. Stretching, squeezing or deforming the balloon neither adds to nor subtracts from the amount of fabric in the balloon. This is important because an expanding universe needs an addition of fabric. The balloon model is therefore insufficient in visualizing a mechanism by which expansion takes place.

Who said the rubber in the balloon exactly represents the fabric of space-time? You're taking an analogy too literally.

 

[Garth]

Okey, something’s not making sense to me. Why does (1) the Universe’s expansion rate slowing to zero after an infinite amount of time not imply (2) the Universe will asymptotically approach a maximum volume?

The expansion of the universe, without the influence of DE that makes the expansion accelerate, can be compared to a projectile leaving Earth at near escape velocity.

If it is launched at just below escape velocity it will eventually fall back to Earth and there will be a maximum altitude that it will reach.

If launched at above escape velocity it will carry on into 'outer space' to infinity always at some positive velocity.

If launched at exactly escape velocity it will be "slowing to zero after an infinite amount of time", yet it will still reach an infinite altitude but asymptotically approaching zero velocity as it does so.

That is it will reach 'inifinity' and take an 'infinite' amount of time to do so!

The really significant point is that its velocity will only approach zero at 'infinity', i.e. it will never actually do so, it will go on and on to infinity at slower and slower velocity but never reach zero velocity wrt the Earth.

The principle of parsimony--Occam's razor. Since apparently there is no empirical evidence against the existence of a boundary, and no empirical evidence in favor of infinite space (instead, only talk of 'best fit', conceptual clarity, etc.), I will judge a theory based on its simplicity. I have never encountered the infinite except in the abstract (in mathematics). Everything I have ever encountered is finite. Everything else in physics is finite—masses, velocities, stars, galaxies, clusters, superclusters, black holes, supernovae, etc. Why should the Universe be any different? Unless there’s evidence to say it is, you’ve still got work to do--or so it seems to me.

I also hold Occam's Razor in high regard, read my signature (the first one), and see my avatar.

I repeat my question, "What (observational) evidence do you have for the hypothesis of the existence of a boundary?"

Garth

 

[KingOrdo]

The expansion of the universe, without the influence of DE that makes the expansion accelerate, can be compared to a projectile leaving Earth at near escape velocity.

If it is launched at just below escape velocity it will eventually fall back to Earth and there will be a maximum altitude that it will reach.

If launched at above escape velocity it will carry on into 'outer space' to infinity always at some positive velocity.

If launched at exactly escape velocity it will be "slowing to zero after an infinite amount of time", yet it will still reach an infinite altitude but asymptotically approaching zero velocity as it does so.

That is it will reach 'inifinity' and take an 'infinite' amount of time to do so!

The really significant point is that its velocity will only approach zero at 'infinity', i.e. it will never actually do so, it will go on and on to infinity at slower and slower velocity but never reach zero velocity wrt the Earth.I also hold Occam's Razor in high regard, read my signature (the first one), and see my avatar.

I'm sorry; I'm still not getting it. I don't dispute that what you're saying is right; it's just not clicking for me. It seems to me that if something is getting slower and slower, and we know the numbers involved, we can calculate a maximum distance. Could you perhaps give a more mathematically rigorous example of this sort of motion?

Also, a related question: Even if in cases when Omega=1 the Universe has no maximum volume, is there any value for Omega for which the Universe will (1) stop expanding (like in Omega=1), and (2) have a finite maximum volume? Thanks.

I repeat my question, "What (observational) evidence do you have for the hypothesis of the existence of a boundary?"

And I repeat my answer: The impetus is on you, not me, to prove your theory. We encounter bounded physical things all the time: stars, black holes, masses, velocities, etc. We never encounter physically boundless things. Matter can only be divided so far. Things can only go so fast. And so on. Yet you claim that the Universe goes on forever. Fine: you might be right. But you need to adduce empirical evidence for such a view.

At worst, we might say that since both the bounded case and unbounded case have no empirical evidence weighing one way or the other (which apparently is true in practice, and what I've been wondering throughout the thread), we need to choose one model on other grounds (e.g. Occam's razor). My intuition, as discussed here and elsewhere, is that the bounded model is simpler, more common sensical, and less 'faith based'.

