When we have an expanding balloon, there exists a point of symmetry (center) for the balloon's 2D dimensional universe, which is the center of the sphere which can only be described using an additional dimension of length.
Can we say that our universe could also have a center (a point of symmet... (more)
Can we say that our universe could also have a center (a point of symmet... (more)
Jonathan's Answer
... and also a topic of great interest to me for many years.
It largely depends on whether your conceptualization of the universe claims that the domain and range of the Lorentz Transformation equations are all events, future and past, or if you put some arbitrary limit on the Lorentz Transformation equations--saying, for instance, they cannot affect events in the distant past, or that they cannot affect events billions of light-years away.
The Cosmological Principle states that the universe must be both homogeneous and isotropic. In such a case, then there cannot be a single center point of the universe. There is only one structure that meets these two criteria--one that has distant parts of the universe moving faster than the speed of light, but at any given moment, it is perfectly homogeneous. This model of the universe renders the Lorentz Transformations irrelevant, by adding another variable to the distance measurement... a cosmological scale factor, usually denoted as
However, if you permit some modification on the Cosmological Principle, and permit the Lorentz Transformations. You can have a universe that appears, from all locations LOCALLY to be homogeneous (within the nearest 3 or 4 billion light years) but actually does come from a single point in space and time, Generally at or near the (x,y,z) coordinates of any given observer.
This idea was first presented by E. A. Milne (See Relativity Gravitation and World Structure : E.A. Milne : Free Download & Streaming : Internet Archive )
You can see a second-hand article about Milne and his model here Cosmology: Methodological Debates in the 1930s and 1940s. The description here of Milne's model bears only the most tangential resemblence to what is in the actual book. In Milne's book, for instance, he gives the clear definition of homogeneity, only to dispel the concept by reductio ab adsurdam. However, if you read the second-hand-article, you get the impression that Milne invented the idea of homogeneity in order to make it a part of his own model!
And it is interesting to note, that references to the actual book "Relativity Gravitation and World Structure" are not permitted on Wikipedia, because it is a Primary Source. Furthermore, direct quotes from Relativity, Gravitation, and World Structure are considered "original research" and are not permitted on Wikipedia.
You can see plainly in the text here, "The particles near the boundary tend towards invisibility as seen by the cntral observer, and fade into a continuous background of finite intensity."
He is talking about what is now known as the Cosmic Microwave Background radiation.
But yes, if you look at the diagram in the picture, you can see a center-point in that sphere; an (x=0,y=0,z=0) and if you back up in time to the event where all of this expansion started, it is (x=0,y=0,z=0,t=0). That is, a single event in four-dimensional space.
Except that no, he's not. It may well have been a perfectly lovely theory at the time it was published, but there's a reason why it isn't taught today, namely that we actually have data now, and that theory doesn't match it.
1. There's a difference between cosmological redshift and Doppler redshift (see: Page on cwru.edu).
2. The CMB has features that are inconsistent with being distant nebulae / galaxies, e.g.,Baryon acoustic oscillations. Many of the same observations and arguments that falsified Hoyle falsified this as well.
I'll never understand why people insist on looking up old theories of cosmology and adopting them without checking whether they even match modern observations. Trying to research cosmology in 1930 was like trying to research medicine in 1300. You have some information, so you might get some things right, but you're missing so much that it would be insane for someone to pick up that research and uncritically accept it because it sounds reasonable.
In Milne's model, this observed surface is simply moving away at nearly the speed of light, and thus red-shifted by the relativistic Doppler effect.
In the standard model, this observed surface is ... whatever the standard model proponents are saying it is doing, but it is redshifted by cosmological redshift.
There are some major features of the apparent universe that do differ significantly from Milne's model. For one, the observed universe appears to be at least 40 billion light years in radius, while the apparent age, according to Hubble's Law puts it around 13.7 billion years.
Both models can explain this by inflation. However, Milne's model actually has a strong explanation for inflation in the already well-known "twin paradox".
I've never got access to the data but here are some features that I would be looking for (as evidence for Milne's model) if I had the opportunity.
(1) at about 6-7 billion light years away from here, there shoud be a statistically significant peak in type I supernovae... Because this would represent a secondary explosion within an older and larger existing universe.
(2) beyond 7 billion light years away, Measurement of Hubble's constant would go down by a factor of 13.7/40 or so, if my figures above are correct. Also, there should be an asymmetry in these values along the same axis as the CMBR dipole anisotropy.
