Requiem for Relativity

Unpublished Wall Street Journal letter

Here is the letter I mailed (no response received) to the Wall Street Journal (a Murdock publication headquartered in New York) postmarked Nov. 27, 2009.

"Re: Global Warming with the Lid Off [title of WSJ editorial]

Regarding your Nov. 24th editorial on 'hiding the truth about climate science': it proves the need to be scientifically self-reliant, now! Don't wait for a journal editor to tell you the Mayan Long Count, 5125 years, is a common multiple of the orbital periods of Jupiter, Saturn, and Uranus. Likewise, Joseph Scaliger set Julian Day Zero, 6295 years before the start of the Gregorian Calendar, because he knew an astronomical cycle.

"Brauer dates the Younger Dryas climate change (related to the nanodiamond 'Black Layer' and Clovis human extinction) at 12,683 years before 2012AD. Half that time ago, another partial human extinction removed most cranial diversity in North America and most linguistic diversity in western Eurasia (leaving mainly proto-Indoeuropean); there were simultaneous bicoastal Australian megastsunamis and frequent North Pacific volcanoes. Accurate interpretation of 'Sothic Dates' puts Year One of the Egyptian calendar at 4328BC. Real researchers are needed.

"Sincerely,
Joseph C. Keller, M. D., B. A. cumlaude (Mathematics) Harvard, 1977"

The Asteroid Resonance - Part 3 (Review)

"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
- Shakespeare, Hamlet, Act 1, Scene 5

The asteroids. From two lists of the most massive asteroids as determined by gravitational interactions (one list on Wikipedia, and one by Dr. Hilton on the USNO website) and also Wikipedia's list of asteroids of largest dimension, I compiled a list of 25 especially massive asteroids. All these had rotation periods and sufficiently precise orbital periods given on Wikipedia. (I always excluded Trojan asteroids.) The IRAS survey gives 72 more asteroids of estimated average diameter > 150km; 15 of these had, on Wikipedia, rotation periods and sufficiently precise orbital periods, so were added, to make 40 total on my list of sufficiently studied, massive asteroids. (My internet searches failed to find adequate data on any asteroids when such data were lacking from Wikipedia.)

The rotations. Assuming no change in Luna's density, and conservation of angular momentum, Earth's rotation period would have been 5.05h, when Luna was at its presumed formation distance at the fluid-body Roche limit. Early Luna would have been less dense; assuming the density ratio early Luna::present Luna = "broken basalt"::basalt, Earth's rotation period at Luna's formation would have been 5.13h. On my list, two of the 40 asteroids, 511 Davida and 39 Laetitia, have rotation periods 5.13h and 5.138h, resp. (Davida is named for David Todd, who happened to be the first astronomer to predict the position of the trans-Neptunian planet.) Five asteroids have rotation in the range [4.148h, 4.84h]. The other 33 are in the range [5.18h, 29.43h].

The "first", "second", and "third" periods. The "first period" I discovered, is Barbarossa's orbital period according to the four sky survey images: 6340 +/- (conservatively) 9 yr. Many other solar system periods and historical phenomena resonate with this period; using these, the best estimate I can make of its true value, is 6339.364 Julian yr.

The "second period" is approximately the Mayan Long Count. Using modern values, the closest possible common multiple of all important solar system periods or half-periods, is 5124.58 Julian yr.

The "third period" is 5124.58*sec(36) = 6334.329 Julian yr. Cos(36) is half the "golden ratio". Cos(36) also is the abscissa of my recent discovery, the "Jacobi 2 Resonance". At cos(36), families of Jacobi polynomials show major peaks (e.g., the Legendre polynomials) or troughs (e.g., the Chebyshev polynomials) in the strength of the periodicity of their logarithms, for period equal to log(2). Like the "first" and "second" periods, the "third" period resonates exceptionally well with solar system periods.

The resonances of 511 Davida and 39 Laetitia. At the winter solstice, 2012AD, Barbarossa's extrapolated heliocentric ecliptic longitude (J2000.0 coords.) is 176.37deg. According to the online JPL ephemeris (my conversion to ecliptic coords.), at 0h UT Dec. 21, 2012, the heliocentric ecliptic longitudes (J2000.0) of 39 Laetitia and 511 Davida will be 174.39 and 170.71+180=350.71, resp. The closest approach of Laetitia's orbit to Barbarossa, is at longitude 173.74. The closest approach of Davida's, is at about the same longitude, 173.39. So, the same two asteroids which show the pristine 5.13h rotation period, also align with the Barbarossa-Sun axis, with only +0.75 and -2.6 degrees longitude error, at the end of the Mayan Long Count, 12h UT Dec. 21, 2012.