 

[SpaceTiger]

At worst, we might say that since both the bounded case and unbounded case have no empirical evidence weighing one way or the other (which apparently is true in practice, and what I've been wondering throughout the thread), we need to choose one model on other grounds (e.g. Occam's razor). My intuition, as discussed here and elsewhere, is that the bounded model is simpler, more common sensical, and less 'faith based'.

There's a whole community of trained scientists who disagree with your view. Adding a boundary adds at least one free parameter to our model of the universe. Furthermore, there is no plausible physical origin for such a boundary, while a universe obeying the cosmological principle arises naturally in many early universe theories.

You don't have to accept that the universe obeys the cosmological principle on scales beyond what we can see to accept the mainstream cosmological model, but I think the issue of which is "simpler" boils down to the number of free parameters needed in the model. In this regard, we are always drawn to the cosmological principle.

 

[KingOrdo]

There's a whole community of trained scientists who disagree with your view.

I have never found appeals to consensus very persuasive. If there is empirical evidence, I would like to hear it.

Furthermore, there is no plausible physical origin for such a boundary, while a universe obeying the cosmological principle arises naturally in many early universe theories.

Well, there's no plausible physical origin for an infinite Universe, either. Those aren't physical questions. And indeed, the cosmological principle is not an empirical one--it's a faith-based leap that in my view is on very shaky ground (compare it to the well-founded Copernican principle). The clever Bedouin who believes that all human beings are surrounded by desert because he is is wrong. What I've been asking is: Is there any empirical evidence against a bounded Universe? N.B. even if not, that doesn't mean the Universe is bounded. But since there is no empirical evidence that the Universe is unbounded, we have to decide the matter on non-empirical grounds: Occam's razor, for example. And my intution seem to differ from others'.

 

[SpaceTiger]

I have never found appeals to consensus very persuasive. If there is empirical evidence, I would like to hear it.

I do not find appeals to popular opinion very convincing, but when faced with the opinion of an untrained layman and a community of scientists, I am more convinced. The trouble is that your intuition is not developed for the problem you're attempting to tackle, while a cosmologist's is. I've already cited some empirical evidence for inflation (the truth of which would also suggest the applicability of the cosmological principle) yet you haven't responded.

Well, there's no plausible physical origin for an infinite Universe, either.

The arguments that we're making do not necessarily suggest an infinite universe. You are aware that a finite universe can exist that does not have a boundary?

Those aren't physical questions. And indeed, the cosmological principle is not an empirical one--it's a faith-based leap that in my view is on very shaky ground (compare it to the well-founded Copernican principle).

The Copernican principle is more abstract than the cosmological principle and the two aren't really comparable. The cosmological principle is very straightforward -- it posits large-scale homogeneity and isotropy. In contrast, the Copernican principle states rather vaguely that we are not "special" and that theories which suggest that we are should be treated with suspicion. I certainly agree with this statement, but think it's much less clearly defined.

Furthermore, the cosmological principle can be tested empirically within our observable universe. Beyond this, we can't test any theory -- for all we know gravity and electromagnetism are completely different outside of our observable universe. Does this mean that the law of gravity cannot be tested empirically?

But since there is no empirical evidence that the Universe is unbounded, that means we have to decide the matter on non-empirical grounds: Occam's razor, for example. And my intution seem to differ from others'.

Occam's Razor can be formulated more rigorously as the statistical maximization of entropy. When we introduce a boundary, we need to specify its location and extent, free parameters that act to decrease the entropy of the theory. A universe that obeys the cosmological principle is simpler in this regard. Any other use of the word "simple" would be irrelevant to the discussion.

It's not clear to me that you understand the problem fully enough to be reaching such sweeping conclusions. If you're confused about something, please ask. This forum is primarily designed to have experts answer the questions of non-experts, not for the formulation of personal theories. Please be careful that this does not turn into one.

 

[marcus]

Oh, I certainly accept that as a possibility. Like you said, if the evidence comes in for Omega > 1, then that's it: the Universe is S^3, no boundary, it makes perfect sense to me why, etc. Nice, elegant, and all tied up.

I will say that I think the fact that Omega appears to be so darned close to 1 might give some extra support to Omega=1. I mean, of all the possible values of Omega, it's right near the critical value? There might be some anthropic reasoning there, though, that I haven't taken account of; I haven't thought too much about that.

