From Jackson (page 319 in the second edition):

"The general usage is to take the group velocity of the dominant frequency component as the signal velocity and velocity of transport. This suffices in most circumstances, but with sensitive enough detectors the signal velocity can evidently be pushed close to the velocity of light in vacuum, independent of the medium."

How do you catch that?

Is not the vacuum the medium? Where is the in dependency?

No this applies also to the transmission in glass, in water, or even in a metal.
But it is a statement of principle, it does not mean it is technically feasible.
It even does not imply that the signal will be higher that the thermal noise.
Therefore, strickly speaking, not only the detector should be as sensible as necessary, but the temperature (noise) should also be as low as necessary.

Principles should become valid when they have the highest probability of becoming feasible. A vacuum is devoid of mass including glass, water, etc.- what you say seems contradictory. This sounds like a description of free space velocity- a medium, an environment, mostly devoid of mass, which allows the signal to propagate most efficiently. Is the point of this exercise, to demonstrate the limits, of our apparatus?

Anonymous

When dealing with the instant theory, "the delay" is magnified greater at near or small levels- but at larger levels, such as observing the sun, the calculations become instant.

This is the same as relativity. Relativity says that on the large scale measures such as the viewing of the sun, normal Newtonian mechanics prevail and we do not feel the need to involve the speed of light, until we reach the small measures involved in electrodynamics, or any micro-atomic theory.

GogoJF,

I could not understand you last posts.
However, your first answer suggested me you had understood the point:

"Is not the vacuum the medium? Where is the in dependency?"

After all, any material -like glass- is made of atoms in vacuum.
In the steady state, the speed of a wave is determined by the by the reactions of the medium.
However, when switching-on a wave, the front of the wave propagates without experiencing any previous excitation of the medium.
The front is then attenuated as it leaves energy to the medium, but some energy is left and should in the end go through the material at the speed of light. The whole question is then: how much energy would be left?

Therefore, I tend to agree with this comment by Jackson in edition 2.
However, I was surprised that I could not find this comment in edition 3.
This suggests me that this remark might be less obvious that it seems to me right now.

The classical Electrodynamics of continuous mediaý usually considers steady state excitation (harmonic excitation).
Standard use of the Fourier transform could allow anybody to go from the usual harmonics point of view to the transient point of view and to analyse the propagation of a wave front.
Therefore, cheking the Jackson ed 2 claim should be not more than an algebraic problem.
However, there is a practical obstacle: the material properties should be know for the complete spectrum. At least this is my guess.

This claim by Jackson is really interresting, I found.

From: www.setterfield.org/000docs/cx3.html


e page

Return to Research Papers



Part 3: Fizeau and the Toothed-Wheel Experiments



H. L. Fizeau
The results
Enter Cornu
Cornus Results
The Young/Forbes Result
Perrotins Procedures
Perrotin and Prims Results
Conclusions from Toothed-Wheel Experiments
Table 5: Toothed Wheel Experimental Values



H. L. Fizeau

The two methods of measuring the velocity of light, c, that have been considered to date have both been astronomical. However, back in 1638, in his Discorsi, Galileo suggested the basis of a terrestrial experiment over a number of miles using lanterns, shutters and telescopes to timed flashes of light. The Florentine Academy in 1667 tried the idea over a distance of one mile without any observable delay. Just nine years later the reason became apparent: Roemers value for c was so great in comparison to human reaction times in operating the lantern shutters that there was no hope of observing the finite travel time delay for c over one mile (or 1609.344 meters).

It was not until 1849 that the French physicist H. L. Fizeau overcame the problem in the following fashion. In the first place it was desirable to have as large a distance as practical involved, instead of just one mile. Fizeau used as his base-line the distance between two hills near Paris, Suresnes and Montmartre, measured as 8633 meters.1 As he had arranged to observe the returning beam of light, the total distance traveled was thus 17,266 meters. Though this distance was large in comparison with the single mile used with lanterns, it was the second shortest base-line ever used in this type of experiment.

