Spatial Foreshortening and the Pioneer Anomaly

On Tue, 27 Nov 12, " wrote:
I'm afraid I (and probably others) don't really know what "strictly time-lag dependent" actually means.

You know, in one year light travels 1 light year, that's all. I could
not say "distance" because of the question of spatial foreshortening.

While you're at it, please provide a prediction for a body at 7 Mpc (redshift v = 450 km/s).

Model predicts redshift in km/sec = C x distance / 10^10 LY
= 300,000 km/sec x 7,000,000 pc x 3.26 LY/pc / 10^10 LY
= 685 km/s.

Bearing in mind that the Einstein radius of 10^10 LY is an
approximation.

In article , Eric Flesch
writes:

some sort of 1/z cosmology which is also observationally wrong.

Obviously the reason I bring it up is because it is observationally
right, e,g Fig 5 in Nilsson et al, 1993 ApJ 413 453 who dared to
include the 1/z line in their LAS/z chart (and remarked that it "in
fact agrees well with the data"),

There are an infinite number of curves which agree with the data within
the errors.

and in the previous thread about
http://arxiv.org/abs/1211.3663 which shows in Fig 16 a z=10 galaxy
which entirely misses the FRW size curves and would have fit the 1/z
line reasonably had it only been plotted.

How do you measure the size of a galaxy at z=10? Note that (at least in
standard cosmology) the surface brightness is proportional to
(1+z)^4, in a finite band to (1+z)^5 and thus signal-to-noise is
proportional to (1+z)^10. Add to that appreciable evolution and any
sort of isophotal diameter is difficult to relate to some "standard
rod".

At least you acknowledge the evidence is against you. Will that be the
end of the inquiry?

The Pioneer anomaly obviously does not support the 1/z static model,
but the Einstein Radius calculation I presented for it was off by 50%,
and in fact it hits the 10^10 LY size like a bullseye. I will have to
make a summary posting for that on its own merit, since it is (at
least) such a remarkable coincidence.

The question is how remarkable it is and, even if it is remarkable, what
this tells us. What does the remarkable coincidence that the angular
sizes of the Sun and Moon are the same tell us?

On Tuesday, November 27, 2012 5:18:06 AM UTC-5, Eric Flesch wrote:
On Tue, 27 Nov 12, " wrote:

I'm afraid I (and probably others) don't really know what "strictly time-lag dependent" actually means.
.....
While you're at it, please provide a prediction for a body at 7 Mpc (redshift v = 450 km/s).

Model predicts redshift in km/sec = C x distance / 10^10 LY
= 300,000 km/sec x 7,000,000 pc x 3.26 LY/pc / 10^10 LY
= 685 km/s.

It's unclear if you are claiming that your model would *add* 685 km/s to the cosmological redshift; or if you are saying that the actual redshift should be 685 km/s instead of 450 km/s.

Either way, it doesn't matter. The "foreshortening" model has a problem because of NGC 4258. NGC 4258 is a unique galaxy because it has both a bunch of cepheid variable stars and a orbiting gas which makes water maser emission.

The cepheid period properties tell us how distant the galaxy is in Megaparsecs. Using the Hubble distance-redshift relationship, this puts it at ~450 km/s, which is close to the true redshift of the galaxy, not your predicted 685 km/s.

You might argue that the Hubble relation was calibrated with Cepheids and therefore the distance is somehow invalid, but that is only partially true: there are several other techniques used to measure the Hubble relation.

One of those other techniques comes from water maser measurements. NGC 4258 has water maser emitters embedded in a nearly keplerian disk circulating around the central compact object. It's possible to measure both doppler shift as well as proper motion of the maser blobs. Together, these observations completely constrain the system including the central mass and inclination, AND the distance! This distance agrees to within a few percent with the distance derived via cepheids. It's a remarkable confirm
ation that the cepheid technique is working well. (I've already referred to Herrnstein; Caputto; more recently Argon et al 2007)

The "foreshortening" model incorrectly predicts 685 km/s when the actual redshift of NGC 4258 is ~450 km/s based on both of these techniques. The error is not just a few percent, but almost 50%. Is that another inconvenient fact?

By the way, you might be tempted to argue that NGC 4258 is some kind of fluke or due to peculiar motion. I picked NGC 4258 because I remembered it off the top of my head and is the most whopping big maser emitter. But it is not alone. Some quick searches show that the Megamaser Cosmology Project has done similar efforts for the galaxies UGC 3789 and NGC 6264. These galaxies are at distances of 50 Mpc and 140 Mpc respectively, which are even more stringent tests (and rejections) of the "foreshortening" t
heory. More inconvenient facts?

CM

References
Argon et al 2007 ApJ 659 1040

On Thu, 29 Nov 12, " wrote:
Eric Flesch wrote:
= 685 km/s.

It's unclear if you are claiming that your model would *add* 685 km/s to the cosmological redshift;
or if you are saying that the actual redshift should be 685 km/s instead of 450 km/s.

The model's cosmological redshift for the distance you stated.

NGC 4258... ~450 km/s, which is close to the true redshift of the galaxy, not your predicted 685 km/s.

Hmm, and you know the proper motion of that galaxy, normal to us, is
zero? And not 300 km/sec toward us like Andromeda?

similar efforts for the galaxies UGC 3789 and NGC 6264.
These galaxies are at distances of 50 Mpc and 140 Mpc respectively

Do tell us the redshifts. But remember that I have said my model is
speculative, and I was simply answering your request to do a
calculation. So I am not invested in the outcome.

