zotero-db/storage/5KDMV57H/.zotero-ft-cache

PACS №: 03.30. +p
H`ector A. Mu`nera, Daniel Hern`andez-Deckers, Germ`an Arenas, Edgar Alfonso
Department of Physics, National University, Bogota`, Colombia
Observation During 2004 of Periodic Fringe-Shifts in an Adialeiptometric Stationary Michelson-Morley Experiment

Contents

1. The evidence for a constant speed of light in 1900

70

2. The MM experiment: a huge blunder?

73

2.1. Was the MM experiment negative? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.2. Eﬀect of solar motion upon the velocity of the laboratory . . . . . . . . . . . . . . . . . . . . . . . 75

2.3. Eﬀect of solar motion upon the interference fringe-shift . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.4. Analysis of solar motion in Michelson, MM, and Miller works . . . . . . . . . . . . . . . . . . . . . 79

3. Our adialeiptometric experiment at CIF

80

3.1. Design of our experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.2. Description of our experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.3. Expected fringe-shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.4. Operational tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.5. Data recollection and raw data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4. Analysis of data

85

4.1. Environmental eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2. Typical corrected fringe-shift curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3. Solar velocities consistent with observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5. Closing remarks

87

Abstract
Adialeiptometry means unceasing or continuous measurements. We have carried out continuous measurements with a stationary Michelson-Morley interferometer at our CIF laboratory in Bogota (Colombia) for almost two years from the end of 2003 to June 2005. The paper reports the results for year 2004, during which we identiﬁed large periodical fringe-shifts, after correcting for environmental variables. To provide a context for the new experimental results presented in this paper, we start by discussing the meaning of speed of light at the time of Einstein, and present next the evidence then available for its constancy. We argue that the evidence provided by the original MM experiment and its repetitions is not as strong as usually believed, thus justifying a new experiment that corrects for the main weaknesses uncovered. The observed periodical variations are consistent with the predicted curves using a constant speed of light in a preferred frame, that adds vectorially to the laboratory velocity using Galilean addition. The solar motion that explains our observations is similar to other modern estimates of solar velocity.

1. The evidence for a constant speed of light in 1900
To provide a context for the new experimental re-

sults presented in this paper, we start by discussing the meaning of speed of light at the time of Einstein, and present next the evidence then available for its constancy. Section 2 argues that the evidence provided by the MM experiment and its repetitions is not as

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Observation During 2004 of Periodic Fringe-Shifts in an Adialeiptometric Stationary Michelson-Morley Experiment

strong as usually believed, thus making it reasonable to carry out a new experiment, described in section 3, that corrects for the main weaknesses uncovered. Section 4 summarizes our main empirical results, and section 5 closes the paper.
Einstein’s special theory of relativity (STR) is based on two assumptions: the postulate of relativity, and the postulate that the speed of light is independent of the state of motion of the observer. The ﬁrst postulate is a philosophical principle that nearly everybody accepts in one form or another; for instance,the principle of Galilean relativity is ﬁrmly entrenched in classical mechanics. Contrariwise, the second postulate has empirical nature and constitutes a testable assertion. The obvious question arises: was there any empirical evidence at the turn of the 20th century for the second postulate? As discussed in the following, the importance of the negative interpretation of the famous Michelson-Morley (MM henceforth) experiment [1] is that it constituted the main direct evidence to support the second postulate; on the contrary, any positive result in a MM-type experiment would falsify the postulate.
In the spirit of Newtonian mechanics, that was the dominant paradigm in 1900, let us consider that motion is relative to a preferred frame of reference Σ, and that time is universal, in the sense that all observers in the universe may agree on a common scale. Let us determine the speed of light in the laboratory. A photon1 moves in straight line (deﬁned by the light path itself) from a light source at A to a photon detector at B, stationary in the laboratory and located at a distance D measured with rod sticks. If the time of ﬂight from A to B is tAB, the one-way speed of light over the line segment AB is

cAB

=

D tAB

(1)

The speed deﬁned by eq. (1) is, of course, an average over the segment AB, and has the familiar meaning of everyday language. For any lay person it is extremely surprising to realize that the one-way speed of light was unknown during Einstein lifetime, and still is unknown today! Although various suggestions to measure the one-way speed of light have been proposed over the years [2–5], to our knowledge, no successful experiments with B stationary in the laboratory have been carried out, let alone with B in motion. That is, when detector B moves with respect to the laboratory along the light path, up to date there is no empirical evidence indicating whether the one-way speed of light varies, or does not.
The diﬃculty to determine the one-way speed of light entirely resides in the measurement of tAB, which
1Our analysis is done in the Newtonian context, from a modern vintage point. Then, ether is not mentioned, and light is treated as a particle. The wave-particle duality appears in interference phenomena.

is the diﬀerence between the time at B when the photon arrives, and the time at A when the photon is emitted. There are two aspects: (i) Then on-existence of clocks with a resolution high enough to measure the extremely short time intervals involved in a laboratory experiment, and (ii) The diﬃculty to synchronize the two clocks at A and B.
All the classical experiments to determine the speed of light in the laboratory (Fizeau, Foucault, Michelson [6,7]) measured c2 the average speed of light along a two-way straight line from A to B, and back to A, deﬁned by

c2

=

2D tAB + tBA

⇒

2 c2

=

1 cAB

+

1 cBA

(2)

Table 1 summarizes the values at the beginning of 20th century for the speed of electromagnetic radiation, in free space according to textbooks [8,p.847]. Note, however, that experiments have never been made in “free space”,whatever it is; the majority of values correspond to the measurement of c2 for light propagating in air in our terrestrial laboratory, which moves with some unknown velocity V(t) relative to Σ. The speed for light propagating in a vacuum in our terrestrial laboratory is calculated by adding a correction based on the index of refraction in air, which is a function of air density.The latter depends of air composition (mainly humidity), and ambient pressure and temperature at the moment of the measurement. For instance, Michelson based his correction on mean2 pressure and temperature [7, p.2, footnote 2], and added the same correction of 67 km/s to all his speeds in air during the 1924 and 1926 experiments, undoubtedly made under diﬀerent ambient conditions [7, p.2, 4, 5,9, 10, 11]. By the way, this cavalier procedure to obtain the vacuum speed casts some doubts on the correctness of the small uncertainty of 4 km/s quoted by Michelson for his 1926 experiments [7, p.12], and shown in table 1.
In the experiments of table 1 the positions of the mirror at B and the detector at A do not change with respect to the laboratory, so that they do not give clues on how the motion of the observer with respect to the laboratory would aﬀect the value of the two-way speed of light. Regarding the motion of the laboratory with respect to the preferred frame, the earth’s orbital speed around the sun is about 30 km/s, smaller than the uncertainty of 30 to 60 km/s, that was attainable by the end of the 19th century (see table 1). Hence, the measurements available in 1905 for the two-way speed of light could not possibly uncover any eﬀect arising from the orbital motion of the observer.
However, if the high resolution of 4 km/s quoted by

2Michelson does not specify what is “mean” in this context. Is “mean” the average during the summer months at the time of the observations, or is it the diurnal average during the summer months, or is it the 24-hour daily average over the summer months, or is it the 24-hour daily average over the whole year...?

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Table 1. The two-way speed of electromagnetic radiation in terrestrial laboratories [8], speed and uncertainty in km/s

Date 1849 1862 1876 1880 1883 1883 1906 1923 1924 1926

Experimenter Fizeau (France) Foucault (France) Cornu (France) Michelson (USA) Newcomb (UK) Michelson (USA) Rosa-Dorsey (USA) Mercier (France) Michelson (USA) [6,7] Michelson (USA) [7]

Method Toothed wheel Rotating mirror Toothed wheel Rotating mirror Rotating mirror Rotating mirror Electromagnetic theory Standing waves Rotating mirror Rotating mirror

Speed 313,300 298,000 299,990 299,910 299,860 299,853 299,781 299,782 299,802 299,796

Uncertainty -
500 200 50 30 60 10 15 30 4

Michelson for his 1926 experiment is correct, such experimental set up was capable of uncovering the variations in c2 due to the diurnal variation of the projection of V(t) along AB (arising from rotation of earth), and due to the annual variation of V(t) resulting from the orbital motion of earth. In an experiment designed with this objective in mind, observations should be made at diﬀerent times of the day during the whole year, so that the possible diurnal and annual periodicities may be identiﬁed (see section 2.2). Michelson?s observations were carried out during the 1926 summer only, so that the eﬀect of velocity could not possibly be observed. Nonetheless, for a diﬀerent reason, Michelson noted that hew anted to repeat the experiment in December 1926 [7, p.12].
There existed since the end of the 19th century a procedure to determine diﬀerences in the two-way speed of light. Indeed, Michelson invented his interferometer in 1881[9] to compare c2 (1), the two wayspeed of light along arm 1, to c2 (2), the two wayspeed of light along arm 2. The interferometer was improved for the1887 MM experiment [1]. According to MM’s negative or null interpretation , they did not observe any diﬀerence between c2 (1) and c2 (2), hence they concluded that the two-way speed of light in our moving terrestrial laboratory is constant along any direction. Next section 2 discusses whether the MM experiment was properly designed to observe what MM wanted, the relevant issue in this section being whether Einstein was aware of the null interpretation of the MM experiment while developing his ideas about the second postulate.
Einstein occasionally made the statement that he did not know the results of the MM experiment before 1905:“When I asked him [Einstein] how he had learned of the Michelson-Morley experiment, he told me that he had become aware of it through the writings of H. A. Lorentz, but only after 1905 had it come to his attention! ‘Otherwise,’ he said, ‘I would have mentioned it in my paper’ ” emphasis in the original [10, p.48]. This

