Requiem for Relativity

There is "new physics" at 53 AU. The Kuiper belt ends suddenly there. Two of the three main tracking anomalies of Pioneer 10, occurred, or began, there; these anomalies are quantitatively or qualitatively inconsistent with gravitational influence by Kuiper belt objects and furthermore such objects would be encountered in the densest part of the belt (42-50 AU) not precisely at its edge (53 AU) (graph from JD Anderson, "Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration", ArXiv.org internet paper, 27 Aug 2001).

The amplitude of the Kimura (Astronomical Journal, 1902) phenomenon is known only to 30% accuracy, but to this accuracy, its amplitude, and also period and phase, are consistent with aberration of starlight determined when the light crosses the 53 AU barrier, not when the light reaches Earth. The two oscillating ("beating") or elongated stars occulted by Saturn's rings (Alexander, "Saturn", 1962) are consistent, to order-of-magnitude accuracy, with this same aberration difference, between starlight originating beyond 53 AU and starlight re-emitted from transparent gas in Saturn's rings.

The "anomalous deceleration" of Pioneer 10 doesn't have any obvious connection with 53 AU, but one of the other anomalies, was an erratic variation in radio frequency occurring mainly near 53 AU. Mainly this was two apparent reductions, of one and two weeks duration, by 18 cm/s, in Pioneer 10's speed. I noted in my 2002 paper ( Aircraft Engineering & Aerospace Technology 74(3) ) that this is consistent with temporary loss of 3/4 of Pioneer 10's relativistic time dilation relative to the sun.

The other Pioneer 10 tracking anomaly was an oscillation in frequency beginning at about 53 AU and remaining about constant thereafter. The period, phase and amplitude of this are consistent with a relativistic time dilation dependent, not on relative speed when the signal reaches Earth (as calculated) but rather on relative speed when the signal reaches 53 AU.

Two theoretical correlates of this 53 AU distance now have been discovered. In my 2002 paper, I remarked that if a proton exists in the smallest (Gaussian) matter distribution allowed by the Heisenberg uncertainty principle, then 53 AU is the distance beyond which the gravitational field vector becomes directed away from the sun, at some points within the proton (i.e., maximum proton gravity exceeds solar gravity). In another recent post, I remarked that 53 AU ( +/- 20% depending on the kind of mean considered) is where the mean speed of electrons at the cosmic background temperature, equals solar escape speed.

If the mean of v^1.5 is considered, that distance is 52.6 AU. (I added the planetary masses to the sun's mass, neglecting other masses; and used T = 2.726.) The 1.5 exponent could be justified as giving the mean square root (as for Brownian motion) of the rate of kinetic energy transport v*v^2 = v^3. (The 1.5th moment of the error function isn't in the CRC tables; I used Jahnke & Emde, 4th ed., pp. 20, 14.)

If both the proton and the electron theories above, explain the 52.6 AU limit, then the CMB temperature is determined. It follows that the CMB is a product of the edge of the solar system. Its symmetry is due to the symmetry of the sun's gravitational field. The CMB dipole might be due to some cosmic vector. The quadrupole and higher moments would be unexpectedly small, and correlated with the plane of the ecliptic; this is so (see MNRAS, Mar. 21, 2006).

The r.m.s. electron radial velocity of 6.43 km/s would give r.m.s. deviation in the CMB temperature, of 2.14 * 10^(-5). Per RB Partridge's 1995 book, "3K: the Cosmic Microwave Background Radiation", pp. 252, 254 & Fig. 7.19, the least upper bound for the rms deviation of CMB temperature, was determined in 1989 to be 1.9 * 10^(-5). (To make this into an explanation, one might assume that large parts of the sky somehow moved with that speed.)

Alternatively, a body near the 53 AU barrier could provide, say, 1/25,000 of the sun's gravitational force, yet negligible gravitational energy. This would move the barrier outward by one part in 50,000, and reduce the apparent CMB temperature by 2*10^(-5). Such bodies would have orbital periods of about 380 yr., so the CMB variations ("shadows on the wall") might move 11 degrees between the COBE (launched Nov 1989) and WMAP (launched June 2001) studies. This would be disguised by the effects of multiple bodies moving different directions. An object with the density of Earth and the typical moderately large "Kuiper Belt Object" diameter of 100km, would need to be 0.01 AU from the barrier; its depression in the CMB temperature would be of diameter roughly 80 arcsec.