Something is special about the 5.13h rotation. That's why this is posted in the thread, "Requiem for Relativity".

Also, both these asteroids resonate with the "first", "second" and "third" periods:

Remainder on division
"First" period
39 Laetitia 0.024
511 Davida 0.896
"Second" period
39 Laetitia 0.342
511 Davida 0.337 (both are thirds; difference = 0.005)
"Third" period
39 Laetitia 0.931
511 Davida 0.003

(The "first" and "third" periods differ by about the orbital period of a typical main belt asteroid, so those resonances aren't independent.)

The Asteroid Resonance - Part 4

Apparently, something maintains 511 Davida and 39 Laetitia, at one and the same axis of rotation. The most recent determination I've found, of Davida's rotation axis, is that published by Conrad in 2007, the result of one night's observation with the Keck telescope: Davida's axis is ecliptic longitude 297, latitude 21. The most recent determination I've found, of Laetitia's axis, is that published by Kaasalainen in 2002, a restudy of observations from 1949-1988: Laetitia's axis is longitude 323, latitude 35. The angle between Davida's and Laetitia's axes, 27 deg, is small, at significance p = 5%.

An earlier analysis of Laetitia's data, by basically the same Finnish group, was published by Lumme & Bowell in 1991: longitude 327, latitude 36. However, differences between studies often show that the errors in axis determination are bigger than would appear from the standard error bars. That is, there is systematic error much bigger than the measurement error.

A review article (Cunningham, Minor Planet Bulletin, 1985) states that 180 deg ambiguity is one of the common errors. For Laetitia, I combined the five published determinations listed in Cunningham's Table 1, with the two by the Finnish group, adding 180deg to the longitude, when needed to make the measurements believably similar. I then averaged the seven longitudes (range 283-327) and latitudes (range 10-61) to find longitude 307 +/- 6 (Standard Error of the Mean), latitude 38 +/- 6 (SEM) for Laetitia's rotation axis.

For Davida, I combined the two in Cunningham, with the one by Conrad, again adding 180deg to the longitude when needed. I then averaged these three longitudes (range 297-306) and latitudes (range 10-34) to find longitude 302 +/- 3 (SEM), latitude 22 +/- 7 (SEM) for Davida's rotation axis. This comprehensive result indicates that Davida's and Laetitia's axes are only 17 deg apart; p = 2%. The difference in latitudes, between Davida's axis and Laetitia's, amounts to 1.7 sigma, p = 9%, two-tailed. Thus the similarity of the rotation axes is more significant than their dissimilarity.

For greater accuracy, I add the axes vectorially, instead of averaging the longitude and latitude. This gives the same result for Davida, and for Laetitia gives long. 309, lat. 39.

The unweighted vectorial average for all ten published determinations, is (long,lat) = (306,34). Abad, A&A 397:345+, 2003, gives the Hipparcos solar apex motion according to the distance or spectral type of the reference stars. Relative to Type O & B Hipparcos stars (these are thought to be very young stars, whose velocities might approximate that of interstellar gas) the solar apex motion is toward (long,lat) = (271,45) with sigma about 5deg. This is a separation of 29deg, p = 12%, two-tailed.

A novel way to estimate the solar apex motion, is to find pairs of nearby, Type O or B or early A, stars, whose motions relative to the Sun, are the same. I checked the twelve Type V stars with Hipparcos parallax > 30mas and Johnson B-V < 0.020. Using Hipparcos parallax and proper motion, and Wilson/Evans Radial Velocity (VizieR online catalog by Duflot), the Sun's motion directions relative to these stars are almost equal in four pairs, where each pair of stars is separated by ~ 90deg:

1. Sirius and Alioth (1st & 4th nearest of the 12). The Sun's motion relative to these stars, is 18.4km/s toward (RA,Decl)=(132,+43), and 16.1km/s toward (122,+31), resp. The solar apex directions differ only 14deg, and the stars are 105deg apart in the sky.

2. Vega and Regulus (2nd & 3rd nearest). The Sun's motion relative to these, is 19.0km/s toward (RA,Decl)=(256,+1), and 28.7km/s toward (253,-4), resp. These solar apex directions differ only 6deg, and these stars are 109deg apart in the sky.

3. Deneb el Okab (zeta Aquilae) and Algorab (delta Corvi) (5th & 6th nearest). The Sun's motion relative to these, is 27.5km/s toward (RA,Decl)=(289,+39), and 33.4km/s toward (285,+36), resp. These directions differ only 4deg. These stars are 102deg apart in the sky.

