Requiem for Relativity

The theory of the Hawaii bubble

In nuclear magnetic resonance spectroscopy, one speaks of "the magic angle" of precession, which in the nonrelativistic approximation is arcsin(2/sqrt(2*3)) = 54.7356deg. According to nonrelativistic quantum mechanics, there is another, closely related angle of precession: arcsin(1/sqrt(2*3)) = 24.0948deg. Merzbacher's quantum mechanics text, among others, derives these angles. Another quantum mechanics text in the library at Iowa State Univ., happens to consider the relativistic correction to these angles, and finds that it is of order (v/c)^2, hence negligible for, say, hydrogen, but not for uranium, because for the innermost Bohr atomic electron, v/c = N/137, where N is the atomic number and 1/137 the fine structure constant. Let's suppose that the nonrelativistic (e.g. hydrogen atom) magic angle, 24.0948deg, is accurate for the Hawaii bubble.

Statistical combination of my two methods of estimating the start time of the bubble, gives 13:38:38.5 UT, only 34.5sec before Luna's southern limb reaches the plane tangent to Earth at the North Pole, at 13:39:13. At 13:39:13, Luna's center projects, according to the azimuths given by the online JPL ephemeris, onto the longitude line 125.836W. Now there are two important vectors associated with Earth: the vector Z from Earth's center to the North Pole, and the vector X, parallel to Earth's equator, from the North Pole to the southern limb of Luna.

At a point on Earth's surface, also there are two important vectors: the outward vector U which is normal to Earth's surface (more precisely, the outward normal to the approximating "reference spheroid"), and the vector V which is that point's rotational velocity (i.e. eastward parallel to the line of latitude). There are two points on Earth's surface, such that U and Z form the "magic" angle arcsin(1/sqrt(6)), and so also do V and X. For only one of these points, is Luna visible above the horizon. That point has longitude 149.931W and geographic latitude 24.095N.

Including a small correction for Earth's curvature, I find that the azimuth of this point, seen from Mauna Kea, is 50.1deg. This compares well to my estimate from the Subaru video (see earlier post), 51deg. This point, if fixed in the geocentric celestial frame, would move, relative to Earth's surface, 269m/s toward the left as projected on Mauna Kea. It is 743km from Mauna Kea. In eight minutes of time, this would be about 10 degrees of motion. I do not yet have an accurate estimate of the amount of motion in the videos, but according to the Japanese astronomer who posted online, the bubble achieved ~45deg diameter (during its >8 min duration). I did estimate from the videos that the bubble center moved upward 2x as fast as the center moved leftward, and that the bubble top moved upward 2x as fast as the bubble center moved upward; thus 40deg size after 8min implies about 10deg leftward motion in 8min. So, my predicted leftward motion of the bubble, corresponds at least roughly to the leftward motion observed.

Also it might be that the bubble, whose center apparently moved upward at about a 60deg slope, really moved upward along another "magic angle" slope, namely 45deg = arcsin(1/sqrt(1*2)), because arctan(tan(60)*cos(50.5)) = 48deg. Here cos(50.5) accounts for the projection as seen from Mauna Kea, using the azimuth angle of the great circle line of sight at the bubble.

The monthly bubble

According to the previous post, the bubble should recur at intervals of almost exactly one sidereal month. There should have been a bubble near Karachi, Pakistan, to the SW over the Arabian Sea, at 21:36 UT July 19 (02:36 July 20 Pakistan Standard Time); and near Key West, Florida, to the SW over the Gulf of Mexico, at 05:34 UT August 16 (01:34 U.S. Eastern Daylight Time).

According to the online service "Weather Underground", classic.wunderground.com/history/airport/ , Key West had clear skies and 10 mile visibility until at least 02:53 EDT on August 16, but there was a thunderstorm early that morning. The thunderstorm began at about 04:42 EDT. During the prior four hours, surface wind direction had ranged from W to SSW at speeds ranging from 3.5 to 6.9 mph. By my calculation, the bubble started 33 mi away from Key West at compass point "S by W" (slightly W of S); the bubble's center moved westward but its eastern side remained about stationary due to expansion. Soon the bubble covered about the western half of the sky at Key West, but if illuminated by Luna with more backward than forward scattering, the bubble might have been hardly visible from underneath. Thunderstorm clouds to the southwest likely partly blocked the view of the bubble, but could not have blocked it completely unless for some reason it were much smaller than the bubble seen from Hawaii. Also according to "Weather Underground", Karachi was "mostly cloudy" continuously from 18:25 July 19 to 16:30 July 20 Pakistan Standard Time.