But again: If we got an errorbar like the one you mentioned, S^3 and no boundary it is.
...

thanks for your reply, KingOrdo. my thoughts on this are similar. it's an important issue what the current best Omega errorbar is, so I try to stay posted.
Personally the most authoritative and recent source I know is March 2006
http://arxiv.org/abs/astro-ph/0603449

Everybody cites it----it's the official implications for cosmology part of a multipaper series reporting the 3rd year data from the WMAP satellite.
If you look on page 50, caption to figure 17, you see a 68 percent errorbar for Omega which is [1.010, 1.041]
The errorbar is based on combined data from four major projects: WMAP CMB, supernova, the Sloan digital sky survey, and the 2-degree-field galaxy redshift survey.
As of 2006 that was about as good as it gets, and I haven't seen anything since then that is more highly cited.

To me that 1.01 is not SURPRISINGLY close to one. Reasons have been offered why, if the universe is spatially S^3, one would nevertheless expect it to be very expanded and so have a small curvature----to be near flat in other words.
The errorbar being close to one is not especially remarkable. What is remarkable IMO is that it does not contain one---it is all on the upside.

So what [1.010, 1.041] says to me personally is that they already HAVE an errorbar that says S^3, they just don't have enough confidence on it. 68 percent is not enough to disfavor the infinite R^3 case. So I could conclude something if I saw a similar errorbar like [1.010, 1.041] and it had 95 percent confidence.

There are technical issues about how you interpret. Like this particular figure assumes dark energy had constant pressure/volume ratio, but they let the constant ratio take on various values. And people can argue should they have allowed time-varying dark energy, or maybe should they have forced the ratio to always be exactly one etc etc. But the technical details don't change the overall sense I get that nowadays the Omega errorbar tends to be mostly over to the > 1 side-----saying "nearly but not exactly" flat. And that the confidence is not high enough to reject the flat case, so one says it is still "consistent with the data" (i.e. flat is not ruled out.)

 

[Wallace]

But since there is no empirical evidence that the Universe is unbounded, we have to decide the matter on non-empirical grounds: Occam's razor, for example. And my intution seem to differ from others'.

Occam's Razor is an often misused concept. As Space Tiger (and others I think) have pointed out several times, adding an edge when one is not observed is adding more parameters and hence complexity to the model. Hence it's an open and shut case that assuming, via the mathematical model for the Universe, that it is infinite is the simpler option clearly favoured by Occam's razor. Less parameters = simpler model, and that is a purely objective way of evaluating model simplicity, without having to get a straw poll of people's intuition.

The point is that if our model describes an infinite Universe, whereas in fact we are in a Universe that is very very big (much bigger than the observable Universe) then the model works perfectly well. If in the future we discovered the Universe was in fact finite, but much much bigger than the observable Universe we would for most cases simply use the infinite model, since the difference between the two is vanishingly small and the calculations are easier in the infinite model. We do things like this all the time, for instance we think General Relativity is the true theory or gravity, however we usually use Newtonian gravity for most things since the Newtonian model is simpler and easier to work with and the two models give the same answer for most questions we have.

This is how science works, we seek to find models that match what we observe, described in the simplest way possible, rather than making metaphysical statements about the extent of reality. If the infinite model works we'll use it, it doesn't matter if whether or not the Universe is truly infinite, that's not the point of the assumption or the model.

 

[Garth]

I'm sorry; I'm still not getting it. I don't dispute that what you're saying is right; it's just not clicking for me. It seems to me that if something is getting slower and slower, and we know the numbers involved, we can calculate a maximum distance. Could you perhaps give a more mathematically rigorous example of this sort of motion?

If \Omega = 1 and with no Dark Energy (DE) or other forms of pressure or cosmological constant then we have the Einstein de Sitter model in which the scale factor

a(t) = a(t_0)(\frac{t}{t_0})^{\frac{2}{3}}

and so as t \rightarrow \infty so a(t) \rightarrow \infty.

Also, a related question: Even if in cases when Omega=1 the Universe has no maximum volume, is there any value for Omega for which the Universe will (1) stop expanding (like in Omega=1), and (2) have a finite maximum volume? Thanks.

Yes, In the absence of DE or the cosmological constant the universe will have a maximum volume if
\Omega > 1.

However, with the present understanding of DE the universe will continue to expand, and accelerate in its expansion, even if \Omega > 1.

And I repeat my answer: The impetus is on you, not me, to prove your theory. We encounter bounded physical things all the time: stars, black holes, masses, velocities, etc. We never encounter physically boundless things. Matter can only be divided so far. Things can only go so fast. And so on. Yet you claim that the Universe goes on forever. Fine: you might be right. But you need to adduce empirical evidence for such a view.

