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[Boud Roukema]

On Wed, 29 Oct 2003, szajtan odwieczny wrote:

> > On Tue, 28 Oct 2003, szajtan odwieczny wrote:
> >
> > > What I think we can say for sure is that, although we're not sure about
> > > the actual curvature of our obserwable universe, and thus we're not sure
> > > if the space go on and on to infinity, it seems that it's quite sure that
> > > our universe is accelerating (q<0), and from this point of view we can say
> > > that if we send out a probe into the space even at the velocity of light,
> > > it's likely that it will never return regardelss of the the curvature
> > > of the universe, because it just won't overpass the expantion rate of the
> > > universe unless there is some nontrivial topology involved. The Big Crunch
> > > never happens in area where q<0 on Omega_l, Omega_m plane. So from our
> > > point of view we can say the spacetime is infinite if we're thinking in a
> >
> > We can't say "the spacetime is infinite". What you mean is

> why not ?

Because "x is infinite" means that
"for every y \in {Real numbers}, x > y".

If the Universe has positive curvature with curvature radius R_C (and
is a perturbed FLRW model, as we think), then there exists a maximal
length spatial geodesic X_s and a maximal length space-time geodesic
X_st .

Then, there exist y \in {Real numbers} greater than these values and
there are no longer any x in the Universe greater than y. So it's not
infinite.


> event horizon accounts for all evolution of expantion according to assumed
> model. if it's less than the curent curvature radius then we won't see the
> probe, if it's bigger we mae but not must see it, for the curvature
> radius is changing in time.

i'll let you do the calculations here, but they are irrelevant for the
question of infinity.

>
> > "the http://www.wikipedia.org/wiki/Event_horizon is less than
> > 2 \pi times the radius of curvature even if comoving space is a hypersphere".
>
> last time I checked the page expired so don't know what was there, but did

So have a look again.

> anyone said something about the relation of the event horizon to the
> curvature ratius.? (this should be calculated)

i'd be surprised if there's any simple relation, unless you restrict
to special cases like \Omega_\Lambda=0 or at least some family of FLRW models.

> >
> > This is true even when \Omega_\Lambda = 0   - the Big Crunch happens
> > before we can see the back of our head.
> >
> even better - another reason for which we will never see the sent signal
> (probe), but with CDM=.3 and DE=.7 or anything close to it we have no big
> crunch at all.

OK

> > > way of traveling in it. If we think just of a space as a slice in some
> > > moment of time the quiestion is still open, but what is use of thinking
> >
> > i think you mean here "in some spatial section at constant cosmological time".
>
> yes

:)

> > > about space this way - it just cannot be separated from time right ?
> >
> > It's the fundamental nature of the model, so we ought to think about it.
>
> the fundamental nature of the model is that going in space we also move in
> time.

This is extremely confusing language. What do you mean by "going in
space", "moving in time" and "we"?  If you mean there's a second time
variable representing the time variable of a thought experiment, then
it makes sense.  Or if you're talking about a physical particle, then
two different time variables are the local (proper) time of the particle
and the cosmological time.

But it's perfectly possible to imagine comoving space without needing
any time variable to "go" through it (though having a local psychological
time variable is convenient).

> eg. Imagine that that space is closed, and expands slow enough that
> a photon emited from your flashlight can round it, but as the time passes
> expansion rate mae grow up, event horizon falls, (say cosmological
> constant starts dominate) and the photon won't make it eventually.

IMHO this is a different theme to the universe being infinite or not

> > If you can think of an alternative model which only models our past
> > time cone, fine.
> btw.
> if the accurate model predict things in the past, I see no reason why
> it should not predict also things in the future.

You can't predict things in the past. Astronomers doing models often talk about
"predicting" observations already made, but this is just astropolitics.

The reality is that you can only postdict the past, and that if you make
predictions they will usually be wrong. Moreover, you're more likely to
get observing time/grants if you postdict the past (and say that you're
predicting it) rather than if you make real predictions.

As for accuracy, the model below is extremely accurate, by definition.

> below this this point I don't follow ;)

Another way of describing the model is that the Universe the inside of a
6k-light-year sphere and that initial (and continuing) boundary conditions
on the sphere have been designed in such a way that people trying to
understand them conclude with a series of simple (but wrong) physical
laws. Initial conditions throughout the sphere were also set up with
the same intention (e.g. fossils, distribution of continents, genetic
mixes of people and other animals, isotopic ratios of uranium etc...)

Maybe another way of describing it is that we live inside a planetarium
of radius 6kly and that The Designer is pretty good at designing fun
models with just enough clues that we remain interested and think we
can understand the model represented in the planetarium.

> > But personally this reminds me of the Christian
> > fundamentalist cosmology model where the Unvierse is only 6000 years
> > old, as written in the Bible.
> >
> > It's a model which perfectly fits all cosmological observations,
> > including those of WMAP. ;) The Universe in this model is the inside
>
> gash, does it says about CMB fluctuations ?

No: but since human beings have interpreted these in terms of a simple
set of physical laws, the Christian fundamentalist model is satisfied
- there are simply a new set of boundary conditions designed to make
physicists interpret them this way.

> meaybe I should review the bible instead of Peebles, etc :)
>
> > of a sphere of radius 6000 light-years, on which EM radiation of all
> > sorts of wavelengths (and we could add other particles) was generated
> > 6000 years ago on this surface, emitted in the direction of the Sun
> > (and it continues to be generated) in such a way to reproduce a
> > "naive" model that makes it (more or less) easy for human beings to
> > interpret these in terms of simple laws of physics. The being "God/Bóg"
> > which generates the emission wants human beings to have an easily
> > interpretable Universe, he/she/it is extremely intelligent and able
> > to generate such complex emission patterns of radiation. Just like
> > he/she/it set up species of animals 6000 years ago in a way that
> > makes biologists think there must have been lots of evolution...
> >
> > Personally i find the model ridiculous, but it perfectly fits all the
> > observations and avoids "extrapolation" into times with which we have
> > no written contact (prehistorical), and the Universe is only 6000
> > years old.
>
> pozdrawiam
> bartek.



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