The next bubble, according to my theory, will be 13:31:16 UT September 12, 2011 (00:31:16 Sept. 13, Okinawa Standard Time). Since the observed time in June, according to my best estimate, was 35sec earlier than given by my theory, my best estimate for the bubble start time this month, is 13:30:41 UT. The starting location will be 131.960 E long., 24.095 N lat. This is SE of Okinawa over the Pacific Ocean, about as far away as it was from Mauna Kea.

Let's all encourage Japanese astronomers to look for the next bubble! I did email the head of the Subaru observatory but got no reply; my emails to the two junior Subaru astronomers who might have been responsible for the messageboard (elsewhere) post cited in the online newspaper, "Hawaii 24/7", both bounced. If others would email the head of the Subaru Telescope observatory, there might be a response because we would not be a "lone nut"!

Perfect agreement between bubble start and geometric alignment?

Previously I found that Luna's south limb sat on the tangent plane to Earth's North Pole, at 13:39:13 UT June 22, 2011. Combining my two methods of estimating from my seven bubble diameter measurements, the bubble start time, I found 13:38:38.5 +/- sqrt(5.5^2/2+7.0^2/2+(17/2)^2)=10.6sec. Agreement becomes perfect if I assume that the frequency response of the system is such that the 18.6 yr nutation of Earth's axis is averaged out.

On June 22, Luna's geocentric ecliptic latitude was maximum, when Luna's geocentric RA was 23h27m. Luna's orbit was tilted toward 12h, so the 18.6 yr nutation displacement, would be that due to the slower precession that happened when Luna's orbit was tilted toward 18h, a quarter cycle earlier. That is, Earth's N Pole would be tilted 9" toward 12h, due to the 18.6 yr nutation. There are other nutation terms, but the next largest has amplitude only 0.6" parallel to the ecliptic, and furthermore is near zero when Earth is near its apsides. So the North Pole was tilted, due to nutation, an extra 9" away from Luna (Luna's RA was 23h17m observed from the North Pole at 13:39). Luna's elevation was increasing 11.85"/minute according to the JPL ephemeris, so if the 9" nutation disappeared from consideration, Luna would have risen 46sec earlier, i.e. 13:38:27, only 1.1 sigma less than my combined estimate of the bubble start time, and only 1sec less than my second estimate, 13:38:28 +/- 7, which averaged every possible quadratic extrapolation.

Elephantine Island observatory: under the bubble, on the Tropic, and artificial

One of Egypt's main astronomical observatories, in the New Kingdom and probably earlier, was on Elephantine Island. The German Archaeological Inst. ( www.dainst.org ) gives the latitude of the island as 24deg05'20", and Wikipedia says it is 1200m, i.e. 39", long from north to south.

"There are records of a temple to Khnum on the island as early as the third dynasty [the Giza pyramids date to the 4th dyn. - JK]. Most of the southern tip of the island is taken up by the ruins of a later temple to him." - Wikipedia article, "Elephantine"

Arcsin(1/sqrt(6)) = 24deg05'41"

Today this is approximately the latitude of the northern tip of Elephantine I. However, Petrie's measurements revealed that the Giza pyramids are several arcminutes askew from true north, which Petrie interpreted as a small pole shift, arguing quantitatively that such a pole shift could occur from major alterations in ocean currents. If the pole changed a few arcminutes in direction from Giza, likely it also moved a few arcminutes nearer or farther from Giza. According to Wikipedia, the pyramids of Khufu and Menkaure are centered 75" and 99" S of exactly 30degN, resp. If Egyptian latitudes have decreased by 99", then an Old Kingdom observatory under the bubble track, now would be latitude 24deg04'02", slightly south of Elephantine I; the temple of Khnum at the south end of the island, would have been as close as possible on dry land.

In many posts above, I've cataloged evidence of a 6339.5 yr solar system cycle ending about 2013.0AD. The 1990 Astronomical Almanac gives a 3rd degree polynomial for Earth's obliquity as a function of time. Fitting a unique sinusoid + constant term to this polynomial, so that the Maclaurin series terms through the third are the same, I find period 41,203 yr (reassuringly, the Milankovitch period usually is given as 41,000 yr) and the obliquity for 2013.0AD - 6339.5 yr, 24deg08'23". (The value given by the published Almanac 3rd degree polynomial is 24deg 08'01".) Again assuming a 99" decrease in latitude in Egypt today vs. Old Kingdom and earlier times, the 24deg08'23" line would be 24deg06'44" now in Egypt. So, under these assumptions, the latitude of the geometric center of Elephantine I., 24deg05'20", is 84" S of the line that was the Tropic of Cancer in the summer of 4328BC, and 78" N of the line that presumably was at geographic latitude arcsin(1/sqrt(6)) in Old Kingdom and earlier times. It is as if the founders of Elephantine I. knew both values, split the difference and built an artificial island there.