recollection by Einsteinis contrary to the most recent documental evidence contained in Einstein’s Love Letters [11, 12], showing that Einstein was aware of the MM experiment before1905 both indirectly and directly, as follows:
Indirect knowledge of MM experiment. Einstein read the work of Lorentz by the end of 1901 and the beginning of 1902, as attested by letter 48 dated in Schaﬀhausen (Switzerland) on 28 December 1901 where Einstein writes to Mileva: “I want to get down to business now and read what Lorentz and Drude have written about electrodynamics of moving bodies” [12, p.72]. These books were the 1895 theory of Lorentz [13], and the 1900 optics book by Drude [14]. The empirical basis for Lorentz’ work was the “negative” interpretation of the MM experiment. Indeed, Lorentz was closely following Michelson’s work right from the beginning and send him a correction to the 1881 experiment [9] that was acknowledged by MM in the 1887 paper [1, p.451] . Evidently, Lorentz continued quite worried about Michelson’s “negative” results, as attested by a letter to Lord Rayleigh on 18 August 1892; Lorentz asked: “Can there be some point in the theory of Mr. Michelson’s experiment which has as yet been overlooked?” [15, p.32]. In addition, Einstein learnt about Lorentz work, and its physical basis, through Drude’s book. The English translation of this book says in the introduction to chapter VIII [14, p.457]:“The assumption which will be adopted here is that the ether always remain completely at rest. Upon this basis H. A. Lorentz [13] has developed a complete and elegant theory. It is essentially this theory which is here presented emphasis in the original.
Direct knowledge of MM experiment. In the same chapter VIII, Drude explicitly discusses the empirical evidence, including Michelson’s 1881 experiment in great detail [14,p. 478-481], and the 1887 MM experiment in less detail [14, p.481-482], i.e.,from Drude’s work Einstein learnt about the constancy of the twoway velocity of light in January 1902. But Einstein had

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Observation During 2004 of Periodic Fringe-Shifts in an Adialeiptometric Stationary Michelson-Morley Experiment

previous information on the same subject. In letter 11 dated in Milan around 28 September 1899 Einstein says:“I read a very interesting paper by Wien from 1898 on this subject” [12,p.15]. Wien’s paper [16] describes 13 experiments related to the detection of the motion of earth relative to the ether.
The MM experiment is in the list of 10 experiments with negative results [12, p.85]. The explicit text is:“If the ether is at rest, then the time a light ray needs to travel back and forth between two glass plates must change if the plates are moving [with velocity v]. The change depends on the quantity ν2A2 [A is the reciprocal of the speed of light], but should be observable by the application of interferometry. The negative result is incompatible with the assumption of an ether at rest. This assumption can only be maintained by means of the hypothesis that the linear dimensions of rigid bodies are altered by motion through the resting ether in the same ratio, so as to compensate for the lengthening 3 of the path of the light ray” [11, p.46]. Hence, Einstein read about the “negative” interpretation of the MM experiment as least as early as September 1899.
The foregoing new evidence casts serious doubts on the conventional view propounded by Holton [17, 18] that the role of the MM experiment was minor in the genesis of STR. It is clear that Einstein knew at least since 1899 that, according to the experimental evidence, the two-way speed of light was independent of direction, and that such a fact necessitated some appropriate physical explanation.
This being so, one may be tempted to say with Edwards [19, p.485] that the second postulate should be amended to explicitly state that the constancy of light assumed by Einstein refers to the two-way speed of light; if that were the case, the second postulate would contain no information about the one-way speed of light. However, given Einstein’s concern for economy of thought, it is more likely that Einstein was thinking in his second postulate about the one-way speed of light. In that case it holds that cAB = cBA, and eq. (2) would immediately imply that the two-way speed is c2 = cAB the same for any orientation of the segment AB. In both interpretations, the second postulate may be falsiﬁed if the two-way speed of light depends of direction, that is,if a MM experiment yields positive results. Notice that to falsify the second postulate there is no need to measure the one-way speed, thus making moot the conventionalist stance that it is impossible to measure it [20].
Einstein was deeply aware that a positive result in a MM experiment would destroy his theory. Regarding Miller’s work (brieﬂy discussed in next section), Einstein wrote:“the existence of a not trivial positive eﬀect would aﬀect very deeply the fundament of theoretical physics as it is presently accepted” [21, p.2283].
3We ask: Is it shortening rather than lengthening?

2. The MM experiment: a huge
blunder?
In retrospect, it is very surprising that Michelson’s work regarding the MM experiment was not closely scrutinized in his epoch, especially for the very deep implications it had. It is well known that both Lord Kelvin and Lord Rayleigh urged Michelson to repeat the 1881 experiment [15, p.25], and that in1900 Kelvin urged Morley and Miller for a repetition of the 1887 MM experiment[15, p.33; 22, p.208]. The uneasiness of Lorentz is reﬂected in his 1892letter to Rayleigh quoted above [15, p.32]. Towards1900 there were several minor criticisms to some aspects of the setup of the MM experiment, that we have listed elsewhere [23, 24], but the only signiﬁcant critical appraisal of the whole process was done by Hicks in 1902 [25]. The most disturbing aspect, however, is Miller’s claim [22] that the MM experiment was always positive. We turn now to that subject and to two new criticisms thatwe have recently advanced [24, 26].
2.1. Was the MM experiment negative?
Firstly, it must be noted that MM did not obtain a zero shift of the reference fringe, as ﬂatly expressed in both relativistic and classical mechanics textbooks,without any caveats whatsoever. Rather, they found that “the relative velocity of the earth and the a ether is probably less than one sixth the earth’s orbital velocity, and certainly less than one fourth” [1, p.458].This means that according to their data reduction process they found a motion of earth relative to the preferred frame that certainly was less than 7.5 km/s, and probably less than 5 km/s. These values are no doubt smaller than their incorrectly expected 30 km/s (see section 2.2), but certainly they were not zero.
It is most striking that the 1887 MM paper [1] contains no analysis of experimental error,which was roughly done for the 1881 experiment [9]; even the straight forward statistical error analysis is missing. Consequently, there are no error bars in their famous ﬁgure 6 [1, p.458] upon which MM based the conclusion quoted in previous paragraph. Moreover, ﬁgure 6 is obtained from the data listed in two tables of the original paper [1, p.457] by an additional reduction process that is unexplained by MM; this weakness in the MM paper went unnoticed until quite recently [27]. We have calculated elsewhere [24, 26] the statistical error associated with the whole reduction process. The very large error bars preempt the conclusions drawn by MM. On the contrary, one may argue that the observations are compatible with MM’s original expectation of 30 km/s.
Additionally, we also revisited all the original MMtype experiments up to 1930, and we found that all of

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them presented small, but non-zero fringe-shifts [23]. Such small fringe-shifts were interpreted as negligible by the experimenters, and therefore in support of the STR. Miller [22] was the only author that interpreted his results as positive fringe-shifts.
Michelson left Cleveland in 1899. From 1902 to his retirement in 1906, Morley teamed up with Miller to repeat the experiments with more sensitive interferometer shaving light-paths of 32 m, about three times the path of the 1887 MM apparatus[22, p.208-217]. Observations were made in August 1902 and June 1903 consisting of 505 turns of a wood apparatus, and with a steel interferometer in July 1904 (260 turns) and July, October,November 1905 (230 turns). Morley and Miller obtained positive eﬀects between 7 and 10 km/s shown in ﬁgure 4 of Miller’s ﬁnal paper [22, p.207]. Miller also recalculated the original 1887 MM results, applying a linear correction suggested by Hicks for thermal shift [25], and obtained “a velocity of 8.8 km/s for the noon observations and 8.0 km/s for the evening observations” [22, p.207], similar to MorleyMiller results.
It may be noted that the Morley-Miller experiments involved 995 turns of the interferometer in the period 1902-1905, while the MM experiment only consisted of 36 turns of the apparatus in the period July 8-12, 1887. It is quite astonishing that the scientiﬁc community accepted the negative interpretation of the latter, and rejected the positive interpretation of Morley-Miller, based on 30 times more data. Technological design of the experiment, and its environmental control were similar in both cases.
Miller resumed alone the interferometer experiments in 1921. During 1921 and 1924 he made observations at Mount Wilson involving 1,181 turns of the interferometer,during 1922-1924 he took data in Cleveland involving 1,146 turns of the apparatus, and again at Mount Wilson in April 1, August 1, and September 15, 1925 and February 8, 1926 Miller performed 6,402 turns of the interferometer. Once again, Miller observed positive results between 9.3 to 11.2 km/s, and additionally uncovered an annual periodicity in the variation of light-speed [22, p.217-230].
By the time that Miller completed his analysis of data around 1930, Einstein’s STR was ﬁrmly entrenched and his results were received with great skepticism.Shankland and collaborators [28] analyzed Miller’s work in 1955; they acknowledged that Miller’s velocity variations were not random, but surprisingly concluded that Miller’s periodical changes were caused by thermal (presumably periodical) variations. Miller had passed away in 1941 and could not defend himself, but this particular issue was empirically checked many years before by Miller during the 1922-1924 tests. From his tests Miller hadal ready concluded that thermal variations could not possibly lead to the periodical eﬀects that he had observed [22, p.220]. For further arguments in support of Miller’s claims see De

Meo’ revision of Miller’s work [29].
Since the 1990’s, there has been a renewed interest in Miller’s work; several authors independently consider that Miller’s results are real and not mere experimental artifacts [23,29-35]. In particular, Allais [32,34] has uncovered new annual periodicities in Miller’s data. Then, if Miller’s results represent real variations of the speed of light caused by the motion of the laboratory, what is the origin of the small amplitude of the variations (hence, the small laboratory velocity) observed by MM and by Miller? This is the remaining puzzle in the whole history. In our earlier work [35, pp. 192-193; 36, pp. 474-475]the clue has been oﬀered: the MM and the Miller experiments were designed to measure fractions of wavelength, larger variations were recalibrated away. To solve this problem, we analyze in next section 2.2 the eﬀect of solar motion upon the readings in any interferometer.
For completeness, let us note that the vast majority of the physics community does not take seriously Miller’s claims. They argue that after 1930 the MM experiment has been repeated many times using modern technology, and that the results have always been in accordance with the original MM experiment. A precision is required here.Starting with the KennedyThorndike (KT) experiment [37], the data reduction process suﬀered a change. Up to this turning point, the fringe-shifts were analyzed in an eﬀort to detect variations that would lead to a measurement of diﬀerent velocities of light along the two arms of the interferometer. About that time a consensus emerged that the (presumably) null-results of the MM experiments could be interpreted as empirical proof of the lengthcontraction predicted by STR. For instance Robertson [38, p.380] stated: “No signiﬁcant diﬀerence in times was found, and since the original experiment and its repetitions were carried out at various orientations and at various times of the year, we would seem justiﬁed in interpreting this null-result as [independence of direction]”. It is amazing that Robertson completely ignored in 1949 the results of Miller’s experiments that were published in the same journal in 1933.
The experimental setup in the KT experiment is very similar to previous MM experiments (except for the length of the arms which is not the same4), but the analysis of data is quite diﬀerent. In the KT experiment, it is assumed that the length of the arms of the interferometer are shorter than the physical value,
4For most authors this is a very important diﬀerence; in our opinion it is negligible. The reason being that in the MM experiment the length of arm 1 equals the length of arm 2 up to macroscopic accuracy (at best, some tenths of millimeters). This accuracy is meaningless relative to the variations of tenths of a wave-length of visible light that are involved in the shift of an interference pattern. On the other hand, if the lengths of the arms are adjusted to the same length using the interference pattern itself, then we are begging the question because we are using as a standard of length the same ruler whose variation we are trying to measure.

