Big Bang and PreExisting Void?

[awktrc]

How do we know that the Big Bang did not expand into a preexisting void?

What is the justification for this knowledge/belief?

[zhermes]

The BB didn't expand "into" anything (in the way you're suggesting). Space(-time) itself is what was expanding, not just the matter in it. It doesn't make sense to describe it as expanding "into" something.

[Chalnoth]

How do we know that the Big Bang did not expand into a preexisting void?

What is the justification for this knowledge/belief?
If you examine what a universe would look like "from the outside", so to speak, it would look like a black hole. Because the new universe looks like a black hole from the outside, it is unable to expand into the pre-existing universe. But it has no trouble expanding from the perspective of somebody within the new universe.

That is, if a new universe was generated from a vacuum fluctuation in an existing universe, it would look like a microscopic black hole that came into existence for a moment, then rapidly evaporated away. One way of looking at it is that the space-time of the new universe "pinches off" from the old one, and almost instantly the new universe is all on its own, with no connection to where it came from.

[Chronos]

Painting on a canvas is a classical argument - suggesting matter must be superimposed over a preexisting 'space'. There is no valid theoretical or observational evidence supporting that premise.

[granpa]

lets assume that it did expand into a preexisting space. Then where did that space come from? Another Big Bang? Did that Big Bang expand into a preexisting space?

At some point there had to be a Big Bang that created space itself.

[Chiclayo guy]

lets assume that it did expand into a preexisting space. Then where did that space come from? Another Big Bang? Did that Big Bang expand into a preexisting space?

At some point there had to be a Big Bang that created space itself.

If cold is the absence of heat, and dark is the absence of light, why can’t an infinite and eternal space be the absence of matter? To me asking the question where did space come from doesn’t make any more sense than asking where did dark or cold come from. There does not seem to be consensus on this forum as to whether space existed prior to or was created by the bb.

Okay…back to lurk mode for me.

Tom

[granpa]

If cold is the absence of heat, and dark is the absence of light, why can’t an infinite and eternal space be the absence of matter? To me asking the question where did space come from doesn’t make any more sense than asking where did dark or cold come from. There does not seem to be consensus on this forum as to whether space existed prior to or was created by the bb.

Okay…back to lurk mode for me.

Tom

infinite and eternal space of how many dimensions? 3? why not 1,826,548,356,657 dimensions?

[justwondering]

And it still may safely be assumed that no information could 'pass' through the Big Bang event. i.e. No matter formation 'instructions' at any scale level, or anything else. Everything that took place after has just been random chance out of perhaps a near infinite range of possibilities?

[MoonlitFractl]

well, the big bang itself seems to over-ride a fundamental law in biology where spontaneous generation (eg- a universe [XD]) is impossible, unless being that there can be apparently be another creating force to do it.

Also in statement, having an infante number of dementions seems to sasify this as well, as in an infante number of universes may have existed previously. Furthering that, with an infante number of dementions, there could be an infante number of different results in each of the other universes created from other "big bangs" occuring in other dementions. Furthering that, having an infante number of dementions with universes ending to an infantle variable rate they'd be destroyied/created.

..the big-bang was technically random?


Or can alternate dementions interact? For example, if universe "A" was being destroyed. While inside universe "A" another random universe was being created. (having an infante number of detementions within a demention) Due to the fact a universe may be random. Now, this new "internal" universe, universe "B" was expanding and universe "A" was being destrioed. Apon Universe "A"'s destruction, universe "B" was able to form fully. Any such that was aware of universe "B" was able to excape to it. And any such unaware of universe "B" was destroied.

(why does this sound like economics, cancer, and the molting of an animals skin.....?)

Now in this example, there is only now universe "B" but all the such lone in the destruction of universe "A", does this mean the remniants create a NEW universe??? Kinda like the "seeds" of a tree that was chopped down.

O_o... (why does this sound religious, philosophical, and strangely like the book "the lord of the flies"...?)


And due to the fact these lone such are in hyper space, they can expand without any other universe holding them back by those universes forces.


0_o...

[Oldfart]

The BB didn't expand "into" anything (in the way you're suggesting). Space(-time) itself is what was expanding, not just the matter in it. It doesn't make sense to describe it as expanding "into" something.

Getting back to this for a moment, could it not be that a void surrounded the BB which was not comprised of spacetime but rather was a simple void which had no characteristics or properties? Could multiple universes be "housed", surrounded in a void soup of sorts? It outwardly seems to me that the existance of a void of this sort could never be proven or disproven.

I love this thread, very interesting!

[Dmitry67]

In such case there should be a border between 'ordinary' and how you call it 'simple' void. You would face many difficult questions like:

Why both types of void have the same number of dimensions?
What happens in places where ordinary space is curved?
What is a border between 2 types of voids?
Is it sharp or smooth?
What happens to an object or particle going thru the edge?
In any case, go thru all theories (QM, EM, Gravity) and incorporate such type of object there.

Purely hypotetically, if our spacetime could have edges in space, such edges would emit enourmous quantities of hawking radiation because of the pair production, when 1 component of the pair dissapears behind the edge. Contrary to Black Holes, that radiation is not redshifted by gravity and is EXTREMELY intense. Very soon it curves space because of its enourmous energy density and creates real black hole with a 'normal' event horizon :)

[twofish-quant]

How do we know that the Big Bang did not expand into a preexisting void?

We don't.

We can however say that the observations of the universe are inconsistent with any void existing any part of the universe we can observe or which influences the behavior of anything that we can observe.

[twofish-quant]

Painting on a canvas is a classical argument - suggesting matter must be superimposed over a preexisting 'space'. There is no valid theoretical or observational evidence supporting that premise.

Let me rephase that to something stronger. The observations say that for the parts of the universe we have any data of, that the universe is not spreading into a void. If the universe was spreading into a void, you'd see the effects of the void. You don't.

[twofish-quant]

And it still may safely be assumed that no information could 'pass' through the Big Bang event.

Not true. Anytime someone "assumes" something, you should ask why we are assuming that.

Some of the current work in cosmology is to work on models of what the universe might of looked like before cosmic inflation happened and to see if any of the "pre-inflation" universe could have any effect on observable things like the CMB power spectrum.

This is important because relating theory to observations is what science is about.

[Oldfart]

Dmitry67, thanks for your convincing reply, this stuff makes my brain hurt after 74 years of experience with edges and boundaries. One final idiot question:

Assuming the existence of multiple universes for a moment, it appears that they cannot be separated from our universe by any sort of boundary, like a border fence. Do they then co-exist within our own universe, separated from us by different dimensions or time? If our universe is infinite/flat, where else could they be? (Brain hurts again.)

[Dmitry67]

Oldfart, our universes our 4 dimensional, so they can coexist in higher dimensional space without any intersections. That hypotetical super-space is called BULK. However, lets wait for TOE to get clearer picture.

For the classification of types Universes in Multiverse (I, II, II and IV) google Max Tegmark Mathematical Universe Hypotesis.

[Oldfart]

Oldfart, our universes our 4 dimensional, so they can coexist in higher dimensional space without any intersections. That hypotetical super-space is called BULK. However, lets wait for TOE to get clearer picture.

