History of the Speed of Light Experiments

Barry Setterfield

| Preface | Part 1 | Part 2 | Part 3 | Part 4 |

Preface:

The following paper was started by Barry Setterfield in 1987.  Shortly after the data and rough paper were complete, he was asked by a senior research scientist at Stanford Research Institute International to put together a white paper for internal study.  This paper was done with Trevor Norman, then of Flinders University in Adelaide Australia.  The paper was published by Flinders University due to internal reorganization at SRI at that time.   At that point, Gerald Aardsma, then of Creation Research Institute in southern California, telephoned both SRI and Flinders and asked them if they knew that Setterfield was a young earth creationist.  This information caused both Flinders and SRI to retract support for the paper, although the Flinders staff had, before that telephone call, been interested enough in the paper to ask for a seminar hosted by Setterfield and Norman regarding the subject of the speed of light and the statistical analysis.  The seminar was cancelled, Setterfield was told he was unwelcome on the campus from that time on, Norman was instructed not to have anything further to do with Setterfield if he wanted to keep his job at the university.  Norman later resigned his position.  The paper, however, had been published and is available on the web here. 

The massive responses to the Norman-Setterfield paper caused the paper which follows here, the history of the research of the speed of light up to the mid twentieth century, to be put on hold.   This material has now been completed and included in Cosmology and the Zero Point Energy, published 2013. The book has numerous illustrations not available here.

Thank you.

Helen and Barry Setterfield

 Part 1:  Early Measurements

An Infinite Speed of Light?
Ole Roemer
Analysis of Roemer’s Work
A Modern Look at Roemer’s Work
Delambre
Glasenapp
Sampson and the Harvard Values
Miscellaneous Values
Conclusions from Roemer-type experiments

An Infinite Speed of Light?

For many ages, men thought that light had no speed.  It simply was.  It was instantaneous.  If speed was referred to, it was referred to as infinite.  The Greek philosophers generally had followed Aristotle's belief that the speed of light was infinite. However, there were exceptions such as Empedocles of Acragas (c.450 B.C.) who spoke of light, "traveling or being at any given moment between the earth and its envelope, its movement being unobservable to us," (The Works of Aristotle translated into English, W.D. Ross, Ed.; Vol. III; Oxford Press, 1931: De Anima, p. 418b and De Sensu, pp. 446a-447b). Around 1000 A.D., the Moslem scientists Avicenna and Alhazen both believed in a finite speed for light (George Sarton, Introduction to the History of Science Vol. I; Baltimore, 1927; pp. 709-12).

Both Roger Bacon (1250 A.D. ) and Francis Bacon (1600 A.D.) argued against an infinite speed for light.  Francis Bacon wrote, "Even in sight, whereof the action is most rapid, it appears that there are required certain moments of time for its accomplishment...things which by reason of the velocity of their motion cannot be seen -- as when a ball is discharged from a musket" (Philosophical Works of Francis Bacon; J.M. Robertson, Ed.; London, 1905; p. 363). However, this was the same year that Kepler maintained the majority view that light speed was instantaneous, since space could offer no resistance to its motion (Johann Kepler; Ad Vitellionem paralipomena astronomise pars optica traditur Frankfurt, 1804).

It was not really considered debatable.  Of course the Bacons were wrong and the speed of light was infinite!  Nevertheless, such a consistent scattering of scientific philosophers through the ages disputed an infinite speed of light that it occurred to Galileo that there should be some way to check this and settle it once and for all. 

In his Discorsi, published in Leyden in 1638, Galileo proposed that the question might be settled in true scientific fashion by an experiment over a number of miles using lanterns, telescopes, and shutters. The Accademia del Cimento of Florence reported in 1667 that such an experiment over a distance of one mile was tried, "without any observable delay" (Essays of Natural Experiments made in the Academie del Cimento; translated by Richard Waler, London; 1684; p. 157). However, after reporting the experimental results, Salviati, by analogy with the rapid spread of light from lightning, maintained that light velocity was fast but finite.

But some things were coming together which would allow the speed of light to be measured.  Galileo had discovered the first four satellites of the planet Jupiter in January of 1610.1  This would provide a source of measurement, as it was discovered later that the moons would eclipse behind Jupiter at regular intervals.