In place of the shutters on lanterns, Fizeau used a rotating wheel with 720 teeth and driven by clockwork made by Froment.2 Light from an intense source was focused on the rim of the wheel, then made into a parallel beam by a telescope, and traversed the 8633 meters. There it was received by another telescope which focused the beam onto a concave mirror, sending the light back along the same path that it had just traveled. The returned beam was viewed between the teeth in the wheel. The system was focused with the wheel at rest and with the light shining between the gap in the teeth. The wheel was then rotated, automatically chopping the beam into a series of flashes like the lantern shutters.
Stroboscope Method

diagram courtesy ofhttp://home.iprimus.com.au/longhair1/chap6.htm
(this diagram is for the net article only. A more detailed original diagram will be in the book)



The results

Initially, as the wheels rotation rate was increased from zero, the observed light intensity dropped, until the light flash that had passed between the teeth on the way out struck the next tooth on its return. The observed light intensity was then at its minimum. However, by increasing the wheels rotation rate, a situation arose where the returning flash went through the next gap to the one it passed through on the way out. This gave an observed maximum intensity. Fizeau found the first minimum occurred with the wheel rotating at 12.6 turns per second and the first maximum followed at 25.2 turns per second.3 The flash of light had thus traveled the 17,266 Km distance in 1/(25.2 x 720) seconds. Hence, in one second, the light traveled 25.2 x 720 x 17,266 Km. This gives Fizeaus value for c as 313,300 Km/s. This is the usual figure given in textbooks.

Although this value for Fizeaus result is often quoted,4 the technical literature prefers another value for the following reason. Fizeau stated that his result was the mean of 28 measurements that gave c as 70,948 leagues of 25 to the degree per second (70,948 lieues de 25 au degre).5 As Dorsey points out, the meter was meant to be 1,10,000,000 part of the earths meridional quadrant and hence Fizeaus league became equal to 40/9 Km. Multiplication of 40/9 by 70,948 gives the technically accepted result of 315,300 Km/s as Fizeaus value for c, the speed of light.6

Fizeaus experimental details were not given in his report, and one promised later after further work seems not to have been found. However, in a quote from the French journal L/Astronomie, with no exact reference given, two further values appear against an 1855 date that are presumably Fizeaus.7 They give c as 305,650 Km/s and 298,000 Km/s, thought this latter value may be a bad citation for Foucaults initial work in 1862.

Enter Cornu

In 1872, A. Cornu used Fizeaus method to determine c over a base-line of 10,310 meters from the École Polytechinque to Mont Valerien.8 This was in the nature of a preliminary experiment, and was refined later. Of the 658 measurements made, 86 were determined using a weight driven motor and the remaining 572 using a clockwork spring drive. The results obtained were later rejected by Cornu9 as being affected by serious systematic errors.10 Dorsey states that The apparatus was crude; the precision was low.11 This preliminary result that Cornu rejected was 298,400 Km/s in air or 298,500 ± 300 Km/s in a vacuum.12

In 1874, the Council of the Paris Observatoire, headed by LeVerrier, who was the Observatory Director, and Fizeau, decided to ask Cornu to obtain a definitive value for c. The date was April 2, and the reason was that a transit of Venus was to occur on December 9th of that year. A value for c accurate to one part in a thousand would be needed by astronomers observing the event. Cornu complied with the request.

The sending telescope was mounted on the Paris Observatory and the light flashes sent to the tower of Montlhery where the collimator lens returned the chopped beam. The base-line was 22,910 meters. Four smoked aluminum wheels of 1/10 to 1/15 mm thickness were used. Three had pointed teeth numbering 144, 150, and 200 respectively. The fourth wheel of 40 mm diameter has 180 square teeth. The wheels could be rotated in either direction, which eliminated a number of errors.

