Introduction
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One of the main assumption of Einstein's relativity is the 
round-trip anisotropy of the speed of light.

It is based on a series of interferometrical experiments,
the older one being the one performed by Michelson and
Morley. None of those experiments have been able to detect 
the motion of Earth through the putative ether. 

Let's however consider Lorentz's interpretation of the null result 
of the Michelson and Morley experiment:

L is the length of the perpendicular arms of their interferometer,
and v is the velocity of the apparatus in the ether.

The round-trip transit time of light along the horizontal arm is
straightforwardly calculated as t(h) = (2L/c)/(1-v^2/c^2).
The round-trip transit time of light along the vertical arm is
straightforwardly calculated as t(v) = (2L/c)/sqrt(1-v^2/c^2)
As t(h) is observed to be equal to t(v), L has been assumed 
by Lorentz to contract by sqrt(1-v^2/c^2). 
Hence, t(h) = (2L*sqrt(1-v^2/c^2)/c)/(1-v^2/c^2) = 
(2L/c)/sqrt(1-v^2/c^2), which is identical to t(v).

Einstein's interpretation of the null result of the MMX and
similar experiments is that, for some unspecified reason,
motion through the ether is a meaningless concept, and that
only motion relative to material bodies has physical significance.
From that assumption, he based his special theory of relativity on
two postulates:
1. The laws of physical phenomena are the same when stated
    in terms of either of two inertial frames of reference.
2. The velocity of light is independent of the motion of its
    source.
An inertial frame is one in which the law of inertia is true, i.e.
relative to which a body that is free from external influence and
at rest remains at rest. Hence, the relative motion of two inertial 
frames can only consist of a uniform translation.
The first postulate is obviously not self-evident, and is
only intended as a hypothesis to be tested by comparing
deductions from it with experimental observation.

In all experiments conducted this far, the round-trip transit
time of light between two points has only been assessed
by interferometry. A direct experimental measure of the
round-trip time is thus needed to confirm or falsify Einstein's 
theory of relativity.

Luckily, direct observations are available, but have not yet
been analysed from the above angle.
The observations in question have been made by a series
of lunar laser ranging stations, i.e. the McDonald Observatory
(University of Texas at Austin), the French CERGA station
at Grasse (Observatoire de la Côte d'Azur in France), the 
German station at Wettzell and the LURE Observatory on 
the island of Maui.

An introduction to Lunar Laser Ranging (L.L.R.)
_______________________________________
(Source)

Up to the beginning of the sixties, the lunar theory, a 
major problem for astronomers, had reached a dead end 
and a breakthrough was needed. The space race provided the 
answer.Reaching for the moon opened the door for scientific 
and technical progress. 

We developed the application of laser technology, using 
precision timing with the atomic clock and data processing, 
resulting in the Lunar Laser Ranging (L.L.R.) technique. 

How do we use this technique to measure the earth-moon 
distance? The laser, a high energy, high density light beam, 
is aimed at targets on the moon's surface. These targets, 
reflectors, were put in place during the Apollo and Lunokhod 
missions. We measure the time taken by the light signal to
travel to the moon and back. Of course these measurements 
need to be very precise (it only takes two and a half seconds 
for the light to cover the distance) so we use the atomic clock. 

As the reflectors are relatively small and as a laser beam loses
its intensity, only a minute part of the signal makes it back. 
However the information is sufficient for precise calculation of 
the earth and moon's movement: speed of rotation, axial variation 
and orbital deviation, of course taking into account the influence 
of other celestial bodies such as the sun. 

Despite the increasing complexity of this relativity new technology, 
it appears that the limits of this experience are far from being 
reached. In 1985 to be within an accuracy of 18 cm was considered
 as a reasonable limit, today 5 mm is the going rate and we are 
talking about even less than one mm! 

It is currently more accurate than measuring the time it takes 
Concorde to fly from Paris to New York within an accuracy 
of one tenth of a millionth of a second! 


The following excerpts from a report by P. J. Shelus, 
R. L. Ricklefs, J. G. Ries, A. L. Whipple, and J. R. Wiant 
of the McDonald Observatory give a good idea of the
quality and interest of the observations:
_______________________________________________

"Lunar laser ranging (LLR) has turned the Earth-Moon 
system into a laboratory for a broad range of scientific 
investigations.  The unique contributions already accomplished 
include a three orders-of-magnitude improvement in the 
accuracy of the lunar ephemeris, a several orders-of-magnitude 
improvement in the measurement of the variations in the 
Moon’s rotation, and the verification of the principal of
 equivalence for massive bodies with unprecedented 
accuracy.  Complementing and supplementing other 
observational disciplines, the LLR analysis has also provided 
measurements of the Earth’s orbit precession, the 18.6 year 
nutation, the Moon’s tidal acceleration, lunar rotational energy 
dissipation and the Moon’s free librations, Earth orientation, 
and the determination of the obliquity and the equinox".
(Report for October  1993, McDonald Laser Ranging 
Operations (NAS5-30942)).


