The Overlooked Phenomena in the
Michelson-Morley
Experiment
Paul Marmet
Abstract.
We
show that Michelson and Morley used an over simplified description and
failed to notice that their calculation is not compatible with their
own
hypothesis that light is traveling at a constant velocity in all
frames.
During the last century, the Michelson-Morley equations have been used
without realizing that two essential fundamental phenomena are missing
in the Michelson-Morley demonstration. We show that the velocity
of the mirror must be taken into account to calculate the angle of
reflection
of light. Using the Huygens principle, we see that the angle of
reflection
of light on a moving mirror is a function of the velocity of the
mirror.
This has been ignored in the Michelson-Morley calculation. Also,
due to the transverse direction of the moving frame, light does not
enter
in the instrument at 90 degrees as assumed in the Michelson-Morley
experiment.
We acknowledge that, the basic idea suggested by Michelson-Morley to
test
the variance of space-time, using a comparison between the times taken
by light to travel in the parallel direction with respect to a
transverse
direction is very attractive. However, we show here that the
usual
predictions are not valid, because of those two classical secondary
phenomena,
which have not been taken into account. When these overlooked
phenomena
are taken into account, we see that a null result, in the
Michelson-Morley
experiment, is the natural consequence, resulting from the assumption
of
an absolute frame of reference and Galilean transformations. On
the
contrary, a shift of the interference fringes would be required in
order
to support Einstein’s relativity. Therefore, for the last century, the
relativity theory has been based on a misleading calculation.
1 -
Assessment
of the Problem.
The
aim of the Michelson-Morley experiment (1-10)
is to verify “experimentally” whether the time taken by light to travel
a distance in a direction parallel to the velocity of a moving frame,
is
the same as the time to travel the same distance in a perpendicular
direction.
The experiment is based on the assumption that the velocity of light is
constant in an absolute frame considered at rest.
The
Michelson-Morley
apparatus (1)
is illustrated on figure 1. After light is emitted by the light
source,
a central semi-transparent mirror M, splits the beam of light between
two
perpendicular directions. The distance L traveled between point A
(on mirror M) and point B on mirror M2
is equal to the distance L between the point A on mirror M and point C
on mirror M1.
In
our experiment, let us consider that light moves downward at velocity
c,
while the moving frame also moves down but at velocity v, as
illustrated
on figure 1. In order to verify the hypothesis that the velocity
of light is c with respect to an absolute frame of reference, (in
opposition
to a constant velocity equal to c in all moving frames), Michelson and
Morley have calculated the time interval taken by light to travel in
the
longitudinal direction (between A and B) compared with the time for
light
to travel in transverse direction between A and C. Therefore they
suggested building an interferometer to test their hypothesis as
illustrated
on figure 1. According to the Michelson-Morley predictions, who
affirm
that the optical distance traveled by light between each arms of the
interferometer
must be different when in motion, consequently, there must be a drift
of
interference fringes on mirror M where the beams join together, when
the
apparatus is rotating. No such drift, having the amplitude
predicted
by Michelson-Morley has ever been observed. Let us examine their
calculation.
In
the Michelson-Morley experiment, it is assumed that light travels at a
constant velocity with respect to an absolute frame assumed at
rest.
In that experiment, Michelson and Morley calculate the time t(A
BA)
taken by light to complete the trip from A to B, and return from B to
A,
while the frame is moving at velocity v. We see that when the
frame
is moving away from the point of origin of light, light passes across
the
moving frame (from AB)
at velocity (c-v), while covering the moving distance L. When
light
returns from BA,
then light passes through the moving frame at velocity (c+v), while the
equal distance L is again completed. These two time intervals are
added in the following equation:
 |
(1) |
Since
the last term in brackets of equation (1) is larger than unity, light
takes
a longer time to complete that return trip, than when the frame
velocity
is zero. Therefore, light must travel an extra distance between
locations
ABA,
when the system is in motion. Using a series expansion, equation
(1) can be written:
 |
(2) |
In
equation (2), to
is
the time taken by light to travel the distance 2L, when the frame
velocity
is zero. Also tv, is the time when the frame velocity
is v. We have to,
is equal to:
 |
(3) |
When
the light paths between locations ACA),
move transverse to the light velocity c, in the absolute frame, the
light
path is seen as an isoscele triangle in the rest frame. Using
geometry,
we find that the time taken by light is then:
 |
(4) |
Equation (4)
gives
the time interval t(ACA)
for light to travel through the moving locations (ACA).
