DECELERATION CONTINUES
Clifford E Carnicom
Nov 08 2003
Edited Nov 14 2003
A detailed statistical analysis of time over a period of four months
continues to support the hypothesis of an earth in a state of
deceleration. The magnitude of the deceleration, if confirmed, is
sufficient to anticipate unusual geophysical activity in the
foreseeable future.
The magnitude of the deceleration is currently best estimated at
approximately 0.3 milliseconds per day. Any deceleration component of
rotation of the earth is to be regarded with the greatest of interest,
as an apparent small acceleration (deceleration) will result in
significant velocity differentials and accumulated time differentials
over a relatively short period of time if sustained. A deceleration
component of 0.3 milliseconds per day will result in a velocity change
of approximately 0.1 seconds per day at the end of a one year period.
This same deceleration component would lead to an accumulated
difference of approximately 20 seconds of time after a one year
period. These are phenomenal magnitudes relative to any historical
basis that is available.
Small changes in time will translate to large changes in the kinetic
energy of the earth. One second of time change per year corresponds
roughly to the energy contained within all of the fossil fuels of the
earth. Data under collection and analysis indicates that a significant
multiple of the historical level of approximately one second per year
may now be occurring. This indicates the prospect of significant
energy and subsequent geophysical changes occurring in future times.
Further data that is accumulated with additional timepieces over a
greater interval of time will continue to clarify the findings that
are under examination. The independent time system now consists of 14
quartz clocks with measurements on a regular basis. The deceleration
bias that is under detection remains thus far regardless of the subset
of timepieces examined or of the interval over which a constant rate
of rotation is assumed.
Readers may also wish to be aware of the anomalous time measurements
over this same period as recorded in the earlier articles, Time, Time
To Start Watching Time ,Time, Energy and Earth Changes, The Waistline
of Rotation, and Time and Rotation Changes Sustained.
Additional notes related to the computation of time differences are
presented below.
--------------------------------------------------------------------------------
The following table presents an example spreadsheet statistical
analysis of an independent timekeeping system using 8-14 quartz clocks
over a four month period. The column descriptions and weighting
functions will be described in more detail below.
n
rirms^2
racc^2
di
do
ai
bi
delta d
Weights
Unweighted
Errors
%
SET 1
4
0.92
0.87
122.4
74.5
0.000286
-0.022
365
5.0E+09
27.6
-9.67
0.79
-1.6
18.8
9.4E+10
75.97
SET 6
4
0.77
0.54
64.9
61.9
0.000258
-0.016
365
3.7E+06
23.5
-6.83
0.49
-1.0
17.1
6.4E+07
0.06
SET 3
4
0.98
0.96
122.4
105.4
0.000512
-0.054
365
1.5E+09
56.7
-25.40
2.84
-5.7
34.1
5.1E+10
22.57
SET 4
4
0.82
0.7
64.9
48.8
0.000300
-0.014
365
9.2E+07
25.7
-5.79
0.36
-0.7
20.3
1.9E+09
1.40
SET 5
4
0.81
0.47
64.9
55.3
0.000232
-0.012
365
2.8E+07
20.5
-5.04
0.36
-0.7
15.8
4.4E+08
1.84
t11
1
0.12
0.21
59.8
50.2
0.000203
-0.008
365
3.5E+05
17.5
-3.32
0.26
-0.4
14.3
5.0E+06
0.02
Wgt.
22.2
Total
Seconds
Error
6
4.2E+01
0.833
1.0E+00
var 7.1
sigma 2.7
E90 4.4
Lower 17.8
Upper 26.6
Additional notes on columns and weighting factors:
Column 1 :
The set number.
Column 2 : n
The number of clocks in the set.
Column 3 : rirms2
The root mean square (RMS) of the r2 correlation coefficients of the
clocks within a set. The linear regressions within the set model the
drift rate of the individual clocks. No variation in the rate of the
rotation of the earth is assumed over the interval of the regression.
The model for each clock is of the form: Drift rate per day in seconds
(DRo) = a1d + b1 where d is the number of days since the point of
synchronization with UTC for each clock. The coefficients of the
regression are a1 and b1. At d = do, no variation in the rotational
rate of the earth is assumed, and the coefficients of the regression
and the correlation coefficients are computed for each clock at that
point in time.