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Observation During 2004 of Periodic Fringe-Shifts in an Adialeiptometric Stationary Michelson-Morley Experiment

according to the Lorentz length-contraction; hence, light apparently takes a shorter time to travel along the shortened arms. The observed fringe-shift (null, or otherwise) is then interpreted as a measure of time dilation with respect to the diﬀerence of apparent travel times along the two shortened arms. Since the observed data are subject to various manipulations during the interpretation of a KT experiment, it is quite diﬃcult to assert from the data reported in the open literature whether a particular KT experiment exhibited fringe-shift relative to absolute space, or not.
As an example consider the excellent, and often quoted, experiment by Brillet and Hall (BH henceforth), who started their paper stating that:“Our conventional postulate that space is isotropic represents an idealization of the null experiments of Michelson and Morley” [39, p.549]. Note that BH talked of an “idealization”, and did not claim that their experiment was exactly the same as MM experiment; indeed, a couple of paragraphs below BH explicitly compared their results to the experiment of Jaseja and coworkers using infrared masers [40]. The latter belongs to a group of experiments headed by Prof. Townes on the isotropy of space [40-42]. Cedarholm and Townes explicitly state that “the experiment is more closely related to the Kennedy-Thorndike experiment than to that of Michelson and Morley” [42,p.1351, ﬁrst column]. Other contemporary experiments either belong to the KT class [43], or have built-in corrections, whose interpretation is not clear-cut [44]. A recent paper even suggests that the theory behind resonant cavity experiments (as the BH experiment) may be more complicated than expected [45].

2.2. Eﬀect of solar motion upon the velocity of the laboratory
The absolute velocity of earth’s center of mass V(t) is the vector addition of V0(t) , the orbital motion of the center of mass of earth around the sun, plus Vs the solar system motion:

V(t) = Vs + V0(t)

(3)

Miller used the same conceptual model for his analysis of the 1925-26 observations, he even built a mechanical model [22, p.22]. Of course, solar motion is formed by the velocity with respect to the center of mass of our galaxy, plus the motion of our galaxy with respect to Σ. For the observation periods of a few years relevant to this paper, Vs is assumed to be constant.
For the calculations, let us adopt celestial equatorial coordinates (see any book on practical astronomy [46, 47]) with the celestial equator contained in the Z-X plane and the celestial northern pole along the Y-axis. To calculate orbital velocity V0(t) the following approximate model is used: (i) the earth moves circularly on the plane of the ecliptic, (ii) the orbital period is 365.25 solar days, (iii) the tangential speed

Fig. 1. Equatorial system of coordinates attached to absolute space. The Z-axis points towards the ﬁrst point of Aries, which is a ﬁxed point in space, on the date of the vernal equinox. At left, the earth as seen from the celestial north ernpole. At arbitrary time t a plane containing the Greenwich meridian makes angle σ with the plane deﬁned by the Y-Z axes. An observer at longitude φ is rotated through an angle ρ relative to the Y-Z plane.

V0 is 29.8 km/s; (iv) the origin of time is noon of March 21 every leap year. It is assumed that at t = 0 an observer G on the Equator (latitude λ = 0) at the Greenwich meridian (longitude φ = 0) sees the Z-axis
The observer G rotates counterclockwise on the ZX plane with a period T = 365.25/366.25 = 0.99727 solar days. At any arbitrary time t (in solar days) observer G has rotated through an azimuth angle σ relative to the Z-axis given by

σ = 360◦mod[t, T ]

(4)

The angle σ is shown in ﬁgure 1, and is a good proxy

for sidereal time. As an aid to reckon daily fringe-

shifts, the number of days elapsed until the ﬁrst day

of each month since the beginning of a 4-year cycle

starting March 21, 2000 is included as Annex 1.

As usual, local civil time t∗ (in solar hours) may be

converted to universal time t (also in solar hours) by

using

t

=

t∗

−

24φT imeZone 360

(5)

where φT imeZone is the nominal longitude for the international time zone, positive (negative) to the
east (west) of the Greenwich meridian. For the calculations used in this paper: φT imeZone = −75◦ for Bogota (Colombia) and Cleveland (Ohio),and φT imeZone = −120◦ for Mount Wilson (California).
In the spherical coordinates associated with the
equatorial celestial coordinates shown in ﬁgure 2, so-
lar velocity Vs is described by magnitude Vs, right ascension angle α and declination angle δ so that

VXS = VS cos δsin α,

VYS = VS sin δ,

(6)

VZS = VS cos δcos α

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Fig. 2. The earth moves on a circular orbit with speed V0 on the plane of the ecliptic deﬁned by the Ze-Xe axes. The equatorial system of coordinates XYZ is ro-
tated through an angle ε with respect to the ecliptic; the directions of the Z and Ze axes coincide. At left, solar velocity Vs in spherical coordinates (Vs,α, δ) in the equatorial system of coordinates.

To calculate the orbital motion of the earth around the sun, ecliptic coordinates are used with the plane of ecliptic contained in the Ze-Xe plane. The Ze-axis has the same orientation as the equatorial Z-axis: towards the ﬁrst point of Aries (see ﬁgure 2). At t = 0 the orbital velocity of earth is Ve (t = 0)= -V0ie. Since the motion of earth is counter-clockwise,at any time t the orbital velocity in ecliptic coordinates is

Ve(t) = V0 (−iecos ω0t + kesin ω0t)

(7)

where ie, je, ke are the unit vectors along the Xe, Ye, Ze-axes and the angular orbital speed is ω0 = 2π radians/365.25 solar days. The inclination of the plane of
the ecliptic relative t0 the equatorial coordinates is = 23.44◦,so that orbital velocity V0(t) in celestial equatorial coordinates is obtained by rotating the system
around the Ze-axis to get:

V0(t) = RεVe(t) = V0 (−icos ω0tcos ε − jcos ω0tsin ε + ksin ω0t) (8)
where Rε is the rotation matrix from ecliptic to equatorial coordinates (see table 2). In equatorial coordinates,the velocity of the earth is then
V(t) = i(Vs cos δsin α − V0 cos ω0tcos ε) + j(Vs sin δ − V0cos ω0tsin ε) + k(Vs cos α + V0sin ω0t) = iVX + jVY + kVZ (9)
The rotation of the earth around her axis does not contribute, of course, to the velocity of her center of mass relative to Σ, and the contribution of earth’s rotational velocity to the total speed of a laboratory on the surface of earth is certainly negligible. However, earth’s rotational motion has an extremely signiﬁcant eﬀect on the magnitude and direction of the projection of V(t) on the plane of the interferometer, eﬀect

that has been often overlooked by other investigators.
Consider a laboratory located on the surface of the
earth at latitude λ (positive north of the equator) and
longitude φ (positive east of Greenwich), and let a measurement be performed at local civil time t∗ (in hours). At t∗ the plane deﬁned by the local meridian
and the axis of rotation of earth makes angle ρ with
the plane deﬁned by the Z-Y equatorial axes:

ρ=σ+φ

(10)

A rotation of coordinates Rρ around the Y-axis through ρ aligns the Z-axis with the local meridian (see ﬁgure 1). A further rotation of coordinates Rλ around the X-axis through angle λ directs the Z-axis towards the local zenith.In this way the local horizon system of Cartesian coordinates is obtained with the X-axis oriented to the local east (E), the Y-axis oriented to the local north (N) and the Z-axis oriented to the zenith (U = up).
In local horizon coordinates the absolute velocity of the center of mass of earth is then

VL(t) = VEeE + VN eN + VU eU = RλRρV(t) (11)
where e is the unit vector along each direction, and the rotation matrices RλRρ are deﬁned in table 2. Substituting (9) into (11) we explicitly get

VE = VX cos ρ − VZ sin ρ

VN = −(VX sin ρ + VZ cos ρ)sin λ + VY cos λ

VU = (VX sin ρ + VZ cos ρ)cos λ + VY sin λ

(12)

The absolute velocity of the solar system is not known with certainty. On the contrary, the experiment reported in this paper could be used to obtain its value [36]. Table 3 presents the values of solar velocity used by Michelson in the design of his experiments in 1881 and 1887 (items 1 and 2). Items 3 and 4are the two values derived by Miller from his observations in the 1920’s. Item5 is the solar velocity obtained by Marinov in the late 1970’s in an experiment with two rotating coupled interferometers [48]. Finally, item 6 is the velocity of earth relative to background radiation, obtained by means other than interferometric experiments [49].
For two of the scenarios above, ﬁgure 3 presents the variation of terrestrial motion in Cleveland, Ohio (φ =81◦ −39 W , λ=41◦ −30 N ) during 8 July 1887,which was the ﬁrst day of the MM experiment. It may be seen that at the time of the experiment (noon and 6 p.m.) the speed towards the east was much larger than the 30 km/s incorrectly expected by MM, and the speed towards the north was not zero as incorrectly expected by MM. On the contrary, both component of velocity are in general much larger than 30 km/s. These two facts immediately imply that the MM experiment was incorrectly designed. This is a novel and deep failure in the MM experiment, that we recently recognized