For the classification of types Universes in Multiverse (I, II, II and IV) google Max Tegmark Mathematical Universe Hypotesis.

Thanks again, Dmitry67! I checked some of Max's stuff, did not understand it, but then, what's new? Is there a book or two out there that sort of gently leads a layman by the hand through our infinite, expanding universe? You can see by inquiries in this thread that some of us have conceptual problems, need help. (Though I fear that the math involved may greatly limit communication between us.)

[BoomBoom]

If the universe was spreading into a void, you'd see the effects of the void. You don't.

What effects would a void have? Wouldn't said void, by definition, be empty of anything that would cause an effect that could be detected?

[Chronos]

There is a word they use in physics for anything that is entirely uninteractive - nonexistent.

[Oldfart]

There is a word they use in physics for anything that is entirely uninteractive - nonexistent.

Dang, Chronos, I've spent at least ten minutes trying to figure out whether your statement is helpful or simple sarcasm...

OK, lets see if I've got this figured out. Assuming the universe is flat/infinite, it didn't just get infinite one day but always has been, even at the start of the BB, when it was, lets say, the size of a pea. Correct? OK, us folks that have this mental picture of the BB expanding into a void are mentally sitting in this void, outside the BB, and watching this thingy expand, and thinking yep, it's expanding into a void, alright! But this cannot be a correct way of thinking, as this would mean placing the observer beyond infinity. The observer, and the void for that matter, cannot possibly exist beyond infinity. Correct?

Having made the void impossible, I am now left with only the minor mental problem of stuffing an infinite universe into a pea...

[Chronos]

It makes more sense if you picture expansion creating its own space as it evolves, and that space is created in the vast gulfs between galactic clusters. Empty space is endowed with a peculiar property called dark energy, and this dark energy is accelerating the expansion of the universe.

[bcrowell]

Looking at this thread, I see that the OP has asked a question, 20 answers have been given, the OP hasn't posted again, and virtually all of the answers are not answers to the OP's question. The OP asked, "how do we know X?," and virtually all the answers are "X is true! X is true! Let me explain X to you!"

Let me rephase that to something stronger. The observations say that for the parts of the universe we have any data of, that the universe is not spreading into a void. If the universe was spreading into a void, you'd see the effects of the void. You don't.

Twofish-quant has tried to answer the OP's actual question here. Hurrah!

I'm not completely satisfied with twofish-quant's answer, however. Maybe it could be improved upon.

Our observations can only reach out to a certain distance. If all we know is that we don't see a surrounding void, that doesn't seem like a very strong argument to me, since maybe we just don't see the surrounding void because it's too far away.

Here is a possible alternative approach.

(1) General relativity has passed a variety of experimental tests, so we think it's probably pretty accurate. (2) We observe that the redshifts of distant supernovae follow a certain dependence on their distance from us. (3) We also observe that the cosmic microwave background has fluctuations on certain angular scales.

Smart people have tried very hard to find a model that fits 1, 2, and 3. All they've managed to come up with is a particular model in which there is no preexisting void. In fact, the observations fit that model extremely well. On the other hand, nobody has ever found a model *with* a preexisting void that fits 1, 2, and 3. That makes us suspect that there is no preexisting void.

Another line of attack is that if we only assume 1 above, then the Hawking singularity theorem http://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems , plus some relatively crude observations of the present state of the universe, tells us there must have been a singularity in our past. Such a singularity, as described by GR, has features that are incompatible with the idea of an explosion in a preexisting spacetime. In particular, if GR is correct, then timelike world-lines can't be extended backward through that singularity.

[Oldfart]

It makes more sense if you picture expansion creating its own space as it evolves, and that space is created in the vast gulfs between galactic clusters. Empty space is endowed with a peculiar property called dark energy, and this dark energy is accelerating the expansion of the universe.

OK, maybe your explanation "makes more sense", but you are running ahead of me. Is there anything in my previous explanation that is incorrect? And why does your explanation make more sense, it doesn't seem to relate to the "void" issue. Duhh...

But thanks for getting back!

[twofish-quant]

Our observations can only reach out to a certain distance. If all we know is that we don't see a surrounding void, that doesn't seem like a very strong argument to me, since maybe we just don't see the surrounding void because it's too far away.

Quite true. But what we can say is that there are no voids within *X* billion light years of the earth, right now I think the limit of *X* is 60 billion light years of the earth. There could be voids 1.2 trillion light years from year, or not....

On the other hand, nobody has ever found a model *with* a preexisting void that fits 1, 2, and 3. That makes us suspect that there is no preexisting void.

Who is "us"? All I can say is that with our current knowledge of the universe, there are no detectable anisotropies and inhomogeneities within 60 billion light years. There could very will be massive voids 1.2 trillion years out.

I can also say that when I do my GR calculations I *assume* that there are no voids at all, because it makes the math easier.

In particular, if GR is correct, then timelike world-lines can't be extended backward through that singularity.

The trouble is that it is known that GR is wrong once you get to planck's length.

[bcrowell]

Who is "us"? All I can say is that with our current knowledge of the universe, there are no detectable anisotropies and inhomogeneities within 60 billion light years. There could very will be massive voids 1.2 trillion years out.
I think we should distinguish logically between a large but finite void and the case where there is an infinite, preexisting, asymptotically flat void. The latter is really what the OP was asking about.


I can also say that when I do my GR calculations I *assume* that there are no voids at all, because it makes the math easier.
It is certainly easier to do calculations with an assumption of homogeneity and isotropy, but it's also impossible to cut and paste a Big Bang singularity into an infinite, preexisting, asymptotically flat void. A BB singularity, which we know exists because of the Hawking singularity theorem, has geodesic incompleteness, so it can't arise out of a preexisting void.


The trouble is that it is known that GR is wrong once you get to planck's length.
True. Everything I'm saying is in the context of classical GR.

[Chronos]

If the universe is surrounded by an infinite void, it is difficult to explain why the cmb intensity is identical in every direction.

[bcrowell]

If the universe is surrounded by an infinite void, it is difficult to explain why the cmb intensity is identical in every direction.

Interesting point. Although our planet could of course just happen to be located at a special center of symmetry, or the void could be beyond the current horizon as seen from earth.

[nunogirao]

If the universe is surrounded by an infinite void, it is difficult to explain why the cmb intensity is identical in every direction.

Imagine you have two BigBangs in the preexisting void, separated by a distance greater than the actual size of our universe. Before the two BB frontiers (cmb) reach each other, you have no effect for someone that is inside each own universe.
And the cmb intensity is nor identical in every direction. Could this fluctuations in the cmbr been caused by other universes created by other BB?
Maybe our expanding universe just needs more time until it bumps with another one.. in this preexisting void. I like the idea.

[Oldfart]

I still need help with this -- anyone?

IF our universe is infinite, can it be surrounded by a void (beyond infinity??). Or is that OK, since an absolute void is, after all, um, nothing?

