Data

The data set used in the 1987 Report

Note June 2, 2003

Indications from the data

Oscillations and the Data

Challenges

December, 2009, question and comment on the statistical use of the data

The data set used in the 1987 Report

From Lambert Dolphin regarding the statistical analysis of Atomic Constants, Light, and Time

When Alan Montgomery and I decided to look at the measurements of c back in 1992 we gathered each and every published measurement from all known sources. This gave us a master list to start with. We could not find any additional published data points or we would have added them to this master list. The master list includes (a) published original actual measurements,(b) "reworkings" of many of these original data points by later investigators, (c) subsequent published values of c which are not new data but actually merely quoted from an original source. (For instance a value published in Encyclopedia Britannica is probably not an original data point).

Naturally we needed to work with a unique data set which includes each valid measurement only once. In some cases we had to decide whether the original measurement or a later reworking of a given measurement was to be preferred. In the data set a couple of data points were so far out of line with any other nearby measurements that they are easily classified as outliers.

What was humorous to Alan and me is that if we take all the data from the master list, that is, all the raw data from all sources, including spurious points, outliers, duplicates and do a statistical analysis of THAT (flawed) data set the statistical result is STILL non-constant c. (Alan and I did this for fun when we were selecting our "best data" set).

We did our calculations on an Excel spread sheet with embedded formulas so we could easily generate various subsets of the data. What we found was that our conclusion of non-constant c was still implied. In other words we tried everything we could think of to prove ourselves wrong, hence our continuing desire to receive valid criticisms of our statistical methods. If anyone has additional c data points that are not on our master list, let us know.

Our complete data sets are available: http://ldolphin.org/cdata.html

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Note: Due to the specific criticism that none of those supporting the Setterfield material had actually supported the statistical use of the data in the 1987 report, but had re-worked the data and arrived at the same conclusion Setterfield and Norman had arrived at, a request was made to Lambert Dolphin for a statement in this area.  He submitted the following statement June 2, 2003:

When Alan Montgomery and I originally decided to check Barry Setterfield's data on the speed of light in 1991 our interest was two-fold. Had Setterfield inadvertently erred in his mathematics?

Secondly, was there additional data he had missed that we could find and add in to the suite of available measurements on c? The entire exercise was very useful for our own edification. All said and done, we found that Barry was correct in his 1987 analysis and conclusions. Alan and I believe we have only confirmed and further strengthened his work so that it stands on even more solid ground.

Ten years later both Alan and I are eagerly waiting for someone to write us challenging our work and Barry's work before us.

Lambert Dolphin

June 2, 2003

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Indications from the data concerning lightspeed

Question: When was the secondary maximum of c?

 

Questions:  If light was traveling faster in the past, but slowed down to c_now by the time it reaches us at the present, so that past events are viewed in "slow motion", wouldn't it be the case that EVERY event we observe gives the impression that light has the speed c_now?  So, then, there would never be any way to determine that c changes, unless subsequent measurements of c_now change, or unless there are events where we observe the speed of c "after the fact", rather than determine c from the events as they happen (e.g. observing _effects_ of radioactive decay from material dated at several Mya rather than observing the radioactive decay itself). Is this correct, according to Barry's cDK theory?  If so, is there evidence of, say, increased biological degradation in preserved animals as a result of the increased radiation dosages caused by a larger c_past? Or do measurements over the decades show a decrease in c_now (I've heard claims to this effect, but I've never seen a plot of c vs. t *with error bars*)?

Setterfield: As the Vc (variable light-speed) theory is currently formulated (I am working on some changes that may be relevant to this discussion), your assessment of the situation is basically correct. You ask if there is any evidence to show that 'c' has changed since measurements began.  Indeed, I believe there is.  The 1987 Report canvasses that whole issue along with all the measured data of light speed, Planck's constant and other physical quantities which are associated by theory, being tabulated and treated statistically. The data provide at least formal statistical evidence for a change in c. The error-bars are graphed and can be viewed in the 1987 Report.  It is fruitful to look at Figure 1 where the c values by the aberration method from Pulkova Observatory are plotted.  Here the same equipment was used for over a century. Importantly, the errors are larger than for most methods, but the drop in c far exceeds the errors. Also tabulated in the Report are the values of c by each method individually, and each of these also displays a drop with time.  Again, when the same equipment was used on a second occasion, a lower value was always obtained at the later date.