I do not claim the universe goes on forever, it could be finite yet unbounded, the standard theory describes a homogeneous and isotropic universe, in this case if \Omega \leq 1 the universe will be infinite and unbounded.

What type of boundary are you thinking of anyway?

Garth

 

[KingOrdo]

I do not find appeals to popular opinion very convincing, but when faced with the opinion of an untrained layman and a community of scientists, I am more convinced. The trouble is that your intuition is not developed for the problem you're attempting to tackle, while a cosmologist's is.

I think you've got things backwards. Sometimes that "untrained layman"--whom, do not forget, may be far smarter than you--has a more veridical intuition because he is approaching things fresh. A good example would be Einstein in 1905. How did that "untrained layman" catch something so obvious, beautiful, and simple (viz. Special Relativity) that the initiated missed? Do not mistake dogmatism for erudition.

I've already cited some empirical evidence for inflation (the truth of which would also suggest the applicability of the cosmological principle) yet you haven't responded.

Assume inflation is true. Then the observable Universe is causally disconnected from other parts of the Universe. That does not weigh in on whether the Universe does or does not have a boundary.

The arguments that we're making do not necessarily suggest an infinite universe. You are aware that a finite universe can exist that does not have a boundary?

You have obviously not read my posts. How many have I devoted to S^3 geometries?

Furthermore, the cosmological principle can be tested empirically within our observable universe. Beyond this, we can't test any theory -- for all we know gravity and electromagnetism are completely different outside of our observable universe. Does this mean that the law of gravity cannot be tested empirically?

You're missing the point. You can test gravity all the time. That's why it's a valid scientific theory. But it would be wrong to drop a ball at one point on the Earth and then claim that, due to that single measurement, gravity holds everywhere on the Earth. You have to test it and test it and test it--under different conditions, in different places, and so on. In addition, gravity fits in a relation of coherence with our other scientific theories (e.g. the Standard Model).

It's not clear to me that you understand the problem fully enough to be reaching such sweeping conclusions. If you're confused about something, please ask. This forum is primarily designed to have experts answer the questions of non-experts, not for the formulation of personal theories. Please be careful that this does not turn into one.

You should take due care not to insult. I have been polite and honest throughout the thread; I expect the same from you. I have asked questions, and solicited answers. Remember that some of us are smarter than you, and some of us are more important than you. Perhaps not me; but some of us. Be nice.

 

[KingOrdo]

Thanks, Garth--this is really helpful.

Yes, In the absence of DE or the cosmological constant the universe will have a maximum volume if
\Omega > 1.

I should have been more specific: Are there any cases where the Universe will have a maximum volume and not recollapse? That is, reach a maximum size and just stop? If so, what would Omega have to be?

What type of boundary are you thinking of anyway?

No bloody idea. When I think about it I just imagine stopping. You're in the vacuum, everything is black, and you can't go any farther. Put as much energy into it as you like and you can't penetrate. But maybe I'm wrong and it's the Pearly Gates (I'm an atheist)!

 

[SpaceTiger]

I think you've got things backwards. Sometimes that "untrained layman"--whom, do not forget, may be far smarter than you--has a more veridical intuition because he is approaching things fresh. A good example would be Einstein in 1905. How did that "untrained layman" catch something so obvious, beautiful, and simple (viz. Special Relativity) that the initiated missed? Do not mistake dogmatism for erudition.

Ugh, not this again. Einstein was a trained physicist, not a layman. It does not matter how intelligent you are or think you are, if you don't know enough about the problem you're trying to solve, you won't solve it.

Assume inflation is true. Then the observable Universe is causally disconnected from other parts of the Universe. That does not weigh in on whether the Universe does or does not have a boundary.

It does, in fact. I suggest you do some reading on eternal inflation, the most favored form of it right now.

You have obviously not read my posts. How many have I devoted to S^3 geometries?

And yet you don't understand how they're distinct from a flat, matter-dominated universe that is infinite in extent?

You're missing the point. You can test gravity all the time. That's why it's a valid scientific theory. But it would be wrong to drop a ball at one point on the Earth and then claim that, due to that single measurement, gravity holds everywhere on the Earth. You have to test it and test it and test it--under different conditions, in different places, and so on. In addition, gravity fits in a relation of coherence with our other scientific theories (e.g. the Standard Model).