[Chalnoth]

Imagine you have two BigBangs in the preexisting void, separated by a distance greater than the actual size of our universe.
This doesn't actually make a difference. The thing is, space-time is not some absolute thing, so even if you have two big bang events born within some other space-time separated by some distance, those two big bang events still can never interact in any way, shape, or form. The new space is generated within each individual event, and cannot effect either the parent universe or anything else.

One way to see this is to just look at the Schwarzschild radius of a black hole with the mass of our observable universe. It turns out that that Schwarzschild radius is larger than our observable universe, which in turn means that if there is an edge to our universe, from the outside it must necessarily look like a black hole.

So we have a picture where when a new universe is formed, it forms within the parent universe as a microscopic black hole which rapidly evaporates, forever disconnecting the new universe from the parent universe, leaving no way for the two to interact whatsoever. The space-time of the new universe, almost immediately after the new universe is formed, is entirely self-contained and cannot interact with any other universe.

[nunogirao]

This doesn't actually make a difference. The thing is, space-time is not some absolute thing, so even if you have two big bang events born within some other space-time separated by some distance, those two big bang events still can never interact in any way, shape, or form. The new space is generated within each individual event, and cannot effect either the parent universe or anything else.


I don't know if the space-time was created in the BB or if it is something that ever existed (and there we go to the «when/why» it was created).
So, is the void just the space-time fabric, where BBs occour?
And, could it be possible that different types of universes (with different rules) populate the same void? Could a «neutrino type» universe exist that just transverse our universe, without influencing it?

[Chalnoth]

I don't know if the space-time was created in the BB or if it is something that ever existed (and there we go to the «when/why» it was created).
However it started, space most definitely expanded. It may have started from a pre-existing space-time, as I mentioned. But entirely new space is produced as the universe expands. The expansion of the new universe cannot ever possibly be observed in the old universe.

And, could it be possible that different types of universes (with different rules) populate the same void?
From what we know of high energy physics today, it definitely appears that different regions of space-time, both within a universe and between them, may well have different low-energy laws of physics. We really can't say much at all about the extent of this variation just yet. For now, the only variation from place to place that we have at least some confidence of is the electroweak symmetry breaking event, which appears to have a particular parameter that is random and varies from place to place (as in it is likely different some place far from our observable universe, but is the same everywhere we can see).

Could a «neutrino type» universe exist that just transverse our universe, without influencing it?
Well, unless you want to talk about higher-dimensional theories like string theory, it just isn't sensible to talk about another universe existing transverse to our own. In General Relativity, our space-time is self-contained and cannot overlap with any other universe.

However, in string theory, the "true" universe has 10 space-time dimensions (11 in M-theory), and we might exist on a brane with 4 space-time dimensions, which could, in principle, be close to another 4-dimensional brane, rather in the same way that two sheets of paper can be placed close to one another. Most forces are stuck on the brane, so that we could not observe the other brane through them, but gravitational interactions always remain, and we could interact with this other universe through gravity.

[yogi]

How do we know that the Big Bang did not expand into a preexisting void?

What is the justification for this knowledge/belief?

We don't - unless we are creatures that are simply satisfied to collect data, some degree of speculation cannot be avoided (Eddington). And when it comes to beginnings, there is no dearth of speculative theories. Most of these are based on what we observe within the confines of the Hubble sphere centered upon our observational position on earth - but there is much evidence that leads to the notion that the actual universe of matter in the form of particles is at least 3 times the Hubble scale - this in part due to an extrapolation of redshift data that shows nebula receding from one another at velocities in excess of c.

I personally have come to speculate upon a pure de Sitter exponentally expanding background space - with neither beginning in time nor space - an interesting twist on the big bang as an initial expansion is a symmetry breaking withing some small volume of the de Sitter background space leading to an abrupt contraction of that volume into a dense volume of proto particles - followed by later expansion to its present limit defined by a de Sitter horizon.

When it comes to beginnings, some are better than others - but there is not much possibility of being proved wrong even if your ideas are as far out as mine.

[JDoolin]

How do we know that the Big Bang did not expand into a preexisting void?

What is the justification for this knowledge/belief?

If you go back to the original source "Relativity, Gravitation, and World Structure" you will see that Milne's model described a Big Bang expanding into a preexisting void. He reassured the reader that nothing could ever get in from outside because the outside edge of the explosion consists (now and forever) of a surface with infinite density traveling at the speed of light.

In fact it only comforts me a little, because if there were another universe in the same infinite void, it's density in its outer shell would also be infinite, and moving toward us at the speed of light. The good news is, if something hits you at the speed of light, you won't ever see it coming until it gets there.

As far as the justification for rejecting the Milne model, I have been trying to figure that out as well. So far, all I've found is that they already have whatever they want with the standard model, and they have read so much misinformation about the Milne model that they find it ludicrous. In fact, you can't even so much as print up the density function for the Milne model on Wikipedia because it is "original research." I imagine, if you quote anything by Milne and put it up under the article for Milne's Model, it will be taken down, because Wikipedia relies on "Reliable Secondary Sources." Unfortunately, the few remaining copies of Relativity Gravitation and World Structure are probably to be burned, and the idea, whether correct or not, will be forever lost.

[JDoolin]

If the universe is surrounded by an infinite void, it is difficult to explain why the cmb intensity is identical in every direction.

If WE, and everything we see came from the same point and the same time, then wouldn't it make sense to expect it all to look the same in every direction?

[twofish-quant]

If WE, and everything we see came from the same point and the same time, then wouldn't it make sense to expect it all to look the same in every direction?

Only if you happen to be lucky enough to be near the center of the explosion, and that is a very weird coincidence. If all of the places in the universe that you happen to end up, how is it that you ended in the middle?

[twofish-quant]

If you go back to the original source "Relativity, Gravitation, and World Structure" you will see that Milne's model described a Big Bang expanding into a preexisting void.

And if you go back to that era, you will find that it's only one of about a dozen ideas that people had that made perfect sense with the data that they had available. Something that I like students to do is to look at old scientific papers and see what they were arguing about at some decade. The reason for this is that the way that we look at people in the 1930's is how people are going to look at us in the 2050.

Personally, if I had been around in 1960, I would have been a strong opponent of big bang because its much less elegant than steady-state. Looking the arguments, I probably would have considered the first measurements of CMB in 1965 to be experimental errors (and there were lots of reasons to think that they would have been wrong) and I probably wouldn't have been converted until the early 1970's.

I wouldn't be terribly surprised if five years from now, someone quotes me bashing Webb's results on the changing fine structure constant which will be standard knowledge at that time.

As far as the justification for rejecting the Milne model, I have been trying to figure that out as well.

It doesn't fit the data. People have been extremely patient explaining why it doesn't fit the data.

Unfortunately, the few remaining copies of Relativity Gravitation and World Structure are probably to be burned, and the idea, whether correct or not, will be forever lost.

If it's right, then people will stumble on it in the end. Continental drift and black holes were two ideas that were dormant for decades before someone observed something. Also scientists are more open minded that I think you give them credit for.

[twofish-quant]

For now, the only variation from place to place that we have at least some confidence of is the electroweak symmetry breaking event, which appears to have a particular parameter that is random and varies from place to place (as in it is likely different some place far from our observable universe, but is the same everywhere we can see).