Column 4 : racc2
The RMS of the r2 correlation coefficients of the linear regressions
of the non-linear components of the clocks within a set. The
determination of this value is as follows:
DRo is applied to a measured drift rate at d >= do by subtraction. In
other words, the effect from assuming a constant rotation rate of the
earth is applied to a measured drift rate at all times exceeding do.
Therefore, the non-linear component of the drift rate is modeled by
DR1i = DRmeasured - DRo at d >= do. A linear regression is then solved
for the mean of the non-linear components of the drift rates for each
clock, after the mean of the non-linear components is subtracted at d
= do. An attempt is therefore made to remove any bias of the set
resulting from a non-linear component of the drift rate. The model for
each clock is therefore DR1 = a2d + b2 where DR1 represents the mean
of the non-linear components minus the mean of the non-linear
components at d = do, to be computed at d >= do. The coefficients of
regression are a2 and b2.
Column 5 : di
The day number at which the complete error analysis is computed. A
condition of computation is that di >= do. This day number is the
number of days that has elapsed since the point of synchronization
with UTC for each clock, or subset of clocks that have been
synchronized on the same day within a relatively short interval of
time.
Column 6 : do
The day number at which it is assumed that the rotation rate of the
earth is constant, that the drift rate for each clock can be
adequately modeled by linear regression, that the correlation
coefficients measure the success of the modeling process, and at which
the reference drift rate function for each clock is therefore
determined.
Columns 7 and 8: ai, bi
The coefficients of regression for the non-linear terms for each set
of clocks as described for column 4. The ai term can be interpreted as
a bias in the change of the difference between a measured drift rate
and a modeled drift rate at any point where d >= do. It can therefore
be interpreted as an acceleration component of time, measured in units
of seconds per day. If the congregation of timepieces demonstrated
random non-linear variations, no aggregate bias (statistical signing)
in these coefficients would be evident.
Column 9 : delta d
The number of days after d = do in which the projected and accumulated
time differences are determined. A value of 365 corresponds to the
projected time differences at the end of a one year period past the
point of d = do. Assuming a constant acceleration rate, both velocity
and accumulated time differentials can be derived.
Column 10 : Weights
The weighting factor applied to the determination of the total time
differential accumulated at d >= do. This factor is currently computed
as:
wi = n * rirms2 * racc2 * di * do2 * (di - do)2
Column 11 : First term of accumulated time difference function:
The first term of the accumulated time difference function determined
as:
t1 =( ai*((delta d) + do)2) / 2
Column 12 : Second term of accumulated time difference function:
The second term of the accumulated time difference function determined
as:
t2 = bi* ( (delta d) + do)
Column 13 : Third term of accumulated time difference function:
The third term of the accumulated time difference function determined
as:
t3 =( ai*(do)2) / 2
Column 14 : Fourth term of accumulated time difference function:
The fourth term of the accumulated time difference function determined
as:
t4 = bi* do
Column 15: The accumulated time difference over the interval of delta
d, determined as:
TE = t1 + t2 - t3 - t4
Column 16 : The contributions to the numerator of the weighted average
of the accumulated time difference, determined as:
Weighted Average (contribution to numerator) = wi * TEi
Column 17 : The contribution of the weight factors expressed as a
percentage of the sum total of the weights.
Individual Entries to the spreadsheet are described as follows:
1. Wgt. Total Error : The weighted average of the accumulated time
difference over the interval of delta d, determined as:
Wgt. Total Error = ( sum (wi * TEi) ) / sum (wi)
2. var: The weighted variance of the weighted average of the
accumulated time difference over the interval of delta d, determined
as:
var = ( sum ( ( wi %) * ( TEi - Weighted Average) ) ) / ( ( ( n -1 ) /
n ) * sum ( wi% ) )
where wi% are the weights expressed as a percentage / 100.
3. sigma : the weighted standard error of the weighted average of the
accumulated time difference over the interval of delta d, determined
as:
sigma = sqrt (var)
4. E90 : the 90th percentile error estimate of the weighted standard
error of the weighted average of the accumulated time difference over
the interval of delta d, determined as:
E90 = 1.6449 * sigma
5. Lower : the lower E90 confidence limit of the weighted average of
the accumulated time difference over the interval of delta d,
determined as:
Lower = weighted average - E90
6. Upper : the upper E90 confidence limit of the weighted average of
the accumulated time difference over the interval of delta d,
determined as:
Upper = weighted average + E90
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