I hope the enclosed material
is of interest to you.
Beelzebub's Buried Dog
The Mathematical Problem of the "Precession-Time
Paradox"
There is no doubt anymore - outside the
solar system, Einstein's complicated Theory of a non-linear
gravitation does prevail considerably over Newton's linear. Can the
so-called THEORY OF
EVERYTHING be unraveled at
last?
Experts at the
International Astronomical Union, the NASA's Jet Propulsion
Laboratory, the US Naval Observatory, the Max-Planck-Institute for
Astrophysics, the Royal Astronomical Society, the National Research
Council of Canada and other renowned institutes, as well as famous
physicists like Dr. Stephen Hawking are not able to solve the
problem, since they do not comprehend the fundamental physical and
mathematical principles of the civil-calendar.
"The last time
we had a real expert on these matters was with Fr. Clavius,* about
400 years ago."
Christopher J.
Corbally, Vatican Observatory Research Group
*(Christophorus Clavius - the distinguished mathematician,
who participated in the calendar reform of 1582)
In scientific
textbooks it is generally claimed, that our Earth is like a
gyroscope. Viewed as a physical exception, Earth is suppose to
precess opposite to its direction of rotation. The period of its
complete precession cycle is said to take about 25 800 years. During
this time period, it is claimed Earth supposedly goes through one
retrograding rotation relative to the inertial system of the fixed
stars. An additional time interval of one year of about 365 days must
occur simultaneously. But since this time interval cannot be
substantiated by actual time measurement, hence the theory of the
Earth's precession does not have a proven scientific
foundation.
A simple mathematical example shall explain the
physical aspect of this precessional motion:
A_______B____________________________________________________C
A gyroscope at point B on the
line A-C makes n
rotations with respect to the central point A in one
complete period of revolution around A.
Logically, the gyroscope must make n + 1 rotations with respect to the distant point
C.
Assuming the gyroscope makes 365.24219878 rotations per
revolution around A, and
within a certain time period it makes 25800 revolutions, the total
amount of rotations with respect to A must
equal:
n × R =
365.24219878 × 25 800 = 9 423 248.73
Assuming
further that the gyroscope precesses and describes a complete
retrograding precession cycle in 25800 periods of revolution, how
many rotations does the make in that time period with respect to
A?
a) 365.24219878
rotations × 25 800 minus one rotation, equals 9 423 247.73
rotations
b) 365.24219878 rotations × 25 800 minus one revolution,
equals 9 422 883.49 rotations
"Why one revolution?"
In order to
understand this mathematical problem, we must analyze the
time-discrepancy caused by this precession:
Please,
refer again to the above diagram. Imagine the Earth standing still at
point "B" in its orbital plane on the line "A-C" between the sun "A"
and the fixed star "C". We will assume that the Earth has already
completed its 25 800 revolutions of 365.24219878 rotations each,
without precession.
Now we will make up mathematically for the one
retrograding or precession motion of the Earth at point "B" in its
orbital plane - first with a vertical and then with a 23‡°
inclined Earth's axis:
1) In the
vertical position of the axis, the sun is always directly over the
equator during the one retrograding motion of the Earth. This results
in a change from a day to a night.
This time
interval corresponds to one rotation relative to the sun or the stars
in a period of 25 800 years, which is equivalent to about 3.34 s per
year* or about 9.12 ms per day.
*equivalent to
the regression of the fixed stars by yearly 50.26" on
average
2) In the
23‡° inclined position of the axis, the result is completely
different. Not only does the change from a day to a night occur, but
since the sun is now directly over the ecliptic of the Earth, also
four seasons have to appear successively during this same
retrograding motion.
That time
interval corresponds to one revolution of the Earth around the sun,
implying more than 365 solar days in a period of 25 800 years, which
is equivalent to about 1223 s per year or about 3.34 s per
day!
Is this
time-discrepancy a physical fact or an illusion?