(3) beyond 7 billion light years away, there would be greater deviation in the Hubble's constant.
>>I'll never understand why people insist on looking up old theories of cosmology and adopting them without checking whether they even match modern observations.
What I can never understand is how someone who clearly doesn't understand a theory, can claim to have found the data that disproves it.
What I would need to see, before I stopped insisting on bringing up this theory is for someone to demonstrate an understanding of the idea, with sufficient clarity that they convinced me that they understood the idea. Then, they could point to the data which disproved the idea...
And then, what would I do? I might not give up just yet. Because I might have another idea.
Why shouldn't an idea from the 1930's evolve? This is the way the standard model has been evolving for many decades. They will make a prediction, then it doesn't fit with their expectations, and they will introduce another idea... Dark matter... Dark energy... cosmological constants... scale factor... cosmological redshift.... whatever they need to get the idea to work. They have had the ability to see the data, and adapt their theory to that data.
The only additional adaptations that I want to have allowed for Milne's model, that Milne didn't originally appear to think of is Brownian motion in the early universe, and a few rather mysteriously massive hypernova explosions, later on.
If the standard cosmological model is correct, additional data and analysis is going to tell you precisely the number for the cosmological constant--exactly how much dark energy, and dark matter, precisely how the scale-factor of the universe is changing.
If Milne's model is correct, then an analysis of the data should show you the locations where huge cosmological events happened in the distant past.
I'm a PhD student in cosmology, so you don't have to tell me what the surface of last scattering is.
>> In Milne's model, this observed surface is simply moving away at nearly the speed of light, and thus red-shifted by the relativistic Doppler effect.
In the standard model, this observed surface is ... whatever the standard model proponents are saying it is doing, but it is redshifted by cosmological redshift.
As I have already said (and posted a reference for), there are differences in how cosmological redshift and Doppler redshift depend on distance in an expanding Universe. We observe the former.
>> beyond 7 billion light years away, Measurement of Hubble's constant would go down by a factor of 13.7/40 or so, if my figures above are correct.
Hubble's constant goes up as you go back in time (and, thus, far away in distance).
>> What I can never understand is how someone who clearly doesn't understand a theory, can claim to have found the data that disproves it.
I can also tell you that a flat-Earth theory is wrong without needing to understand its nuances. The model of an actual explosion of stuff into empty space doesn't work. I would be happy to go into more detail if you gave me Milne's theory in more detail.
>> Why shouldn't an idea from the 1930's evolve? This is the way the standard model has been evolving for many decades.
Sometimes things are minorly wrong, and need tweaking. Sometimes things arefundamentally wrong, and trying to tweak it just gets embarrassing (see: Fred Hoyle).
>> They will make a prediction, then it doesn't fit with their expectations, and they will introduce another idea... Dark matter... Dark energy... cosmological constants... scale factor... cosmological redshift.... whatever they need to get the idea to work.
The possibility of a cosmological constant has been around since the beginning (almost a century now). As has the idea of a scale factor, which was a fundamental part of even early versions of Big Bang Theory. Cosmological redshift is a straight-forward result that falls out of General Relativity, and was not "added in". Dark matter was first postulated for astrophysical reasons, not cosmological ones, although we now have cosmological evidence of dark matter as well (and there's nothing at all in the original theory that would be in tension with the existence of dark matter; it's just an extra thing to plug in). Dark energy is (in our current models) the same thing as the cosmological constant, so you can't really count it twice.
Looking at that list of stuff you just mentioned, and the way you described it, it's clear you don't particularly know what you're talking about in this area. The irony of writing a list like that after railing against criticising things you don't understand is astounding.
Do you think the scale factor was a fundamental part of Milne's model?
By the way, a quick look on Wikipedia explains the contradictions between Milne's model and observations: Milne model.
"Because GR is Minkowski space when there is no curvature."
"Perhaps you mean SR (not GR) is Minkowski space when there is no curvature."
(No, they were right the first time... GR without curvature is SR.)
The fact that Milne may not contradict the things that you personally know about cosmology does not mean that the two are consistent. Making claims that contradict the scientific consensus, without actually studying the field in detail, is rather silly.
You might think it is silly to go by what I personally know. But I think it is rather sillier to go by what you don't personally know.
That was one particular example out of many (both in that Talk page and in our exchanges), and you directed me to the Talk page as counter-evidence to the page itself, which describes contradiction with observation.
