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Similarly to the Michelson and Morley experiment, the Brillet and Hall experiment is also designed to test the symmetry of space. Brillet and Hall use a large Fabry-Pérot “etalon of length” to stabilize the frequency of a He-Ne laser, rotating with respect to a fixed reference laser. It is measured that there is no apparent change of frequency between the two lasers, during the rotation of the Fabry-Pérot etalon. There is an error in the Brillet and Hall calculation, which is due to the fact that when the cavity moves sideways, light inside the Fabry-Pérot cavity needs to use an extended optical path to fill the cavity. When we take into account that ignored phenomenon, we find that the conclusions presented in the Brillet and Hall experiment are due to that disregarded change of light path in the transverse direction. We show here that the resonant frequency of the Fabry-Pérot cavity does not change in Galilean space after a rotation of 90

**1-
Distance Traveled by Light in Parallel Velocity.**

The Brillet and Hall experiment has much in common with the
Michelson-Morley experiment. In both experiments, we compare
the
time
taken by light to travel a constant distance moving parallel to
the
moving frame, with the distance when they travel in perpendicular
directions. We have seen that, according to the
Michelson-Morley
calculation, in Galilean space, the total time light takes to
travel
the constant length of the etalon in the parallel direction
has
been
calculated
to
be
different
from
the corresponding total
distance in the transverse direction. The
symbol
means that light travels in a direction, which is parallel to the
velocity of the moving frame. The symbol corresponds
to the
direction of light after a rotation of 90^{0}
of the moving frame.

The constant length of
the
etalon in the frame moving at velocity v is defined as L. We
can
see that in the parallel direction, in the
Brillet
experiment, the total time [t(total)] taken by
light
is equal to the time in the forward direction t(forward),
plus the
time in the backward direction t(backward), before
completing
the two-way trip inside the cavity. This gives:

1 |

2 |

3 |

The corresponding parameters are also calculated in the transverse direction when the moving frame has rotated by 90

4 |

5 |

** 2
- The Brillet and Hall’s Instrument.**

The aim of the Brillet and Hall experiment is to verify Einstein’s
hypothesis, which assumes that there is an asymmetric distortion
of
space (or matter) when the frame is moving. In the case of
the Michelson-Morley experiment ^{(1)},
such
an
asymmetric
distortion
has
been
claimed
following the zero
shifts of the observed fringes. However, we
have seen ^{(2)} that this
zero
shift must be reinterpreted.

The principle of the Brillet and Hall experiment ^{(3)},
consists first in having a constant reference length using a
Fabry-Pérot etalon. A He-Ne laser is servo
stabilized with respect to
the Fabry-Pérot etalon as illustrated on figure (1).
Therefore, it is
usually claimed that the stability of the frequency of the He-Ne
laser,
which is servo controlled, should be as good as the length of the
etalon. The Fabry-Pérot etalon with the servo
stabilized
He-Ne laser
can rotate, as illustrated in the lowest part of figure (1).
The
frequency of the light signal transmitted on the axis of that
rotating
frame is compared with a non-rotating reference laser shown on the
upper part of figure (1). In order to make sure that the
length
of the
Fabry-Pérot etalon is highly stable, it is made of low
expansion
glass-ceramics and temperature stabilized inside a vacuum tube.
The
very high stability of the length of that etalon is hopefully
replicated to the frequency of the servostabilized He-Ne laser.
Therefore, any change of length of the etalon (or a change of
velocity
of light) should be detected as a corresponding change of
frequency of
the rotating servostabilized He-Ne laser, with respect to an
independent non-rotating exterior stable laser.

The
mechanical length of the Fabry-Pérot etalon in the Brillet
and
Hall
experiment is “L” as illustrated on figure (1). The
conventional
demonstration of the Michelson-Morley
experiment ^{(1)}has
been interpreted as an asymmetric space contraction in the
transverse
direction with respect to the parallel direction. Therefore
that
assumed space distortion, when measuring a moving length must also
be
reproduced similarly in the Brillet and Hall experiment, using the
Fabry-Pérot etalon, after a rotation of the moving
frame. Brillet and Hall report ^{(3)},
that
their
experiment
gives
a
null
result
during a rotation.

Assuming that everything above is right, this leads to believe
that
there is an asymmetric space distortion between the parallel and
transverse direction.
In this paper, we show here that that claim is erroneous because,
in
their calculation, Brillet and Hall ignore the fact that in
Galilean
space, they did not consider the needed change of path, due to an
angle
that makes the light path [1/Cos a]
times
longer. In this paper, we reconsider the calculation of the
Brillet
and Hall experiment, taking into account the increase of length of
the
trajectory of light inside the Fabry-Pérot etalon when it
is
moving
sideways, as explained below.