First of all we
must understand what this enormous time-discrepancy really means, as
the additional time interval of one year is only seemingly 'created'.
How else can one explain a retrograding rotation of the Earth with an
inclined axis, which has four seasons appear at the same time?
Ultimately, this phenomenon would imply that the vernal equinox has
to retrograde around the sun by not only 50.26" per year, but per
day!
At some point in history the theory was put forward -
maybe out of ignorance or even intentionally – that a
precession of the Earth is the cause for the steady regression of the
fixed stars, a phenomenon already observed since ancient times. It
was realized, that due to such a precession a gradual shift of the
seasons has to occur. In order to mathematically justify this theory,
a sidereal year was 'invented'. Its time interval is suppose to be
about 20 minutes longer than the precisely defined tropical year of
31 556 925.9747 seconds - the fundamental physical time interval for
the definition of the SI second, an internationally accepted Standard
of Physical Measurement.
Paradoxically,
this so-called sidereal year of 365.256361 mean solar days, said to
be the truest measure for Earth's period of revolution around the sun
with respect to the fixed stars, has no physical relevance or
practical application in astronomy and specifically in
astrometry!
At the
beginning of the 1950's, when accurate clocks and methods of sidereal
time measurement were available to precisely determine the tropical
year, it became evident that a precession of the Earth cannot exist,
as it was believed. Instead of accepting this truth, it was decided -
for whatever reason - to obscure this knowledge by introducing the
new and complicated reference-system of the vernal
equinox*.
* ".... a base
position from which the mean time can be calculated was established.
This base position is the vernal equinox, an imaginary point in the
sky that is, nevertheless, calculated with great accuracy by
astronomers. Practically, the location of the vernal equinox is found
by reference to the position of the fixed stars." Funk &
Wagnall’s New Encyclopedia
The natural and
dependable system of the 'sidereal-time-clock' became obsolete. New
star catalogues and elaborates tables including formulas to
pre-calculate the positions of stars were now available, which made
the actual measurement of sidereal time unnecessary. It could not
have been made any easier, especially for hobby-astronomers. Since
there were no skeptics there was no suspicion that something was not
right about the theory of the precession of the Earth.
If precession is
considered to be a physical fact, then one should also be able to
measure and substantiate the additional physical time interval of
more than 1223 seconds per year.
Any time-delay in a
planet's rotation period with respect to the inertial system of the
fixed stars due to a precessional motion of the planet’s
axis, can never have any influence on the planet’s actual
revolution period around its sun.
Completely
contradictory to this statement is therefore the assertion about the
time period of the so-called true sidereal year, which only appears
to exist in the supposition that a precession of the Earth exists.
But this would mean that the time interval for each consecutive
revolution period of the Earth around the sun with respect to the
position of the fixed stars should be about 20 minutes longer than
the tropical year (the absolute physical measurement standard for
time). This is in reality
not the case.
"Or does
one seriously believe, that because of precession the Earth can
'loose' an entire year after 25 800 revolutions around the sun, only
to have 25 799 tropical years completed?"
In order to visualize this absurdity, the sun and the
stars will have to rise and set one additional time in about every 71
years throughout this whole precession cycle. And this extraordinary
cosmic phenomenon has to occur without being noticed, despite precise
methods of time-measurement. But then again, how is it possible to
measure something that does not exist?
"The following
measurements are proof, and they are factual, that the average figure
for the regression of the fixed stars is about 50.26" annually, and
it has nothing to do with a precession of the Earth, but is due to
the effect caused by our entire solar system orbiting a 'central
sun'." Karl-Heinz Homann
Practical
Observation and Measurement of Sidereal Time with respect to
Sirius:
My meridian tansitition time measurement with respect to
Sirius (using the UTC atomic-time radio signal
from WWV Fort Collins/Colorado), which I conducted over a period of 5
consecutive years, resulted in the following mean sidereal rotation
time for the Earth.
