Ben Rudiak-Gould wrote:
Spoonfed wrote:
Actually, my idea is that k=0 and a(t)=1.
What does t denote here? Are you saying that a is a constant function of
time, i.e. that the universe is not expanding? Or are you saying that
a(now) = 1? The latter is not a hypothesis, just a normalization convention.
I'm not convinced that you "speak the language" yet; it looks like you're
just copying stuff from recent posts by Tom Roberts without understanding it.
These are terms from the FLRW metric.
I'd go farther than this and say that they only have meaning in the context
of the FLRW metric, i.e. in the context of big bang cosmology. If you're not
talking about the big bang theory, I don't even understand what you mean by
saying that k=0.
As far as the cosmological constant goes, I don't even
know what it is, let alone what value it might have.
You can ignore it for the time being; conceptually speaking, it's a detail.
Ben, you successfully identified my model as an Omega = 0 model. To
first order, it matches the diagram in Ned Wright's Cosmology page
http://www.astro.ucla.edu/~wright/cosmo_02.htm
I disagree with his definition of the word "now" as using the event of
a distant galaxy reaching 13.7 billion years as a definition of our
"now" is completely at odds with Einstein's methods of defining
simultaneous events in Special Relativity.
As far as the FLRW metric goes, I meant a(t)=1 as in, it is constant.
If I understood right, Tom told me that the FLRW metric was the family
of solution to some differential equation when you assumed that the
cosmological constant was zero. And yes, I repeated that back to him,
and I believe he confirmed it. So, in that respect, yes, I was simply
copying stuff from his posts without really understanding it. I
understood it well enough to answer your accusations that my model was
an Omega=0 model, to which my answer is guilty, as charged.
But it gets even simpler than that. Not only do I assume that Omega =
0, but I also assume that of the many possible solutions available in
the family of FLRW metrics, I am choosing the very most simple one.
If you take the FLRW general metric
ds^2 = dt^2 - a(t)(dr^2/(sqrt(1-k r^2)) + r^2
(d(theta)^2+sin^2(theta)d(phi)^2))
and set a(t)=1 and k=0, this becomes, (unless I've made a horrible
blunder)
ds^2 = dt^2 - dx^2 -dy^2 - dz^2
which is the definition of the differential space-time interval between
two differentially separated events.
Now, everything that I have been bringing up, which you have said I
should preface by saying "in my model" is based on this very simplest
possible metric which should, in my opinion, be the most well explored,
well known model of space-time. When I bring up my answers, the
experts should say, "Oh yes, of course, in the trivial, simple model
where Omega is equal to one and the scale factor is constant, and the
curvature, k is zero, of course that would be true, but we live in a
much more complex universe than that."
Ben, I congratulate you on doing just this. You came right out and
told me that I had an Omega=0 model, and after looking into it a little
deeper, I find that you are right.
By accelerating toward a receding object, but not matching pace with
it, we enter a frame of reference where the space between us and the
receding object is length uncontracted. It will be moving away more
slowly, but also more distant. In this way, the distance will be
greater than you would expect from its velocity. Likewise, the
faintness would be more than you would expect from its redshift.
I think you should stop talking about frames of reference and phrase things
in terms of what we can actually see, which is a 2D projection of our past
light cone. In particular, how should we define the distance of the
astronomical objects that we can see?
Here's an SR conceptual question which may be pertinent. At one end of Main
Street is a clock tower. Alice is running along Main Street toward the clock
tower at a relativistic speed. Bob is standing stationary on Main Street,
looking at the clock tower. At the moment Alice passes Bob, they compare the
times they see on the clock face. Does Alice see an earlier time, a later
time, or the same time?
Alice and Bob see the same moment on the clock face. However, Alice
sees the clock-face further away, and measures that the event happened
longer ago than Bob measures it to have occurred.