The apparatus was powered by a weight-driven, friction-brake controlled device. An electric circuit automatically left a record of wheel rotation rates on a chronograph sheet advancing 1.85 cm/s. A 1/20 second oscillator was used to subdivide the one second intervals of the observatory clock. Times were estimated to 0.001 second were claimed. The main difficulty in observation was the determination of the exact moment of total eclipse of the returned flash as the background is always slightly luminous. The speed of the wheel corresponding to the disappearance of the beam was noted, as was the speed for its re-appearance and a mathematical averaging procedure was adopted.13

Cornus Results

In his initial report of December 1874, Cornu announced that his preliminary reductions of the data resulted in a value for c of 300,330 Km/s in air.14 Multiplied by a refractive index for air of 1.0003 gave the vacuum velocity of 300,400 ± 300 Km/s. After final reductions of the data gave a result of 300,170 Km/s for air, Cornu felt obliged to apply a correction for possible vibrations of the wheel which resulted in a value of 300,350 Km/s in air.15 The addition of the 82 Km/s to bring the value to that of a vacuum gave his final result again as 300,400 ± 300 Km/s to four figures. In all, he claimed to make 630 measurements of c for this toothed wheel determination. However, he records 624 sets of observations, of which he appears to have used 546 in the reduction process.16

Following the publication of the initial report, Helmert noticed that, for low speeds of the wheel, the c values were higher than the mean value, while for high wheel speeds, the values were lower than the mean.17

This suggested that a systematic error was affecting the result such that c* = c (H/q) where c* was the reported value of c, and H = 7.1. The q term was the order of the eclipse so that for higher rotation speeds q was also higher. Dorsey derived a similar function.18 Helmerts correction was generally discussed, verified, and accepted, even as late as 1900, despite Cornus protestations at the treatment.19 The Cornu-Helmert value was 299,990 ± 200 Km/s. Dorsey, after considerable analysis, decided that The best value one can derive from the observations seems, from these data, to be 299.8 metametres/sec. in air with a possible range of ± 0.2.20 After applying a refractive index correction, the final Cornu-Dorsey vacuum c value was 299,900 ± 200 Km/s.

The mean dates for Cornus experiments were 1872.0 for his preliminary work at the Ecole Polytechnique, and 1874.8 for those at the Paris Observatory. It should be noted that Newcomb gives incorrect dates for these determinations and also attributes the value of 299,900 to a re-discussion of Cornus results by Listing.21 Though Listing had just published a paper (Astron. Nachr., Vol. 93, p. 369, 1878) on solar parallax, Cornus results were accepted without discussion. This misinformation was transmitted by Michelson in his Tables22 and by Preston (The Theory of Light, p. 511, 1901). Michelson furthermore quotes the value as Listings even when referencing a work that correctly attributes it to Helmert (Phil. Mag., 6th series, Vol. 3, 1902, p. 334). Later Michelson gave the result as 299,950 Km/s, different from Cornu, Helmert or Listing, leaving the origin of this figure lost in obscurity.23

The Young/Forbes Result

One of the main problems facing the toothed wheel method was the estimation of the exact moment of eclipse of the light beam. Cornu overcame the problem by making pairs of observations on either side of the exact eclipse position and further pairing with reversed wheel rotation. Young and Forbes in England in 1991 used a different technique. From an observing station at Wemyss Bay, light was sent to two distant reflectors, instead of the normal one, in the hills behind Inellan. The reflectors were in the same line but the nearer one was 16,835.0 feet from the observation post, and the other was at 18,212.2 feet distance. The two images so formed were observed simultaneously. The position of the eclipses or the maximum was not needed. The speed of the cogwheel was measured instead at the time when both images appeared to be of equal intensity.

The advantage of this method is that the eye is extremely sensitive to slight differences in the intensity of adjacent images. The extreme disadvantage of their arrangement consisted of the short base-line. Even taking the most distant reflector, the base was only 5551.07 metres long. This was by far the shortest for this type of experiment being not quite two-thirds of Fizeaus base-length. The problems of the short base asserted themselves, as did other experimental features that were not conducive to obtaining good results. This determination was severely criticized by both Newcomb24 and Cornu.25 It is omitted in the definitive list of best c determinations treated by Birge.26 Dorsey comments, it is generally admitted that their work is seriously in error, and is reported unsatisfactorily.27 This Young/Forbes result was given as 301,382 Km/s28 with an unwarranted accuracy but they give no probable error.29

Perrotins Procedures

Joseph Perrotin was born in 1845 and was appointed as the Director of the Observatory at Nice in France during the late 1800s. His assistant at the Observatory was Prim, who had the details of their determination of c by Fizeaus method published in 1908.30 Cornu was still alive at the inception of the project in 1898, and gave his counsel throughout its duration. Cornu died in 1902, the year in which the experimental proceedings were finalized. Perrotin died shortly after, in 1904, before completing the discussion, leaving Prim to release the final calculations in 1908.