In about 1986, RD Davies found a CMB anisotropy about 10 degrees wide, near RA 217 Dec +40. This could be caused by an Earth-size "Planet X" with 900^2 times more mass than the above, i.e., 10,000km diam, and roughly 9 AU from the barrier: i.e., outside, at 62 AU, because the negative 2nd derivative plotted, implies a maximum of temperature. The planet might be somewhat bigger if it really lay at +35 or +45. Based on Halley's and two other comets, JL Brady, of Lawrence Livermore Labs, in Publications of the Astronomical Society of the Pacific 84:314+, pp. 319 & 322, 1972, predicted a Jupiter-size "Planet X", 63 AU from the sun, with eccentricity 0.07, and 1946 position RA 75 Decl +67. Brady's planet lay outside Tombaugh's search; mine too close to the edge of the search, to tell. Brady's planet and mine are too far apart to be identical.

From the positions of the giant planets during data collection, the difference in the magnitude & galactic longitude of the CMB dipole, between COBE (DMR) & Wilkinson (WMAP), is predicted by this model. See the post below.

Error bars include not only measurement errors, but also variations due to physical effects yet unknown. So, the error bars on the CMB dipole really are upper bounds of the measurement error; the measurement error might be much less. Even accepting the error bars as published, there is a significant difference between the "COBE DMR" and "Wilkinson WMAP" determinations of the CMB dipole's galactic longitude.

One-, two- and four-year COBE reports, and one- and three-year WMAP reports, have been published. No matter which COBE or which WMAP reports are considered, the magnitude and galactic latitude of the CMB dipole, given by COBE & WMAP, differ by less than one (joint) standard deviation. On the other hand, no matter which reports are considered, COBE and WMAP give galactic longitudes differing by *more* than one (joint) standard deviation, with COBE exceeding WMAP. COBE & WMAP always are consistent with themselves, though, within one (joint) standard deviation. For the 4-year COBE & 3-year WMAP, the difference in galactic longitude, 0.40 degrees, is 1.2 joint standard deviation, p = 11.5%, one-tailed. For the 2-year COBE & 3-year WMAP, the difference is 2.65 s.d., p = 0.3%, one-tailed.

One can see on the Norton atlas galactic chart, that the directions of increasing galactic and ecliptic longitude are almost parallel at the location of the CMB dipole vector. Furthermore, the CMB dipole vector is only about 12 degrees from the ecliptic. From published articles, I gleaned the start and stop dates of the above data sets; data collection apparently was very steady (99.4% efficient for the last two years of WMAP and almost that good for the first year). From the Astronomical Almanac (formerly American Ephemeris & Nautical Almanac) I found the heliocentric ecliptic longitudes of the giant planets Jupiter, Saturn, Uranus and Neptune near the midpoint of each of the five observation periods. Using the approximation that the CMB dipole lies on the ecliptic at lambda = ecliptic longitude = 171.4 degrees (found using published celestial coordinates for the COBE 4-year report, and graphical conversion on the Millenium atlas), I found the theoretical effect of the giant planets, on the CMB dipole, using the above theory. (Even for Jupiter over 4 yrs, the error of using sin(mean(theta)) instead of mean(sin(theta)), was only 5%, and Jupiter will prove to have, on average, only 1/10 the effect of Neptune.)

First, I found by successive interpolation using a "BASIC" computer program, accurate "barrier" distances (i.e., equal total gravitational *force* at 52.6 AU in superior conjunction, and "r" AU in inferior conjunction) for the two extreme positions of each planet. The difference, in total potential energy, between these distances, divided by the total potential energy, divided by two, gives a dipole strength. The ratio of this dipole, to the CMB dipole, gives the radians maximum deviation, in CMB dipole ecliptic longitude, that the planet can cause.

