Quantized redshift anomaly

Charles H. Fort, "New Lands", Part 1, Ch. 7:

"In Bradley's day there were no definite delusions as to the traversing by this earth of another path in space...About a century later by some of the most amusing reasoning that one could be entertained with, astronomers decided that the whole supposed solar system is moving, at a rate of about 13 miles per second from the region of Sirius to a point near Vega,..."

The apparent apex speed is changing. Proper motions (predominantly measured by HL Alden, c. 1920-1923) have been compared to those for the same stars about 20 years earlier (mostly by Boss, c. 1900)(SA Mitchell et al, Astronomical Journal No. 778 v. 33(10):79-86; also Nos. 796, 803, 808, 823). The second time derivative of right ascension is positive for R.A. 6-->18h (+:- = 111:76) and negative for R.A. 18-->6h (+:- = 118:142). The latter ratio is significant only at p=7% (one-tailed), but fitting a cosine curve to ratios for twelve two-hour blocks, gives phase=12h R.A., correlation coefficient = +0.70, p=0.6%. The stars appear to be accelerating toward the apex.

Laboriously I tried to confirm this by entering stars individually into SIMBAD. Using whichever I could of Mitchell's first, main list, with ID numbers ending in 1 or 6, I found for R.A. 6-->18h, +:- = 8:4; for R.A. 18-->6h, +:- = 13:12. The percentage change was about the same for all groups. So, the 1900-1920 trend might or might not have persisted 1920-2000.

By my unrefined estimates, the median parallax of the above stars was 0.05". The 13th percentile absolute change in R.A. PM (needed to give 56.5% agreement)(those with zero change weren't used) was 0.004"/yr. The average value of sin(phi) on the sphere is pi/4, so the needed change in apex speed is roughly 4/pi*0.004/(0.05*2)*30/(pi/2)= 1 km/s in 20 years.

The best fit to Dayton Miller's ether drift (observed 1925-26) is, in the component parallel to Earth's axis, the contemporaneous unculled RV-based apex speed determination of Campbell (c. 1913), using Campbell's compromise declination of 30 degrees. The discrepancy, only a few percent, is consistent with Campbell's and Miller's error bars.

The Boss vs. Alden comparison shows that the rate of change of PM is only half as large on the Orion arm's side of the sky. Suppose this is because the integral of that rate, i.e., the apparent apex motion, is only half as large within a spiral arm, because the amplitude of the ether wave is half as large there. Then gas and the blue stars formed from it, settle in the spiral arm like snow along a path of reduced windspeed. The Orion arm is about 200 pc across; suppose the sun were 100 pc centripetal to the arm's inner edge. Then PM-based apex speeds would be slightly more than 3/4 as large, using stars 100pc < d < 300pc, as for d < 100pc; also, the apparent speed would partially recover using stars d > 300pc. This was observed by Hipparcos (Abad, 2003). Stars 100 to 200pc farther from the galactic center than we are (the farthest such bin), showed a similar reduction (some of them would be above or below the arm, reducing the effect).

Similarly, Fehrenbach's quadratic reduction with distance, of apparent RV-based apex speed, could be due to curvature of the Orion arm, toward the apical line. However the relatively minor increase in speeds obtained from RVs of stars at d < 100pc, and the very large speeds obtained from the PMs of very close stars (e.g. absolute mag > +5) suggest multiple parallel channels, of much-reduced wave amplitude. The abs mag > +5 stars would be nearer us than the closest channel, and this closest channel would explain the RV-based speed for d < 100pc.

The cosine term of the ether wave has the smaller coefficient, hence probably is changing the most. The apex speeds determined from RVs and from PMs are decreasing proportionately. As for RVs, Fehrenbach's bin < 100 pc most resembles Campbell's unculled sample, in distance and speed. Campbell obtained 19.9 km/s, Fehrenbach 16.9, a 15% decrease. Fehrenbach's sample was deliberately (apparent)magnitude-limited and Campbell's roughly was.