Obviously, as indicated by the adjective mean all
variations in time caused by periodic or any other fluctuations of
the Earth's axis, as well as the assumed precession of the axis, must
be included in the 5-year observation period. Technically speaking
this is still the easiest and best available method to measure and
determine a mean sidereal day.
First meridian
transition time of Sirius on 20.04.1994 at 20:16:48.5
hours
Last meridian transition time of Sirius on 19.04.1999 at
20:21:34.5 hours
The total time
span between those two measurements is exactly 157 680 286
seconds.
(5 calendar years
including one leap day is 5 × 365 days of 86400 s each, plus the time
difference of 286 s on the last day)
In this same time
interval exactly 5 × 366 sidereal days (meridian transitions) were
completed. As a result, the mean sidereal day with respect to
Sirius is:
157 680 286 s ÷ 1830 = 86164.09071 seconds.
Note: The mean
sidereal day is officially published with 86164.091 s mean solar
time, while the mathematically calculated mean sidereal day is
exactly 86164.0905382 seconds. Therefore, my precise measurement of
86164.09071 s with respect to Sirius is within the acceptable range
of accuracy.
A maximum error in observation of ± 0.5 seconds
between the two (first and last) meridian transition of
Sirius during the period of 5 years would have the
following results:
minimum: 157 680 285.5 s ÷ 1830 meridian transitions
= 86164.09044 s
maximum: 157 680 286.5 s ÷ 1830 meridian transitions
= 86164.09098 s
Due to the apparent precession, the measurable mean
sidereal day should be about 86164.09966 seconds, since logically the
actual mean rotation time of the Earth by 86164.0905382 seconds can
only be measured with a delay in time relative to the inertial
position of the fixed stars. In other words, if precession were
indeed to occur, absolutely no fixed star can ever have a mean
meridian transition time of 86164.0905382 seconds.
This physical fact would imply that my measurement with
respect to Sirius
contains an error of
observation by about 16.7 seconds (5 × 3.34 s per year), not to
mention the +1223 s with each sidereal year!
Note: Many
'experts' have suggested to me to "correct" or "compensate" my
observation for precession by either adding or
even deleting
about 9.12 ms daily
!
It can be
concluded, that the annual regression of the fixed stars by 50.26" on
average allows for only two explanations:
- a precession
of the Earth's axis
- a revolution of our entire solar system around a central
sun
Since it was
proven that a precession of the Earth cannot exist as claimed,
Earth's mean sidereal rotation time of 86164.0905382 s can only
coincide with one true "axis-star", which is orbited by our solar
system.
"And because our
Earth has this decisive mean sidereal rotation time with respect to
Sirius, the Dog Star, there can no longer be any doubt about the
central position of Sirius relative to our solar system. The
mathematical proof, the observations and measurements, as well as a
complete understanding of the fundamental physical and mathematical
principles of the civil-calendar will bring the theory of gravitation
- at least concerning the gravitation outside of our solar system -
into a completely new light. Has Einstein's theory of a non-linear
gravitation been greatly underestimated, and is this not the basis to
finally unravel the so-called 'theory of
everything'?"
Time Deviation and Adjustment of the Civil Calendar to the
Tropical and Sidereal Year
The assumption that Earth's polar axis precesses opposite
to its direction of rotation, whereby the Earth, after completing a
retrograding precessional cycle around the sun, looses one year of
about 365 mean solar days with respect to the apparently true
sidereal year of 365.256361 mean solar days, although paradoxically
one additional tropical year must occur due to precession, does also
completely contradict the precise mathematical time-keeping of our
civil calendar.
It is an undisputed fact, that our civil calendar is
mathematically synchronized to the actual revolution period of 31 556
925.9747 seconds. This physical time interval for the Earth to
complete its orbit around the sun with respect to the inertial system
defined by the position of the fixed stars is still the absolute
criterion for time.
Please, refer
once more to the previous simple diagram.