Question: Are you saying that 'c' is no longer decaying? The graphs you use seem to show the rate of change going to zero now.  Do you mean "nearly zero" compared to what  it may have been at the time of creation?

Setterfield:  No, I am not saying c is no longer decaying, but the exponential decay has an oscillation superimposed upon it.  The oscillation only became prominent as the exponential declined.  The oscillation appears to have bottomed out about 1980 or thereabouts.  If that is the case (and we need more data to determine this exactly), then light-speed should be starting to increase again.  The first minimum value for light-speed was about 0.6 times its present value.   This occurred about 2700 - 2800 BC.  This is as close to ‘zero’ as it came.  The natural oscillation brought it back up to a peak that had a maximum value of about 310,000 -320,000   km/sec.  This was in the neighborhood of about 1000 AD.  Today the value is 299,792.458 km/sec.

Oscillations and the Data 

The following question has to do with this graph.

Question: The plot presents a current C ~ 2.4 m/sec., while modern measurement yield a C Nearer to 2.998 m/sec.  How can you be so far off? What is confusing is that the article containing this plot was discussing an accelerating C.

Setterfield:  It should be pointed out that the graph was developed by a comparison of radiometric dates compared with historical dates. The discrepancy between the two dates is largely due to the behaviour of lightspeed since that is the determining factor in the behaviour of all radiometric clocks. It will be noted that the data points show a scatter which is largely due to the 11 to 22 year solar cycle which affects the carbon 14 content in our atmosphere.

The problem as stated in the above question results from a misreading of the graph. If you look carefully, you will note that the years AD are on the left, while the years BC are on the right. In other words, reading the graph from left to right takes us backwards in time. If you notice, the graph on the left hand end finishes at today’s value for c.

The reason for the oscillation is that a static universe in which the mass of atomic particles is increasing is stable, but will gently oscillate. This has been shown to be the case by Narliker and Arp in Astrophysical Journal Vol. 405 (1993), p.51. As you know, the quantized redshift evidence suggests that the universe is static and not expanding, but evidence of the oscillation is also there. In terms of the Zero Point Energy (ZPE) this oscillation effectively increases the energy density of the ZPE when the universe has its minimum size since the same amount of Zero Point Energy radiation is now contained in a smaller volume. The result is that lightspeed will be lower. Conversely, the energy density of the ZPE is less when the universe has its maximum diameter and the speed of light will be higher as a result.

I trust that this clears up the confusion.

 Challenges

for Statistician Alan Montgomery: I have yet to read a refutation of Aardsma's weighted uncertainties analysis in a peer reviewed Creationary journal. He came to the conclusion that the speed of light has been a constant. --A Bible college science Professor.

In Aardsma's work he took 163 data from Barry Setterfield's monograph of 1987 and put a weighted regression line through the data. He found that the rate of decrease was negative but the deviation from zero was only about one standard deviation. This would normally not be regarded as significant enough to draw a statistical conclusion.

In my 1994 ICC paper I demonstrated among other things the foolishness of using all the data--those methods with and without sensitivity to the data to the question. You cannot use a ruler to measure the size of a bacteria. Second, I demonstrated that 92 of the data he used were not corrected to in vacuo and therefore his data was a bad mixture. One cannot draw firm conclusions from such a statistical test.

I must point out to the uninitiated in statistical studies that there is a difference between a regression line and a regression model. A regression model attempts to provide a viable statistical estimate of the function which the data exhibits. The requirements of a model are that it must be:

(1) a minimum variance (condition met by a regression line);

(2) homoskedastic - data are of the same variance (condition met by a weighted linear regression) and

(3) it must not be autocorrelated - the residuals must not leave a non-random pattern .