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Table 2. Rotation matrices used in the calculations

Rε

Rρ

cosε −sinε 0 cosρ 0 −sinρ 1

Rλ

0

0

sinε cosε 0 0 1 0 0 cosλ −sinλ

0

0 1 sinρ 0 cosρ 0 sinλ cosλ

Table 3. Some estimates of solar velocity

Item Name

Description

VS, km/s

α

δ

1 Michelson1881[9] Estimate in 1881

30

18 hr

+26◦

2 MM1887 [1])

Solar speed ignored (1887)

0

X

X

3 Miller1[22,p.231] Initial evaluation (1928)

200

17hr − 30min

+65◦

4 Miller2[22,p.234] Recalculation in 1932

208

4hr − 54min −70◦ − 33

5 Marinov [48]

Rotating interferometers 303 ± 20 14.28 ± 0.33hr −23◦ ± 4◦

6 SGM [49]

Background radiation

390 ± 60 11.0 ± 0.6hr +6◦ ± 10◦

Fig. 3. Components of terrestrial motion in Cleveland (Ohio) on 8 July 1887, the ﬁrst day of the MM experiment for two scenarios of solar motion in table 3 (see text): item 4 = Miller2, and item 6 =SGM. The Cartesian components of the velocity of the laboratory present large diurnal variations, whose shape depends of solar velocity.
[24], after being unnoticed for more than 120 years. This subject is expounded in next section 2.3.
Figure 3 also shows that at noon and 6 p.m. the magnitude of each speed is rapidly varying. Hence, during the duration of a session of the MM experiment (say, between 30 and 60 minutes) there is a signiﬁcant change on the eastern and northern components of speed. This immediately implies that the initial fringeshift at position 0 is not the same as the ﬁnal fringeshift at position 165, despite the fact that at both
5MM rotated the interferometer in 22.5◦ steps with respect to a local direction, say the east. Arm 1 to the east is position 0, arm 1 at 22.5◦ relative to the east is position 1, and so on.

positions the apparatus has the same orientation with respect to the laboratory. This additional fringe-shift at position 16 is a cumulative process that steadily grows during the 6 turns of the MM interferometer. The overall result is the monotonous drift present in MM data [1], which did not merit any comment from MM but was recognized by Hicks [25], who ascribed it to“thermal eﬀects”. On the contrary, in our opinion, the change in the position of the reference fringe at position 16 is a signature of absolute motion, which accounts, at least partially, for the observed monotonic drift [35, 36].
2.3. Eﬀect of solar motion upon the interference fringe-shift
The MM experiment was designed in the context of Maxwell’s theory. For our purposes, the basic assumption is that the speed of light is a constant c with respect to the preferred frame Σ, independently of the direction of propagation, and of the velocity of the emitter. Regarding the latter, there exist alternative theories where the motion of the source aﬀects the speed of light [50]; the evidence in favor of independence of c with respect to the motion of the source has been provided by astronomical observations (for instance, De Sitter observation of twin stars) and by laboratory experiments [51]. For a revision of evidence see [52]. For the time being, we simply assume that c
Position 16 is a full turn.

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is independent of the motion of the source. Also, from the isotropy assumption, it follows that c may be interpreted as a one-way velocity. For an observer at rest in Σ, the two-way velocity eq. (2) has exactly the same value c.
An observer in motion with respect to Σ will measure a diﬀerent speed according to Galilean velocity addition.In a Michelson interferometer light propagates along two diﬀerent directions (arms 1 and 2) orthogonal to each other. For an apparatus on the surface of earth the time-dependent components of the terrestrial velocity VE , VN , VU deﬁne the response of the interferometer. For instance, a vertical stationary interferometer with one arm oriented along the WE axis, and the other perpendicular to the local horizontal plane is controlled by VE and VU . More relevant to the analysis in this paper is a stationary horizontal interferometer with arm 1 oriented from west to east, and arm 2 oriented from south to north, where components VE and VN control the operation of the apparatus.
Consider a stationary interferometer with L1 the length of arm 1 oriented WE, and L2 the length of arm 2 oriented SN, and let Tj be the two-way time of transit of a light-ray along arm j=1,2 of the interferometer. Then, the diﬀerence in the time of transit as given by the time-delay of the light signal is

∆T

=

T1

− T2

=

LβI2cos 2γ c(1 − βI2 )

+

∆L(4 − βI2) c(1 − βI2 )

(13)

where

∆L =

L1

− 2

L2

,

L=

L1

+ 2

L2

,

β1

=

VI c

(14)

and the projection of earth’s absolute velocity upon the plane of the interferometer is VI (t) given by

VI = VN2 + VE2

(15)

tan γ

=

VN VE

(16)

Eq. (13) is also applicable to asymmetric interferome-

ters with diﬀerent arm lengths; the equation may also

be used for error analysis. If the interferometer arms

are identical, and if VI is small, then eq. (13) reduces

to

∆T

=

LβI2cos 2γ c

(17)

In a rotating interferometer eq. (17) becomes

∆T

=

LβI2cos 2(θ c

− γ)

(18)

where θ is the angle between arm 1 and WE axis. The conventional expression used by MM for the interpretation of their experiment is a particular case of eq. (18) with VN = 0, and γ = 0. From ﬁgures 3

Fig. 4. Components of terrestrial motion in Cleveland (Ohio) on 8 July 1887, the ﬁrst day of the MM experiment, for two scenarios of solar motion in table 3 (see text): item 4 = Miller2, and item 6 =SGM. The projection of earth motion on the plane of the interferometer depicts large diurnal variations, whose shape depends of the actual value of solar velocity. The magnitude VI is at left, and the azimuth φ is at the right side.

and 4, the latter condition is utterly wrong, as noted at the end of previous section 2.2. In a previous paper [23], the leading author has already discussed this systematic error in the analysis of all MM-type experiments.
As usual, the fringe-shift F is proportional to the time delay, so that in the MM rotating interferometer

F

=

ν∆T

=

LβI2cos 2(θ Λ

−

γ)

(19)

where ν and Λ are the frequency and wave-length of the light used in the interferometer. As shown in ﬁgure 4, calculated for 8 July 1887 with the same solar velocities used in ﬁgure 3, both VI and γ depend of the time of day and epoch within a year. For the Miller2 solar velocity, VI at noon and 6 p.m. respectively are 197 and 122 km/s, whereas for the SGM solar velocity these values are 330 and 248 km/s. All of them are much larger than the 30 km/s used by MM to calculate their expectations.
MM compared the fringe-shift for θ = 0 with the fringe-shift for θ = 90◦,

∆F

=

F (0) −

F (90◦)

=

2LβI2cos 2γ Λ

(20)

Table 4 shows the absolute value of fringe shift ∆F to be expected in a MM experiment for the various scenarios of solar velocity in table 3.
In general,fringe-shifts of several wave-lengths are to be expected, rather than the small 0.4 fringeshift predicted by MM. Notice also the strong dependence of the time of day. However, as is well known, the MM experiment and subsequent repetitions,including Miller’s, was designed to read only fractions of wavelength,completely ignoring the integer number of fringes. Consequently, the amplitude observed in experiments is much lower than it should

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Table 4. Expected fringe-shifts for the MM experiment on 8 July 1887

Solar velocity Michelson81 MM87 Miller1 Miller2 Marinov SGM

Noon 6 p.m.

0.08

0.37

14.3

13.1

21.5 40.4

0.10

0.20

6.4

2.8

18.7

0.8

be, and the estimate of velocity from eq. (20) is lower than it should. In a recent paper we have simulated the response of the MM interferometer, assuming the SGM solar velocity, when only fractions of fringe are read [24]. The apparent fringe-shift amplitude under the incorrect data gathering procedure only amounts to 3.2% of the amplitude that would be observed if the whole fringe-shift were measured, thus explaining the consistently low values of laboratory velocity obtained in all MM-type experiments.
2.4. Analysis of solar motion in Michelson, MM, and Miller works
For completeness and fairness, we brieﬂy review in this subsection the analysis of solar motion performed in the early experiments. In 1881, while at Helmholtz laboratory in Berlin, Michelson invented his interferometer and performed his ﬁrst experiment. Regarding solar motion he stated [9, p.124-125]: “At this time of the year, early in April, the earth’s motion in its orbit coincides roughly in longitude with the estimated direction of the solar system – namely,toward the constellation Hercules. The direction of this motion is inclined at angle of about 26◦ to the plane of the equator, and at this time of the year the tangent of the earth’s motion in its orbit makes an angle of 23.5◦ with the plane of the equator; hence we may say the resultant would lie within 25◦ of the equator. The nearer the two components are in magnitude to each other, the more nearly would their resultant coincide with the plane of the equator. In this case, if the apparatus be so placed that the arms point north and east at noon, the arm pointing east would coincide with the resultant motion, and the other would be at right angles” Therefrom Michelson estimated the ensuing fringe-shift. This solar motion of 30 km/s was included in table 3 above as MM1881.
In the same paper Michelson also considered the possibility that “the proper motion of the sun is small compared to the earth’s motion” [9, p.125], and estimated the corresponding fringe-shift. He considered both scenarios equally likely because we went on to take “the mean of these two numbers as the most probable” [9, p.120].It is noteworthy that Michelson did not