Using a series expansion of equation (4), the time taken by light in
the
transverse direction can be written:
 |
(5) |
According
to Michelson and Morley, we have seen in equation (2) that, when light
moves parallel to the frame velocity (between ABA),
light must travel during an additional time equal to: to(v2/c2),
with respect to the system at rest. However, in equation (5),
when
the direction of the frame is transverse to the velocity of light
(between
ACA),
then the additional time, due to the proper velocity of the frame is
different.
It is now only half of the other value. The difference of time is
(to/2)(v2/c2).
It is that difference of time interval between axes, which led
Michelson
and Morley to predict that there should be a shift of interference
fringes
between the arms of the interferometer. From equations (2) and
(5),
we see that, between the parallel direction (AB)
and the transverse direction (AC),
there is a difference of time equal to:
 |
(6) |
There
is a difference of distance DL,
corresponding
to the difference of time given in equation (6). That difference
is equal to the velocity of light c, times the difference of time Dt
(see equation (6)). Therefore, the difference of distance
traveled
by light between the parallel and transverse arm of the interferometer,
as given by equation (3) and (6) gives:
 |
(7) |
When
rotating the interferometer through 
= 90 degrees, the two beams exchange lengths, giving a
total
path difference
DL(rotation 90o)
between the two rotating perpendicular axes. Using equation (7),
the difference of path length DL(rotation 90o)
due to that rotation is:
 |
(8) |
According
to Michelson-Morley, equation (8) gives the difference of distance
traveled
by light between the parallel and the transverse direction, when the
apparatus
is rotated by 90o.
Following these calculations, the Michelson-Morley experiment was made
and repeated by many researchers under various conditions and at
different
locations. Most importantly, it was observed experimentally that
the observed shift of interference fringes was, if any, quite
negligible,
and therefore much smaller than predicted by Michelson and
Morley.
Consequently, scientists decided to consider some esoteric hypothesis
to
explain these experimental observations. We show here that this
Michelson-Morley’s
demonstration is seriously over simplified. In fact we show below
that the unexpected result is due to an erroneous prediction.
2
- Reflection of Light on a Moving Mirror.
We show here
that there are at least two crucial physical phenomena, which have been
ignored in the Michelson-Morley calculation. The importance of these
phenomena
changes radically the Michelson-Morley prediction. One of these
phenomenon
takes place on the reflected light on the semi transparent mirror M of
the interferometer.
In the
Michelson-Morley
experiment, it is considered that light is reflected at 90o
because the mirror is at 45o.
However, we show here that it cannot be so, because of the proper
velocity
of the mirror. Whenever a mirror possesses a velocity with
respect
to the stationary frame in which light travels at velocity c, we see
here
that the usual laws of reflection on moving mirrors are not compatible
with a constant velocity of light in that frame.
On
figure 2, let us consider first the motion of mirror M at 45o,
moving in the same downward direction as the incoming light. The
position of the mirror at time (tm
=1) is represented by the narrow line between the pair of labels (tm=1).
At time tw=0,
(labeled
with four 0’s in the wavefront) we see the incoming wave. We
consider
light arriving progressively on mirror M. At time tw=1,
(labeled with 1's), we see that the incoming wavefront, just reaches
the
left hand side of mirror M. Since it takes time, for that
wavefront,
to move downward and reach the right hand side of the mirror, the
mirror
M moves a short distance downward, while the wavefront of light is
moving
down much faster. The continuous progression of the wavefront on
the mirror (while the mirror is moving down) is illustrated in four
steps.
During each step, the (moving down) mirror is shown between each pair
of
labels tm=1, tm=2,
tm=3, and tm=4.
Let us now
consider the motion of the wavefront. The labels on each
wavefront
(tw=0, 1, 2, 3
or
4) are repeated at each individual quarter of wavefront. After
the
initial time tw=0,
that
same
wavefront is shown at different later times at: tw=1,
tw=2, tw=3
and tw=4,
(inscribed
on each segment) during light propagation. All wavefronts
(labeled
tw=1, tw=2,
tw=3 and tw=4
) drawn on figure 2 correspond to the same wavefront at different
times.