My paper thus went a step further in identifying a proper statistical representation of the data. If I did not point it out in my paper, I will point it out here. Aardsma's weighted regression line was autocorrelated and thus shows that the first two conditions and the data imposed a result which is undesirable if one is trying to mimic the data with a function. The data is not evenly distributed and the weights are not evenly distributed. These biases are such that the final 11 data determine the line almost completely. This being so caution must be exercised in interpreting the results. Considering the bias in the weights and their small size, data with any significant deviation from them should not be used. It adds a great deal of variance to the line yet never adds any contribution to its trend. In other words, the highly precise data determines the direction and size of the slope and the very low imprecision data makes any result statistically insignificant. Aardsma's results are not so much wrong as unreliable for interpretation.

The Professor may draw whatever conclusions he likes about Aardsma's work but those who disagree with the hypothesis of decreasing c have rarely mentioned his work since. I believe for good reason.  ( October 14, 1999.)

Note added by Brad Sparks: I happened to be visiting ICR and Gerry Aardsma just before his first Acts & Facts article came out attacking Setterfield. I didn't know what he was going to write but I did notice a graph pinned on his wall. I immediately saw that the graph was heavily biased to hide above-c values because the scale of the graph made the points overlap and appear to be only a few points instead of dozens. I objected to this representation and Aardsma responded by saying it was too late to fix, it was already in press. It was never corrected in any other forum later on either, to my knowledge.

What is reasonable evidence for a decrease in c that would be convincing to you? Do you require that every single data point would have to be above the current value of c? Or perhaps you require validation by mainstream science, rather than any particular type or quality of evidence. We have corresponded in the past on Hugh Ross and we seemed to be in agreement. Ross' position is essentially that there could not possibly ever be any linguistic evidence in the Bible to overturn his view that "yom" in the Creation Account meant long periods; his position is not falsifiable. This is the equivalent of saying that there is no Hebrew word that could have been used for 24-hour day in Genesis 1 ("yom" is the only Hebrew word for 24-hour day and Ross is saying it could not possibly mean that in Gen. 1). Likewise, you seem to be saying there is no conceivable evidence even possible hypothetically for a decrease in c, a position that is not falsifiable.

Comment: I looked at several papers published after Humphreys', yet found only ONE reference to it. The objections that Humphreys raised have not been answered by Setterfield, Montgomery, Dolphin, Bowden or anyone else that I can see. If I have missed it then please let me know.

The one reference I did find was this from Montgomery: "Humpreys [14, p42] questioned why the rate of decrease of c should decrease in direct proportion to our ability to measure it. Humphreys gave no evidence that this was true."

But if you read Humphreys CRSQ paper, he DID give evidence that this was true - in the sentences IMMEDIATELY preceding the reference that Montgomery cites above! Furthermore, the very next sentence in Montgomery's paper says: "As yet no paper has properly addressed this important issue of the sensitivity of the data" - which is essentially admitting that this is a problem!

There was also another vague reference to Humphreys' personal correspondence with Goldstein over the Roemer data. Bowden pointed out that Goldstein himself seems to have bungled some of his calculations and that Mammel has corrected them. But the point Humphreys was making in his paper was that Setterfield was using a 2nd hand quotation and didn't bother to check with the source, or do his own verification. Indeed, it was Mammel who found the problems with Goldstein's calculations not Setterfield or Bowden.