consider the other logically possible alternative: that the speed of the sun could be larger or, much larger than earth’s orbital velocity (as it is, according to current knowledge). Perhaps, the logically possible alternative was not a physically possible alternative in Michelson’s age...
In the 1887 MM experiment, for unknown reasons the emphasis was on orbital motion only: “In what precedes, only the orbital motion of the earth is considered. If this is combined with the motion of the solar system, concerning which but little is known with certainty, the result would have to be modiﬁed” [1, page458]. Since this is the best known paper, most writers believe that in a MM experiment orbital velocity is the only relevant motion, for instance Lodge [53, page 854]. For completeness, a null solar motion is entered in table 3 as MM1887. In the experiments carried out by Morley and Miller from 1902 to 1905 [22, 54], solar motion was assumed very much as Michelson did in 1881. The magnitude of terrestrial motion was about 33.5 km/s [54, p.684], which resulted of a “combination of the diurnal and annual motions of the earth, together with the presumed motion of the solar system toward the constellation Hercules with a velocity of 19km/s. On the dates chosen for the observations there were two times of the day when the resultant of these motions would lie in the plane of the interferometer, about 11:30 A.M. and 9:00 P.M.” [55,p.353], emphasis added; see also [22, p.210].
Miller did not notice that the solar motion used by Michelson, MM and himself contained a signiﬁcant weakness until 1925; this recognition was prompted by a detailed calculation of expected outcomes [56], very similar to our calculation in section 2.2 above.In his words: “At the end of the year 1924, when a solution seemed impossible, a complete calculation of the then expected eﬀects, for each month of the year, was made for the ﬁrst time” [55, p. 356-357],emphasis added. Miller then understood that “the well-known motion of the solar system towards the constellation Hercules, with a velocity of 19 km/s, is only a relative motion of the sun with regard to the group of nearby stars and it may give no information as to the motion of the group as a whole” emphasis in the original [22, p.223]. Then, for his large and ﬁnal series of experi-

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ments during1925-26, Miller introduced a new experimental design: continuous rotation of the interferometer day and night without assuming any azimuth for VI .The analysis of his results led him to obtain the two estimates of solar velocity labelled Miller1 and Miller2 in table 3 above.
Miller’s experimental design introduced a new concept in the design of experiments that has not been duly emphasized: continuous repetition of an experiment, under constant conditions with respect to the laboratory, for long periods of time. The goal is to uncover small eﬀects that are missed by the conventional design, for instance, the eﬀect of the velocity of earth with respect to absolute space.To describe this class of experiments we hereby propose a new word: adialeiptometry, from the Greek words αδιαλειπτ oσ and µετ ρoν meaning unceasing, or continuous, measurement. Other examples of adialeiptometry are Buﬀo’s daily observation of a Foucault pendulum during 8 years in the 1940’s and 1950’s [57], Allais observation of a paraconical pendulum during several months day and night in the 1950’s [31], our ongoing research with paraconical pendulums, and our research with the stationary interferometer reported elsewhere [35,58], and in the present paper.
Summarizing section 2, the MM experiment can not be interpreted as a demonstration that the two-way speed of light is independent of the observer. Indeed, under the incorrect data gathering procedure used by MM and by Miller the result was not null. If MM and Miller had used the correct procedure of measuring the total shift (integer fringes plus fraction of a fringe), they should had obtained a much larger amplitude, and hence a much larger velocity of the laboratory.6 In addition, MM did not provide error analysis for their results; the missing statistical error bars are quite large and do not permit a negative conclusion,as MM did. Furthermore, the fact that there is one experiment (Miller’s) that apparently contradicts the predictions of STR warrants, in our opinion, a repetition of the experiment using modern technology.
3. Our adialeiptometric experiment at CIF
3.1. Design of our experiment
From the foregoing discussion one concludes that a correct design of a MM experiment should be based on the identiﬁcation of a large number of fringe-shifts
6To obtain the velocities listed as Miller1 and Miller2 in table 3 above, Miller introduced a correction factor of about 20 to convert observed velocity into ﬁnal velocity [22, table V, p.235]. He obtained this value from an analysis of the observed direction of earth’s motion. Our claim is that if Miller had measured integer fringe-shifts, then ﬁnal velocity would have resulted,without any ad hoc correction.

during one rotation of the interferometer. A possible approach towards this end is to make many observations during one rotation, say every 1◦. The experimenter should be reasonably certain that in passing from an arbitrary position θ of the interferometer to the next, say θ + 1◦, the reference fringe has moved less than 1 fringe. In the few turns of the MM experiment [1] and in the many repetitions by Miller [22], measurements were made every 22.5◦ so that it was completely impossible to know how many fringes the reference fringe had moved. They rotated the interferometer from θ to θ + 22.5◦ and observed that the reference fringe was at a diﬀerent position and naively concluded that the fringe had moved through less than one fringe! In many of the famous repetitions of the experiment, like those by Kennedy [59] and by Illingworth [60], the situation was even worse: the experimenter determined the initial position of the reference fringe and then rotated the apparatus through 90◦. Obviously, nobody knows how many fringes shifted past the ﬁducial marker during such a massive rotation of the apparatus. However, without hesitation and without evidence, all experimenters up to date have interpreted that their reference fringe moved less than one wavelength!
Another weakness in the design of the original MM experiment is implicit in Miller’s writings [22, p.228]: “these observations have involved the taking of over 200,000 readings of the positions of the interference fringes, requiring that the observer should walk in a small circle, in the dark, while making the readings, a distance of about 160 miles”. Sir Oliver Lodge, an acid critic of Miller, noted with irony that “it is rather surprising that the readings were made by a peripatetic observer, with the instrument in constant and not very slow rotation. . . one would have thought that a stoppage of the frame and a reading of the fringes by a seated observer in many azimuths, would have been more satisfactory” [53, page 854, second column], emphasis added.
Our experimental design solves the two weaknesses noted in previous two paragraphs. A stationary interferometer performs a slow rotation at the earth’s angular speed, and can be read by a seated observer (a video camera connected to a computer) at short intervals of time. During the setup process the ﬁrst semester of 2002, we started with measurements every 15 minutes, which amount to rotations of the interferometer through 3.75◦. The interference pattern from one observation to the next showed diﬀerences that could be appreciated by the naked eye. We tried shorter time intervals, until ﬁnding that observations taken every 2 minutes appeared identical to the naked eye. Thus, the initial experiments in 2002 were manually made at 2 minute intervals [35]. Starting in 2003 we implemented an automatic system for data gathering, and have used ever since 1minute intervals. In this way we are reasonably certain that, if a shift of the

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reference fringe does exist, it is smaller than one wavelength.7 During 1 minute the earth rotates through 0.25◦, which means that the spatial resolution of our experiment is 22.5/0.25 = 90 times better than MM setup.
3.2. Description of our experimental setup
As previously described [58], a symmetric Michelson interferometer was mounted on top of a reinforced concrete anti-vibration table 4.48 m long, 2.57 m wide,0.32 m thick, that weighs 13.5 metric ton; the height of table relative to the ﬂoor is 0.77 m. The table is placed inside a room with dark walls, and polystyrene thermal insulation in the former windows, located in the ground ﬂoor of the CIF institute (Centro Internacional de Fisica =International Center of Physics), housed at the campus of National University in Bogota, Colombia, located at φ = 74◦ − 05 W , λ = 4◦ − 38 N ,and 2,556 m altitude above mean sea level.
The light source is green (Λ = 532 nm)produced by a Nd: YAG diode pumped laser, model DPY 325/425II, manufactured by Adlas (Germany), whose maximum output power is 200 mW. The laser light propagates along the West-East direction, the apparatus being located at the SW corner of the interferometer, on top of a metal supporting plate (35×35×5cm), fastened to the main concrete table. The laser’s power supply is placed outside the anti-vibration table. The horizontality of the laser beam was checked with a precision level (0.1 mm in 1 m).
The light beam splitter is a prism (equivalent to the semi-transparent mirror in the original MM setup), located on top of another independent metallic supporting board (81 × 81 × 5cm), attached to the main concrete table. The mirrors are placed on top of small brass tables (10 × 10 cm), with legs of adjustable height fastened directly to the concrete table, and placed at the end of each arm. The length of each interferometer arm is given by the distance from the center of the beam splitter to the face of each the east and north mirror, L1 = L2 = 2.044 m as measured with a metallic tape8.
The interference pattern is observed with a Sony video camera focused upon a small frost glass screen (6 × 4 cm) placed about 1 mm in front of the camera lens; the glass screen is 20 cm south from the beam splitter. The camera is oriented along the S-N direc-
7A rigorous critic may note another possibility. The variations in the fringe-shift may be so fast that they cannot be observed by the eye. The video camera, however, has a temporal resolution higher than the eye and did not show any instabilities in the interference pattern. Additionally, during 2005 we also took some series of observations every 15 seconds; the interference patterns were similar from one observation to the next. Hence, we stay reasonably certain in our claim that fringe-shifts between successive observations are smaller than 1 wavelength.
8Macroscopic length measured with an accuracy of 0.5mm.