I attempted to make a demo of this phenomenon here
http://www.spoonfedrelativity.com/files/timetravel.swf
realized it was pretty badly written and tried to do it again he
http://www.spoonfedrelativity.com/files/newYears2.swf
Unfortunately it is still pretty bad, and probably doesn't get the
point across. The main issue is that the images are observed (by the
moving Speedy T and by the stationary Green Clark) at the centers of
the light spheres.
(Thanks for the set-up there, Ben. Really nice when somebody tosses a
question to me that I've got a demo for.)
Imagine at the dawn of the universe, we were being pushed HARD from
below by that hot part of the CMBR.
"Below"? Are you saying that the universe was not isotropic? What was the
distribution of matter? Is it still anisotropic in the present era?
On further research, I find that the direction I called "Below" is more
commonly known as Galactic North. Roughly 13 hours Right Ascension, 27
degrees, declination. Virgo Supercluster is 12 h 30 m, RA, 12 degrees
declination, where the Sandage Team measured Hubble's Constant at 57
km/sec/MPc. Ned Wright's page says there is a large excess of bright
galaxies in the "northern part of the sky" which I can only guess means
galactic north. This is the direction that I called "down" earlier.
And YES, my theory says the distribution of matter is anisotropic in
the present era--at least the parts of it we can see. The dark areas,
I believe, are still isotropic--undisturbed from the original
explosion.
Starting at around this point I can barely understand at all what you're
trying to say. I seriously have trouble distinguishing it from schizophrenic
raving, and I would dismiss it without a second glance if your relativity
tutorials didn't show obvious evidence of sanity. If you're going to make
this theory comprehensible to anybody, you're going to have to put a lot of
effort into clearing up the exposition. The first step in doing this is to
learn the current dominant theory of cosmology, and how to extract simple
predictions from it. Then you can describe how your theory differs from
that. For example, are you aware that the big bang theory predicts that
beyond a certain redshift, galaxies which are *farther* away will appear
*larger* in the sky? I assume your theory does not match this prediction.
This does not necessarily exclude your theory, because I don't know whether
this prediction of the big bang theory has been directly verified.
I really appreciate the extra time you are taking to give it a second
glance. I am developing it further, and perhaps it will become clearer
as I fill in more gaps, both in my explanation, and my understanding of
the standard model. For instance, I do see that gravitational lensing
actually happens, but I have my doubts that gravity can effect the
redshift of passing photons.
As my model does nothing to the scale factor of space, I would say that
distant galaxies should not appear larger than nearby ones.
If you
make clear predictions like this which differ from the big bang theory and
are not excluded by experiment, there is a chance that people might take you
seriously. At least they will understand what you're trying to say.
The simplest difference I know of is that I predict that a 600km/second
change in velocity would not significantly effect a measurement of the
CMBR dipole. This is very much at odds with the explanation for the
dipole given by NASA.
The neat thing about my explanation, though, is that it fits the data.
I'm sorry, but this is almost certainly just wishful thinking. It may fit
the data on whose basis you originally formulated it. But there is a lot
more data than you realize.
It's hopeful thinking. My prejudiced eyes see confirmation everywhere
I look.
Read through Ned Wright's cosmology pages:
http://www.astro.ucla.edu/~wright/cosmolog.htm
They're full of charts showing the agreement of various cosmological
theories with the data. How confident are you that you can match all of
those data points?
Ned Wright's pages are, incidentally, the most accurate popular introduction
to big bang cosmology that I've ever seen. This is a great place to learn
more about thine enemy.
-- Ben
Well, it's interesting, but I lose him when on page:
http://www.astro.ucla.edu/~wright/cosmo_02.htm
I lose him when he defines D_now as any event on the same hyperbola
instead of on the horizontal plane. That would be fine if he just said
"interesting idea" and moved on, but he appears to use it throughout
the rest of the tutorial as though it were the actual distance. Is he
correcting for this error in judgment when he introduces the scale
factor?
Jonathan Doolin