Planets such as Neptune which are not near the sun, give a much smaller dipole, for given extreme values (small bodies very near 53 AU give negligible dipole integrated over the sphere). The unique 4th-degree polynomial having the properties of ordinate and slope, needed to correct for this, is (1-(r/52.6)^2)^2, and this was applied for all planets. Neptune showed ten times the dipole strength of Jupiter, and five times Saturn or Uranus.

The sines of the angles between the planets and the dipole, indicated that, using the largest COBE and WMAP reports, the galactic longitude should differ 0.466 deg (one must multiply by sec(48.2) because the galactic longitude lines are closer together than at the galactic equator) between COBE and WMAP. The actual difference was 0.40 +/- 0.33 deg. However the predicted and actual difference were opposite in sign; maybe there is some reason for this sign reversal.

It also was predicted that the 3-yr WMAP dipole magnitude should be 9 microKelvins less (assuming sign reversal of the effect as above) than the 4-yr COBE dipole magnitude. Actually it was 5 microK more, but with such error bars and variable results between data sets, that there is neither confirmation nor denial.

N Jarusik et al, ArXiv.org May 15, 2006, Fig. 12, especially the 6th & 7th of the 8 maps produced by various subtractions and averagings, shows a band of increased (CMB) "delta(T)/T" (as shown by the mixture of dark blue and green dots), roughly 45 degrees wide, crossing the center at the angle of the ecliptic. This suggests that Kuiper belt objects indeed cause CMB anisotropy.

J Davies, "Beyond Pluto" (Cambridge Univ. Press, 2001) Fig. 8.1, p. 150, combines five studies into a chart indicating that the number of Kuiper belt objects greater than a given mass, is roughly inversely proportional to that mass. Thus the total mass of the Kuiper belt objects could be very large (almost a divergent infinite series in either direction).

RB Partridge ("3K...", op cit) Fig. 7.19, p. 254, reproduces a graph from ACS Readhead et al, ApJ 346:566+, 1989, showing that for small angular sizes of sky, the rms deviation of the CMB, decreases as the reciprocal of the square root of the area of the sky patch; I think this is a manifestation of the textbook sqr(N) sampling formula. For larger sky patches, the rms deviation increases again as the area of the sky patch. This would occur, if the mass of the largest object goes as d^3, where d is the edge of the cube; thus the height of deviation goes as d, the area of deviation goes as (sqr(d^3))^2, and the overall deviation due to that object, as d^4. Dividing this by the area, gives deviation proportional to the area, as observed.

The 0.3 x 0.3 degree pixels of WMAP, with its 60 microK sensitivity, imply that objects would need to be about 400km diam to be detected by WMAP if the above mechanism is correct. The upper bound in Allen & Bernstein's article, together with the N = 1/M law, implies an upper bound of 40 such detectable objects near enough to either side of the 53 AU barrier (i.e., < 40 maxima or minima of the CMB temperature). Furthermore, COBE's poorer resolution & sensitivity would give COBE only a fraction this many maxima & minima. If smaller objects usually occur in clusters like the Trojan asteroids, then the effective number of objects might be several times larger.

The CMB quadrupole from COBE (4-yr) is given as 10 (+7 or -4) microK; also, by the alternative method of data analysis, it is estimated at 15.3 (+3.8 or -2. (Bennett et al, ApJ 464:L1+). I multiplied the dipole theoretically produced by each giant planet, by a 4th-degree polynomial estimating factor, 1-(1-(r/r0)^2)^2, to obtain its theoretical quadrupole. Neptune gave 14.5 microK, Uranus gave 1/10 that, Saturn 1/50 and Jupiter 1/300. For COBE (4-yr), Neptune and Uranus were only 3 degrees apart on average, so the predicted quadrupole would be 16 microK.