As for PMs, Walkey obtained 20.5 km/s but his sample was culled by almost the same criterion as Campbell's 17.85 sample. So Walkey's unculled result can be estimated at 20.5*19.9/17.85=22.9. Hipparcos gave 21.8 for all stars, but sampling correction adjusts this downward by up to 3 km/s for comparison with Walkey, because both these PM samples were effectively both (apparent)magnitude- and distance-limited. Thus the extremes of absolute magnitude were removed. This sampling effect would be greater for Walkey's sample. The apex speed determined from Hipparcos stars of median absolute magnitude, is 18.6 km/s, 3.2 km/s less than that from the entire star sample (Abad, op. cit., 2003). Hence the true decrease is 5 to 19%.

A 15% decrease in A, in 80 years, from an initial A/B=0.2, i.e., theta=11.3 degrees, is equivalent to a period of 17,000 years. (The rough estimate from PM changes, amounts to a 5% change in 20 years, or a period of 13,000 years.) This suggests a relation to spiral arms. The apex direction is almost parallel to our (Orion) arm of the galaxy (Gupta, Astrophysical Journal 451:722, Fig. 4 has a good chart); indeed the Sirius-Vega line is a reasonable definition of the local direction of the Orion arm.

At great distances toward apex or antapex, the effective value of B is reduced appreciably by the factor sin(x)/x. Grenier et al (A & A Supp. 135:503) has cataloged RVs for, inter alia, B8-9 southern hemisphere stars; the web address for downloading the list is printed in the article. Using the B8-9 stars on Fehrenbach's hardcopy list (A & A Supp., v. 95) I found reduced RV near the apex at the greatest distances: -16.1 km/s (N=23) for apparent magnitude [9.0-10.0) and -19.9 km/s (N=14) for apparent magnitude [8.0-9.0). Using the typical temperature of B8-9 stars (13,500 K) and the Hertzsprung-Russell diagram, the absolute magnitude was obtained and hence the distances, 2060 and 1300 lt-yr, resp. Using a 15,000 lt-yr wavelength, we would expect 19.9*1.25/1.3*0.88 (resp. 0.95)= -16.8 (resp. -18.2). Jaschek's apex speed based on Type B8-9 stars is 20.3, or slightly larger if mixed groups are also included (at fractional weight), but perhaps this should be multiplied by 1.3/1.4 to account for the tendency of B stars to lie in the Orion arm at great distances (i.e., near the apices). So I might as well use Campbell's 19.9.

Quoting Joe Keller:

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Both could be aspects of the sinusoidal variation of some parameter of interstellar space.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

With all due respect, Joe, is it not dangerous to introduce voodoo effects?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
Solar apex speeds determined from RVs (e.g. Campbell, Fehrenbach) are consistently less than those determined from proper motions (e.g. Boss, Hipparcos). As a function of the distance of the star sample, Fehrenbach's result extrapolates parabolically to 17 km/s at the origin. Using the two nearest star samples, the Hipparcos result (Abad et al, Astronomy & Astrophysics, Jan 2003) extrapolates parabolically to 26 km/s at the origin. Maybe neither the proper motions nor RVs signify motion. Both could be aspects of the sinusoidal variation of some parameter of interstellar space.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

With all due respect, Joe, is it not dangerous to introduce voodoo effects?

Thomas, you write on your website:

"The Hubble law for the large scale redshift of galaxies is usually taken as evidence (if not proof) for the picture of an expanding universe in general and the Big Bang theory in particular. However, recessional velocities have by no means been actually measured and the assumption of the Doppler effect being responsible for the shift is only reached due to the absence of other known physical explanations. In fact, the Hubble law appears to be based on rather limited data sets, and in particular has not been examined for its strict validity throughout the whole of the electromagnetic spectrum (in fact, it is known that the redshift factor for certain spectral lines from the same object differs by up to 10% even within the visible part of the spectrum itself)."

I have some questions:
A. You state that "recessional velocities have by no means been actually measured ", can you confirm this for me? Is it a fact?

B.You state that: "the assumption of the Doppler effect being responsible for the shift is only reached due to the absence of other known physical explanations." Can you confirm this also? Is Doppler redshift an assmption?

C. You state that: "...the redshift factor for certain spectral lines from the same object differs by up to 10%..." And can you confirm this too?

I don't know how you would confirm all this, are there published papers available?

