Good News for Big Bang theory

In article , Oh No
writes:

In the Einstein static universe there would be a finite
amount of radiating matter. The two problems being that the Einstein
static universe is contradicted by the observation of Hubble expansion,
and that it turned out not to be stable, and is not a valid model of
physics for that reason.

It's ruled out by observation; we agree on that. I think it is
interesting that the Einstein-de Sitter universe is ALSO an unstable
fixed point, and no-one used that as an argument against it. (Though
that argument, in a roundabout way, WAS used to justify inflation,
saying that because of this the universe can't be just near Einstein-de
Sitter, but must be VERY near it. I don't buy this argument, but that
has been discussed here at length.)

Thus spake Phillip Helbig---remove CLOTHES to reply
LOTHESvax.de
In article , Oh No
writes:

Thus spake "
Oh No wrote:

The large scale distribution of galaxy clusters is also observed to be
extremely homogeneous. But actually, what would be really difficult is
justifying the formulation of a theory which did not obey the
cosmological principle.

The Perfect Cosmological Principle is probably a myth. A good
discussion of strong and weak versions of the cosmological principle
can be found in Mandelbrot's The Fractal Geometry of Nature, and
subsequent journal papers by him. Within the fractal paradigm the
degree of homogeneity and adherence to the CP are a function of the
particular scales you are sampling, as is the case on atomic, stellar
and galactic scales. The fractal paradigm says nature does not
mysteriously switch to ideal homogeneity and a perfect CP at just about
the scale that our observational capabilities peter out. Rather, the
fractal paradigm says what we have observed from subatomic to atomic to
stellar to galactic to supercluster scales probably continues to higher
scales. The latter idea seems much more natural to me, and more
consistent with observations.

I don't think that is what cosmological principle says. I agree that
perfect homogeneity is not expected - indeed locally the distribution is
matter is not homogeneous, but the cosmological principle does not say
it should be. The cosmological principle simply says that fundamental
local laws of physics of physics are always and everywhere the same.

Normally, by the "cosmological principle" one means that the universe is
everywhere the same. This means a) that the laws are everywhere the
same and b) that (averaged over a large enough volume), the universe
LOOKS the same to observers there.

Thanks for pointing this out. I confess it strikes me as a little odd.
Really these are two distinct principles, and not only that but they are
principles of quite a different character. a) is a principle concerning
a fundamental principle of physical law, and b) is a statement about
matter distribution, normally summed up as homogeneity and isotropy.

The "perfect cosmological principle"
extends this to all times as well. (And makes a definite prediction:
the steady-state model. Note that in the steady-state model the LAWS
are the same for all times; it is the additional requirement that the
universe LOOKS THE SAME at all times which leads to the steady-state
model as contrasted with, say, models based on GR.)

I am not so interested in principles which I don't think are properties
of nature. The principle I want to express is that the fundamental
behaviour of matter is always and everywhere the same. From this I infer
infer the principle of general relativity, local laws of physics are the
same irrespective of the observer.

The former principle makes no mention of an observer, so I have not
thought it right to call it an expression on the general principle of
relativity, but as a fundamental principle from which it is possible to
formulate physical law it seems to me it ought to have a name. Any
ideas? Perhaps it is just an expression of the general principle of
relativity.


Regards

--
Charles Francis
substitute charles for NotI to email

Martin Hardcastle wrote:


Since the Big Bang model just says that the universe was hotter and
denser in the past, the obvious predictions involve the mean density
of the universe and temperature/energy density of the CBR as a
function of redshift.

I generally agree with these reasonable statements about what has been
demonstrated with the Big Bang model. I also agree that these
conclusions have undergone significant scientific testing, and have
passed those early tests.

Rob

Phillip Helbig---remove CLOTHES to reply wrote:

Of course, there are inhomogeneities in the CMB, which are directly
related to structure formation. If everything were EXACTLY homogeneous,
I wouldn't be here.

So, perhaps authors need to be careful with their terminology. When
the unqualified term "homogeneity" is repeated thousands of times, the
less discerning members of our community, as well as the general
public, could actually begin to believe in such over-idealizations.

Phillip Helbig---remove CLOTHES to reply wrote:

The same remark applies to GR. The point is that it is wrong to suggest
that a good theory must "predict everything".

Well, then how about you just predict "something".

When you clearly define by what you mean by that paradigm.

Define the BB paradigm any way you prefer, and then use your model to
make a new prediction that is prior, quantitative, testable and
non-adjustable.