The absolute
center of the Earth "B" has completed one full 360° revolution
around the sun "A" after exactly 31 556 925.9747 seconds or one
tropical year.
Assuming for the moment, that the Earth's rotational axis
does not precess, an observer on the Earth's surface, for example,
would measure with the aid of a meridian-transition instrument
exactly 365.24219878 rotations of the Earth with respect to the sun
"A" and exactly 366.24219878 rotations with respect to the inertial
point of reference or fixed star "C", since:
365.24219878 ×
86400 s = 31 556 925.9747 s = 366.24219878 × 86164.0905382 s
.
According to the generally accepted claim that it takes
the Earth about 25 800 years to make one retrograding precession
cycle, the following celestial-mechanical process would have to occur
after a period of 6450 years:
The fixed star
"C" will appear to our observer approximately 21 600 seconds later in
his meridian-transition instrument, since he will notice a time-delay
of about 9.12 milliseconds per day* or about 3.34 seconds per year
with respect to the fixed star "C". Of course, the same is true with
respect to the sun "A".
*(Note: 86400 s ÷ 25800 revolutions equals about 3.34
s per revolution or 9.12 ms per rotation)
Interestingly, our observer will also notice another
phenomenon taking place during this quarter period of precession,
because the 23‡° inclined Earth's axis has changed its direction
in space with respect to the sun or the fixed stars. In other words,
the sun "moved up" by 23‡° along the ecliptic during those 6450
years, while for example the fixed star "C" appears 23‡° lower
in our observer's meridian instrument.
If we were to choose a specific point in time when the
Earth "B" crosses the imaginary line "A-C", say January 1 at 00:00 h,
then after 6450 revolutions of the Earth "B" exactly 6450 × 31 556
925.9747 s have elapsed with respect to the sun "A". However, due to
the assumed precessional motion of the Earth's axis, our observer
still has to consider the time delay of 21 600 s.
Since the Gregorian Calendar* has a defined length of
365.2425 days, it is only about 26.03 seconds longer (365.2425 ×
86400 s = 31 556 952 s) than the tropical year of 31 556 925.9747
seconds. Therefore, after 6450 revolutions of the Earth a time
difference of 167 893.5 s or 46.64 hours must occur and our calendar
must then indicate December 30, instead of January 1. Due to the
assumed precession the 21 600 s have to be deducted now from the 167
893.5 seconds; 46.64 h minus 6 h = 40.64 h
Consequently, the total time difference that our calendar
needs to be corrected for is almost 2 days.
* See my attached diagram: Time deviation and adjustment of the civil calendar
to the tropical- and sidereal year
(IMPORTANT: USE DIN A4 SIZE PAPER FOR A
PRINT-OUT OF THIS MS-WORDDOCUMENT)
As indicated earlier, the change in direction of the
23‡° inclined Earth's axis in space due to precession does
create a unique problem:
It was said,
that after exactly 6450 revolutions of the Earth, while crossing the
imaginary line "A-C" at point "B" on January 1 at 00:00 h, our civil
calendar will indicate December 30. However, in those 6450 years the
position of the sun relative to the Earth's equator has also changed
at point "B", and instead of winter on the Northern Hemisphere it is
spring. Based on further calculations, this paradoxical shift in time
appears to create an additional difference in time of 91.31 days (º
year) in 6450 years or about 20 minutes per year:
91.31 days × 86400 s/day ÷ 6450 years = about 1223
s/year
Here we have
those mysterious 20 minutes of time-manipulation, resulting from each
revolution of the Earth around the sun; i.e. a time difference of
about 1223 s between the tropical-sidereal year of 365.24219878 mean
solar days and the apparently true sidereal year of 365.256361 mean
solar days
This yearly time difference can be
calculated mathematically, but based on observation and according to
physical laws it cannot exist in reality.
