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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

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To be published in Physics Essays

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Version, January 8, 2005

Corrected, Jan. 27, 2005

Paul Marmet

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