Every independent patch of space that we observe is a test of the cosmological principle -- it is not wrapped up in "one point" as you put it. Observing the universe from the Virgo cluster would only increase the data a very small fraction, since only a small portion of the "outside" universe would be revealed.

You should take due care not to insult. I have been polite and honest throughout the thread; I expect the same from you. I have asked questions, and solicited answers. Remember that some of us are smarter than you, and some of us are more important than you. Perhaps not me; but some of us. Be nice.

I'm surprised that you think that you have been polite to the people responding to you, but the last paragraph in my post was not meant as an insult, but as a warning. Unless you are claiming that you actually are an expert on cosmology, you should not be selling you ideas or "intuition" as fact. The debate over Occam's Razor is a good example of what I'm talking about.

 

[KingOrdo]

Ugh, not this again. Einstein was a trained physicist, not a layman. It does not matter how intelligent you are or think you are, if you don't know enough about the problem you're trying to solve, you won't solve it.

I'm not trying to solve a problem. I'm asking questions. When someone tells me 'B', I ask why and they say, 'Because either A or B', I'm going to wonder what's up.

It does, in fact. I suggest you do some reading on eternal inflation, the most favored form of it right now.

If I could find the answer to this question, I wouldn't be asking it in this forum. Again: If there is empirical evidence (i.e. not magic), please tell me what it is.

And yet you don't understand how they're distinct from a flat, matter-dominated universe that is infinite in extent?

I do. Read the thread.

Every independent patch of space that we observe is a test of the cosmological principle -- it is not wrapped up in "one point" as you put it. Observing the universe from the Virgo cluster would only increase the data a very small fraction, since only a small portion of the "outside" universe would be revealed.

Right. This is induction.

I'm surprised that you think that you have been polite to the people responding to you, but the last paragraph in my post was not meant as an insult, but as a warning. Unless you are claiming that you actually are an expert on cosmology, you should not be selling you ideas or "intuition" as fact. The debate over Occam's Razor is a good example of what I'm talking about.

I don't understand what your problem is, but I've certainly been polite to everyone--even you. And I'm not "selling" anything. I'm asking questions. You obviously don't want to answer them. Fine--go somewhere else. (Cf. Garth's posts if you need an example of how to be helpful.)

 

[cristo]

I suggest you do some reading on eternal inflation, the most favored form of it right now.

What exactly is eternal inflation, SpaceTiger? (or anyone else who's reading!) My gut instinct says it must have to do with a scenario in which inflation continues forever in some regions. Is this something to do with the way in which the inflaton decays at the end of inflation; i.e. the way in which the inflaton decays into radiation is a quantum mechanical process, and so all regions will not have inflation ending at the same time. I guess this implies that in some regions inflation will never end? This latter point is getting towards how structure formation is explained, isn't it?

Any review papers you can suggest will be appreciated!

 

[Dozent100]

I am a scientist by trade, so I know how the process works. Discussion here is much more pedagogical, but the basic mode of discourse is the same. If what you have to say is supported by scientific research and/or general knowledge, then say it and present your support. If not, then you can either ask about it or keep it to yourself.[/QUOTE]

AMEN to that!

 

[SpaceTiger]

If I could find the answer to this question, I wouldn't be asking it in this forum. Again: If there is empirical evidence (i.e. not magic), please tell me what it is.

I already gave you some empirical evidence for inflation. If you need clarification, please ask, don't ignore it.

I don't understand what your problem is, but I've certainly been polite to everyone--even you. And I'm not "selling" anything. I'm asking questions.

You certainly have asked questions, but after having them answered, you've quickly formed a position against the person responding to your question. If your intentions really are to learn, then I have no quarrel with you, but your responses suggest to me that you consider your ideas to be not only contrary to mainstream science, but more reliable than the mainstream because you're thinking outside the box. Perhaps you can see why this might ring warning bells for a moderator of an internet forum.

What exactly is eternal inflation, SpaceTiger? ...
Any review papers you can suggest will be appreciated!

Certainly, here's a review by Guth himself:

http://xxx.lanl.gov/abs/astro-ph/0002156"

 

[Dozent100]

But The universe has at least 4 dimensions by the most conservative estimate and 11 or 12 dimensions as the normally accepted Number. S or R =3?