In the initial work, centering about 1900.4, the base-line was from the Nice Observatory to the village of La Gaude, a distance of 11,862.2 metres. In the more extensive series, that centered around 1902.4, a longer path of 45,950.7 metres to Mont Vinaigre was employed. In the La Gaude series, a total of 1540 measurements of c were made, 607 by Perrotin and 933 by Prim. The Mont Vinaigre experiment totaled 2465 measurements with Perrotin making 1452 and Prim 1013. In all the complete exercise made 4005 measurements to come to the final value for the series.31

With Cornu as advisor, much of the equipment and procedure was the same. The illuminator and the powering apparatus were those Cornu used, as were the chronograph, pendulums, and 1/20 second oscillator. The microscope with variable magnification was also that used by Cornu in his determination.32 The only essentially different equipment items were the sending and collimator lenses and the toothed wheel itself. This latter was 35.5 mm. diameter, and comprised 150 triangular teeth. It differed from Cornus 150 toothed wheel only in the thickness of the aluminum, being 0.8 mm thick. The stage was thus set for an interesting comparison between Cornus results and those of Perrotin, using virtually the same items of equipment, but separated in time by about 28 years.

Perrotin and Prims Results

As soon as the necessary reductions had been carried out by Perrotin, it was announced that the La Gaude series gave a value of 299,900 ± 80 Km/s.33 The mean date was 1900.4. Under similar circumstances, Perrotin published the Mont Vinaigre result as 299,860 ± 80 Km/s for a mean date of 1902.4.34 On this occasion, he discussed both results and issued their average as 299,880 ± 50 Km/s, the mean date being 1901.4.35 This later figure was frequently quoted as Perrotins final definitive value.

Perrotin began writing up all the details of the two series, but had not completed the task at the time of his death in 1904. Prim continued writing the discussion, issued in 1908, re-working the calculations in the process. Prims discussion makes no mention whatever of the reports that were issued earlier. Instead, he derived a value for the La Gaude series of 300,032 ± 215 Km/s. However, he was unhappy with the method used to obtain the result. The other option that he considered was a least-squares treatment, but he felt that the number of observations over the La Gaude path was too few to justify this approach. Consequently, this La Gaude value was completely discarded as unsatisfactory.36 Prim then re-appraised the Mont Vinaigre experiments and treated them by the least-squares method to yield a final value of 299,901 ± 84 Km/s at the mean date of 1902.4.37 Although Dorsey criticized this value (he did not comment on the earlier reports), he did not derive a better one, despite extensive analysis.

The issuing of this final discussion resulted in some confusion, particularly since Prims final declared value of 299,901 Km/s for the Mont Vinaigre path was so close to the Perrotin value for the La Gaude path of 299,900 Km/s. Many failed to realize that they were from a different series of experiments over a different base-line. Even Michelson fell into this trap, quoting this final declared value as having been obtained over the shorter La Gaude path.38

Conclusions from Toothed-Wheel Experiments

Table 5 summarizes the above results by listing the fourteen values obtained by this method. A least squares linear fit to all these data points gives a light speed decline of 164 Km/s per year, while a fit to the most reliable values, marked [*], gives a decline of 2.17 Km/s per year. The confidence interval was 99.4% that c was not constant at its present value during the period covered by these experiments. The Fizeau values have been described as pioneering experiments that were admittedly but rough approximationsintended to ascertain the possibilities of the method.39 The remaining unstarred values were rejected by the experimenters themselves or have been severely criticized as outlined above. Nevertheless, when all the data points are included, the decrease in the speed of light is even more evident.

The comparison between Cornus re-worked values and those obtained with substantially the same items of equipment by Perrotin is of great interest. The Cornu mean is 299,945 Km/s, while the Perrotin mean is 299,887 Km/s. The drop measured by this same equipment is thus 58 Km/s in 26.6 years. It is fascinating to note that both Perrotin and Prim, despite problems with the analysis, independently obtained results in which the earliest determination resulted in the higher value for c.