Let
us consider the progression of the wavefront. At time tw=1,
(on figure 2) the left hand side of the wavefront of light just reaches
the left hand side (bold segment) of mirror M, (segmented in four
parts).
At that time, the first segment (bold line) of the mirror is at mirror
location tm=1.
Then,
the
wavefront keeps moving down. At time tw=2,
the second quarter of the same wavefront reaches the second quarter of
the mirror, (see bold segment at mirror location tm=2),
which has then moved downward due to the velocity of the mirror.
Similarly, at time tw=3,
the third segment of the wavefront reaches the third section of the
mirror,
(see bold segment at mirror location tm=3),
which moved still further down during that time. Finally, at time
tw=4, the
reflection
of the wavefront on the mirror is completed after the fourth quarter of
the wavefront is reflected on the fourth section of the mirror (bold
segment
at mirror location tm=4),
which has moved still further down due to the mirror velocity.
Consequently,
even if the mirror makes exactly an angle of 45 degrees with respect to
the incoming wave, that wave is reflected by a mirror making
effectively
a larger angle, because the mirror has the time to move down, during
the
time of reflection on the whole surface of the mirror. The
“effective
moving mirror” is illustrated on figure 2, as the sum of the four bold
segments of the moving mirror, formed by the wide set of narrow lines
(crossed
by three parallel lines), covering the average location of the four
bold
sections of the mirror. That effective mirror makes an affective
angle a (with respect to 45 degrees) as
illustrated
on figure 2. The angle a between the
instantaneous
and the effective moving angle of the mirror is shown separately on
figure
2 (bottom left). It can be shown that this angle a,
represents half of the increase of the angle q
of reflection of light due to the mirror velocity. However, here,
the angle of reflection of light will be calculated using a more direct
method.
Let
us calculate the change of angle of the reflected wavefront, after
reflection,
due to the velocity of the moving mirror. The projected width of
the wavefront on mirror M is equal to P (see fig. 2). The
“instantaneous”
position of the mirror with respect to the wavefront is exactly 45o.
Since light is moving downward at a velocity (c-v) with respect to the
moving frame, let us calculate the time interval T1
needed to reach the opposite edge of the mirror. Since the mirror
is at 45o, the
vertical
distance (of projection) P is the same. The time T1
taken by light to travel the vertical distance P is:
 |
(9) |
We can see
that
the change of distance P in the vertical direction, due to the motion
of
the mirror leads to a correction implying a higher power of v/c, which
is negligible. During the same time T1,
while light travels downward toward the right hand side of the mirror,
the previously reflected light on the left hand side of the same mirror
travels horizontally toward the right hand side. The horizontal
velocity
of light is equal to c. Let us calculate that horizontal distance
D, traveled by light at velocity c, during the same time interval T1.
Using equation (9), we find:
 |
(10) |
The
distance D is illustrated on figure 2. In
equation
(10), we take into account that the relative velocity of the mirror
(which
is the velocity of the Earth around the sun) is very small (i.e.
1/10000)
compared with the velocity of light. Higher powers of v/c are
neglected
when appropriate (as seen in equation (10).
Let us use
the Huygens method of light propagation. From figure 2, we see that,
after
reflection on the upper left corner of the mirror, the Huygens wave
method
show that light has traveled a larger horizontal distance D,
than the X-coordinates “P” on the right hand
side
of the mirror. Therefore this produces the angle q
on the reflected wavefront. From equation (10), we find that the
additional distance (D-P) is:
 |
(11) |
From
figure 2 and equations (10) and (11), the tangent of angle q
is:
 |
(12) |
Therefore,
light
is reflected at (90o+q),
when the static angle of the mirror at 45 degrees is moving at velocity
v. Figure 2 also illustrates the wavefront (of the wave drawing)
(label tw=4) after total reflection by the moving mirror
with
the additional angle q due to the mirror
having
an effective angle a.
It
is important to realize that the angle q
also
appears when the moving frame travels in different directions.
Instead
of having the mirror moving downward in figure 2, using the same
method,
we can show that the increase of angle q of
the wavefront is the same when the mirror moves toward the left hand
side.
Using the same method as above, we can also show that when the mirror
is
moving in a direction opposite to the velocity of light (upward) or
toward
the right hand side, the effective angle of deflection of light then
decreases
by the angle q degrees.