It was not until almost fifty years later, however, that a device which could be used accurately enough in timing was invented.   In 1657, Huygens had invented a clock with a free-swinging pendulum,2 capable of counting seconds.  This was improved upon with his 1673 version.3 

 Descartes (who died in 1650) strongly held to a belief in the instantaneous propagation of light and, accordingly, influenced the generation of scientists who were confronted with the results of Roemer’s experiments in 1675. These scientists usually accepted Descartes arguments. He had pointed out that we never see the sun and moon eclipsed simultaneously. However, if light took, say, one hour to travel from earth to moon, the point of co-linearity of the sun, earth, and moon system causing the eclipse would be lost and visibly so (Christiaan Huygens, Traite de la Lumiere...; Leyden; 1690, pp. 4-6, presented in Paris to the Academie Royale des Sciences in 1678). In 1678 Christiaan Huygens demolished Descartes' argument by pointing out, using Roemer's measurements, that light took (of the order of) seconds to get from moon to earth, maintaining both the co-linearity and a finite speed.

However, only Bradley's independent confirmation published January 1, 1729 ended the opposition to a finite value for the speed of light. Roemer's work, which had split the scientific community, was at last vindicated. After 53 years of struggle, science accepted the observational fact that light traveled at a finite speed. Until recently, that finite speed has been generally been considered a fixed and immutable constant of the universe in which we live.

Scientifically speaking, the velocity of light is the highest known velocity in the physical universe. The present value has been fixed (by definition) since 1983 and declared to be an absolute constant at 299,792.458 kilometers per second. Almost everyone rounds this off to 3x10^8 meters/second, or 186,000 miles/second. Electronics technicians often prefer to remember the approximate speed of light as one foot per nanosecond in air or vacuum-the distance light travels in one-billionth of a second. In dielectric media the velocity of light (electromagnetic waves) is slower than in the vacuum of space.

Ole Roemer

More was needed.  Ole Roemer, born in Denmark on September 25, 1644, had begun studies in mathematics and astronomy at Copenhagen University in 1662.  Ten years later, in 1672, he was appointed to the newly constructed observatory in Paris.  In 1675, he discovered that the epicycloid was the best shape for teeth in gears and communicated to Huygens that such gears would be advisable in his clocks.4  This resulted in an improvement so significant that clocks of this caliber made the determination of longitude possible. 

With such accurate clocks and the knowledge that Jupiter’s moons eclipsed regularly, it was now theoretically possible to measure the speed of light, and determine whether or not this speed was really infinite.  The eclipses provided a regular astronomical phenomenon that was visible from both a standard observatory and the place whose longitude was to be determined.  The Paris Observatory was chosen as the standard.

One more thing was needed, however:  accurate tables were needed to predict eclipse times. Picard, then later Cassini and Roemer, made a series of observations so that the tables could be prepared.  Cassini published the first reliable times for these astronomical events.5  Roemer collected more than seventy observations by Picard and himself of Jupiter’s inner moon, Io, from 1668 to 1677.  Of these, half came from the period 1671-1673, when Jupiter was at the most distant point in its orbit and consequently moving the most slowly as seen from earth.

At any given time, Io would take approximately one day, 18 hours, and 28.5 minutes to complete one revolution around its giant parent planet.  The times when it either went into eclipse behind Jupiter, or emerged from eclipse could thus be accurately predicted.  The giant planet itself takes about 12 years to go around the sun once.  The earth in its orbit thus periodically comes its closest to Jupiter, then swings away, until 6 months later, at the opposite part of its orbit, the earth is a its furthest point from Jupiter.

During the course of these observations, Roemer noticed something:  as the earth drew away from Jupiter, the eclipse times of Io fell further and further behind schedule.  However, once the furthest point in our orbit was passed, and the earth began to approach Jupiter, the eclipse times began to catch up again.  How could the position of the earth in its orbit affect the time it took Io to go around Jupiter once and be eclipsed?  It didn’t, said Roemer.  What is happening is that the light carrying the information from the Jupiter-Io system is taking time to travel across the diameter of the earth’s orbit, so the eclipse information takes longer to get to the earth when it is at the furthest point in its orbit.

This was the discovery that Roemer announced to the Paris Academie des Sciences in September of 1676.  He then predicted to them that the eclipse of Io that was due on November 9 of 1676 at 05 hours, 25 minutes and 45 seconds would, in fact, be ten minutes late.  They listened.  They doubted.  Then they watched.  

On November 9, 1676, the eclipse was observed at the Observatoire Royale at precisely 05 hours, 35 minutes, and 45 seconds, exactly as Roemer had predicted, evidently because of the time it took the light to travel.