** 3 –
The Fabry-Pérot Etalon.**

In the Brillet and Hall experiment, the Fabry-Pérot etalon
is
moving at
velocity v with respect to the stationary frame. L is the distance
between mirrors A and B of the Fabry-Pérot etalon, as
illustrated on
figure 2. The Fabry-Pérot etalon is alternatively
oriented
so that
light, inside the etalon, in a Galilean space, moves either
parallel or perpendicular
to the velocity of
the frame.

On figure 2A and 2B, a large extended parallel beam of light,
projects
monochromatic light (from the left hand side) through a pair of
highly
reflecting parallel mirrors (A and B). On figure 2A, we see
that
the
incident light, which is parallel to the axis of the mirrors, is
reflected many times between mirrors A and B. Some light
emerges
each
time, through mirror A after each two-way collision. Then,
that
light
is focused by a lens on a light detector, forming the central spot
shown on figure 2A.

Figure 2B is just
added here to
complete the illustration of the Fabry-Pérot cavity, when
the
incident
light arrives at an angle with respect to the axis of the
interferometer. On figure 2B, we see then that that light coming
out of
the interferometer can produce a circle around the central spot of
the
Fabry-Pérot interferometer. Other concentric circles
are
formed,
corresponding to a larger integer number of wavelengths. However,
on
figure 2B, we notice that the distance traveled by light when
completing the two-way travel is one wavelength longer than in
figure
2A. Therefore the natural resonant frequency of the cavity,
which
is
compatible with that extra wavelength (N+1) on figure 2B is lower,
because the light path inside the cavity is longer due to the
angle
inside the cavity. In reality, figures 2A and 2B are
generally
superimposed. Figure 2B is not directly relevant here, but it
helps to
understand the fundamental mechanism taking place inside the
Fabry-Pérot etalon.

**4
–Resonant Frequency of the Cavity of a Rotating
Resonator. **

Returning to figure 2A,
we
need to calculate, the total time t taken by light to
travel the
two-way distance inside the cavity, in both parallel and
perpendicular directions.
We consider here on figure 2A, the instant when the distance
traveled
by light during a two-way reflection on mirrors A and B, is
exactly
equal to an integer number N of wavelengths. Number N must
be an
integer, in order to obtain a constructive interference, so that
the
phase of the wave could be the same, at the same spot, after
multiple
two-way reflections. Then, the two-way distance D(total)
traveled
by
light
is
given
by
the
number of wavelengths N,
times the fundamental resonant wavelength l.
This gives:

6 |

**4
-A
– Resonant Frequency in Mode. **

In this problem, the simplest way to calculate the resonant
frequency
of a cavity is finding time light takes to travel a full two-way
trip
inside the cavity corresponding to one cycle of oscillation.
We
know
that the resonant frequency “F” of a cavity is the inverse of the
time
taken by light to complete its two-way reflection inside the
opposite
mirrors of the cavity between mirrors B and A. In the
Brillet-Hall
experiment, we wish to determine whether the resonant frequency of
the
cavity is the same in the parallel as in the
perpendicular directions.
We
have
F(cavity)
is
the
resonant
frequency
of
the cavity in the
parallel mode. Therefore the simple knowledge of the periods
P(cavity)
and
P(cavity)
is
sufficient
to
determine
the
validity
of the
Brillet-Hall experiment. In the parallel direction, the
period “P(cavity)” of the cavity is:

7 |

8 |

9 |

** 4
-B
– Resonant Frequency in Mode. **

Let us now calculate
how the
** “effective”**
length of the Fabry-Pérot cavity changes, when moving in
the
transverse
direction in Galilean space, after a rotation from the
parallel
direction, to the
transverse direction.
Only the rotation of the moving frame at a constant velocity “v”
needs
to be considered here. We need to calculate only light
reaching
the

Let us now examine the
light
path inside the etalon when light travels in the transverse direction,
as
seen
by
the
stationary
observer
for
which
the velocity of light is
always equal to c in the Galilean frame. Figure 3 shows an
illustration of the light path inside the moving
Fabry-Pérot
etalon.
The mirrors A and B are highly reflective and slightly
transparent. On
figure 3, the small concentric circles on the upper left of the
image
represent the light source. The Fabry-Pérot etalon
appears
as six
vertical cylinders on figure 3, moving toward the right hand side,
as
illustrated at six different instants. Let us notice that
the
multiple
reproductions of the ** same **moving
Fabry-Pérot
cylinder having a length L, are ended by mirrors A and B (see
figure
3).