For WMAP, agreement is poorer. WMAP (1-yr) showed a CMB quadrupole of 8 +/- 2 microK (G Hinshaw et al, ApJ Supp 148:135+) though Neptune & Uranus were only 16 degrees apart on average. Due to a change in terminology, expressing the quadrupole "power" in different fundamental units, I don't know how to express the 3-yr WMAP result in comparable form; but CG Park, C Park & R Gott, ArXiv.org Aug 5, 2006, do give the direction of the quadrupole as l=241, b=67; and of the octupole as l=235.5, b=63 (midranges of six close results). Apparently these vectors are to the pole of the "m=0" (i.e., lowest) spherical harmonic of a given order n. They lie about 10 degrees above the ecliptic and about 145 degrees from Neptune (coordinate conversion with the online utility on www.realuniverse.nao.ac.jp ).

If the CMB originates at an average distance of circa 400 million light years, then as I outlined months ago on this messageboard, a long wave of comparable half-wavelength, affecting the value of the Hubble parameter, could cause the CMB dipole; but then there also would be a quadrupole of similar magnitude. Really, the quadrupole is about 1/300 of the dipole.

Only within the solar system, but at great distance from the sun, is there known to be such symmetry as the CMB shows. The sum of the planets' masses is 0.134% the sun's mass; the CMB dipole is 0.123% the CMB temperature.

Graphically I estimate the ecliptic longitude of the CMB dipole as 171.4. On March 6, 2006, the sun achieved the yearly minimum "B0" of -7.23deg (solar latitude of center of sun's disk): the ecliptic longitude of the sun would have been 180 - (20 - 6) = 166. That is, the sun's rotation axis, the principal axis of the solar system, and the CMB axis are nearly coplanar (the use of the principal axis of the solar system makes the CMB dipole 8 degrees out of the plane, instead of 171-166=5). By analogy with the coplanarity of the moon's rotation axis, the moon's orbital axis, and the ecliptic axis: the CMB axis might be the sun's true orbital axis as part of a larger system. Apparently a small CMB quadrupole and octupole also lie in this direction.

Hi Joe. As, without a doubt, the thickest reader of this board [] I think it's encumbent on me to ask you to give a little primer on multipoles. That should open up the debate a bit more.

Some really dumb observations [8D][] Let's say we've got an electron and this bit of matter has an atmosphere of "space" ether, whatever. So half its energy, at rest, is space, half matter. Push it and its kinetic energy goes up and it potential energy goes down. The energy density of the ether can change with velocity. (joules per cubic metre [][][] but what do I know[] )

Note that from that equation of Robert Carroll, the ether "atmosphere" falls off as an inverse fourth power i.e. a quadropole.

A question: a perfect spherical planet would have this quadropole but we don't get them, so I'll bash the planet with a big mallet. Now it's got a quadropole. Do I need to do that? Or, is the quadropole moment a consequence of the ether "atmosphere"?

Multipoles; we've got the sun's space, which contains planets, which have their own space. So I took a look at Legendre polynomials en.wikipedia.org/wiki/Legendre_polynomial

Yuck [] hard sums! Though I have to say, that graph of values for n looks promising [] Start with a big ball of gas, bash it with a supernova, and see if we can get a multipole set up that gives us Bode's "Law."

I blame my parents[]


(Edited) From another thread; if we consider the ether to be a Bose Einstein condensate of neutrino pairs, analogous to Cooper pairs, then a ftl graviton could "see them as paired particles, rather than as a boson. On pasing through ether then, I think we have a very rapid Lorenzian contraction for some ftl gravitons. However, as they slow down, the neutrino pairs become increasingly fuzzy. A graviton which has lost its energy to the ether and is at light speed, then sees a boson and, i presume, passes sraight through it. Yep [] needs work[)]

[Stoat] "Push it and its kinetic energy goes up and it potential energy goes down."

In general this is not true because not enough information is provided. An unspecified push on a system with unspecified starting conditions can result in both types of energy increasing, decreasing or remaing unchanged in all possible combinations.

[Stoat] "Yep, needs work."

And a little attention to the basics. If you stick with it, you will get there.

We've all made ambiguous claims like this, and eventually learned how to avoid them. It begins with realizing that they are ambiguous. And that it usually matters.

Regards,
LB