>> You might think it is silly to go by what I personally know. But I think it is rather sillier to go by what you don't personally know.
Holding off on making claims about things you don't know is reasonable. That's not what you're doing, though... you're making negative claims. That's not supportable. When people who have studied the field in more detail try to tell you that something doesn't work, you should consider listening to them, instead of standing by a long-falsified theory that the world of science moved on from ages ago.
This is exactly the problem.
I think this is interesting that you getting near having a PhD in cosmology and you don't know whether Milne's model has a cosmological scale factor or not.
>>(No, they were right the first time... GR without curvature isSR.)
Thinking a little more about what 2006 me said, I think I was right the first time. (You did not nail 2006 me... 2006 me was actually correct, though now I can express my point with greater clarity.)
GR without curvature still has this scale factor
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Edit: This really was in error.
GR without curvature would have
My point was that the FLRW metric, even if mathematically identical to
That generalization should really not be extended to all of General Relativity, but it does apply to the Friedmann-Lemaitre-Robert
===========
In SR motion of objects; even the most distant objects, would be modeled by
There is no need for a cosmological scale factor.
While
When Galileo set Ptolemy's model and Copernicus' model side-by-side to prove that Copernicus was more correct, he did not do so by failing to acknowledge that Ptolemy's model existed. Rather, he accepted Ptolemy's model for what it was, and then used evidence to show that one model fit the data better than the other.
What cosmologists are doing with Milne's model is failing to acknowledge that it ever existed.
Why is it essential for me to know the details of a theory that was falsified and abandoned decades before I was born?
>> Thinking a little more about what 2006 me said, I think I was right the first time. (You did not nail 2006 me... 2006 me was actually correct, though now I can express my point with greater clarity.)
No, 2006 you was wrong. If you no longer agree with that statement, then congratulations, you just removed your "that was 9 years ago" defense; 2015 you is also wrong.
>> GR without curvature still has this scale factor a(t)=1/t. That is NOT the same as SR.
This is entirely false, in many, many ways. What made you think this?
>> In SR motion of objects; even the most distant objects, would be modeled by distance=initialposition+
There is no need for a cosmological scale factor.
Indeed, there is no scale factor.
>> While a(t)=1/t would be observationally identical to a universe modeled by distance=velocity∗time, it is NOT THE SAME.
I have no idea what you're talking about, and I don't think you do, either. You seem to be confused about what a scale factor is, but I can't tell from what you're saying quite what you do think it is.
>> What cosmologists are doing with Milne's model is failing to acknowledge that it ever existed.
We tend to stop talking about things once they've been falsified, except in a context where they are of historical interest. Every time there's a new epidemic, do you see people considering the Miasma Theory of disease again? No. We already know it doesn't work. We've moved on.
I erred. (Correction added above)
I should have said
I was referring to the Robertson Walker Scale factor (cosmology)
Have they got rid of that with the Lambda-CDM model?
No, it's still there.
Lambda-CDM model
But they've nailed it down, at least...
>>We tend to stop talking about things once they've been falsified, except in a context where they are of historical interest.
Precisely... But I would think that the falsification of a claim would also be of historical interest, if such a falsification existed.
Apparently not, actually... apparently, you were talking about the Hubble parameter, which is very different. Are they related? Of course. But if the Hubble parameter is constant, then the scale factor grows exponentially, so you can't really interchange them.
>> Have they got rid of that with the Lambda-CDM model?
No, it's still there.
You initially wrote something nonsensical. You have since corrected it to something completely different, which is less nonsensical, although it still assumes a power law for the scale factor (which is only a good approximation during some time periods). You do not get to make snarky comments implying that I was somehow ignoring the presence of the scale factor in ΛCDM, when I was the one who explained its history in the first place.
>> But they've nailed it down, at least...
This comes directly from the definition of redshift and the fact that wavelength is proportional to scale factor. It's a trivial corollary of cosmological redshift, and has been "nailed down" for almost a century.
Why do you insist on trying to explain things to me that you clearly don't understand?
>> Precisely... But I would think that the falsification of a claim would also be of historical interest, if such a falsification existed.
Sometimes yes, sometimes no. There are far too many false hypotheses to teach all of them, and it's often irrelevant to current science. If you want to study history of science, great, study history of science. If you want to study science, you mostly study the stuff that actually works, with however much historical context is necessary to explain each particular concept. We don't have time to spend weeks on all the incorrect models of electromagnetism, we jump straight to Maxwell.