Fig. 5. Diagram of our experimental setup. L1 = L2 = 2044 mm, A = intensity absorber, BS = beam-splitter, M1 and M2= end mirrors, P =polarizer, S =frost glass screen. Only one laser is on at a given time. To decrease eﬀects due to air motion, the optical trajectory is enclosed inside a plastic tubing (approximately 3 cm diameter). To stabilize the air temperature, the tubing is surrounded by polystyrene insulation (approximately 5 cm thick). The beam splitter is also covered with thermal insulation fabricated of the same material. The small tables supporting the mirrors are also surrounded by polystyrene insulation; additionally, there is another layer of thermal insulating material mounted on wood. This second level of protection is intended to decrease eﬀects due to vibration of the mirrors induced by sonic vibration of the air (i.e. to control noise from the street, and from low-ﬂying airplanes). Additionally, there are cloth curtains surrounding the main concrete table along the south and west sides, to avoid noise vibrations from a main street (outside the campus) that is about 100 m away.
tion, and is placed on the south border of the concrete table. The video signal is sent by a 1m cable to a computer placed in the same room, but outside the concrete anti-vibration table. Figure 5 is a diagram of the experimental setup.
Each end mirror has two screws for vertical and horizontal adjustment. They are used to obtain an interference pattern containing some 7 fringes, each fringe has a width of 1 to 2 mm. The interference pattern is very stable, and remains the same over weeks. The laser has a built-in stability control; occasionally, after being in operation for more than 30 hr, the laser entered into recalibration mode. The measurements were then ended, and resumed when the laser was back into stable mode.
3.3. Expected fringe-shifts
The fringe-shifts to be expected in our interferometer can be calculated from eq. (17). To compare observations taken in diﬀerent sessions we follow the usual

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Fig. 6. Prediction of fringe-shifts at our CIF laboratory in Bogota (Colombia) for four scenarios of solar velocity, at four epochs during the year. Note the large variations in the shape of the curves, and their amplitudes, as a function of solar velocity. For further discussion see the text.
procedure of comparing against an arbitrary reference value, that, for the MM experiment, was the reading at the initial position of the interferometer.Since our interferometer is stationary let us take midnight (mn) as the reference position, so that the relative fringeshift ∆F is given by

∆F = F (t) − F (midnight)

=

L Λ

βI2 cos 2γ − βI2(mn) cos 2γ(mn)

(21)

As discussed in section 2, the shape of the curve ∆F versus local time of day t∗ will depend of the actual value of solar velocity, which is unknown. Figure 6 shows the expected response of our interferometer for four scenarios of solar velocity in table 3: Miller1, Miller2, Marinov, SGM.
For a given solar velocity there are variations over the year. The shape of the curve may depict signiﬁcant variations over the year, as in the case of Miller1 and Miller2, where the direction of solar motion is more or less perpendicular to the equatorial plane. If solar motion is nearly parallel to the equatorial plane, as in Marinov’s and SGM’s scenarios, the shape of the curve remains constant over the year, with the position of the minima shifting according to civil time. However, as shown in ﬁgure 7, the position of minima remains more or less stationary in sidereal time. The magnitude of solar velocity in the four scenarios is about the same, ranging from 200 to 390 km/s. The expected amplitude of fringe-shift shows a much larger variation, which is of fractions of wavelength in the case of Miller’s estimates, to several fringes in the

Fig. 7. Prediction of fringe-shifts at our CIF laboratory in Bogota (Colombia) for four scenarios of solar velocity, at four epochs during the year, in terms of sidereal angle σ, which is a proxy for sidereal time. Despite the large diﬀerences in the shape of the curves, the minima are concentrated in a small region (compare to ﬁgure 6 in terms of local civil time). The variations in position are larger for large declinations of solar velocity (Miller1, Miller2).
other two scenarios. These diﬀerences are caused, of course, by the diﬀerent directions of solar motion. As argued elsewhere [36], the shape of the relative fringeshift curve ∆F versus t∗ may be used to obtain solar velocity. Section 4 describes the preliminary results of that exercise.
3.4. Operational tests
The design and setup of the experiment was carried over the year 2002. As mentioned in 3.1, the interval of measurement was chosen during the ﬁrst semester of 2002 to assure that the interference pattern is almost identical from one measurement to the next. During that period we also checked for the possible existence of periodic vibrations in the concrete table and/or the video camera support. For this, we measured acceleration with an apparatus capable of discriminating 0.001g (where g = 9.77m/s2 is the local gravitational acceleration); measurements were performed at different times of the day, and in particular during the evening rush hour (17:00 to 20:00), when heavy trucks and low-ﬂying airplanes can be heard passing by. Accelerations along two horizontal directions (W-E and S-N) and along a direction normal to the concrete table were checked. Acceleration readings do not show periodic behavior, and the amplitude is at the noise

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level (0.001g).
The interference pattern itself is extremely sensitive to ambient noise. However, only about ﬁve readings were lost during several weeks of tests. The reason for the high success rate is that the concrete table returns to rest within a few seconds after entering in vibration by, say, the passage of a heavy truck. The only perturbing external inﬂuence that completely destroyed the interference pattern during intervals of one to two minutes was the operation of an air compressor in a nearby laboratory. This is most likely due to the excitation of resonance modes in the damping system of the table. When the compressor was operating, we did not measure. Fortunately, the compressor was moved by the end of 2002 from that particular place.
We used two thermal sensors to check the thermal stability of the air around the interferometer. One of them was located next to the beam splitter, on top of the supporting table. The other one was located inside the laser beam enclosure, alternatively on the W-E and S-N arms. Most of the time, temperature is constant, within ±0.2◦C (sensor sensitivity). Occasionally,during a 24-hour run there is one change of temperature either of +0.4◦C, or −0.4◦C. Humidity and illumination were also checked during the experimental sessions. Illumination is constant because the room is always dark, but humidity is variable and is more or less periodic, with variations associated with solar motion. Hence, the eﬀect of humidity must be corrected from our data (see section 4).
During the setup period it was also noted that the most diﬃcult time to perform stable measurements was about the peak of the evening rush hour (18:00 to 19:30). To avoid the noisy environment during the week, it was decided to carry out our observations during weekends and holidays, as indeed done during 2003. Analysis of data from 2003 did not show peculiarities in the Friday evening data (when the interferometer started operation) [61], so that by the end of 2004 we started collection of data collection also during weekdays.
During October 2002 the temperature in the room housing the interferometer was continuously changed using four electrical oil-heaters. A variation in the room air temperature over a couple of degrees Celsius produced a severe change of the shape of interference patterns, which would make completely meaningless any experiment. Since November 2002, all measurements are made without any heating.
To check whether the observed variations in the fringe-shifts could possibly be ascribed to intrinsic periodic oscillations of the laser equipment we installed an alternative source of light: a conventional He-Ne laser manufactured by a Belgian company, also shown in ﬁgure 5. Consecutive series of data were taken with the green laser and the red laser in the period November 2002-October 2003. As reported elsewhere, the interference patterns taken with both lasers exhibit the

same cyclic behavior [58, 61]. Hence, the observed periodicities are not due to intrinsic cyclic variations of the light source.
After observing periodic behavior of the interference pattern during a whole year, both with the green and red lasers, it was also checked whether such behavior could be induced by periodic variations of the power supplied to the laser sources. This was done in November 2003. Large variations of voltage were imposed to the laser apparatuses that did not produce proportional eﬀects on the interference patterns [61]. Hence, it may be concluded that the periodic oscillations in the fringe-shifts are not due to the daily voltage drops during the hours of high electricity consumption.
The analysis of the 2003 data suggests some instability in the laser apparatus during several hours immediately after turning the laser on [61]. Hence, from mid 2004 it was decided to use the green laser only, without ever turning it oﬀ after an experimental session.
3.5. Data recollection and raw data
A video camera permanently observes the image of the interference pattern on the frost glass screen (ﬁgure 5). This color image is captured every minute and stored in the computer using software developed by the Owaha Group of the Department of Systems Engineering of National University, for a total of 1440 images produced each day. Since each experimental session lasts several days, several thousand images in TIF format (about 300k each) are collected in each run. Each image is labeled with the date and civil time at the moment that the image was stored. Although the whole image is not required for our data reduction, we are keeping them all as evidence of our work, and for possible future re-analysis.The images obtained up to June 2005 occupy 306 CDs.
In the period 14 December 2002-18 October 2003 we took 30 runs with the green laser and 16 runs with the red laser. After being convinced that the periodicities were not instrumental artifacts, we decided to use only one laser. The green laser apparatus was exclusively used from 18 October 2003 to 10 June 2005; about 60 experimental runs were carried during this period, of which 41 series correspond to year 2004. During the year 2005 several runs of more than 10 days were taken. The laser was continuously powered from October 2004 to June 2005, when it entered a recalibration mode that did not reset itself; observations were stopped at that time.
Since 13 January 2003 onwards, during each experimental run we also registered temperature, humidity and light intensity at the end of each arm using small sensors manufactured by Hobo (USA); the sensors are located inside the wooden box enclosing the end mirrors. Temperature inside the eastern mirror enclosure varies at most 0.2◦C during a weekend, but

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Table 5. Correlation coeﬃcients R between data from diﬀerent sensors

Series T(east mirror) vs. T(concrete table) vs. T(concrete table) vs. H(east mirror) vs.

T(north mirror)

T(east mirror)

T(north mirror)

T(north mirror)

1

0.69

0.53

0.49

0.94

2

0.62

0.00

0.00

0.96

3

0.69

0.45

0.28

0.91

4

0.17

0.01

0.09

0.95

5

0.63

0.00

0.00

0.82

6

0.67

0.46

0.31

0.94

7

0.40

0.48

0.39

086

8

0.24

0.00

0.00

0.97

9

0.45

0.30

0.38

0.89

10

0.47

0.00

0.00

0.83

mean

0.50 ± 0.20

0.21 ± 0.27

0.15 ± 0.25

0.90 ± 0.06

temperature variations inside the northern mirror enclosure are somewhat larger; this eﬀect is most likely due to variations in temperature outside the building (which are very large in Bogota) that are communicated through a former window covered with polystyrene, that is close to that end of the interferometer. Temperature of the concrete table immediately below the optical path of the WE arm is also recorded; its value is constant almost all time. Table 5 shows the coeﬃcients of correlation between temperature T and relative humidity H at the eastern and northern mirrors, for 10 typical series during 2004 (one per month, the actual dates for each series is in ﬁgure 10). As expected, humidity is highly correlated, but temperature is not, due to the inﬂuence of external ambient temperature through the former window near the northern mirror. The zero correlation between mirror temperature and table temperature is produced by a completely constant temperature of the concrete table during the whole duration of the run. The average values in last line of table 5 were calculated for all 41 series taken during 204.
After collecting the images, the next step is to obtain the position of a fringe as function of time; this is done oﬀ-line using a computer program written by one of us [61]. A digital proﬁle of each image is obtained across a thin two-dimensional window placed upon the

image. The position (in pixels) of this window is the same during a given run. The light intensity in the image is converted to a scale between 0 (= dark) to 255 (= bright). In the digital proﬁle a minimum value is a dark fringe, while a maximum value corresponds to a bright fringe; our analysis is based on the position of dark fringes in the image taken at local time t∗. The position of a certain dark fringe is followed in all consecutive images taken during a given run. This process immediately produces fringe position in pixels versus local civil time. To increase the robustness of our measurement, we calculated the average fringeshift of two or three consecutive fringes in each image, relative to the ﬁrst image in a run.The average fringeshift versus local civil time, obtained by the computer program without direct human intervention, constitutes the empirical output from an observational run. Figure 8 is a typical example of a run with the green laser during the period from 02 to 08 September 2003. The periodical behavior of the fringe-shifts is evident, and is similar to the expected curves shown in ﬁgure 6. Figure 8 is labeled “raw data” in the sense that no corrections have been applied to the data so far; the input to our analysis, which strictly is the raw data, is formed by the images of the interference patterns.