This particular parameter is the fine structure constant which happens to be set to 1/137.(something) which is a number that looks pretty random. There are a number of experiments trying to see if the fine structure constant varies over space and time. One group has reported yes. Everyone else has reported no, and the details are in another thread on this forum.

[Chalnoth]

This particular parameter is the fine structure constant which happens to be set to 1/137.(something) which is a number that looks pretty random. There are a number of experiments trying to see if the fine structure constant varies over space and time. One group has reported yes. Everyone else has reported no, and the details are in another thread on this forum.
Actually, no, I wasn't talking about the fine structure constant, but rather the weak mixing angle. I don't think we have any indication that the fine structure constant could be different from place to place, but as I understand it the weak mixing angle is expected to be a result of a spontaneous symmetry breaking event, which would produce different angles in different locations (though it is definitely the same everywhere within our observable universe).

[twofish-quant]

When it comes to beginnings, some are better than others - but there is not much possibility of being proved wrong even if your ideas are as far out as mine.

Which is why I find this sort of thing surprisingly uninteresting. What happens at t=0 is rather uninteresting to me because you can basically make up anything and there is nothing that can prove you wrong.

This is not true for events at t=3 million years or t=3 minutes. At t=0 you can argue that some giant multidimensional space bird laid an egg that turned into the universe. At t=3 minutes, the temperatures are those that we can simulate in nuclear reactors. So you have to ask why you don't see space birds popping out of fusion reactors. At t=3 million years, you have to ask why you don't see space birds everywhere. There is a boundary point right now, at which if there is a giant space bird, then you such see it with the LHC.

At t=0, you don't know when something strange is happening because everything is strange. That's not true for t=3 million years, so when you see bricks start levitating themselves, then you know something odd is going on.

I'm a little puzzled why people are so fascinated with t=0, and its a religious, cultural and historical thing. Personally, I'm more interested in the "dark ages."

[Chalnoth]

I think it's precisely because it's rather wide-open that people want to talk about it so much: people don't have to actually know anything to say something about what's going on. But when you get into the later universe, we know quite a lot, and just pulling random ideas out of your backside starts to be directly contradicted by experiment. Actually presenting something potentially interesting requires knowledge and serious thought. So I think most people get rapidly discouraged when they get into the areas where we do have ample experimental knowledge.

Of course, we do regularly get people who are genuinely interested in the areas where we know more as well. So it isn't quite so bad as all that.

[twofish-quant]

I don't think we have any indication that the fine structure constant could be different from place to place, but as I understand it the weak mixing angle is expected to be a result of a spontaneous symmetry breaking event, which would produce different angles in different locations (though it is definitely the same everywhere within our observable universe).

My (possibly incorrect) understanding is that the fine structure constant also arises from the same spontaneous symmetry breaking event as the weak mixing angle, and so it's likely to be random for the same reasons. This is why people have suddenly got interested in anthropic arguments because with the current state if HEP, the fine structure constant is basically a totally random value.

Also the reason that people like cosmic inflation is that it provides an explanation for why the universe seems to look the same. What happened was that during and after the SSB event, the universe expanded so much that places with different values of the fundamental constants become unobservable.

[Chalnoth]

My (possibly incorrect) understanding is that the fine structure constant also arises from the same spontaneous symmetry breaking event as the weak mixing angle, and so it's likely to be random for the same reasons.
Hmm, that's conceivable.

Also the reason that people like cosmic inflation is that it provides an explanation for why the universe seems to look the same. What happened was that during and after the SSB event, the universe expanded so much that places with different values of the fundamental constants become unobservable.
Indeed. In fact, it seems that inflation expanded the universe so much that even defects that would have occurred from such a spontaneous symmetry breaking event are so far unobserved (namely, cosmic strings).

[twofish-quant]

Hmm, that's conceivable.

Did some more research on this. It turns out that the fine structure constant is believed to result from broken symmetry at the energies that strong and electroweak forces unify. This is different from the weak mixing angle which happens when EM and the weak forces unify. The latter are energies we can do direct experiments on.

The other interesting thing is that it turns out that we can do lab experiments to show that the fine structure constant isn't constant. As energy increases there are vacuum effects that change the value of the fine structure constant.

Indeed. In fact, it seems that inflation expanded the universe so much that even defects that would have occurred from such a spontaneous symmetry breaking event are so far unobserved (namely, cosmic strings).

One consequence of inflation is that the unobserved universe is a lot, lot bigger than the observed universe. You can get a limit for the size of the unobserved universe. You figure out how many cosmic strings you are likely to generate, you see how much you have to inflate the universe so that you don't see any. That gives you a bound as to how much of the universe is unobserved.

[Chalnoth]

Did some more research on this. It turns out that the fine structure constant is believed to result from broken symmetry at the energies that strong and electroweak forces unify. This is different from the weak mixing angle which happens when EM and the weak forces unify. The latter are energies we can do direct experiments on.
That makes a lot of sense, and it's why I wouldn't go so far as to say we (yet) have good reason to believe that the fine structure constant varies from place to place in the universe. Granted, I think it's highly likely, I'm just not so sure that we're there yet in terms of observation.

The other interesting thing is that it turns out that we can do lab experiments to show that the fine structure constant isn't constant. As energy increases there are vacuum effects that change the value of the fine structure constant.
It's been a little bit since I've looked into this, but from what I understand, this variation is largely understood, and doesn't constitute an actual variation of the coupling constant, but instead some "effective" variation. I'm not entirely certain what this means, but I gather that you can wrap some of the terms in higher-energy interactions back into the strength of the interaction, allowing coupling constants to run with energy.

The effect of this, it turns out, is that at some rather high energy, the variation of these effective coupling constants for the strong, weak, and electromagnetic forces tend towards close to the same value. If we add supersymmetry to the mix, the alignment between the coupling constants at high energy is much better.

One consequence of inflation is that the unobserved universe is a lot, lot bigger than the observed universe. You can get a limit for the size of the unobserved universe. You figure out how many cosmic strings you are likely to generate, you see how much you have to inflate the universe so that you don't see any. That gives you a bound as to how much of the universe is unobserved.
Well, at lower bound, at least! I don't think you could, even in principle, obtain an upper bound from this because this only estimates the amount of expansion after the symmetry breaking event, while there could in principle have been quite a lot of expansion before that event.

[JDoolin]

Only if you happen to be lucky enough to be near the center of the explosion, and that is a very weird coincidence. If all of the places in the universe that you happen to end up, how is it that you ended in the middle?

Quite the contrary. That is no coincidence at all. Every particle in the system is, in its original trajectory, in the center of the explosion.

What is your velocity? In your own reference frame, your velocity is zero. The particles around you have velocities anywhere from zero to the speed of light. Therefore no matter which particle you pick, it is going to be approximately in the center.

This is basic relativity. Think about it.

[Chalnoth]

Quite the contrary. That is no coincidence at all. Every particle in the system is, in its original trajectory, in the center of the explosion.