In
closing, I pose two uneasy questions, which thus far the experts are
unable to answer decisively:
1. Is the exactly defined time period of the
tropical year of 31,556,925.9747s (which is mathematically based on a very precise mean
sidereal day to which even the atomic time second has to be
synchronized) derived from the
about 9.12ms longer sidereal day, although such a sidereal day is not
used in practice for any time-reference or astronomical
calculations?
2. If a true
sidereal reference point for the tropical year is a pre-calculated
imaginary point or direction in space, then what other reference
point or fixed star is used, in order to determine a sidereal year of
365.256361 Earth rotations and consequently a sidereal day, that must
have an additional time-difference of more than 3.3 seconds per daily
rotation of the Earth, since the yearly time-difference between a
sidereal year and a tropical year is supposed to be 1,223.6 seconds
more, with each consecutive 360° revolution of the
Earth?
After carefully
reviewing my arguments regarding "The Mathematical Problem of the
Precession-Time Paradox", please mark the appropriate box(es) below
and send it to the following address:
Karl-Heinz Homann
RR1, Site 19, C2 Peers, Alberta - Canada T0E 1W0
e-mail: UHOMANN @ telusplanet. net
[ ] Your line of
argumentation and your mathematical proof, regarding the
non-existence of a sidereal year of 365.256361 mean solar days and
consequently the precession of the Earth, is wrong, despite the claim
that a precession cycle must cause an additional year with respect to
the sun. "What cannot be, must not be", and I have no time or
interest to deal with this matter.
[ ] I am able to specify and prove to you the following
mistakes you have made in your line of argumentation, regarding the
non-existence of a sidereal year of 365.256361 mean solar days and
consequently the precession of the Earth - see my attached
letter.
[ ] I am willing to have knowledgeable experts review my
mathematical arguments, as well as my experiments or observations to
disprove your arguments regarding your theory of the non-existence of
a sidereal year of 365.256361 mean solar days and the non-existing
precession of the Earth. I understand that you offer a research grant
of $ 10,000. -
US for officially proving
your arguments wrong. I would like to receive more information
concerning this offer.
[ ] Your arguments are mathematically correct and seem
logical. However, I am not sure and would like to have first of all
the following questions answered:
I would also
like to receive more information on this subject:
[ ] Please,
send me additional material, as well as copies of your correspondence
with the National Research Council of Canada, NASA's Jet Propulsion
Laboratory in Pasadena, CA and other renowned institutes, individuals
and responsible government officials.
[ ] I would like to have more information regarding your
time-measurement with respect to Sirius.
[ ] This matter
is very interesting. Your arguments are convincing and I would like
to help you in the following manner:
Name:____________________________________________________________
Address: _________________________________________________________
_________________________________________________________
Date:___________________ Signature:
______________________________
Thank you for your co-operation
Appendix 1:
Description of the Time-Functions
Notice:
