Is the Big Bang Expanding into a Preexisting Void?

[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.