A rough analysis of LLR Cerga observations
____________________________________

Its aim is to illustrate the procedure which could be followed
to detect the motion of the couple Earth-Moon in space.
From the observation of a dipole in the CMBR, it is inferred
that the solar system has an overall velocity of about
370 km/s in the direction of the Leo constellation. Due to
the revolution of the Earth around the Sun, such velocity
should fluctuate according to the period of the year, and
those fluctuations should influence the time taken by the 
laser pulse to travel to the moon and back.

One could select the CMBR rest frame as the ether frame, 
and use an ether theory of gravity. For instance,  
Ilja Schmelzer wrote on Jun 02,1999 
(newsgroup sci.physics.relativity):

"If you use, for example, my ether theory, then there are very 
small but physical effects which depend on the preferred frame.  
In this situation there are physical reasons for the hypothesis 
that the absolute rest frame is close to the CMBR rest frame.
Such frame is preferred by symmetry reasons.  In SR 
approximation, it is also an inertial frame.Of course, there 
is some anisotropy.  But for practical purpose (use as a reference 
frame) that's not important because it is too small."

First of all, the individual round-trip rough data should be
corrected for the angle between the station and the reflector
situated on the moon (via the precise time of observation), the orbital
position of the moon, which determines the distance Earth-Moon,
the temperature and hygrometry of the air, the atmospheric
pressure, etc...

Only the specialists working at the LLR stations are sufficiently 
equipped to perform those corrections, so I had to limit myself 
to the determination of the orbital position of the moon at 
each date of observation.
The calculated times obtained from the double of the distance 
Earth-Moon corresponding to the orbital position of the moon,
divided by the light speed c, can be found in the file "apollo.dat".

Such times would be observed if the couple Earth-Moon were
at rest relatively to the CMBR. The effect of any velocity wrt
the CMBR would be an increase of the round-trip times.
Thus, I have divided the calculated times by the observed times,
and examined the monthly evolution of the corresponding factors,
because any statistically significative pattern would falsify Einstein's 
theory of relativity.

In fact, the factors appear lower for the months April to June, but
the difference with the other months is not significative. It is
clear that the time of observation (hour, minute and even second)
should also been taken into account. Hopefully, some LLR expert
will be interested in performing the proposed analysis.

Summary of the proposed procedure
_________________________________

1) Adjust the LLR raw data according to standard conditions of
   air temperature and humidity, atmospheric pressure, etc...
2) Calculate with the greatest possible precision the distances
   laser source-reflector corresponding to the exact time of
   observation (year, day, hour, minute and second).
3) Divide by c the double of those distances to obtain calculated
   round-trip times.
4) Divide each calculated time by the corresponding adjusted
   observed time. The obtained factors correspond to sqrt(1-v^2/c^2),
   where v is the instantaneous velocity of the couple Earth-Moon
   with relation to the CMBR.
5) Calculate weekly of semimonthly factors, and plot the obtained
   means against time. One should obtain a quasi-sinusoidal pattern.
   A statistically significative pattern would be a strong argument
   in favour of ether theories.


Even if J. Müller and M.H. Soffel [1] have already used LLR data to 
test Special Relativity, and found that they are compatible with it, 
their paper dates back from 1995. As numerous and more precise 
data have been collected since then, a new comprehensive study has
become necessary.

[1] J. Müller and M.H. Soffel, "A Kennedy-Thorndike experiment
using LLR data", Phys. Lett. A 198 (1995) 71

References
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Origin of the used raw data:
CERGA

Raw data: Mnc8799.txt
and their format
 
Apollo XV data (Year, month, day, hour, minute, raw 
round-trip times) selected from the file Mnc8799.txt: 
apollo.dat

Extended Apollo XV data (Year, month, day, hour, minute, 
raw round-trip times, calculated times, factors): 
apollo2.dat

N.B.: 
1) the calculated times are obtained from the double 
of the distance Earth-Moon corresponding to the orbital 
position of the Moon at each date (year, month, day), 
divided by c.
2) the "factors" correspond to the ratio calculated times/
raw round-trip times.

Mean factors for the different years and months: 
Factors


Marcel Luttgens
March 17, 2001