Tommy

From Campbell's culled data (removing speeds &gt; 60 km/s different from expected) (op. cit., Table XI) I found an average RV of +1.39 (+/-)0.55 km/s, weighting his 70 groups by their number of stars (1034 total). The above formula predicts +17.85*0.25/1.3/3=+1.14. Campbell suspected systematic error, but modern values confirm his accuracy. Of the 13 of Campbell's 88 bright stars which were near the apex or antapex, all agreed, to the nearest km/s, with modern RVs except Altair, an exceptionally fast rotating star (230 km/s; Astronomy & Astrophysics, Nov 2005).

The residual RV after correction for the effect of RV-inferred apex motion, fits my graph of Campbell's observations tolerably; the derivative d(RV)/d(phi) fits well for associations of stars.

In the "Starlist 2000" of Dibon-Smith, I added 20 km/s to the RVs in Hercules and Lyra (solar apex), and subtracted 20 from those in Canis Major, Columba and Lepus (antapex). This gave 96 positive RVs vs. 69 negative (uncorrected for sample size: 92 vs. 67).

Near the equator of the sphere with pole at the apex, the difference was barely significant, 102 positive vs. 90 negative (equivalent to +0.6 km/s)(predicted: zero). I used unaltered RVs from all of Crater & Corvus, counterweighted by Pisces (23h --&gt; 1h R.A. only); Virgo, counterweighted by Cetus; and Auriga, counterweighted by Telescopium (&lt;19h R.A. only) & Ara.

The predicted combined mean RV over the poles of the apex sphere is +3.8. Here I used Campbell's unculled apparent apex motion, 19.9 km/s, from a sample of 280 stars (op. cit., pp. 187,188). The apex and antapex RVs from Dibon-Smith gave +2.6, weighting each end equally.

My theory predicts that the apex speed determined from the poles alone is 1.5/1.3 times the apex speed determined from RVs overall. Again using Campbell's unculled 280-star sample, the prediction is 23.0 km/s vs. 25.7 observed from the Dibon-Smith apices above.

My polar sample from Dibon-Smith (N=168) and Campbell's unculled whole-sphere sample (N=280) might suffer equally from the absence of fractions of outliers. Bayesian statistics, considering each outlier as one occurrence of a Poisson distributed variable of a priori unknown lambda, implies doubling the outliers. Fictitiously doubling them changed the predicted and observed divergence (resp. end speed) above to +4.2 and +4.6 (resp. 25.3 and 28.0); without weighting the ends equally, the observed were +3.5 and 27.8. Use also of Hipparcos' Type G apparent apex speed, 26.07 km/s, gives an even larger speed excess at the ends, predicting 26.3 vs. the observed 28.0 or 27.8.

Abad's graph (A & A 397(1):345-351, Jan 2003, Fig. 5) of apparent Hipparcos proper motions fitted to a sine halfwave, reveals the influence of the cos(2*phi) term predicted above. Data for phi=60 to 120 fell under the curve; over:under=89:131. Data for phi&gt;150 or phi&lt;30 (my angle phi is the supplement of the apical polar angle usually employed), gave over:under=32:19. Using an estimated 3 km/s s.d. centrally, there is a 3.6% downward shift of the middle 60 degrees of the curve. What would be expected in an attempt to least-squares fit my formula to a sine, is 4.2%.

The influence of the cos(phi) term in Abad's graph was revealed in the over:under ratio of 18:6 (p=0.01, binomial 1-tailed) near the apex (Abad's phi=0, my phi=180) but 14:13 near the antapex. The actual slopes near the apex (resp. antapex) should be 1.56x (resp. 0.94x) those of the fitting curve; that's roughly what is seen.

The energy needed to change 16 km/s to 18 km/s (let alone 20 km/s) is much larger than that needed to change the direction 6 degrees. In this sense, the consistent difference between solar apex speeds determined from RVs and from proper motions, is huge.

If the first derivatives w.r.t. space and time, of the ether's velocity vector field, are constant, then effects (e.g., the apparent solar apex motion) do not occur: "All inertial frames are equivalent", except for the subtlety that a patch of ether moves with the object, causing a small spatial second deriviative. During relative motion of objects, patches of ether (associated with the moving objects) change relative position, second derivatives appear, and these cause "Special Relativistic" effects (e.g., possibly, a swarm of relativistic objects known as an "electron"). Random internal motion likewise causes ether effects dropping off as r^2, known as "gravity"; the other "General Relativistic" phenomenon, acceleration, directly causes second derivatives in the ether.