If we ignore the bad citation of 1855, the only values that went against the decay trend in the entire of Table 5 were those rejected by the experiments themselves or those severely criticized by others. When combined with the results of the two astronomical type determinations, the decay trend now appears in three different methods of measuring c. These methods have involved about 30 different c measuring instruments, comprising at least six by the Roemer method, at least 21 for aberration, and at least three by the Fizeau method. A decay trend measured by 30 different instruments lengthens the odds against coincidence to roughly one in a billion.


Table 5
Toothed Wheel Experimental Values
(NOED = number of experiments done)

starred values are generally considered the most reliable



Experimenter

Date

NOED

Base line in meters

c value in Km/sec

Comments

Fizeau


1849.5


28


8633


315,300


Base too short (journals)

Fizeau


1849.5


28


8633


313,300


Base too short (textbooks)

Fizeau


1855





8633


305,650


No reference usually omitted

Fizeau


1855





8633


298,000


Bad date citation for Foucault?

Cornu


1872


658


10,310


298,500 ± 300


Rejected by Cornu serious errors

Cornu


1874.8


624


22,910


300,400 ± 300


Flawed analysis 4 figures only

*Cornu/Helmert


1874.8


624


22,910


299,990 ± 200


Reworked in 1876 generally accepted

*Cornu/Dorsey


1874.8


624


22,910


299,900 ± 200


Reworked by Dorsey in 1944

Young/Forbes


1880


12


5551.07


301,382


Usually severely criticized

Perrotin/Prim


1900.4


1540


11,862.2


300,032 ± 215


1908 discarded by Prim

*Perrotin


1900.4


1540


11,862.2


299,900 ± 80


Perrotins published 1900 analysis

Perrotin


1901.4








299,880 ± 50


Perrotins generally accepted mean

*Perrotin


1902.4


2465


45,950.7


299,860 ± 80


Perrotins published 1902 analysis

*Perrotin


1902.4


2465


45,950.7


299,901 ± 84


Prims final declared value



References


1 H. Fizeau, Comptus Rendus, 29:90-92, 132 (1849); also E.R. Cohen et.al., Reviews of Modern Physics, Vo. 27 No. 4, 1955, p. 363

2N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, p. 13

3 K.D. Frooma and L. Essen, The Velocity of Light and Radio Waves, Academic Press, London, (1969), p. 4. Also Martin and Connor, Basic Physics, Whitcomb and Tombs, Melbourne, p. 1377

4 Froome and Essen, pp. cit., p. 4. Also Martin and Connor, op. cit., p. 1378. Also Science, 66, Supp. x, Sept. 30, 1927 in quoting an article from LAstronomie, no exact reference given.

5 H. Fizeau, Comptus Rendus, 29:90-92, 132 (1849); Also, de Bray, Nature, Vol. 120, October 22, 1927, p. 603. Also N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, p. 13

6 De Bray, Nature op. cit. Also Dorsey, op. cit. Note: W. Harkness, Washington Observations for 1885 Appendix III p. 29 lists this value erroneously as an in vacuo result.

7 Anon, Science, 66, Supp. x, Sept. 30, 1927. No exact reference quoted.

8 A. Cornu, Journal de LEcole Polytechnique, 27 [44]:133-180, (1874)

9 A. Cornu, Annales de LObservatoire de Paris Vol. 13, (1876), p. A 298, footnote

10 de Bray, Nature, Vol. 120, October 22, 1927, p. 603 Note (3)

11 N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, p. 15

12 Dorsey, ibid. p. 16. Also de Bray, op.cit., p. 603

13 A. Cornu, Annales de LObservatoire de Paris Vol. 13, (1876), p. A 298, footnote. Also Cornu, Comptus Rendus, Vol 79, (1874), p. 1361. Also Dorsey, op. cit., pp 18, 19

14 Cornu, Comptus Rendus, Vol 79, (1874), p. 1363

15 A. Cornu, Annales de LObservatoire de Paris Vol. 13, (1876), p. A 293. Also N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, pp 34, 35 lists it as 300,340 Km/s.