 

[KingOrdo]

I already gave you some empirical evidence for inflation. If you need clarification, please ask, don't ignore it.

I responded to that remark. You have failed to explain yourself--you essentially said, 'No, you're wrong'. And that is not an argument.

You certainly have asked questions, but after having them answered, you've quickly formed a position against the person responding to your question. If your intentions really are to learn, then I have no quarrel with you, but your responses suggest to me that you consider your ideas to be not only contrary to mainstream science, but more reliable than the mainstream because you're thinking outside the box. Perhaps you can see why this might ring warning bells for a moderator of an internet forum.

I've had lots of questions answered; none by you. I must say, I don't understand why you've involved yourself in this discussion in the first place, and why you persist in causing trouble. The rest of us are having a nice conversation. If you need examples of how to rigorously respond to inquiries, I recommend looking at the posts of (e.g.) Garth, Wallace, and marcus.

Also, I am not presenting a theory here. This you must understand. I am asking about the justificatory basis of your theory (viz. the infinite Universe). If you have a sound argument, you should be able to present it without difficulty. I'm simply asking for clarification and pointing out lacunae if I see them.

It is sometimes good to have a logician looking over your back, don't you think?

 

[SpaceTiger]

I responded to that remark. You have failed to explain yourself--you essentially said, 'No, you're wrong'. And that is not an argument.

Please see my posts for cited evidence for inflation:

https://www.physicsforums.com/showpost.php?p=1536453&postcount=61"

If you need me to expand or clarify anything, please say so rather than pretending it was never posted. It took several nearly identical explanations of Occam's Razor before you stopped trying to use it in your arguments.

I've had lots of questions answered; none by you. I must say, I don't understand why you've involved yourself in this discussion in the first place, and why you persist in causing trouble. The rest of us are having a nice conversation. If you need examples of how to rigorously respond to inquiries, I recommend looking at the posts of (e.g.) Garth, Wallace, and marcus.

I'm glad you found their posts useful, they are among the more helpful and knowledgeable members here and there is much to be learned from them. Certainly many of my posts were addressing the tone of the discussion, as it is my responsibility to moderate these forums as well as to contribute to them. If you're not finding my posts helpful, then perhaps I'm not communicating myself well, and If you have more questions, I can assure you that I will address them as directly as I can.

 

[Dozent100]

I already gave you some empirical evidence for inflation. If you need clarification, please ask, don't ignore it.
You certainly have asked questions, but after having them answered, you've quickly formed a position against the person responding to your question. If your intentions really are to learn, then I have no quarrel with you, but your responses suggest to me that you consider your ideas to be not only contrary to mainstream science, but more reliable than the mainstream because you're thinking outside the box. Perhaps you can see why this might ring warning bells for a moderator of an internet forum.

Certainly, here's a review by Guth himself:

http://xxx.lanl.gov/abs/astro-ph/0002156"

--------------------------------------------------------------------------------------
I got to go with Space Tiger on this one. I think your questions have been adequately answered several times over. Some very smart people, myself not included, have looked at your problem from several different angles. Cosmology is a not a hard science. There are not a lot of hard facts around to base assumptions on. And we can talk till the cows come home, but if you reject all explanations offered, what are we accomplishing?

My experience is more on the nuclear Engineering side, but I try to keep up with what is going on. I will caution you that There is a lot of Pseudo Science running around and I wonder if this where you are coming from. Psudo-Science attempts to make the science fit the desired outcome, rather than the other way around. And where the facts don't support the theory, the facts are ignored.
There has been a lot of that going around since the Clinton Years.



s

 

[KingOrdo]

Please see my posts for cited evidence for inflation:

https://www.physicsforums.com/showpost.php?p=1536453&postcount=61"

If you need me to expand or clarify anything, please say so rather than pretending it was never posted. It took several nearly identical explanations of Occam's Razor before you stopped trying to use it in your arguments.

I can't make things any clearer to you on this matter. Regarding Occam's Razor: You apparently still don't understand it. It's not: The simplest theory is the best. It is: Do not multiply entities without need. There is a subtle, but important, difference there. You are the one making a positive claim; the burden of proof is on you, not me. You believe that X? Great: adduce some evidence in support.

I got to go with Space Tiger on this one. I think your questions have been adequately answered several times over. Some very smart people, myself not included, have looked at your problem from several different angles. Cosmology is a not a hard science. There are not a lot of hard facts around to base assumptions on. And we can talk till the cows come home, but if you reject all explanations offered, what are we accomplishing?