Alternatively, the 6th degree polynomial given by Bretagnon et al, A&A 400:785-790, Table 2, p. 787 (2003), free online from the SAO/NASA Astrophysics Data System (also quoted correctly with time unit converted to centuries, on the astrological website www.tenspheres.com ) gives for the summer of 4328 BC, obliquity 24deg07'32.45"; subtracting 99" gives 24deg05'53", which is the geographic latitude only 33" N of the center of Elephantine I. A linear extrapolation of the presumed (from Menkaure's pyramid) 99" pole shift vs. ~ 2500BC, to 4328 BC, gives 139"; using this correction instead, gives 24deg05'13", about the middle of the southern half of Elephantine I. Respectively, Khufu's pyramid (75" shift) gives 105" from 4328 BC, hence 24deg05'47", just beyond the north end of Elephantine I. So, the most modern and authoritative formula available, for Earth's obliquity, indicates that at 4328 BC, the Tropic of Cancer overlay Elephantine I., if the present latitude of any of the Giza pyramids is an accurate indicator of the rate of pole shift.

The seven parameters of Bretagnon's obliquity formula, allow fitting with a unique (and rapidly convergent) three-frequency Fourier sum + constant term, if I borrow the 41,203 yr period implied by the 1990 Astronomical Almanac polynomial. This result, again for 6339.5 Julian yr before 2013.0 AD, is 24deg07'33.54", only 1.09" greater than given by Bretagnon's polynomial. Also, according to Bretagnon's Table 3, none of his parameters differ enough from an earlier authority published in 1977, to affect my conclusion much.

The information website www.digitalegypt.ucl.ac.uk , says

"The Geology of Egypt

The three layers

A layer of limestone covers most of the surface of modern Egypt.

Beneath this lies a bed of sandstone, and this earlier sandstone is the surface rock in Nubia and southern Upper Egypt, as far north as the area between Edfu and Luxor.

The oldest ground of modern Egypt comprises outcrops of metamorphic and igneous rocks. ..."

What is the chance, that the most impressive granite outcrop in the Nile, would be at such a special latitude? Megalithic construction at Baalbek, Gobekli Tepi and elsewhere, suggests that engineers of the 5th millenium BC might have been able to roll large granite boulders downstream to construct Elephantine I.

Paleomagnetism in Egypt: Zero at ~ 4268 BC ?

References:
H. Odah, J. Appl. Geophysics 3:205-212, 2004
Odah, Earth Planets Space 51:1325-1329, 1999
Odah et al, J Geomagnetism Geoelectricity 47:41-58, 1995
Knudsen et al, Earth and Planetary Sci Letters 272:319-329, 2008
British Geological Survey webpage www.geomag.bgs.ac.uk

Odah's 2004 paper studies the geomagnetic field strength as recorded for posterity in Egyptian ceramics that are well-dated historically (not by radio-isotope). The dates almost always were known within a very few decades. The field strengths all could be determined within a few percent. Twenty of the determinations were on ceramics from Elephantine Island. Nine more were from a few other major Egyptian archaeological sites.

I will consider only the Elephantine ceramics. Little is to be gained by including such a small number of others: the others covered a smaller range of dates (mostly from the New Kingdom), all but one of them were very close to Elephantine values at similar dates, and a small correction had to be made for the presumed variation of geomagnetism with location (latitude).

Odah's 1999 paper contains dates and strengths from another 13 ceramics from various sites in Egypt. The 1999 paper also alludes to dates and strengths published in the 1995 paper; one of these was 4000BC and one 1990AD. Though the 1999 and 1995 strengths almost all fall near the smooth curve through the data of the 2004 paper, I won't include them in my curve fitting, due to the less refined earlier magnetometry instrumentation and technique, their sometimes inexact dates (e.g. "4000BC") and their geography, scattered over Egypt.

By a computerized three-parameter search, I found the sinusoid without constant term that best gives the geomagnetic field strength as a function of time. (Though this is for Elephantine Island, the other sites in Egypt were similar.) This best fitting sinusoid is zero at 4268BC, rises positively and then falls to zero again 8033 yrs later. The field strengths in 1990AD and c. 2800BC are about half the maximum which occurs c. 500BC.