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Fig. 8. Fringe-shift versus local time, as observed in the period 02 to 08 September 2003 with the green laser. Above: raw data, below: fringe-shift corrected for ambient humidity and pressure. The lower graph shows a residual curve with a periodicity similar to the original curve, with a smaller amplitude, and well deﬁned minima.
4. Analysis of data
4.1. Environmental eﬀects
As noted in section 3.4, environmental humidity of air varies periodically according to the daily rotation of earth, and the magnitude of fringe-shift also varies in a similar manner. If the variation in the fringe-shifts is caused by the humidity variations, then the humidity eﬀect, and any other causative periodical eﬀect, must be subtracted from the “raw data” curve. However, it may happen that humidity and fringe-shift are not causally related, and that the correlation may be due to the existence of a common cause. In that case, a subtraction of the humidity component would amount to elimination of the eﬀect that we are searching for. Finally, it may happen that a part of the fringe-shift variation is caused by environmental eﬀects, and the remaining variation by the common cause directly; in that case a stochastic correction totally eliminating the correlation between fringe-shift and the environmental variables amounts to an over-correction, leading to a residual curve whose amplitude is smaller than it should be.
The inﬂuence of ambient temperature and pressure upon the index of refraction of air was already known to Michelson, who corrected for such eﬀect in his measurements of the speed of light [7], but did not consider them in the interference experiments [1,9]. With

regard to the index of refraction, Michelson’s decision was correct. Indeed, using a modern semi-empirical equation [62], we have estimated the eﬀect of variations of temperature, pressure and humidity upon our interferometer [61, ch.3], to ﬁnd that the fringe-shifts induced by changes in the index of refraction are much lower than the resolution of our experiment.
Ambient temperature was mentioned by Michelson as a signiﬁcant source of experimental error in his1881 experiment [9], but was ignored in the analysis of the 1887 MM experiment[1]. In his analysis of the MM experiment, Hicks [25] suggested that the monotonic drift of fringe-shifts was due to a thermal eﬀect. Miller recognized the importance of temperature and built apparatuses in diﬀerent materials, hence,with diﬀerent coeﬃcients of thermal expansion. Additionally, Miller tried to control for temperature variations, and checked whether it was possible to obtain periodical eﬀects on the fringe-shifts from temperature variations in the interferometer room [22]. In a re-analysis of Miller’s work, Shankland and collaborators attributed Miller’s periodical fringe-shifts to periodical thermal variations [28]. Even the recent Stanford experiment
carried out at a temperature close to absolute zero with an extremely tight control of temperature variation (within 10−5K, according to the authors [63]) attributed the observed periodical frequency-shifts to mechanical eﬀects induced by temperature! However, although the inﬂuence of temperature is usually recognized, no eﬀort is done to eliminate such temperature eﬀect during the data reduction process.
As mentioned above, variation in the index of refraction along the optical path produces a negligible fringe-shift [61], so that the most important eﬀect of temperature is thermal expansion and contraction of the interferometer, thus changing the values of L1 and L2. To decrease the variations in optical length, our experiment is set upon a concrete table that has a low coeﬃcient of thermal expansion. However, the supports for the mirrors, which are ﬁxed directly to the concrete, are fabricated in brass, so that thermal effects due to expansion of the metallic parts must be expected. Theoretical calculation of such expansion would require a detailed knowledge of the distribution of temperature, which is not available.
In view of such diﬃculties, during the analysis of the data taken during 2003 [61], it was decided to implement a stochastic correction for the eﬀect of the three environmental parameters: relative humidity (H), pressure (P), and temperature (T). The correlation between fringe-shift F and each parameter is found for each series. A linear regression is then obtained between F, and, say, H. This gives the maximum value of fringe-shift that could be attributed to the environmental variable H. If this value is subtracted from the raw data, a corrected fringe-shift F ∗ is obtained that is not correlated any longer to H. The same procedure is now applied to the other two envi-

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ronmental variables P and T, using in each case the most recently corrected F ∗.
Due to limitations in the storage of data at the sensors, H and T are taken at intervals that vary from 1 to 5 minutes, depending upon the duration of the run. The correction calculated in previous paragraph is thus applied to the average fringe-shift during the appropriate interval. For pressure we did not have a micro-barometer with the required accuracy. During 2003 we used for the stochastic correction the data collected hourly at the Eldorado International Airport, some 15 km away from the National University campus. So that, for the pressure correction, we had to average the fringe-shifts over one-hour periods, thus decreasing the temporal resolution [61]. For the analysis in the present paper we rather used synthetic monthly pressure curves derived from 20 year averages taken at a meteorological station on the campus of National University [64]. In this way the averaging of fringe-shifts is done over equal intervals for the 3 parameters H, P, and T.
The largest corrections are produced by H and P. After correcting for H and P (in that order), the curve F* has a low correlation with H shown in the second column of table 6 and no correlation with P, but the correlation with T is still large, as shown in the third column of table 6. After applying the correction for temperature, its correlation with T disappears, but the correlations with H and P slightly increase as shown in columns 4 and 5 of table 6. The averages shown in last row of the table are calculated over the 41 runs taken in 2004. We also explored the application of the corrections in a diﬀerent order, say P,H,T; the residual correlations are somewhat larger but still very low.
The lower graph in ﬁgure 8 is a typical example of the residual curve after correction for H and P. Note that, although the amplitude is decreased, the periodicity is enhanced by the correction process. However, the amplitude of the ﬁnal residual curve amounts to several fringes. As shown in last column of Table 6, the ﬁnal curves have a low correlation to the environmental variables, which means that the procedure used here for eliminating environmental eﬀects was successful.
However, as implicitly noted at the beginning of this section, and recalling that variations in the index of refraction can not explain the large observed fringeshifts, there remains a fundamental question: what is the physical mechanism that may explain the large eﬀect of humidity and pressure upon fringe-shift. For this reason, in the following we show both the corrected curves and the raw curves.
4.2. Typical corrected fringe-shift curves.
From the 41 experimental runs during 2004, we have

Fig. 9. Average fringe-shift curve for April (left) and October (right), corrected for H and T as measured at the eastern mirror (continuous line) and northern mirror (dashed line). The months were chosen for having a very low correlation between the temperatures at the two mirrors. The shapes of the corrected curves are similar, independently of the correction process. The one-sigma error band is shown in all cases.
selected a long run (several days) about the middle of each month as typical of that particular month;9 the dates of the runs are indicated in table 7 and ﬁgure 10. Each run is divided into 24 sidereal hours periods, and the fringe-shift at each midnight is taken as a reference for that particular day; this means that the relative fringe-shift at midnight is always zero. The relative fringe-shifts at other times of the day are averaged over the several days in the run. Figure 9 shows the average fringe-shift curve for the month of April, corrected for H and T as measured at the eastern mirror, compared in the same graph to the curves corrected with data taken at the northern mirror. Both corrected curves have the same general shape, thus hinting to an underlying physical process that cannot be removed by the environmental correction. As seen in table 5 (series 4), temperature at the northern mirror was not correlated in April to temperature measured at the eastern mirror. The right-hand-side of ﬁgure 9 shows the same curves for the month of October 2004 (series 8 in table 5). Once again, the temperatures at the eastern and northern mirrors are not correlated, while the corrected curves are quite similar, thus hinting again to the existence of an underlying physical mechanism diﬀerent from the mere environmental variations. The one sigma statistical error bands are also shown in the ﬁgure.
Since the shapes of the corrected curves are similar using the values of H and T measured at either the eastern or the northern mirror, in the following we concentrate on the curves with the corrections based on the eastern mirror. Figure 10 shows the corrected curves for the 10 months analyzed in 2004, with the one-sigma error bands. The error only contains the statistical variation over the several days that form the series. Other experimental and/or data reduction errors are not included; for instance, the error arising from the fact that pressure correction was based on
9Two months are missing during a period of distress (May and June) induced by the robbery of the video camera by the end of April 2004.