I'm not interested in your pet theories, conjecture, poetic impressions, etc. I'm interested in evidence. I'm interested in someone saying: 'Hi, KingOrdo: We know that the Universe is infinite because satellite A measured b. We already know because of law Y that b if and only if c. But if c then d. Therefore d.'

My experience is more on the nuclear Engineering side, but I try to keep up with what is going on. I will caution you that There is a lot of Pseudo Science running around and I wonder if this where you are coming from. Psudo-Science attempts to make the science fit the desired outcome, rather than the other way around. And where the facts don't support the theory, the facts are ignored.

Are you talking about pseudo-science in the Popperian sense? It's not clear to me what you're saying here. I am asking questions about the structure of the Universe.

There has been a lot of that going around since the Clinton Years.

I don't know what you're saying here. I don't see what politics, or my liberalism, has to do with anything.

 

[Wallace]

I'm not interested in your pet theories, conjecture, poetic impressions, etc. I'm interested in evidence. I'm interested in someone saying: 'Hi, KingOrdo: We know that the Universe is infinite because satellite A measured b. We already know because of law Y that b if and only if c. But if c then d. Therefore d.'

I think we are getting somewhat off track in this discussion! No one is suggesting that we can conclusively prove the Universe is infinite but I'm curious to know why you think 'the burden of proof' rests on the 'case for infinite' side of the argument? It could equally be argued that if one was to suggest the Universe is finite, then evidence for this must be presented.

However, neither of the above arguments I just made are reasonable. Clearly we do not have conclusive evidence either way. What we do know is that we have not reason to doubt that the cosmological principle applies for the extent of our observable universe, for this we do have hard evidence such as the isotropy of the CMB (the anisotropies are of course of great interest, but are very small in agreement with the cosmological principle), and the general isotropy of galaxies and QSO's seen in large redshift surveys.

Given this data then, we can see that if the Universe is finite, it is clearly at least much bigger than the observable Universe, and for all intents and purposes is infinite. Assuming the Universe is infinite makes the equations easier to deal with, since there are less parameters.

I'm not sure how to discussion got to the point of demanding conclusive evidence for the infinite nature of the Universe? Surely this is impossible! We can only ever say that was haven't observed something, we can never have proof that is doesn't exist. To make a whimsical example, it is not reasonable to demand that someone who says that talking monkeys with tea-pots for hands do not exist provide evidence for their non-existence. All you can do is point to the evidence that we have not observed such things, and it makes evolution a simpler model if it does not have to explain why monkeys should have evolved tea-pots in place of their hands. To further the silly analogy, we could make theoretical predictions about the problems monkeys would face with tea-pot hands, just as we can make predictions about the problems an edge to the Universe would introduce. In both cases our theories may suggest the non-existence of something but to prove with evidence the non-existence is clearly impossible.

Theories are constructed based upon what is observed, and are made to be as simple as possible given those observations. This is why we assume the Universe is infinite, in full knowledge that this is not absolutely neccessarily the case.

 

[pervect]

Regardless of whether or not there is an edge to the universe, there is a definite edge to this thread. A rather unpleasant one.

So, let's all try to be nice to one another, and get the thread back on track (as Wallace ha noted, it's started to drift).

Otherwise, I'm going to get grumpy and start doing grumpy things...

One thing that pushes my buttons is Ordo's idea that SpaceTiger should have unlimited amounts of time to answer his (Ordo's) questions. In an ideal world, this would be nice, but people have to be able to live with the fact that moderators and mentors may actually have other things in their life other than PF, hard as it may be to believe...

 

[cristo]

Certainly, here's a review by Guth himself:

http://xxx.lanl.gov/abs/astro-ph/0002156"

Thanks

 

[KingOrdo]

I think we are getting somewhat off track in this discussion! No one is suggesting that we can conclusively prove the Universe is infinite but I'm curious to know why you think 'the burden of proof' rests on the 'case for infinite' side of the argument?

Because that's a positive claim: 'The Universe is infinite.' Okey, fine: Maybe you're right. Why is that so? What empirical evidence do you have in support?

It could equally be argued that if one was to suggest the Universe is finite, then evidence for this must be presented.

Indeed. And in a previous post I made precisely this point. If I were prepared to make a rigorous claim that the Universe were finite, the onus would be on me to defend it.

