Ben Rudiak-Gould wrote:
Spoonfed wrote:
The diagrams you have drawn show a Galilean Transformation, showing a
fairly small change in speed, less than ten percent of the speed of
light. This would cover the area within a billion light years of
Earth; within 10% of the radius of the universe.

First, that's the radius of the *visible* universe; nobody knows how big the
whole universe is. Second, in terms of comoving distance the radius of the
visible universe is about 47 billion light years, so one billion light years
is a lot less than 10%.

When we get outside that range, if Hubble's Law still holds true, we
need to use a Lorentz Transformation, as the Galilean transformation is
only an approximation.

As I've said before, the Galilean transformation is a better approximation
than the Lorentz transformation in this situation. More precisely, fix an
object O which is roughly stationary with respect to the CMBR, and choose
coordinates such that time is cosmological time and distance from the origin
is comoving distance from O. The coordinate systems so obtained, for
different objects O, are related by a coordinate transformation which is
similar to the Galilean transformation.

I know we've talked about this before, and I recall you said that you were
aware that your ideas were different from mainstream cosmology. If so, I
think you should tag your posts with "this is just my personal theory,
but...". And you should be aware that your model, if I understand it
correctly, is a special case of the standard big bang model with Omega ~ 0,
but Omega has been known to be about 1 for a long time. For as long as I can
remember, the only debate has been over whether it is slightly larger or
slightly smaller than one. Zero is way outside the error bars.

-- Ben

Actually, my idea is that k=0 and a(t)=1. These are terms from the
FLRW metric. As far as the cosmological constant goes, I don't even
know what it is, let alone what value it might have.

My personal theory, though it is a work in progress, is that the
universe started from (approximately) a point, and expanded outward
into space. Our local section of the universe underwent a huge
acceleration from the beginning. In the massive amount of energy
available in the beginning, Brownian motion caused the primordial
particles of our local universe to undergo immense acceleration.

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.

Imagine at the dawn of the universe, we were being pushed HARD from
below by that hot part of the CMBR. Primordial Andromeda M31 galaxy
and and Fornax supercluster are right over our heads, and SN1997ff,
M87, and Virgo are at our feet. We are forced up, accelerating, and
with each change in velocity, the universe under us is scrunched by
length contraction, while overhead, distances to receding particles are
Lorentz "uncontracted" until we match pace with them... but there are
always more particles outpacing us, so as we continue to accelerate,
the region above us expands to an ancient sphere (as old as it is big),
while we accelerate away from the very edge of that sphere, receding
right under our feet.

Millions of years pass by, and toward the end of our acceleration era,
we match pace with Andromeda galaxy, and start to overtake it so it
starts falling "down" towards us.

Because the area below us is length contracted, Hubble's constant
toward our feet, toward Virgo cluster, is a very tightly packed 55
km/sec/MPc. Meanwhile, overhead, in the length uncontracted region,
toward Fornax cluster, Hubble's constant is a much more loosely packed
80 km/sec/Mpc. These values for Hubble's constant have been argued,
but in my theory, they are both right.

Because of "uncontraction" all the stars overhead (toward Andromeda and
Fornax) are further away than they would be by the formula,
distance=rate * time. They are all dimmer than their redshifts would
indicate. But what about those below?

Our acceleration was right at the beginning of the universe... They
distances to them contracted at once, while the stars at our feet were
still nearby. An expansion of a little distance can get HUGE, but a
contraction of a little distance is still little. These stars may have
been delayed a couple million years in taking off away from us, but
still, they should be very close to matching the distance=rate*time.

They may have even accelerated toward us after we stopped accelerating,
meaning they would have a higher average velocity away from us than
their current velocity away from us... So these stars should also be
slightly dimmer than their redshifts would indicate, although for
different reasons.

But where does that leave SN1997ff? It's a supernova that is much
brighter than it should be, as though it was staying close to us for a
long time, but then all of a sudden, it took off away from us.

Well, there's room in this model for mysteries. I'm guessing that
whatever caused it to go supernova also caused it to shoot downward
toward the near edge of the universe.

That's my theory, as it stands today, after spending most of the day
looking up Right Ascensions and Declinations for a bunch of those
objects. As far as whether it comes close to the standard model, I'm
pretty sure it doesn't, but I'm not 100% certain, because I've never
heard much about the standard model except that you can't understand it
without years of graduate level mathematics.

The neat thing about my explanation, though, is that it fits the data.