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Observation During 2004 of Periodic Fringe-Shifts in an Adialeiptometric Stationary Michelson-Morley Experiment

Table 6. Correlation coeﬃcients R of intermediate and ﬁnal series, after correction with data taken by sensors located at east mirror

Series No. 1 2 3 4 5 6 7 8 9 10 mean

Series corrected with H and P

Correlation with H Correlation with T

−0.01

−0.19

+0.01

−0.25

−0.01

−0.74

−0.10

−0.01

−0.01

−0.64

−0.03

−0.64

+0.04

−0.11

+0.00

−0.31

+0.01

−0.29

−0.11

−0.39

0.00 ± 0.09

−0.26 ± 0.29

Final series corrected with H,P and T

Correlation with H Correlation with P

+0.12

−0.01

+0.09

−0.07

+0.18

−0.06

−0.10

+0.00

−0.11

−0.06

+0.11

+0.03

−0.03

−0.01

−0.12

−0.05

+0.03

−0.05

+0.15

−0.12

0.00 ± 0.12

−0.04 ± 0.09

a synthetic curve rather than on observed pressures. Note that the error band contracts at some points. The amplitude of the residual curves is of several fringes, while the position of the minima varies over the year.
Some of the sessions are identiﬁed by the date followed by the letters INV; some explanation is required. When the fringes move to the right (or up, depending upon the interference pattern), the computer program arbitrarily deﬁnes that sense as an increase of the position of the fringe-curves; however, it could be a decrease in position. This is due to the orientation of the reﬂecting mirrors, that are modiﬁed during the process of calibration of the interferometer.10 Then, the empirical curves may be plotted with the sign assigned by the computer, or with the opposite sign; the latter produces an inversion of the curves, denoted by the letters INV. The curves (direct, or inverted) were selected for consistency with our theoretical expectations.
4.3. Solar velocities consistent with observations.
We turn now to a preliminary analysis of possible solar velocities consistent with our empirical observations. The main features of the fringe-shift curves are the position of the two minima in terms of angle σ in degrees (◦), and the amplitude A in fringes, understood as the diﬀerence between the maximum and minimum values of the curve. Table 7 shows the amplitudes for the original and corrected curves, the latter information is also contained in ﬁgure 10. In general, the environmental correction decreases the amplitude of the fringe-shift curve. The most interesting feature of the corrected curves is the variation of amplitude
10As noted long ago by Hicks [25], this is the same mechanism that produce increasing or decreasing trends during the original MM experiment.

during the year. During the four months from July to October 2004 the amplitude is much smaller than in the rest of the year, which is, of course, conﬁrmed by the partial averages shown in table 7. At ﬁrst sight this empirical observation is counter-intuitive, however, some reﬂection indicates that this result must be induced by the direction of solar motion.
By direct numerical calculation in a simple computer program written in Excel, it is found that when the right ascension of solar motion is in the range 170◦ to 190◦ the observed ordering of amplitudes is reproduced. When right ascension is outside this range, the ordering of amplitudes is completely diﬀerent, for instance, amplitudes during July-October may be the highest. The second half of table 7 shows the amplitudes calculated for two solar velocities, namely: V 1 = 350 km/s, α = 175◦, δ = −50◦, and V 2 = 300 km/s, α = 185◦, δ = −50◦. As expected, the value of the amplitude of the fringe-shift is directly linked to the value of solar speed.
The fringe-shift curves calculated with V 2 are shown in ﬁgure 10. It may be seen that there is a reasonable agreement with the observations, with the theoretical curves within the one-sigma error band in most cases. From the previous qualitative analysis it may be said that the solar motion consistent with our observations may be in the range 300 to 360 km/s, with right ascension from 170◦ to 190◦, and declination between −45◦ and −55◦. No additional quantitative analysis is presented at this stage. This matter will be pursued together with the analysis of the data taken during 2005, that we are currently advancing.
5. Closing remarks
Following Miller’s pioneering eﬀorts, we have carried out an adialeiptometric experiment using a sta-

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Table 7. Amplitudes of the fringe-shift curves in year 2004

Session Original

Corrected

Calculated V1 Calculated V2

No. Dates

A,

A, Partial A, Partial A, Partial

fringes fringes Average fringes average Fringes average

1 Jan19-27 4.0

3.0

3.7

3.1

2.8

2.5

2.2

2 Feb13-16 5.0

4.2

3.0

2.3

3 Mar19-23 6.3

3.5

2.6

2.0

4 Apr16-19 5.1

4.1

2.4

1.8

5 Jul19-24

3.2

2.7

2.2

2.1

2.5

1.5

1.8

6 Aug13-17 2.4

1.6

2.3

1.6

7 Sep10-13 1.9

1.3

2.6

1.8

8 Oct16-19 3.6

2.3

2.9

2.1

9 Nov18-21 3.5

3.9

4.4

3.2

3.2

2.4

2.4

10 Dec17-23 5.4

4.8

3.3

2.5

tionary Michelson-Morley interferometer at our CIF laboratory in Bogota (Colombia) for almost two years from the end of 2003 to June 2005; the present paper reports the results for year 2004. After correcting for environmental variables, we identiﬁed large fringeshifts, whose period most likely is a sidereal day. To provide a context for the new experimental results presented in this paper, we started by discussing the meaning of speed of light at the time of Einstein, and presented next the evidence then available for its constancy. It was argued that the evidence provided by the original MM experiment and its various repetitions is not as strong as usually believed, thus justifying our new experiment, where we tried to correct for the main weaknesses uncovered.
The fringe-shift curves observed in Bogota are consistent with the predicted curves using a constant speed of light in a preferred frame, that adds vectorially to the laboratory velocity using Galilean addition. From the qualitative analysis performed so far, it may be said that the solar motion that explains our observations is in the range 300 to 360 km/s, with right ascension from 170◦ to 190◦, and declination between −45◦ and −55◦. This value is similar to other modern estimates of solar velocity (recall table 3), for instance Smoot and his team [49] found a solar speed of 390 ± 60 km/s, in the direction α = 165◦ ± 9◦, δ = +6◦ ± 10◦, while Marinov [48] obtained 303 ± 20 km/s, α = 214◦ ±5◦, δ = −23◦ ±4◦. The declination is the controlling factor for the relative depth of the two minima in the fringe-shift curves. The value consistent with our curves seems to point towards the southern celestial pole, as in Miller’s observations, and seems larger than the value of either SGM or Marinov.
Finally, it is noted that the recent experiment by the Stanford group [63] amounts to a vertical interferometer. As already pointed out elsewhere [58], the Stanford curves are very similar to our own raw curves, for instance ﬁgure 8, but they were interpreted as caused

by thermal eﬀects. It is noted that the Stanford group tried to interpret (without success) the variation of their parameters in terms of the annual orbital motion of earth. As noted in section 4, and as can be gathered from ﬁgure 10, the shape of the fringe-shift curves does not follow a simple sequence. Then, if a curve is ﬁtted to each monthly fringe-shift curve (as done by the Stanford group) the parameters of the ﬁtting curve do not follow a simple pattern, as incorrectly expected in that paper.
Acknowledgements
This experiment was carried out at the Centro Internacional de Fisica (CIF) in Bogota, using optical and laser equipment kindly provided by Prof. Dr. Eduardo Posada, Director of CIF; J. Garcia and I. Lopez, members of CIF’s staﬀ, designed and built the accelerometer. The data acquisition system was furnished by the principal investigator; Munch Engineering (USA) provided funds for the sensors, and Thomas Goodey (England) provided a new video camera (to replace the original one stolen in April 2004).
For the manual observation of the interferometer during 2002, the authors counted with the help of N. F. Munera, P. R. Gis, C. Carrillo, G. Carrillo and R. Rojas; the latter also manufactured the polystyrene thermal insulation around the interferometer. The software for the automatic data gathering was developed by Professor M. G. Forero and his students C. Gomez and D. Vejar of Owaha Group, Faculty of Engineering, National University. The Faculty of Sciences and the Department of Physics of National University at Bogota have allowed the three authors to use a minor percentage of their working time to carry out this experiment and for advancing the theoretical research. Discussions with our colleagues V. Tapia, R. Amezquita and Y. Mejia are gratefully acknowledged.

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Observation During 2004 of Periodic Fringe-Shifts in an Adialeiptometric Stationary Michelson-Morley Experiment

Fig. 10. Fringe-shift curves corrected for environmental variables for the 10 months observed in 2004. Note the variation of amplitude during the year (somewhat concealed by the diﬀerent vertical scales). The onesigma error band is the standard deviation calculated for the number of days in the series. The theoretical fringe-shift, shown by the crosses, was calculated for a solar motion of 300 km/s in the direction α = 185◦ and δ = −50◦.
Manuscript received May 12, 2006
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H`ector A. Mu`nera, Daniel Hern`andez-Deckers, Germ`an Arenas, Edgar Alfonso

Annex 1. Four year cycle used for the calculations, σ = Sidereal angle at noon GMT

Date 2000-01 Mar 21, 00 Apr 1, 00 May 1, 00 Jun 1, 00 Jul 1, 00 Aug 1, 00 Sep 1, 00 Oct 1, 00 Nov 1, 00 Dec 1, 00 Jan 1, 01 Feb 1, 01 Mar 1, 01 Mar 21,01

t, days
0 11 41 72 102 133 164 194 225 255 286 317 345 365

Sidereal angle σ,◦
0.0 10.8 40.4 71.0 100.5 131.1 161.6 191.2 221.8 251.3 281.9 312.4 340.0 359.8

Date 2001-02 Mar 21, 01 Apr 1, 01 May 1, 01 Jun 1, 01 Jul 1, 01 Aug 1, 01 Sep 1, 01 Oct 1, 01 Nov 1, 01 Dec 1, 01 Jan 1, 02 Feb 1, 02 Mar 1, 02 Mar 21, 02

t, days 365 376 406 437 467 498 529 559 590 620 651 682 710 730

Sidereal angle σ,◦
359.8 10.6 40.2 70.7 100.3 130.8 161.4 191.0 221.5 251.1 281.6 312.2 339.8 359.5

Date 2002-03 Mar 21,02 Apr 1, 02 May 1, 02 Jun 1, 02 Jul 1, 02 Aug 1, 02 Sep 1, 02 Oct 1, 02 Nov 1, 02 Dec 1, 02 Jan 1, 03 Feb 1, 03 Mar 1, 03 Mar 21,03

t, days 730 741 771 802 832 863 894 924 955 985 1016 1047 1075 1095

Sidereal angle σ,◦
359.5 10.3 39.9 70.5 100.0 130.6 161.2 190.7 221.3 250.8 281.4 312.0 339.5 359.3

Date 2003-04 Mar 21, 03 Apr 1, 03 May 1, 03 Jun 1, 03 Jul 1, 03 Aug 1, 03 Sep 1, 03 Oct 1, 03 Nov 1, 03 Dec 1, 03 Jan 1, 04 Feb 1, 04 Mar 1, 04 Mar 21, 04

t, days 1095 1106 1136 1167 1197 1228 1259 1289 1320 1350 1381 1412 1441 1461

Sidereal angle σ,◦
359.3 10.1 39.7 70.2 99.8 130.3 160.9 190.5 221.0 250.6 281.2 311.7 340.3 0.0

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