However, neither of the above arguments I just made are reasonable. Clearly we do not have conclusive evidence either way. What we do know is that we have not reason to doubt that the cosmological principle applies for the extent of our observable universe, for this we do have hard evidence such as the isotropy of the CMB (the anisotropies are of course of great interest, but are very small in agreement with the cosmological principle), and the general isotropy of galaxies and QSO's seen in large redshift surveys.

Thanks for this response. But why isn't the onus on you to justify your claim: 'The universe is isotropic from Earth. Therefore, the universe is isotropic from every point in the observable universe.' That's a leap that does not seem to be entailed by the empirical evidence. The Bedouin would be wrong to say, 'The world looks desert-y in all directions to me. Therefore, the world looks desert-y from all spots on the Earth.' How does going from local isotropy (observationally true) to the cosmological principle not make the same mistake?

Given this data then, we can see that if the Universe is finite, it is clearly at least much bigger than the observable Universe, and for all intents and purposes is infinite. Assuming the Universe is infinite makes the equations easier to deal with, since there are less parameters.

But here's a technical question I asked earlier that has not been answered: Is there any amount of matter that would halt the expansion of the Universe (that is, such that the Universe asymtotically approaches a maximum volume)? If so, the Universe is identical to the observable universe (right?) and if there's a boundary, we could eventually find it (our progeny, that is). Other than the cosmological principle and (your) intuitions about simplicity, is there anything that weighs against a finite universe?

Theories are constructed based upon what is observed, and are made to be as simple as possible given those observations. This is why we assume the Universe is infinite, in full knowledge that this is not absolutely neccessarily the case.

Okey. Our inuitions just differ on this point. Thanks again for your very clear and informative reponse.

-----

One thing that pushes my buttons is Ordo's idea that SpaceTiger should have unlimited amounts of time to answer his (Ordo's) questions. In an ideal world, this would be nice, but people have to be able to live with the fact that moderators and mentors may actually have other things in their life other than PF, hard as it may be to believe...

Are you talking about someone else here? I never claimed any such thing; in fact, I've asked SpaceTiger to stay out of the discussion. Part of being a good scientist--indeed, a good human being--is honesty in argument, pervect.

 

[Valjean]

It may be that condidering the edge of the universe is like considering the edge of time. Many advances in knowledge have come at the expense of contradicting current accepted conclusions. Maybe a different look at the basis would help answer some of the questions...most likely not but maybe. Consider, from the same starting place as the bang, formation of strings and such...nothing. Then a contraction of space into bits of compressed space each surrounded by expanded space, both created by the same action, like a teeter, totter. Just as a compressable spring with equal alternate sections compressed it will expand the other sections and they will pull beteen the compressed sections but not move them if that pull is equal in both directions. Equate that to space, multi-dimensional, spherical. The likeness stops there but it could help understand how the expanded space is necessary to produce attraction between the compressed bits of space. Under this scenario the area we consider an empty vacuum of nothingness is not. It is near infinitely flexible expanded space. It would be the conduit that transfers energy fluctuations from bit to bit and the ever larger units they combine to form. Compressed space (energy) surrounded by expanded space (energy) Some combine to form units around which other individual or smaller units of bits orbit in regular frequencies and amplitudes, increasing and decreasing the level of attraction strength between them and others comensurate with the changing distance. Those we can detect with our instruments. The ones who do not move in regular patterns we can detect would still retain their attraction component (dark matter). And if units combine into large accumulations their attraction increases accordingly and could be the source of what is considered "warped space". This would violate and contradict many currently held notions. But one of the frequenct comments shared by most scientific disciplines is something akin to "Because of this we're going to have to reconsider our conclusions about...". It's those rethinkings that produce progress.

 

[SpaceTiger]

I can't make things any clearer to you on this matter. Regarding Occam's Razor: You apparently still don't understand it. It's not: The simplest theory is the best. It is: Do not multiply entities without need. There is a subtle, but important, difference there. You are the one making a positive claim; the burden of proof is on you, not me. You believe that X? Great: adduce some evidence in support.

Okay, I think it's time to lock this thread. It's clear that the OP isn't going to accept the answers given to them, so for the sake of everyone's time, the discussion should probably stop. Other folks with lingering questions (about eternal inflation, or whatever) should feel free to start another thread. Thanks to everyone who took the time to respond.