Response from Alan Montgomery: At the time I presented my Pittsburgh paper (1994) I looked at Humphreys paper carefully as I knew that comments on the previous analyses was going to be made mandatory. It became very apparent to me that Humphreys was relying heavily on Aardsma's flawed regression line. Furthermore, Aardsma had not done any analysis to prove that his weighted regression line made sense and was not some vagary of the data. Humphreys paper was long on opinion and physics but he did nothing I would call an analysis. I saw absolutely nothing in the way of statistics which required response. In fact, the lack of anything substantial statistical backup was an obvious flaw in the paper. To back up what he says requires that the areas where the decrease in c is observed is defined and where it is constant. If Humphreys is right the c decreasing area should be early and the c constant area should be late. There may be ambiguous areas in between. This he did not do. I repeat that Humphreys expressed an opinion but did not demonstrate statistically that it was true.

Third, the aberration values not only decrease to the accepted value but decrease even further. If Humphreys explanationis true why would those values continue to decrease? Why would those values continue to decrease in a quadratic just as the non-aberration values and why would the coefficients of the quadratic functions of a weighted regression line be almost identical and this despite the fact that the aberration and non-aberration data have highly disparate weights, centres of range and domain and weighted range and domain?

Fourth, if what Humphreys claims is true why are there many exceptions to his rule? Example, the Kerr Cell data is significantly below the accepted value. Therefore according to Humphreys there should be a slow increasing trend back to the accepted value. This simply is not true. The next values take a remarkable jump and then decrease. Humphreys made not even an attempt to explain this phenomenon, Why?

Humphreys paper is not at all acceptable as a statistical analysis. My statement merely reflected the truth about what he had not done. His explanation is a post hoc rationalization.

An additional response from a witness to the arguments regarding the data and Setterfield's responses (or accused lack of them):

"In the [1987] Report it is noted at the bottom of Table 3 that the aberration constant is disputed. There is a systematic error that involves different techniques in Europe to those at Washington and is enhanced by the large number of twilight observations at Pulkova. The details are too lengthy to discuss here. The Washington aberration constant is now accepted as definitive resulting in systematically low c values from the European observations. When this error is corrected for, many values of c in Table 3 increase by about 230 km/s, with some higher. This correction overcomes the perceived problem with Figure I. The zero takes account of this systematic error and is thus not misleading, nor is the decay trend spurious, and the vast majority of values in Table 3 are then above c.

"The aberration values are very useful. The majority of Russian observations were done on the same insturment with the same errors. They display the decay trend well, which cannot be due to instrumental effects nor error reduction. The same comments apply to the results obtained from the Flower Observatory as well as the International Latitude Service. All give decay rates above 4 km/s per year. Far from being 'misleading,' the aberration values only serve to confirm the decay hypothesis."

References for the above:

Simon Newcomb, "The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy," in the Supplement to the American Ephemeris and Nautical Alamanac for 1897, p. 138 (Washington)

E.T. Whittaker, "Histories of Theories of Ether and Electricity," vol. 1, pp 23, 95 (1910, Dublin)

K.A. Kulikov, "Fundamental Constants of Astronomy," pp 81-96 and 191-195, translated from Russian and published for NASA by the Israel Program for Scientific Translations, Jerusalem. Original dated Moscow 1955.

 (Nov. 13, 1999)

Comment: Regarding the Montgomery & Dolphin paper, yet crucial to any consideration of the reality of thehypothesized variability of the speed of light. It is difficult to tell from the paper by how much the authors think the speed of light has changed. They do not settle on any one value for the slope of the line, arguing only that there is one. The one specific number mentioned, in conjunction with Roemer cell experiments, is 27.5 km/sec/year (between tables 5 and 6).

Compared to the defined standard value of 299792.458 km/sec, that's a fractional change of 0.000092 per year, a number just shy of 1/100 of a percent. The error bars on the large majority of the pre-1950 data points are far in excess of that value, and most of the data points in fact lie well outside the range of 299792.458 ± 27.5; the scatter of the data and the probable errors are far in excess of the value of the proposed slope, and that is a major reason for not believing that the slope is physically real.