4. Alpheratz (alpha Andromedae) and Alnair (alpha Gruis) (8th & 10th nearest). The Sun's motion relative to these, is 32.1km/s toward (RA,Decl)=(269,+53), and 31.1km/s toward (265,+49), resp. These directions differ only 5deg. These stars are 81deg apart in the sky.

Enlarging the investigation, I checked the 42 stars (excluding two with obvious large binary motion: a companion in the Duflot catalog within a few arcminutes, that is almost as luminous, hence massive, and has much different RV) with Hipparcos parallax > 20mas, Johnson B-V < 0.030, and Hipparcos Visual magnitude < 6.7 (excluding 14 stars with V > 9; I want only relatively massive stars). These are spectral color types B and early A, types IV & V plus a few III.

Of all 42*41/2=861 possible pairs, the pair ranking third, in closeness of agreement in their direction of motion, is epsilon Hydri (in the south circumpolar constellation Hydrus) and mu Serpentis (in Serpens Caput). Their speeds (relative to the Sun) differ 20%, but their directions of motion differ only 2.7deg. These stars are 107deg apart in the sky. The vectorial mean Sun velocity relative to these, is 22.6km/s toward ecliptic (long,lat)=(310,33), differing only 3 degrees from my meta-determination (see above) of the shared Davida-Laetitia asteroid rotation axis.

More evidence that Davida's and Laetitia's rotation axes are equal, is that the determinations cluster as if systematic errors sometimes were the same. Cunningham's second listed determination for Davida, is (long,lat) = (306,34); his first & third determinations for Laetitia, are (128,38) & (121,37), presumably correctable to (308,38) & (301,37). His first determination for Davida is (122,10); his fourth determination for Laetitia is (130,10).

Mars' published theoretical Newtonian lunisolar, or rather simply solar, precession period is 170,000 yr. If these asteroids had the same oblateness and rotation period as Mars, they would have about nine times that precession period (it is independent of density and radius) but their shorter rotation periods make it about 45 times. Still, because Davida's and Laetitia's orbital semimajor axes differ considerably, the precessions should randomize in ~ 10^8 yr.; really it's probably less than a tenth that, because of the asteroids' irregular shape. An unknown force keeps them aligned.

The Asteroid Resonance - Part 5

Review. After compiling a list of, approximately, the 40 most massive asteroids for which adequate data are available, I found that two of them, 39 Laetitia ("S" or silicaceous type) and 511 Davida ("C" or carbonaceous type), will be, at the winter solstice 2012AD, 0.75deg from conjunction with, and 2.6deg from opposition to, Barbarossa, resp. In itself, this isn't statistically significant, but their rotation periods are nearly equal: 5.138h and 5.13h, resp., a significant clustering, considering the large range of those periods.

The 5.13h period (review). Straightforward calculation, using conservation of angular momentum and accounting for Earth's axis tilt, shows that, assuming Luna's modern density, Earth's rotation period would have been 5.05h when Luna was at the Roche limit. The actual period would have been greater, because the original Luna would have been less dense, hence the Roche limit larger. The result is rather insensitive to Luna's density; use of an authoritative value of the ratio, solid basalt::broken basalt, increases Earth's theoretical primordial rotation period to only 5.13h. Can it be mere chance that this is the rotation period of the two asteroids (among the 40) which are aligned with Barbarossa at the end of the Mayan Long Count?

The 5.13h period (new information). R Duffard et al, "Transneptunian Objects and Centaurs from Light Curves", A&A manuscript 12601, 5 Nov 2009, on arXiv.org, say (sec. 2.2, p. 3):

"...assuming that all objects have single-peaked light curves...A Maxwellian curve was fitted...for a mean period of 5.13 hours."

When the functional form is known (e.g., it is known that it should be a Maxwellian curve), even a moderate number of data points such as Duffard's (n=72), can give a very accurate estimate of one parameter. Duffard states that it is "obviously not true" that all the objects have single-peaked light curves, but Duffard could be wrong.

The Asteroid Resonance - Part 6

The IAU Minor Planet Center lists 511 Davida's rotation period as 5.1294h, and 39 Laetitia's as 5.138h. The mean of these is 5.134h. So, today I arbitrarily investigated all asteroids on the IAU rotation period list, whose rotation periods are within 0.054h of this mean, i.e., from 5.08h to 5.188h inclusive.