It might be expected that with the above information Roemer would pronounce a definitive value for the speed of light (or “c”), but this was not his main purpose.  His prime concern was to demonstrate that light was not transmitted instantaneously, but had instead a definite velocity, as evidenced by the observations.  In this he eventually succeeded.  The main factor that was unknown to Roemer, and that prevented accurate calculation of the speed of light was the radius of the earth’s orbit.  Without that knowledge it was impossible to know exactly how far the light had traveled and thus also impossible to determine its speed.  Today we know the radius of the earth’s orbit to be 1.4959787 x 108 Km,6 a value that is adopted in all the following calculations. 

Due to the precision needed in the measuring devices, there would have been further problems for Roemer if he had tried to calculate the speed of light.  First of all, though Huygenian clocks could count seconds, the metal in the pendulum rod was temperature sensitive.  A rise of 5° C caused a loss of 2.5 seconds per day.7  With temperature variation on a daily scale, it is possible that Roemer’s clocks were accurate only to five seconds.  While this accuracy was quite sufficient to pick up a ten minute time difference in the observations, it was not until 1869, about 200 years later, that temperature effect was corrected for by making only evening transit timings for Jupiter’s moons.  

The other major problem Roemer would have faced had to do with human error in observation.  Io is about 3632 kilometers in diameter, and it goes into or emerges from its total eclipse in a period of 3.5 minutes.  During the time that it goes into eclipse, it becomes progressively fainter until the observer times the disappearance of the last speck of light from the fast-fading satellite.  When Io is emerging from Jupiter’s shadow, the first speck of light is timed.  With a small telescope, this timing can be accurate to within ten seconds,8 which would approximate what Roemer achieved with his equipment.  Obviously, an exact timing of the moment of extinction of the disappearing Io is going to be easier than the exact timing of its re-emergence out of darkness.  Consequently, it comes as no surprise that Roemer’s value for the period of Io in its orbit as timed by its emergence from Jupiter’s shadow varied from 8 seconds up to 29 seconds longer than the timing of its disappearance.  The average variation was about 20.7 seconds.  As the November 9 eclipse timing in 1676 was one of a re-emergence, it is inevitable that it would be timed late.  Roemer’s period for Io’s orbit in November was 27 seconds longer than in June of 1676.9

Analysis of Roemer’s Work

A variety of values for the speed of light have been extracted from Roemer’s figures.  They range from 193,120 Km/s up to 327,000 Km/s.10  If we take Roemer’s delay as being the ten minutes that he quoted, less the 27 seconds due to the late emergence timing for November, less a further 5 seconds for the clock running fast in the cold November weather, we end up with a delay of the order of 568 seconds. 

In 1915, Danish mathematician K. Meyer rediscovered Roemer’s own observations in an original notebook.  Meyer’s calculations show that “the increment in the distance from Jupiter to the earth between August 23 (the last eclipse of Roemer’s list before that of November 9, and the one on which it is probable he based his startling prediction) and November 9 of 1676 was 1.14 r” where r is the radius of the earth’s orbit.11    We thus divide 568 seconds by 1.14, giving us 498.2 second for the delay across the radius of the earth’s orbit of 1.4959787 x 108 Km.  This results in a value for c of 300,280 Km/s -- but this is little more than a ‘guesstimate’.

Roemer estimated the delay across the diameter of the earth’s orbit as about 22 minutes, a result that he obtained by averaging what he considered his best figures.12  In 1686, in his first edition of “Principia”, Newton quoted the radius delay discovered by Roemer as ten minutes, but in his own revision in the second edition, he quotes it as seven or eight minutes.  By contrast, in 1693 Cassini, from his own observations, gave the delay for the orbit radius as 7 minutes and 5 seconds.13 Halley noted that Roemer’s figure of 11 minutes for the time delay across the radius was too large, while that of Cassini was too small.14  Cassini agreed about the delay but debated its cause.  Newton noted the orbit radius delay in 1704 in these words: “Light is propagated from luminous bodies in time, and spends about seven or eight minutes of an hour in passing from the sun to the Earth.”15  Newton quoted the radius delay discovered by Roemer as ten minutes,16 but in his own revision in the second edition, he quotes it as seven or eight minutes.17  In May of 1706, a translation of sections of Newton’s “Opticks” appeared in French quoting the figure as eight minutes.18  This gives a speed of light equal to 311,660 Km/s.