Knudsen et al compiled all Holocene paleomagnetic absolute intensity data extant in peer-reviewed journals; they found good agreement with Odah for the time interval Odah considers, but without a decrease all the way to zero at earlier times as in my extrapolation above. Because Knudsen used absolute intensity data, and the absolute intensity cannot be negative, error will prevent the average from ever being zero, and the error becomes much more considerable, at times earlier than the times considered by Odah.

In my sinusoidal fit, the rate of change at 1950AD is -3.0%/century. Between 1900AD and 2000AD worldwide, the rate of change of Earth's dipole strength, according to the British Geological Survey graph on their webpage, has been a fairly steady -6.7%/century. Also, the value 38 "microT" found by Odah for 1990AD, is slightly less than the value 44.8 microT given by my sinusoidal fit. So, zero geomagnetic field might come in the much nearer future than 3764AD (the prediction of my sinusoid): the discrepancy in ordinate is only (44.8-38)/(70-44. of the approximately quadratic sinusoidal curve, but the discrepancy in derivative is (6.7-3.0)/3.0. The ratio of the two fractions, 4.57 = approx. 9/2, could be due to an additional 9th degree term, which would cause the zero to occur in the 25th century AD.

"The Windsor Hum"

In recent months there have been several local mainstream media reports of the "Windsor Hum" in Windsor, Ontario, across the strait from Detroit. Here's the latest:

"Windsor Rumble Intensifies: 'It was the loudest it's ever been'

By Kristie Pearce, The Windsor Star September 13, 2011

It seemed as if the mysterious rumblings had subsided,...but Sunday night through early Monday the low pitch humming came back with a vengeance.
...inexplicable rumblings she and thousands of Windsorites have reported hearing in the past eight months.
...the noise woke her at home about 5:30 a.m. Monday in the 3000 block of Sandwich Street.
...We went outside and it was almost like it was vibrating your eardrums.
...the noise comes and goes...
The Ministry of the Environment has ruled out industrial sources as the culprit, but Councillor Al Maghnieh wants to know why.
They're not giving us answers, he said.
...[Maghnieh] said he's received thousands of calls, mostly concentrated in the Windsor West area by Brighton Beach.
The ministry ruled out the Windsor Salt mine because the company only blasts once a day in the mid-afternoon.
Most residents find the rumblings more prominent between 1-3 a.m.
Zug Island, lake freighters and plane traffic from Detroit Metro Airport are also not suspected.
The ministry could not be reached Monday for comment.
Multiple Facebook groups have started to log times and locations of the mysterious humming, including The Windsor/Essex County Hum which has 523 members.
The page was flooded with posts describing Monday's occurence as the loudest yet.
...in a basement unit on Curry and Adanac avenues. I want to know what's causing my walls to vibrate.
...hearing...since February.
[Maghnieh]...is also holding a meeting open to residents and officials Sept. 29 at 6:30 p.m. The location has not yet been announced.

Copyright (c) The Windsor Star"


Joe Keller's collection of theories (some original, some not):

1. Pole shift. Windsor, Ontario will be the new North Pole. Most of the English will find themselves at about 35N, but Joe Keller will be living in an igloo at latitude 83N and seeing only circumpolar constellations. Chicago will be under two miles of ice again. (Keller's location in Iowa was only a mile or two inside the edge of the most recent ice sheet, the "Algona" stage of the "Wisconsinan".)

2. Bunker building. The shadowy group known in U.S. populist politics as "the elite", is hunkering down for the Apocalypse. The shore of the Great Lakes might seem a bad place to dig tunnels (high water table) but maybe they need the water for shielding from neutron radiation or something. Giant abandoned factories in Detroit could conceal the tunnel entrances; the bed of Lake Huron or Lake Erie is a good dumping place for the rock tunneled out. The elite likes to do things transnationally, so would dig into Canada from the U.S. to avoid local laws.

3. Underground weapons testing.

4. Impending geological event: volcano or earthquake. According to Wikipedia, many locations on Earth recently have reported similar hums, mainly in recent years, and one such location, the big island of Hawaii, has had a hum correlated with volcanic activity. Citing Dr Tom Moir of the Massey University in Auckland, New Zealand, Wikipedia says the Auckland Hum's power spectrum peaks at 56Hz. If a tetrahedron is inscribed in a sphere of radius equal to Earth's equatorial semidiameter, the time for light to travel one leg of the tetrahedron, is 1/28.8 sec; this frequency, doubled, is 57.6Hz.

5. Extraterrestial/"Ultraterrestrial" (i.e. "alien") activity.