Eric

..... adding to my reply above, I had also stated that the Einstein
Radius of 10^10 LY, used in the calculation as the denominator, is
approximate. Obviously that is a tweakable parameter and would be set
to some optimal value over a large input data sample. Once that
average is found, then the question is how well the fit adheres across
all z. And don't worry, I won't add "dark energy" to make it fit
better.

Eric

On Tuesday, November 27, 2012 4:18:06 AM UTC-6, Eric Flesch wrote:
On Tue, 27 Nov 12, " wrote:

I'm afraid I (and probably others) don't really know what "strictly time-lag dependent" actually means.



You know, in one year light travels 1 light year, that's all. I could

not say "distance" because of the question of spatial foreshortening.



While you're at it, please provide a prediction for a body at 7 Mpc (redshift v = 450 km/s).



Model predicts redshift in km/sec = C x distance / 10^10 LY

= 300,000 km/sec x 7,000,000 pc x 3.26 LY/pc / 10^10 LY

= 685 km/s.



Bearing in mind that the Einstein radius of 10^10 LY is an

approximation.

Except that redshift as a straight linear function of distance is very well known to be wrong. There was a nice little Nobel in physics recently awarded on this.

On Tuesday, November 27, 2012 4:14:41 AM UTC-6, Eric Flesch wrote:
On Mon, 26 Nov 12 21:33:09 GMT, Eric Gisse wrote:

On Nov 26, 9:55�am, Eric Flesch wrote:

... a bulk 3 km/sec redshift of the farthest stars of this Galaxy ...



A 3km/s-effective redshift would systematically shift all spectral

lines. This would have been noticed quite a long time ago.



The farthest stars of the Galaxy are faint and rarely attempted. The

brightest of them could be observed nowadays with a dedicated dynamic

survey, I think, but I don't believe this has yet been done.

As with Oldershaw I do with you:

http://vizier.u-strasbg.fr/viz-bin/VizieR

This is an excellent resource.

On Thursday, November 29, 2012 10:26:21 AM UTC-5, Eric Flesch wrote:
On Thu, 29 Nov 12, " wrote:

Eric Flesch wrote:
.....

NGC 4258... ~450 km/s, which is close to the true redshift of the galaxy, not your predicted 685 km/s.

Hmm, and you know the proper motion of that galaxy, normal to us, is
zero? And not 300 km/sec toward us like Andromeda?

NGC is within the Hubble flow to within a few tens of km/s. Nowhere near 235 km/s.

similar efforts for the galaxies UGC 3789 and NGC 6264.
These galaxies are at distances of 50 Mpc and 140 Mpc respectively

Do tell us the redshifts. But remember that I have said my model is
speculative, and I was simply answering your request to do a
calculation. So I am not invested in the outcome.

Why don't you get invested enough to check the redshifts for yourself? The answer is that the "foreshortening" formula overpredicts by thousands of km/s.

.... adding to my reply above, I had also stated that the Einstein
Radius of 10^10 LY, used in the calculation as the denominator, is
approximate. Obviously that is a tweakable parameter and would be set
to some optimal value over a large input data sample. Once that
average is found, then the question is how well the fit adheres across
all z. And don't worry, I won't add "dark energy" to make it fit
better.

..... and what will happen is that you will end up mimicking the Hubble flow, v = Ho d, in the local universe. Your factor will be equivalent to Ho; you will call it the foreshortening factor (or 1/Reinstein), but it's effectively the same thing as Ho. But then the "foreshortening" model will have problems at high redshifts, just as the standard Hubble law does, where Type Ia supernova remnants demonstrate to us that v = H d is no longer valid.

CM

This is just to close out the thread with a corrected calculation for
the Einstein Radius using the Pioneer anomaly:

At 20AU Pioneer was travelling 12500m/s.
The anomalous sunward acceleration was 9 x 10^-10 m/s^2

Therefore, per each second, the distance travelled was 12500m, and the
anomolous distance shortfall was d=.5a = 4.5 x 10^-10m.

Thus the ratio of the shortfall to distance travelled is 3.6 x 10^-14.

Spatial foreshortening is equivalent to an open Lobechevskian
curvature of the manifold which brings distant places closer. Let's
say that curvature X yielded the above foreshortening at 20AU. Such
foreshortening linearly increases with distance in tandem with the
increasing total curvature, eventually reaching 100% at what we would
perceive to be the edge of the universe. That distance would thus be

20AU / ratio = 3 x 10^9 km / 4.5 x 10^10^-14 = 6.67 x 10^22 km =
7 x 10^9 LY, close to the standard Einstein radius of 10^10 LY.

If this were a true relationship, then the Pioneer anomaly would be
seen to be twice at 40AU as it was at 20AU. I doubt that this would
be found to be the case, but it would be interesting to find out.

cheers,
Eric

On Fri, 30 Nov 12 09:00:17 GMT, Eric Flesch wrote:
the ratio of the shortfall to distance travelled is 3.6 x 10^-14.
...
20AU / ratio = 3 x 10^9 km / 4.5 x 10^10^-14 = 6.67 x 10^22 km =
7 x 10^9 LY, close to the standard Einstein radius of 10^10 LY.

Argh, I used the wrong value for the ratio. Using the right value:

20AU / ratio = 3 x 10^9 km / 3.6 x 10^-14 = 8.33 x 10^22 km =
8.8 x 10^9 LY, close to the 10^10 LY Einstein radius.

I tried to be careful, sorry for the mess,
Eric.