In describing Roemer’s method in the section on Astronomy in the Encyclopedia Britannica for 1711, the conclusion is presented from the latest observations that “it is undeniably certain that the motion of light is not instantaneous since it takes about 16.5 minutes of time to go through a space equal to the diameter of the earth’s orbit…And…it must be 8.25 minutes coming from the sun to us.”19  This gives a 1710 value of c equal to 302,220 Km/s.

Apart from Roemer’s statement about the 11 minutes, it seems that Cassini, Halley, Flamstead, and Newton quote figures that suggest that the speed of light prior to 1700 may have been higher than now.  The orbit delay quoted in the Encyclopedia Britannica tends to confirm this, as does Bradley’s comment about his own method.  Roemer’s statement thus leaves an element of ambiguity that is in contrast with the other observers of his day.  This suggests that a closer examination of Roemer’s figures is needed.

By 1729, Bradley had published his findings on the aberration of light and wrote that “…from when it would follow, that Light moves, or is propogated as far as from the Sun to the Earth in 8 minutes 12 seconds…”.  This gives the result that c was equal to 304,000 Km/s.  Bradley then commented that his result was “…as it were a Mean betweist what had at different times been determined from the Eclipses of Jupiter’s satellites.”20

A Modern Look at Roemer’s Work

In 1973, an attempt was made by Goldstein et al to reanalyze 40 of Roemer’s original observations to come to some definite conclusions.  What Goldstein and his team did was to adopt a model for the Jupiter-Io system and calculate the eclipse times for any given position of the earth.  They chose the forty most reliable eclipse times from Roemer’s diary which were then compared with times from their model.  They concluded that “The best fitting value for the light travel time across one astronomical unite [the radius of the earth’s orbit] does not differ from the currently accepted value by one part in 200.”  Their final statement was that “the velocity of light did not differ by 0.5% in 1668 to 1678 from the current value.”21

Does this negate the idea of any variation in c?  No, it does not.  An immediate problem with the analysis surfaces when we look at what was done in 1973.  As Goldstein and his co-workers point out, their method results in what is known as a “root mean square” (rms) deviation of observed times compared with the model of 118 seconds.   In other words, the predicted times from their model disagreed with Roemer’s observations by an average of almost two minutes!  The claim that c did not differ by 0.5% about 1675 is therefore meaningless.  An rms error of 118 seconds in about 1000 seconds for the observed delay across the diameter of the earth’s orbit is an 11.8% error, which is equivalent to ± 35,000 Km/s in the value of c.  Any suggested variation in c is very liberally covered by this error margin!

Mammel has noted another, even more interesting, difficulty.22 1973 The actual visible phase of Io was not projected back over a period of 300 years to get the exact times of eclipses from the model.  To do this would have involved knowing the orbital period of the satellite to an accuracy of better than one part per billion.  So instead, Golstein et al  calculated via an adjustment made on what was seen now, or the empirical initial point.  .  To get this initial point they used the current value of the speed of light to adjust the average time of observation to get the best agreement with the average predicted time.  Consequently, their answer gave them back the same value of c that they started with!
Instead they should have  been adjusting c to account for the variation in the apparent period of Io. 

In other words, because they started with an assumption that the speed of light was constant, their conclusions included that assumption.

After pointing out this problem, Lew Mammel Jr. went on to correct the conceptual error and do his own calculation from the data used by Goldstein et al.  As he is not a supporter of any variation in c, his results are the more interesting.  He found that he had to subtract 6% of the nominal delay time for each datum to get the best fit.  The predicted delay times were therefore being reduced by 6%, meaning that the value of c was 6% higher than now.  This places Roemer’s value for the speed of light at 317,700 Km/s, with an expected error of 8.6%.  The conclusion is that when Roemer’s data is re-worked by the current Goldstein method, it suggests that c was somewhat above its current value, in good accord with the statements by Cassini, Halley, Flamstead and Newton, who were contemporary observers with Roemer.

It might also be noted here that in the last ten years, since about 1995 or so, observations of Io, the moon that was used for the Roemer data, has shown that its orbit is changing, thus making it virtually impossible to go back in time and determine the exact eclipse times Roemer and his colleagues were seeing.