16 A. Cornu, Annales de LObservatoire de Paris Vol. 13, (1876), p. A266

17 Helmert, Astronomische Nachrichten, 87 (2072), (1876), pp 123-124

18 N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, pp17 and 95, equation (103)

19Rapports presentes au Congres International de Physique de 1900, vol 2, pp225-227. The probable error was estimated by Todd, American Journal of Science, 3rd series, Vol. 19, (1880), p. 61

20 Dorsey, op.cit., p. 36

21 S. Newcomb, Astronomical Papers for American Ephemeris and Nautical Almanac, Vol. 2, part 3, (1891) p. 202.

22A.A. Michelson, Decennial Publications of the university of Chicago, Vo. 9, (1902) p. 6. Also Dorsey, op.cit., pp 76-79

23 A.A. Michelson, Journal of the Franklin Institute, Nov. 1924, p. 627; and Nature, Dec. 6, 1924, p. 831. See also de Bray, Nature, Vol. 120, Oct. 22, 1927, p. 604

24 S. Newcomb, Astronomical Papers for American Ephemeris and Nautical Almanac, Vol. 2, part 3, (1891) p. 119,

25Rapports presentes au Congres International de Physique de 1900, vol 2, p. 229

26 R.T. Birge, Reports on Progress n Physics, Vo. 8, (1941) p. 99

27 Dorsey, op.cit., p. 4

28 Young/Forbes, Phil. Trans., vo. 173, Part 1, (1882) p. 231

29 DeBray, Nature, vol. 120, Oct. 22, 1927, p. 604

30 J. Perrotin and Prim, Annales de LObservatoire Nice, vol. 11, (1908) pp A1-A98

31 Ibid. Tableau III, See also Dorsey, op.cit., pp 40-41

32 See Dorsey, op.cit., p. 37, for comparison of equipment

33Perrotin, Comptus Rendus, Vol. 131, (1900) p. 731

34Perrotin, Comptus Rendus, Vol. 135, (1902) p. 881

35 Ibid. p. 883

36 Dorsey, op.cit., p. 37. See also de Bray, Nature, vol. 120, Oct. 22, 1927, pp. 603-604

37J. Perrotin and Prim, Annales de LObservatoire Nice, vol. 11, (1908) pp A1-A98

38A.A. Michelson, Journal of the Franklin Institute, Nov. 1924, p. 627; and Nature, Dec. 6, 1924, p. 831. See also de Bray, Nature, Vol. 120, Oct. 22, 1927, p. 604

39DeBray, Nature, vol. 120, Oct. 22, 1927, p. 603, quoting Fizeau, Comptus Rendus 29:90 (1949)

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Journal Article Printable view
Dispersion in the Ether: Light over the Water
Dispersion in the Ether: Light over the Water
Journal Physics in Perspective (PIP)
Publisher Birkhäuser Basel
ISSN 1422-6944 (Print) 1422-6960 (Online)
Issue Volume 3, Number 3 / September, 2001
DOI 10.1007/PL00000533
Pages 258-270
Subject Collection Physics and Astronomy
SpringerLink Date Thursday, February 19, 2004

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Abstract

This is an account of measurements of the velocity of light by James Young (1811-1883) and George Forbes (1849-1936) around 1880 based upon an improved version of Fizeau's toothed-wheel method. They presented evidence for a dispersive effect resulting in a difference in the velocity of 1.8% across the visible spectrum. This conflicted with Albert A. Michelson's measurements and prompted discussions by Lord Rayleigh, Arthur Schuster, Léon Gouy, J. Willard Gibbs, and Paul Ehrenfest that led to the conclusion that not the phase velocity but the group velocity was being measured, and that there was no theoretical foundation for Young and Forbes's result.

What does this mean, that there was no theoretical foundation?

Anonymous:
I have been thinking about what you said concerning wave velocity and group velocity. I believe the wave form is the clean form, is the signal form. Conversely, I believe group velocity is a dirtier form, and as a consequence, it becomes "slowed down" in reference to the vacuum, which does not possess glass, mirrors, or metal. So, I would have to say, that in terms of speed, group velocity is less than wave velocity.

In terms of the group form carrying a signal FTL, I would have my misgivings about whether I would want to call it a velocity, or not