What is your velocity? In your own reference frame, your velocity is zero. The particles around you have velocities anywhere from zero to the speed of light. Therefore no matter which particle you pick, it is going to be approximately in the center.

This is basic relativity. Think about it.
Why do you continue to claim this is in any way reasonable? We've already shown that the Milne cosmology only works if the universe is completely empty. It isn't, so it's wrong.

[JDoolin]

If it's right, then people will stumble on it in the end. Continental drift and black holes were two ideas that were dormant for decades before someone observed something. Also scientists are more open minded that I think you give them credit for.

If you're trying to make me feel better, it's working.

But what I'd like is, even if it's wrong, for it to be properly understood, and the reasons for rejecting it to be based on actual experiment, rather than misinterpretation. I'd like to see why it's wrong.

[JDoolin]

Why do you continue to claim this is in any way reasonable? We've already shown that the Milne cosmology only works if the universe is completely empty. It isn't, so it's wrong.

No. You've asserted that the Milne cosmology only works if the universe is completely empty. And that was based on claiming that Milne's metric was not the Minkowski metric, which I already told you was not true.

[Chalnoth]

No. You've asserted that the Milne cosmology only works if the universe is completely empty. And that was based on claiming that Milne's metric was not the Minkowski metric, which I already told you was not true.
Um, no, it wasn't. It was based on the fact that the Einstein tensor vanishes with the Milne metric. The Einstein tensor also vanishes with the Minkowski metric. This changes nothing.

[TrickyDicky]

No. You've asserted that the Milne cosmology only works if the universe is completely empty. And that was based on claiming that Milne's metric was not the Minkowski metric, which I already told you was not true.
You seem to be muddled on this.

Let's see Minkowskian and Milne spacetimes(they are the same spacetime with a change in coordinates that shouldn't affect the physics) are both empty, meaning there is no gravity sources therefore no gravitational field. So the Milne cosmology is defined that way, as empty, and that has nothing to do with anyone's claims.

You are yourself admitting that Minkowski and Milne metrics are equivalent so you are implicitly admitting that the Milne universe is empty, so I don't know exactly where you disagree.

[JDoolin]

You seem to be muddled on this.

Let's see Minkowskian and Milne spacetimes(they are the same spacetime with a change in coordinates that shouldn't affect the physics) are both empty, meaning there is no gravity sources therefore no gravitational field. So the Milne cosmology is defined that way, as empty, and that has nothing to do with anyone's claims.

You are yourself admitting that Minkowski and Milne metrics are equivalent so you are implicitly admitting that the Milne universe is empty, so I don't know exactly where you disagree.

While Milne was attempting to show how ridiculous Eddington's ideas were, he gave an equation which would map comoving world-lines to world-lines that were moving away from a single event at a constant velocity. The equation was nonsense, and Milne's point was that it was nonsense.

However, because his point was also that Eddington's ideas were ridiculous, the Eddington followers latched onto the very equation that Milne was describing as nonsense, and began calling it The Milne Model.

I admit that the Minkowski metric and the real Milne metric are equivalent.
ds^2=dt^2-dx^2-dy^2-dz^2

However when you map in the nonsense equation, and use the metric given on Wikipedia for the Milne Model:
ds^2 = dt^2-t^2(dr^2+\sinh^2{r} d\Omega^2)
where
d\Omega^2 = d\theta^2+\sin^2\theta d\phi^2

... this metric is no longer equivalent to the Minkowski Metric.

[Chalnoth]

And we're back to my previous question: why are you so absurdly opposed to a simple change of coordinates?

[TrickyDicky]

However when you map in the nonsense equation, and use the metric given on Wikipedia for the Milne Model:
ds^2 = dt^2-t^2(dr^2+\sinh^2{r} d\Omega^2)
where
d\Omega^2 = d\theta^2+\sin^2\theta d\phi^2

... this metric is no longer equivalent to the Minkowski Metric.
Well they are not exactly the same if that is what you mean, if you have an aesthetic repulsion towards FRW metrics applied to Milne's model (why? maybe because you see the introduction of a scale factor as artificial or arbitrary in a spacetime that is essentially static? I could understand that, but Milne actually also introduced artificially an explosion in his special relativistic universe that gave particle tests their speeds up to c) that's OK, but you must realize that physically from the point of view of these particles(from their proper time and length)the metric with the scale factor and the Minkowski metric are indeed equivalent, the Minkowski metric is called the "private" frame in Milne's universe and the FRW metric would be the "public" view as seen from an outside point of view.

[TrickyDicky]

Quite the contrary. That is no coincidence at all. Every particle in the system is, in its original trajectory, in the center of the explosion.

What is your velocity? In your own reference frame, your velocity is zero. The particles around you have velocities anywhere from zero to the speed of light. Therefore no matter which particle you pick, it is going to be approximately in the center.

This is basic relativity. Think about it.
This is indeed an interesting property of Milne's model shared by standard cosmology, and shows that isotropy does not necesarily always imply homogeneity, so the cosmological principle is indeed as has been said here before, a philosophical preference that ultimately will have to be confronted empirically since isotropy without homogeneity is also a possibility.

I think the key here is that our cosmology based in GR is basically telling us that there is no center( in this forum"where is the center of the universe?" is a frequent question), so no observer can be in the center, so isotropy without homogeneity doesn't imply any privileged point of view and therefore perhaps the cosmological principle is not philosophically valid in a universe ruled by the theory of relativity.

[Chalnoth]

This is indeed an interesting property of Milne's model shared by standard cosmology, and shows that isotropy does not necesarily always imply homogeneity, so the cosmological principle is indeed as has been said here before, a philosophical preference that ultimately will have to be confronted empirically since isotropy without homogeneity is also a possibility.
At the very least, void models to explain the accelerated expansion without any dark energy have been ruled out already:
http://arxiv.org/abs/1007.3725

I think the key here is that our cosmology based in GR is basically telling us that there is no center( in this forum"where is the center of the universe?" is a frequent question), so no observer can be in the center, so isotropy without homogeneity doesn't imply any privileged point of view and therefore perhaps the cosmological principle is not philosophically valid in a universe ruled by the theory of relativity.
Well, pretty sure that isotropy without homogeneity does imply a privileged point of view. It's just that so far there's no reason to believe our universe isn't homogeneous, as the homogeneous models work, but the inhomogeneous ones so far do not.

[TrickyDicky]

Well, pretty sure that isotropy without homogeneity does imply a privileged point of view. It's just that so far there's no reason to believe our universe isn't homogeneous, as the homogeneous models work, but the inhomogeneous ones so far do not.

The context of the quoted paragraph seems to indicate you meant to say does not imply.
In that case, I agree, perhaps the problem lies not in the cosmological principle in itself, which is quite reasonable and seems to agree with observation so far, but in the interpretation some cosmology books make of the principle.

[Chalnoth]

The context of the quoted paragraph seems to indicate you meant to say does not imply.
In that case, I agree, perhaps the problem lies not in the cosmological principle in itself, which is quite reasonable and seems to agree with observation so far, but in the interpretation some cosmology books make of the principle.
Hmm, perhaps there was some miscommunication here, as I am saying that isotropy without homogeneity does imply a privileged location.