All of this combines to raise many questions about the validity of the conclusion that the speed of light has been historically time variable. The slope uncovered by Montgomery & Dolphin, and Setterfield, is most likely a typical random component of the data set which they have all confused for a physically real variation. That's why I said, and I continue to say, that their results is severely lacking in confidence inspiring clarity. It is not impossible for the trend to be real, based solely on this analysis, but it is unlikely. In light of the much more clear evidence that the speed of light has not varied, there is no confident reason to assume that it has, based on a result so weak as this one.

Response from Alan Montgomery:  This is all drivel. For example, 299792.458 ± 27.5 is drivel. 299792.458 is the speed of light – 27.5 km/sec/year is a linear change to the speed of light . The two values are apples and oranges and any plus or minus stuck between them is meaningless. Or is .000092 = .0092% change per year. This looks very small. But it is like a salesman who sells you a stove for a few dollars per day for 3 years at 18% interest to the finance company. The real question is “Is the change statistically significant?” and according to the model I produced in my ICC paper

c(t) = c(0) + .03*T² or c(t) = (1 + 10^(-7)*t²)*c(0) which is smaller than .000092 and still statistically significant.

In 1994 I presented a paper on the secular decrease in the speed of light.

I used a weighted regression technique and found a quadratic which produced a regression model with significant quadratic coefficients.

This has been reviewed by statisticians with Ph.D s. Some have been convinced and others
are not yet convinced. The technique is, however, acknowledge as appropriate to the data.

Also a systematic search was made for obvious sources of the statistical decrease to find a correlation with some technique or era that might bias the statistics. The result was a systematic low value for the aberration methodology. When these values were segregated from the non-aberration values significant trends were found in both. Thus even the systematic errors that were found only reinforced the case.

These figures having stood for over 10 years, I wonder why so many people still doubt the result when none have produced a better analysis or better data.

Alan Montgomery

December, 2009, question and comment on the statistical use of the data

Question: I looked at the data ( http://www.setterfield.org/report/fig1.jpg).
The r was -0.947. Was that the r or the R2? What was the N? With the N, a calculation may be made on the certainty of the evidence, if that would suit your purpose.

Setterfield: In the 1987 Report, I only used r, not R2.  N is the number of observations involved, right?  Figure 1 is the Pulkova results, as listed for two hundred years from 1740-1940, with the majority of the observations being in the second hundred years.  The lines you see are the error bars (for those unacquainted with a graph like this) and show the measurements have a trend beyond the potential error in any of the given observations.
On the graph that is in the Report are the results of each SET of observations and any given set involved thousands of individual observations.  The number chosen by the Pulkova people in each case represented their statistical analysis of the thousands of observations in each set.  So we have about twenty points on the graphs, representing tens of thousands of observations.  For example, the data for 1935, collected by Romanskaya, had 14,783 observations.  The point for 1935 is then the
measurement they chose as the best data point given all the data.  
Remember, these were not young earth creationists!  In 1922, Kulikov collected 28,542 observations, to give us the best possible measurement for the 1922 date.

This is representative of what was done and the number of total observations may well go past the tens of thousands and into the hundreds of thousands.

Responding comment: From the Pulkova r (-0.947), and the numbers you gave me (14,783 for 1935 and 28,542 for 1922), then the decline in the speed of light was statistically significant at P < 0.0001. Believe that c has declined and you run the risk of being wrong less than one chance in 10,000.

 Scientists accept as true if their risk of being wrong is less than one in twenty, P < 0.05. Very few scientists in the world require P < 0.01. Virtually no scientists worldwide require P < 0.001. Given the r, the numbers, and the probability, no rational person would argue that c has not declined.

It may be stated another way. Given the data, anyone arguing that c has not declined would be wrong more than 10,000 times out of 10,000.

If the audience understands the rudiments of statistical treatments of experimental data, then the probability values may be convincing. 

from Alan Montgomery:  The statistical significance required is subjective. It depends on what you are using it for and how sure you have to be to take a significant action.  It would be a different significance if you are selling light bulbs vs atomic reactors.

Several of the tests I did in my statistical model went beyond the p<.001.
There is definitely a statistical significance to the decrease in c.