There are 19 such asteroids. As I did for Davida and Laetitia, I found the JPL ephemeris' heliocentric Right Ascension predicted for them for 12h UT, Dec. 21, 2012. The two asteroids with rotation period < 5.11, namely 3165 Mikawa & 7895 Kaseda, both will be more than two hours of RA away from heliocentric conjunction or opposition with Barbarossa, which is about the same as being more than two hours RA from 12h RA and also from 0h RA. The nine asteroids with period > 5.1655, namely 132 Aethra, 1011 Laodamia, 33107 1997 YL16, 87 Sylvia, 3086 Kalbaugh, 7816 Hanoi, 1296 Andree, 53435 1999 VM40, & 4713 Steel, likewise will be more than two hours RA away from conjunction or opposition with Barbarossa. Of the three asteroids with period 5.11h, two (153 Hilda & 6260 Kelsey) will be more than two hours RA from conjunction or opposition with Barbarossa, but one (6379 Vrba) will be, only an hour of RA, ahead of opposition. 2292 Seili has period 5.121h; it will be an hour of RA behind conjunction.

The remaining four asteroids, of the 19, have period from 5.1294h to 5.1655h, inclusive. All four are within three degrees either of heliocentric conjunction or opposition with Barbarossa, at the end of the Mayan Long Count. As discussed previously, 511 Davida is 2.6deg behind opposition, and 39 Laetitia is 0.75deg ahead of conjunction. (These values refer to the distance along the orbit, from the orbital point nearest Barbarossa's position). Remarkably, 1717 Arlon (rotation period 5.1484h, diameter ~ 9km) is 3.1deg behind conjunction, and 947 Monterosa (rotation period 5.1655h, diam. est. 27km) is 1.75deg ahead of conjunction.

Thus the four asteroids whose rotation periods are clustered near or slightly above the critical value, 5.13h, all are within 3.1deg or less, of either heliocentric conjunction, or heliocentric opposition, with Barbarossa, at the winter solstice, 2012AD. This is so significant statistically, that it proves a causal relationship between the end of the Mayan Long Count, and either Barbarossa, or if not Barbarossa, something else, near 176deg ecliptic longitude then.

*********

Update Dec. 30, 2009

Let's expand the table in Part 3 (Dec. 22) to include Monterosa and Arlon. I use Wikipedia's value, 4.562yr, for Monterosa's orbital period. Because Wikipedia's value for Arlon's orbital period is given to implausibly many digits, for Arlon I use instead another online value, 3.2534yr, from the website of WR Johnston, Nov. 2008.

Remainder on division

"First" period (Barbarossa's orbital period, est. 6339.364 Julian yr)
39 Laetitia 0.024
511 Davida 0.896
947 Monterosa 0.602
1717 Arlon 0.535

"Second" period (Mayan Long Count; best resonance, 5124.58yr)
39 Laetitia 0.342
511 Davida 0.337
947 Monterosa 0.319 (all are thirds)
1717 Arlon 0.146

"Third" period (5124.58yr * sec(36); see previous posts)
39 Laetitia 0.931
511 Davida 0.003
947 Monterosa 0.512
1717 Arlon 0.007

Thus there is an tendency for these four asteroids' orbital periods, to be whole, or sometimes half, divisors of the "first" and "third" periods, and to have a third left over, when divided into the Mayan Long Count.

Hi Joe, do you mind if I go a little off subject to pick your brains about something we discussed earlier in the thread? You remember that I think that h = c^2 / b^2 is the best bet for the speed of gravity; b being the speed of gravity here. Also, that writing the lorentzian in terms of the refractive index i.e. sqrt(1 - 1 / 1.5009 34) is somewhat similar to the Riemann conjecture, in that we can replace that reciprocal of h by the prime number sequence.

My rough muddle of an idea. At the speed of light there's a phase change, the sign changes from a minus to a plus. In effect it's just the old luxon wall revamped in terms of the speed of gravity. Jump into your space ship and accelerate upto the speed of light; you use a lot of energy to do this but you do have an immense, hidden store of gravitational angular momentum in the core of every particle of your ship. At the speed of light, your relativistic mass doubles. Thereafter your mass starts to fall. You're burning grav energy as fuel after all.

At the speed of gravity your mass has fallen to the square root of two, of twice the ship's mass. A lunatic pilot might e tempted to put his foot down and go faster, But effectively he's in the future of the universe, he'd need to navigate by going everywhere at the same time. Wow!

So back to Rieman, PI(1 / 1 - 1 / p^s

s is a complex number (a +jb) a = 0.5 and b = 14.134725

I get about p^0.5(0.9854 + j 0.1706)and get a value of half e for s.

Frankly I'm pretty naff at maths, so could you check this out for me? Strangely I think we get a devil's stair case. From twice the speed of light to three times the speed of light, your spaceship mass decreases but from three to four it stays the same. That's because four isn't a prime. The question is, does this staircase mirror over to the sublight part of the lorentzian? Would the steps be scaled right down? A fractal space is begining to make a little more sense to me, I suppose the pretty pictures made would be us and the whole shooting match.