Now, bear in mind that the statement of homogeneity is not an absolute statement. Rather it's just a statement that there is a potential choice of coordinates for which the universe appears homogeneous. If it isn't possible to select such a coordinate system, but the universe still looks isotropic to us, then that says we live in a special location.

One way to look at this is that if you can find some small number observers for whom the universe is isotropic, then the universe is also necessarily homogeneous for some choices of observers (IIRC the minimum is three non-colinear observers).

[TrickyDicky]

One way to look at this is that if you can find some small number observers for whom the universe is isotropic, then the universe is also necessarily homogeneous for some choices of observers (IIRC the minimum is three non-colinear observers).

How far apart would they have to be?

[Chalnoth]

How far apart would they have to be?
In principle any distance would do, if we're talking about a hypothetical situation where we have perfect isotropy. Clearly this isn't the case, so you'd want them to be about as far apart as is required to smooth out the small-scale fluctuations, so I'd place them at around 80Mpc or so in our universe, at a minimum.

Obviously we can't do this explicitly, but this isn't the point I'm trying to make. The point I'm trying to make is that isotropy plus no homogeneity equals a special location. The reason being that if you have isotropy at many points, you also necessarily have homogeneity. So the only way you can have isotropy and no homogeneity is if there are only a tiny fraction of the available points that have isotropy, which means that the isotropic location is a special location.

[TrickyDicky]

Obviously we can't do this explicitly, but this isn't the point I'm trying to make. The point I'm trying to make is that isotropy plus no homogeneity equals a special location. The reason being that if you have isotropy at many points, you also necessarily have homogeneity. So the only way you can have isotropy and no homogeneity is if there are only a tiny fraction of the available points that have isotropy, which means that the isotropic location is a special location.
Ok, unless (this is of course a thought experiment,not meant to describe our actual universe) the whole universe was bigger than the observable universe, and the 3 observers fields of view don't overlap, in that case each of them could comply with isotropy, not be in any special location wrt the total universe and this universe could be inhomogenous (but the observers would never know).

The observable part of the universe of each of these observers may or may not be itself homogenous, in case it was confirmed not to be homogenous, they could always hope that a sufficiently bigger sample of the total universe confirmed homogeneity in case it could be observed but they wouldn't be able to prove it ever since it would be outside their limit of observability.

[Chalnoth]

Ok, unless (this is of course a thought experiment,not meant to describe our actual universe) the whole universe was bigger than the observable universe, and the 3 observers fields of view don't overlap, in that case each of them could comply with isotropy, not be in any special location wrt the total universe and this universe could be inhomogenous (but the observers would never know).
Correct, but the point remains that it's a special position within the observable universe. That is enough, I think.

The observable part of the universe of each of these observers may or may not be itself homogenous, in case it was confirmed not to be homogenous, they could always hope that a sufficiently bigger sample of the total universe confirmed homogeneity in case it could be observed but they wouldn't be able to prove it ever since it would be outside their limit of observability.
Well, I don't think most cosmologists think that homogeneity is likely to be more correct on extremely large scales. That is, in order for a region to become nearly homogeneous, it really needs to have some time to reach some sort of thermal equilibrium. But once your distances get large enough, there won't have been any chance for such widely-separated regions to reach thermal equilibrium, and so you expect wildly different sorts of behavior.

Of course, given current observations, we expect this distance to be much larger than the size of our observable universe, but I think we expect things to get less homogeneous eventually as you go beyond our observable region.

[TrickyDicky]

Correct, but the point remains that it's a special position within the observable universe. That is enough, I think.

Right, it is a special location inside the observable universe since in a truly inhomogenous universe, observers on the edge of the observable universe of the original observer would probably loose the isotropy(unless isotropy lies in the eye of the observer, like beauty :) and is intrinsic to relativistic observers no matter what).
I am not sure if that is really enoug, though, as the cosmological principle is applied to the whole universe, not only to the observable part.


Well, I don't think most cosmologists think that homogeneity is likely to be more correct on extremely large scales. That is, in order for a region to become nearly homogeneous, it really needs to have some time to reach some sort of thermal equilibrium. But once your distances get large enough, there won't have been any chance for such widely-separated regions to reach thermal equilibrium, and so you expect wildly different sorts of behavior.

Of course, given current observations, we expect this distance to be much larger than the size of our observable universe, but I think we expect things to get less homogeneous eventually as you go beyond our observable region.
I tend to agree with you, but if I were to speculate about what cosmologists opine on this subject I'd say they pretty much don't think about it and when they do they favor homogeneity from a certain scale all the way to the extreme.
But the more I think of it the more convinced I am that homogeneity cannot be empirically confirmed, only suspected.

[Chalnoth]

But the more I think of it the more convinced I am that homogeneity cannot be empirically confirmed, only suspected.
Well, first of all, I tend to think that homogeneity should be the default assumption, because it is the simplest one in accordance with observation, and that unless pursuing an inhomogeneous universe can explain some observations, it shouldn't be considered reasonable.

One approach that has appeared recently is the attempt to explain dark energy as the result of us living in a large void. But as I linked a few posts back, this has been shown not to work when you look carefully at the details. So it seems we're back to the assumption that fits the data: homogeneity.

[JDoolin]

Chalnoth,

I will try to give you a demonstration of the Minkowski-Milne Model under Lorentz Transformation sometime soon.

I'm not real good with the definitions; but I think what you mean by isotropy is that it looks the same in all the directions (change theta or phi, and it looks about the same), but what you mean by homogeneity is that it looks the same at all distances, (change r, and it looks the same)

The thing is, if you ignore the relativity of simultaneity, then Chalnoth is right. Isotropy without homogeneity would imply a privileged point of view. However, if everything is flying apart from the same event, then you have to do the full analysis with the lines (or planes) of simultaneity. You'll find that every plane of simultaneity for every particle intersects the worldlines of the other particles in such a way that you DO have isotropy from the Point of View of every particle.

But you don't have homogeneity in any particle's point-of-view, because each observer sees the density tend towards infinity at the outer edge of the sphere.

Jonathan

[Chalnoth]

The thing is, if you ignore the relativity of simultaneity, then Chalnoth is right. Isotropy without homogeneity would imply a privileged point of view. However, if everything is flying apart from the same event, then you have to do the full analysis with the lines (or planes) of simultaneity. You'll find that every plane of simultaneity for every particle intersects the worldlines of the other particles in such a way that you DO have isotropy from the Point of View of every particle.

But you don't have homogeneity in any particle's point-of-view, because each observer sees the density tend towards infinity at the outer edge of the sphere.
This isn't what homogeneity means. Homogeneity means that if I move to a different location, I see the same thing as if I stay put.

[JDoolin]

This isn't what homogeneity means. Homogeneity means that if I move to a different location, I see the same thing as if I stay put.

There is some ambiguity in the statement "I move to a different location," but if we define our term "different location" to mean "landed on another inertial particle" then by your definition the Minkowski-Milne model does turn out to be both homogeneous and isotropic.

A physical change in r would represent an instantaneous change in position without changing time, or velocity. What I meant by a change in r was simply to ask what the density of particles was at a distance of r.