For reason of simplicity the time-functions begin 1600 AD instead of
1582 AD, the year of the calendar reform.
x1 = Tropical year of 365.24219878 mean solar days of
86,400s
x1 = Sidereal year of 366.24219878 mean sidereal days of
86,164.09054s
x1a = Sirius (Sothis) year of 366.24219878 mean
Sirius-meridian-transitions of 86,164.09071s*
*this value is
based on own measurements
x2 = x1 plus the
annual time-deviation of 50".26 (regression of the
fixed-stars)
x3 = Gregorian Calendar of 365.2425 days since the
calendar-reform of 1582 AD (because 0.2425 = 97/400 see also
x4)
Note:
After 3,319.88 years, x3
reaches the y-value of '24hrs' and has to be adjusted to x1 by means
of one leap-day
x4 = Civil Calendar
of 365.2500 mean solar days including a 400year-leap-cycle (97 leap
days in 400 years - i.e. at full centuries that cannot be evenly
divided by 400 the leap day is omitted, e.g. 1700, 1800 and 1900
AD)
Note:
The 400year-cycle of
time-function x4 results into the time-function x3
x4a = Julian
Calendar of 365.2500 mean solar days (prior to the calendar reform of
1582 AD)
x5 = Apparently, the true sidereal year (fixed-star to
fixed-star) of 365.256361 mean solar days
Note:
Actually, x5 deviates from the
true time-function x1 noticeable faster than x4a - the ineffectual
time-measure of the Julian year was in fact the cause for the
calendar reform of 1582 AD
Karl-Heinz
Homann Peers, Canada
Appendix 2:
*The Relativity of
the Concept of Time*
"First of all,
you must know that in calculating Time the ...beings of that planet
(Earth) take the 'year' as the basic unit ...and they define the
duration of their 'year' as the time it takes for their planet to
make a certain movement in relation to another cosmic concentration -
that is to say, the period during which their planet, in the process
of 'falling' and 'catching up', describes ...a ... revolution around
its sun." "But since ... you do not yet have any idea of the
exceptional peculiarities of Time, you must first be told that
genuine Objective Science defines this cosmic phenomenon thus:Time in
itself does not exist, there is only the totality of the results
issuing from all the cosmic phenomena present in a given place. Time
in itself no being can understand by Reason or perceive by any outer
or inner being-function. It is possible to evaluate Time only by
comparing different cosmic phenomena occurring under the same
conditions and in the same place where Time is being considered. It
should be noted that in the Great Universe all phenomena, without
exception, wherever they arise and are manifest, are simply
successive, lawful 'fractions' of some whole phenomenon which has its
prime arising on the '... Sun Absolute'.In consequence, all cosmic
phenomena, wherever they proceed, have an 'objective' significance.
Time alone has no objective significance, since it is not the result
of the fractionating of any definite cosmic phenomenon. Issuing
>from nothing, but always blending with everything while remaining
self-sufficiently independent, Time alone in the whole of the
Universe can be named and extolled as the
'Ideally-Unique-Subjective-Phenomenon'. Thus, ...Time ...is unique in
having no source on which its origin depends, and it alone, like
'divine Love' always flows independently and blends proportionately
with all the phenomena present in all the arisings in any given place
in our Great Universe." "...since Time has no source of its arising,
and its presence cannot be precisely established, as can be done for
all other phenomena in every cosmic sphere, Objective Science has,
for its examination of Time, ...(a) standard unit.... Objective
Science has established ....that all ...beings ...sense the
....action, by which they define Time, forty-nine times more slowly
than it is sensed ....on the ... Sun Absolute. Consequently, the
process of the flow of Time is forty-nine times quicker for the
beings on ....planet Earth ....than ...on the Sun
Absolute."
G.I. Gurdjieff
(1872-1949) , "All and Everything - Beelzebub's Tales To His
Grandson"
"If Gurdjieff had intended his meaning to be readily
accessible to every reader, he would have written the book
differently. He himself used to listen to chapters read aloud, and if
he found that key passages were taken too easily - and therefore
almost inevitably too superficially - he would rewrite them in order,
as he put it, to "bury the dog deeper." When people corrected him and
said that he surely meant "bury the bone deeper," he would turn on
them and say it is not the 'bones' but the 'dog' that you have to
find. The dog is Sirius, the dog star, which stands for the spirit of
wisdom in the Zoroastrian tradition."
J.G. Bennett
(1897-1974) , "Gurdjieff - Making a New World"
IMPORTANT: The period of revolution period for
Sirius B around Sirius A
is about 49 years.
Sirius is the central sun
for our entire solar system. Uwe Homann
"The
starting point of creation is the star which revolves round Sirius
and is actually named the "Digitaria star"; it is regarded by the Dogon as the smallest and
heaviest of all the stars; it contains the germs of all things. Its
movement on its own axis and around Sirius upholds all creation in
space. We shall see that
its orbit determines the calendar."
Marcel Griaule and Germain Dieterlen in African Worlds
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