At time t=0, light entering the etalon, passes through the partially transparent mirror B. The time interval between drawings corresponds to half the time taken by light to travel the two-way distance D, between mirrors B and A. After light reaches mirror A, at time t=1, light is reflected toward mirror B and reaches it at time t=2. After another reflection at time t=2 by mirror B, toward mirror A at time t=3, these two last steps have completed the two-way reflection between mirrors A and B.

We see that the distance traveled by light while making the two-way reflection in Galilean space, between each ends of the cavity

**Distance
Traveled
inside
the
Moving Cavity. **

Let us consider light
passing from mirror B at time t=0, to mirror A at time t=1, as
shown on
figure 3.

**a**
– First, we must notice that, in Galilean space, light takes more
time
to travel the distance between mirror “B at time t=0” and mirror
“A at
time t=1”, because light travels a longer distance in the
stationary
frame, which is the side of the isosceles triangle. Light
always
travel at velocity c in the Galilean frame. Therefore,
along the side
of that triangle, the distance D, becomes (1/Cos a)
times
longer.
This
gives:

10 |

For the moving cavity (and the observer), light travels between mirror B at time t=1 and mirror A at time t=1. Therefore, the time taken for light to travel that distance is the same as the time between mirror B at time t=0 and mirror A at time t=1. However, we see on figure 3, that the distance between mirror B at time t=1 and mirror A at time t=1 is Cos(a) times smaller, due to the proper velocity of the moving cavity with respect to the moving wave in the stationary Galilean frame. Consequently, in the moving frame, the relative velocity of light with respect to the moving cavity is reduced. It takes more time for light to fill up the cavity with the wave, and complete the full period P(cavity) inside the cavity. Therefore light reaches mirror A (at time t=1) at a slower velocity than c, because it is moving away. The relative velocity (inside the cavity) between the incoming light and the running away moving frame is V

11 |

Using equations (10) and (11), we find inside the Fabry-Pérot cavity, the total time T(total) light needs to make the two-way trip. This time interval is the time, to complete one full cycle of the resonant frequency F of the cavity. This resonant period P(cavity) of the cavity between mirror A and B is equal to the distance traveled inside the cavity (equation 10) divided by the velocity (equation (11) of the wave with respect to the cavity. Since the cavity is moving away from the wave, the period P(cavity) is longer. This gives:

12 |

13 |

14 |

It is well known that Einstein’s relativity has been based on the erroneous belief that in Galilean mechanics, there should appear a shift of frequencies in the Brillet and Hall experiment and a shift of fringes in the Michelson-Morley experiment when the instrument is rotated. This is an error. Without any space distortion, Galilean physics is compatible with zero shifts during a rotation. On the contrary, in order to be compatible with Einstein’s space distortion, observations should record a well determined positive change of frequency, which has never been observed. Observations are perfectly compatible with the existence of an absolute frame of reference in Galilean space.

**
5** - **Acknowledgments.**

The author acknowledges the precious help from my son Nicolas
Marmet
and Dennis O’Keefe for reading and commenting this paper, so that
that
paper can be completed.

**6 - References**

1
- Albert A. Michelson, and Edward W. Morley, The American Journal
of
Science, “On the Relative Motion of the Earth and the Luminiferous
Ether”. No: 203, Vol. 134, P. 333-345, Nov. 1887.

2 – Paul Marmet, (to be published). Also “The Overlooked Phenomena in the
Michelson-Morley Experiment”. Web address:

http://www.newtonphysics.on.ca/michelson/index.html

3 – A. Brillet and J. L. Hall, “Improved
Laser
Test of the Isotropy of Space”.

Phys. Rev. Letters, Vol. 42, No: 9, Page 549-552, 1979.

4 – Marmet Paul, “Einstein’s
Theory
of
Relativity
versus
Classical
Mechanics” Newton Physics
Books, Ogilvie Rd. Ottawa, Canada, K1J7N4, 200 pages,
(1997). Also on the Web at:

http://www.newtonphysics.on.ca/EINSTEIN/Chapter7.html

----------------------------------

To be published in Physics Essays

----------------------------------

Version, January 8, 2005

Corrected, Jan. 27, 2005

Paul Marmet

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