But you are saying you want to actually move the observer to a the new position, r. If you mean to do this literally, then you will have to increase your velocity toward the "position" where you want to go, then wait until you arrive at the "position" and then change your velocity again to stay at that "position."

This process is fairly straightforward if you have a set of comoving particles. You can take away the finger-quotes around the word "position." Since the worldlines are all parallel, the "position" as defined in the frame of the first particle, and the "position" as defined in the frame of the second particle are the same.

You will, of course, invoke the "Twin Paradox" so the traveler finds on both journeys that the particles have aged more.

However, in the Minkowski-Milne* model, an ambiguity arises; one which can be quickly cleared up by considering the intersection of world-lines, and you will need to use one of the following two definitions of position:
(1) The world-line associated with r="particle distance" which is parallel to your own, before you change velocity.
(2) The world-line of the actual particle.

And the final velocity that you wish to achieve once you get to that position could be either of the following.
(1) return to your own original velocity.
(2) match velocities with the particle and land on it.

If you use idea #1 for both, then you would not see the same thing as if you stayed put. The distribution of matter would still be a sphere, but you would no longer be in the center.

If you use idea #2, you would see essentially the same thing as if you had stayed put. You would be at the center of the sphere after you matched speed with the other particle.

Once again, accelerating and decelerating invokes the twin-paradox, but in the Minkowski-Milne model, the twin-paradox also manifests itself as "inflation" in the experience of the accelerating twin.

Jonathan

[Chalnoth]

There is some ambiguity in the statement "I move to a different location," but if we define our term "different location" to mean "landed on another inertial particle" then by your definition the Minkowski-Milne model does turn out to be both homogeneous and isotropic.
Yes, I would agree. The only way in which homogeneity is sensible is as statement that it is possible to choose a set of spatially-separated observers which all see the same properties of the universe. Not every potential cosmology has this property. But yes, I would agree that the Milne model does.

A physical change in r would represent an instantaneous change in position without changing time, or velocity. What I meant by a change in r was simply to ask what the density of particles was at a distance of r.
Well, there is no non-arbitrary way to connect velocities at one point with velocities at another point. So you are free to choose a different "rest" at every point in space-time, if you wish.

One way to think about it is that in General Relativity, one can move a vector at one point to another point through a method called "parallel transport". This basically consists of moving the vector along a line so that it is continuously parallel with itself. The problem is that if the space-time has any curvature, then the specific path you use to get from point A to point B changes the answer you get.

[TrickyDicky]

Well, first of all, I tend to think that homogeneity should be the default assumption, because it is the simplest one in accordance with observation, and that unless pursuing an inhomogeneous universe can explain some observations, it shouldn't be considered reasonable.

I agree that in practical terms the assumption of homogeneity as default makes things simpler, (the math treatment for instance) but as long as we don't have direct observations that clearly point to either homogenous or inhomogenous distribution of matter at large scales so far we just find the homogenous option more likely for philosophical, historical, model-dependent and practical reasons, not direct observational reasons, that still permit both assumptions.
When I say direct observation I mean that up to the largest range our telescopes allow currently, we haven't yet found strict homogeneity, and instead some disquieting large voids and unexpected distributions of clusters that can still be explained by statistical reasons so they don't point to an inhomogenous universe either. So it is still an open subject from the purely direct observational perspective.

Certainly, though, according to the standard model of cosmology the homogeneity assumption is mandatory and that is why we consider it as the only reasonable assumption allowed by the whole collection of observations about the universe.

For instance in an inhomogenous universe since there is no constant matter density, there is no such thing as a critical density that is ncesary to our model calculations of fundamental parameters. There wouldn't even be a mean density for the universe since it would be a function of location.

[Chalnoth]

I agree that in practical terms the assumption of homogeneity as default makes things simpler, (the math treatment for instance) but as long as we don't have direct observations that clearly point to either homogenous or inhomogenous distribution of matter at large scales so far we just find the homogenous option more likely for philosophical, historical, model-dependent and practical reasons, not direct observational reasons, that still permit both assumptions.
Well, I'd disagree on that. We do definitely have clear observations of isotropy. Given isotropy, we would have to live in a very special location for homogeneity to not also be true, therefore even without additional knowledge, homogeneity is very likely given isotropy.

The fact that we've been able to rule out some specific inhomogeneous models is just icing on the cake, really.

When I say direct observation I mean that up to the largest range our telescopes allow currently, we haven't yet found strict homogeneity, and instead some disquieting large voids and unexpected distributions of clusters that can still be explained by statistical reasons so they don't point to an inhomogenous universe either. So it is still an open subject from the purely direct observational perspective.
Well, obviously when we talk about homogeneity and isotropy, we're talking about statistical homogeneity and isotropy. The exact deviations from this are interesting, but don't undermine the statement that our universe is, on average, highly homogeneous and isotropic.

For instance in an inhomogenous universe since there is no constant matter density, there is no such thing as a critical density that is ncesary to our model calculations of fundamental parameters. There wouldn't even be a mean density for the universe since it would be a function of location.
Well, it's not quite that bad, because you can still talk about a mean density of the universe. This is how we deal with inhomogeneities that exist: consider the universe to be made of some mean distribution plus deviations from the mean. This separation would allow you to model any universe, in principle. The main difficulty is that the Friedmann equations start to give you the wrong answer if your universe gets too inhomogeneous.

[TrickyDicky]

Well, I'd disagree on that. We do definitely have clear observations of isotropy. Given isotropy, we would have to live in a very special location for homogeneity to not also be true, therefore even without additional knowledge, homogeneity is very likely given isotropy.

Yes, I was restricting my analysis to purely direct empirical confirmation. If we add a philosophical assumption (the special location issue) we obviously ge homogeneity.


Well, it's not quite that bad, because you can still talk about a mean density of the universe. This is how we deal with inhomogeneities that exist: consider the universe to be made of some mean distribution plus deviations from the mean. This separation would allow you to model any universe, in principle. The main difficulty is that the Friedmann equations start to give you the wrong answer if your universe gets too inhomogeneous.
I think this comment is purely argumentative . Now you accept inhomogeneity as long as it's not too much? How much inhomogenous can a universe be for you to be acceptable?
In my opinion the universe as a whole is either homogenous or inhomogenous and our preferred model tells us it is the former. There is no in between.

[Chalnoth]

I think this comment is purely argumentative . Now you accept inhomogeneity as long as it's not too much? How much inhomogenous can a universe be for you to be acceptable?
In my opinion the universe as a whole is either homogenous or inhomogenous and our preferred model tells us it is the former. There is no in between.
There most definitely is in between, though, because our universe is absolutely not completely homogeneous (planet Earth is a huge departure from homogeneity, for instance). It is only approximately homogeneous, as near as we can tell.

So it becomes a huge grey area as to whether or not a certain amount of inhomogeneity is "enough" to call our universe inhomogeneous.

Personally, I would approach it from this point of view: the CMB itself offers a natural scale for the inhomogeneities, namely that at the time the CMB was emitted, the universe at that distance from us was homogeneous to within one part in one hundred thousand. If this is an accurate statistical representation of the overall level of inhomogeneity throughout the visible universe at that time, then we can call our universe homogeneous.