Delambre

In 1792 the Paris Academie des Sciences decided to compile a definitive set of tables of the motions of Jupiter’s satellites.  This was accomplished by Delambre in 1809 and published in 1817.23  For this task, Delambre processed all observations of Io and the other satellites in the 150 years since 1667.  In all, nearly one thousand observations of those moons were processed.  Unfortunately, Delambre’s manuscripts containing his calculations have been lost, so that it is impossible to cross-check his results.  Irksome though this may be, all are forced to admit that Delambre’s final result of 8 minutes 13.2 seconds for the earth orbit radius delay was generally received as definitive for the median date of 1738 ± 71 years.  Even Newcomb admitted this and at the same time acknowledged that it was “remarkable that the early determinations of the constant of aberration agreed with Delambre’s determination,” even though “there was an apparent difference of 1 per cent” when they were compared to the c values of the mid-1800’s.24  To see the agreement, Bradley’s value from the aberration constant as mentioned above is 303,440 Km/s, while Delambre’s result is 303,320 Km/s.  The figure is quoted to the nearest tenth of a second, but if the accuracy was about 0.5 seconds, resulting from the known rapid development of both telescopes and time-pieces, the error margin would be about ± 310 Km/s.

Glasenapp

In 1874, S.P. Glasenapp of Pulkova Observatory discussed the results from all available observations of Io between 1848 and 1873 – 320 eclipses in all.25  He analyzed each eclipse according to the following five different correction procedures:

The 5 corrections resulted in the following 5 values

Glasenapp pointed out that the large variation in results was due to the impossibility of determining the exact apparent brightness of Io in absolute units at the moment of the eclipse.  He did not indicate which results were to be preferred.  However, as the first is included in the more comprehensive results of the fifth, it appears justifiable to take the mean of the second, third, fourth, and fifth, and omit the first.  When this is done, the orbit radius delay becomes 498.57 ± 0.1 seconds.  This error has been adopted, as it was the daily accuracy of the timepieces around 1800 that would be checked by daily star transit observations.26  Observational accuracy with larger instruments would be somewhat better than that as times are quoted in hundredths of a second.  Accordingly, an average result for the speed of light of 300,050 ± 60 Km/s for the median date of 1861 can be derived.27

Sampson and the Harvard Values

In 1909, Sampson derived a value for the orbit radius delay of 498.64 seconds from his private reductions of the Harvard observations since 1844.28  However, the official Harvard readings themselves gave a result of 498.79 ± 0.02 seconds, the error being due to the inequalities in Jupiter’s surface.  The Sampson result thus becomes 300,011 Km/s for the speed of light, while the official Harvard reductions give 299,921 ± for the same median date of 1876.5 ± 32 years.

Miscellaneous Values

In 1759, B. Martin deduced a time of 8 minutes 13 seconds for the orbit radius light delay.29  A light speed of 303,440 Km/s results.  In 1770, Richard Price indicated that his research gave a value of 8.2 minutes or 492 seconds for the orbit radius delay, resulting in a light speed, or c, of  304,060 Km/s.30  In 1778, J Bode published a value of 8 minutes 7.5 seconds for the orbit light delay, giving a c of 306,870 Km/s.31 In 1785, Boscovich published his time of 486 seconds, equivalent to 307,810 Km/s.32

These values appear to be the only other independent assessments of the orbit radius delay for light.  Most others appear to take Cassini’s, Newton’s or Roemer’s figures and build upon them.  As various estimates of the radius of the earth’s orbit flourished, so did a wide variety of proposals for the peed of light.  However, the one basic requirement was the measured time delay, and the above appear to be the full compliment of available measurements.  Once that basic fact had been determined, our modern knowledge of the orbit radius allows a consistent treatment of these observations.  This was the one factor lacking in the derivation of c from these basic observations up until the early 19th century.  But by that time, Delambre’s figure of 8 minutes 13.2 seconds was already being widely quoted.

Conclusions from Roemer-type experiments

The above results may be best summarized in a table.  This is done in Table 1 below.  When treated statistically, the Table 1 values yield the following results:

TABLE 1
Roemer-type Experiments

Upon omitting the approximate values of Roemer and Newton, a least squares linear fit to the 9 data points gives a decay of 36.35 Km/s per year.  When the next two most aberrant values marked # are omitted, the linear fit to the 7 remaining data points produces a decay of 28.3 Km/s per year with r = -0.945, which is significant at the 99.93% confidence level.  Furthermore, the mean of these 7 points is 301,860 Km/s, which is 2067 Km/s above the current value of 299,792.458.  The t statistic therefore indicates with a confidence of 98.48% that c has not been constant at this current value during the time covered by these data points.  These c values are thus consistent with a slowing trend.