Phillip Helbig---remove CLOTHES to reply wrote:

Assumption (B) is perhaps the most crucial one in a Big Bang discussion:
given that at all scales so far observed the universe is hierarchical,

This is simply not true. At scales larger than galaxy clusters (still
much smaller than the observable universe), one DOES have homogeneity.

Well, there you go again using the unqualified H-word!

Why not say: "have homogeneity at the x level", or "have approximate
homogeneity", or perhaps best: "appear to have statistical homogeneity
over the x to y range of scales"?

Such differences in science are not mere semantics!

Phillip Helbig---remove CLOTHES to reply wrote:

Or, looking a bit lower, perhaps Uranus (use American pronunciation
here). :-)

To paraphrase Pauli: 'Not even funny'.

The resolution of Olbers's paradox is that the universe is not yet old
enough for enough light to have reached us.

There is more than one way to avoid Obler's paradox. Let us not forget
that.

wrote in message
...
Phillip Helbig---remove CLOTHES to reply wrote:

Assumption (B) is perhaps the most crucial one in a Big Bang
discussion:
given that at all scales so far observed the universe is hierarchical,

This is simply not true. At scales larger than galaxy clusters (still
much smaller than the observable universe), one DOES have homogeneity.

Well, there you go again using the unqualified H-word!

Why not say: "have homogeneity at the x level", or "have approximate
homogeneity", or perhaps best: "appear to have statistical homogeneity
over the x to y range of scales"?

Such differences in science are not mere semantics!

If N is the number of galaxies within a cube of
side length l:

dN/N = 0.5 +/- 0.1 at a box width l = 30h^-1 Mpc

where dN is the standard deviation of N and N is
the mean of N.

Saunders et al 1991 and Efstathiou 1991

Quoted from Peebles "Principals of Physical Cosmology",
eqn 3.24.

I have sometimes wondered how dN/N would vary
as a function of l and I guess I should know but
it's too long since I did any statistics. Anyone
care to put me out of my misery?

George

I think this is getting outside the charter for the
group so I've cross-posted and set follow-ups
to sci.astro.

wrote:
George Dishman wrote:
Of course it is falsifiable. If there were no CMBR, the
model would be in serious trouble and if the universe
were 99.9% hydrogen then our model of nucleogenesis
would be falsified.

I mean falsified in a future definitive test.

By that approach if I make a prediction today
and it is borne out by measurement tomorrow
that is great, but the day after it doesn't count
because it is then in the past. The big bang
model has made many predictions that have
been confirmed, some of which have been
mentioned in these threads. The fact that they
were successfully done some time ago doesn't
diminish their significance.

Predictions must be made
prior to observations in a definitive test. What sense does it make to
say "if there were no CMBR..." and "if the universe were 99.9%
hydrogen"?

The first makes sense because the prediction _was_
made prior to the measurement, other were already
looking when Penzias and Wilson got lucky. The
second makes sense because the prediction is
not based on a free parameter that can be adjusted
to get that value whle still meeting other observations.
The term "prediction" doesn't just refer to whether the
value was calculated prior to its measurement but can
also mean that it is derivable without fitting.

Think of moving forward. How can we test the BB paradigm
vs the discrete fractal paradigm NOW?

I already answered that, the most obvious test to do
is the angular power spectrum. Where is the fractal
prediction? You complain about the big bang model
not making predictions yet you ignore the fact that
you cannot provide that key prediction from your
theory.

However, let me correct another point. You don't test
one theory against another in science, you test each
against observation. Your theory suggests _all_ dark
matter should be in MACHOs, does it not? If so then
the microlensing evidence is strongly against it.

For recent specific predictions, note that the angular
power spectrum of the CMBR was predicted before WMAP
using GR both with a cosmological constant and without
but including quintessence instead as the nature of
dark energy. the subsequent results are a better fit to
the cosmological constant than quintessence so GR made
a prediction and passed the test.

This is mostly model-building, ...

Nope, the predictions were made before the results
were known, not fitted retrospectively. GR passed
the test, you have not yet even provided a prediction.

George

George Dishman wrote:
.....
If N is the number of galaxies within a cube of
side length l:

dN/N = 0.5 +/- 0.1 at a box width l = 30h^-1 Mpc

where dN is the standard deviation of N and N is
the mean of N.

Saunders et al 1991 and Efstathiou 1991

Quoted from Peebles "Principals of Physical Cosmology",
eqn 3.24.

I have sometimes wondered how dN/N would vary
as a function of l and I guess I should know but
it's too long since I did any statistics. Anyone
care to put me out of my misery?

I think the answer to that should be

dN/N = k / l^(3/2)

for a homogenous universe, but corrections will be
appreciated if I'm wrong.

I wonder what Rob's fractal theory predicts.

George