An alternative measure might be from the dynamical point of view, where we can say that our universe is homogeneous if the Friedmann equations are accurate within our observable unierse.

[TrickyDicky]

There most definitely is in between, though, because our universe is absolutely not completely homogeneous (planet Earth is a huge departure from homogeneity, for instance). It is only approximately homogeneous, as near as we can tell.

You know I'm referring to large scale.

So it becomes a huge grey area as to whether or not a certain amount of inhomogeneity is "enough" to call our universe inhomogeneous.
Personally, I would approach it from this point of view: the CMB itself offers a natural scale for the inhomogeneities, namely that at the time the CMB was emitted, the universe at that distance from us was homogeneous to within one part in one hundred thousand. If this is an accurate statistical representation of the overall level of inhomogeneity throughout the visible universe at that time, then we can call our universe homogeneous.

This is all quite arbitrary, makes almost pointless to talk about homogeneity of the whole universe because it almost leaves the concept empty of meaning.
In an infinite universe those departures from homogeneity would become infinite, making to call such universe homogenous meaningless.

[Chalnoth]

You know I'm referring to large scale.
It doesn't actually matter. There are inhomogeneities on all scales. At some point you have to make a more-or-less arbitrary cutoff for how big the inhomogeneities can be before you call the observable universe inhomogeneous.

This is all quite arbitrary, makes almost pointless to talk about homogeneity of the whole universe because it almost leaves the concept empty of meaning.
In an infinite universe those departures from homogeneity would become infinite, making to call such universe homogenous meaningless.
Arbitrary doesn't mean meaningless, though. Such arbitrary distinctions are found all over science, and are actually quite useful.

[JDoolin]

Well, there is no non-arbitrary way to connect velocities at one point with velocities at another point. So you are free to choose a different "rest" at every point in space-time, if you wish.

One way to think about it is that in General Relativity, one can move a vector at one point to another point through a method called "parallel transport". This basically consists of moving the vector along a line so that it is continuously parallel with itself. The problem is that if the space-time has any curvature, then the specific path you use to get from point A to point B changes the answer you get.

This parallel transport is only necessary if you reject the use of Minkowski Space.

In Minkowski space, just because there is more than one way does not mean there is no non-arbitrary way. If you are talking about the non-modified Minkowsiki-Milne model, where all the objects move at constant velocity, in fact, all ways of determining the relative velocity in Minkowski space will be the same.

But if the particles are accelerating, still, in Minkowski space, an object has a clear velocity at any given event, determined as d\vec r /dt; This is the slope of its worldline.

The only ambiguity when you ask, "what is the velocity of a distant particle, now?" is to determine what you mean by now. Should you use a line of simultaneity, and try to match what velocity the particle is going now? Or should you use an inverted light-cone so you can try to match the velocity the particle was going when the image you are now seeing was produced.


When I say direct observation I mean that up to the largest range our telescopes allow currently, we haven't yet found strict homogeneity, and instead some disquieting large voids and unexpected distributions of clusters that can still be explained by statistical reasons so they don't point to an inhomogenous universe either. So it is still an open subject from the purely direct observational perspective.

It appears to me, though that this data has not yet been tabulated in any consistent manner, because all of the studies are done using different metrics. For instance, Hubble's Constant is treated as a universal constant. When one set of data disagrees with another, the astronomers are compelled to find some way to fudge the numbers, or take some kind of average. Wouldn't it be better to assume that the different Hubble-Constants are due to expulsion from different events?


Well, it's not quite that bad, because you can still talk about a mean density of the universe.

Put together with your earlier statement, "there is no non-arbitrary way to connect velocities at one point with velocities at another point" why would there be a non-arbitrary way to connect the density at one point with the density at another point? Wouldn't you need to do the same thing with parallel transport of the meter-stick?

In the Milne-Minkowski model, talking about the mean density of the universe only makes sense if you are talking about the mean density near the center of the sphere at a particular proper time.


(from http://en.wikipedia.org/wiki/Talk:Milne_model)
n dx dy dz = \frac{B t dx dy dz}{c^3
\left(t^2-\frac{x^2+y^2+z^2}{c^2}\right)^2}

This is derived as equation (9), in section 91 of Relativity, Gravitation, and World Structure, and repeated in a summary in section 112 as equation (36). In section 94, Milne proves that this distribution is Lorentz Invariant.

Though the Milne model is homogeneous and isotropic, it's density is not constant in either time or space.

[TrickyDicky]

Arbitrary doesn't mean meaningless, though. Such arbitrary distinctions are found all over science, and are actually quite useful.

Sure, I'm not arguing they are not useful, they help us construct models, my point is that some concepts lose their meaning when this distinction is too vague.

[Chalnoth]

Sure, I'm not arguing they are not useful, they help us construct models, my point is that some concepts lose their meaning when this distinction is too vague.
Well, I don't think comparing the inhomogeneities to the observed anisotropies in the CMB is too vague, though. Basically this just comes down to the assumption that the universe is statistically isotropic, and isotropic in the same way no matter where you are within the visible universe. That's a pretty specific statement about homogeneity.

[Chalnoth]

In Minkowski space, just because there is more than one way does not mean there is no non-arbitrary way. If you are talking about the non-modified Minkowsiki-Milne model, where all the objects move at constant velocity, in fact, all ways of determining the relative velocity in Minkowski space will be the same.
No, all ways of determining relative velocity in Minkowski space-time will not be the same. However, because the space-time curvature is identically zero, parallel transport gives the same answers no matter which path you take, which in turn means that you can use parallel transport to give a unique answer to the velocity at any other point in the space-time.

This is all academic, though, because Minkowski space-time doesn't describe our universe.

It appears to me, though that this data has not yet been tabulated in any consistent manner, because all of the studies are done using different metrics.
This is irrelevant. The coordinates we apply to reality don't change the behavior of reality. This means that the particular choice of coordinates is irrelevant, and since the Milne metric is actually a special case of the FRW metric, we actually test the Milne cosmology every time we perform an observation using the FRW metric, and we find that the Milne cosmology just doesn't fit observation.

Wouldn't it be better to assume that the different Hubble-Constants are due to expulsion from different events?
If it worked, perhaps. But it doesn't work.

Put together with your earlier statement, "there is no non-arbitrary way to connect velocities at one point with velocities at another point" why would there be a non-arbitrary way to connect the density at one point with the density at another point? Wouldn't you need to do the same thing with parallel transport of the meter-stick?
Yes, this is true. The way it's done in FRW coordinates is you define a set of observers that are stationary with respect to the CMB and all see the same CMB temperature as having the same value of the time coordinate. This is clearly an arbitrary choice, but it is a convenient one given the symmetries of our universe. Those symmetries allow us to express coordinate-dependent quantities such as the matter density in a much simpler fashion.

Though the Milne model is homogeneous and isotropic, it's density is not constant in either time or space.
It all comes down to the coordinates you use. If you use the "right" coordinates, the density is constant in space, but not in time.