The
demonstration
which shows that the change of angle of deflection of light reflected
on
a mirror moving in the transverse direction is given in the appendix
of this paper.
3–
Shifted
Direction of Light in a Transverse Direction.
There
is a second phenomenon which also has been ignored in the
Michelson-Morley
experiment.
Let
us
consider figure 3. Just as hypothesized by Michelson and
Morley,
figure 3 illustrates light moving at velocity c with respect to a
stationary
frame. After emission, that light forms circular wavefronts
around
the instantaneous location of the emitter. Then, the circular
wavefronts
get bigger with time. However in the problem here, the “light
source”
is not stationary, but moves sideways on Earth at the same time as the
interferometer. On figure 3, we illustrate that both, the light
source
and the interferometer move at velocity v toward the right-hand
side.
Let
us consider a wavefront of light emitted at time t(-2). Of
course,
at the instant light is emitted, the mirror M of the Michelson-Morley
interferometer,
is located just below the light source, where the interferometer is
shown
(ghost image). Two units of time later, at t(0), that
spherical
wavefront of light [emitted at t(-2)] reaches mirror M of the
Michelson-Morley
interferometer (new location of the interferometer drawn with dark
lines).
Simultaneously, the light emitting source also moves toward the right
hand
side. Therefore, both the source and the interferometer still
have
similar relative positions (same vertical axis) as seen experimentally.
This description corresponds to the Michelson-Morley experimental
apparatus.
We see that
light reaching location A on mirror M, originates from a location where
the source of light was located two units of time
previously.
We see clearly that light makes an angle q
with
respect to the Y-axis, in order to reach the mirror M at location A of
the interferometer and beyond, (toward B’). Therefore due to the
velocity
of the frame, even if the source of light is instantaneously always
located
exactly above the mirror M of the interferometer, it must be understood
that light traveling toward mirror M2,
either
can
be considered to move at velocity c at the angle q
in the rest coordinates, or at velocity [c Cosq]
along
the
Y axis of the moving coordinates. Of course, as seen on
figure 3, these two calculations are indistinguishable. However,
the function Cosq has been ignored in the
moving
frame by Michelson and Morley. This will be taken into account
below
in figure 5.
Let us
recall
that the M-M calculation is a completely classical calculation (not
relativistic).
Recalling that the M-M calculation is totally classical, "with an
absolute
frame" whatever the observations of the moving observer are, let us
consider
again how much time light takes to travel from point A on mirror M to
mirror
M2 (figure 3), independently of the
location
on the surface of mirror M2. We
see
that even if the observer in the moving frame perceives that light
moves
along his moving Y axis, the time interval taken by light to travel
that
distance is (L/Cosq)/c (because the frame is
moving). Since this is a classical calculation, there is no
space-time
distortion involved in that calculation, as expected for the M-M
calculation.
It seems that we are so much involved with relativity theory, that we
sometimes
overlook "when" exactly we must apply relativity or classical
physics.
It is not because the moving observer cannot see directly the angle q
that the time interval between mirrors M and M2
is changing! The transit time is longer because, in the M-M
experiment,
light traveling from mirrors M to M2
must
necessarily travel at the angle q.
A similar
phenomenon happens when two fast cars, emitting sounds in stationary
air,
are moving parallel. The observer in both cars will detect sounds,
apparently
coming from a direction perpendicular to their velocity, but the time
interval
taken by sound before reaching the opposite car increases as (L/Cosq)
with the velocity of the cars.
The fact
that
the light path reaching the interferometer makes an angle q
with respect to the observed direction inside the moving frame is
related
to another well known phenomenon, discovered
by Bradley (11)
in 1725. This phenomenon explains how
an
observer in the moving frame can see light coming from a direction
which
is parallel to the Y-axis, even if in fact, the light source is an
angle
q.
Consequently, it becomes obvious that light takes more time to travel
between
mirrors M and M2 than when the frame
is
at rest. This is taken into account below.
4
- Application to the Michelson-Morley Apparatus.
Figure
4, represents the Michelson-Morley apparatus moving in a direction
parallel
to the velocity of light. On figure 4-A, the interferometer moves
downward away from the light source.
The
velocity
of light is c in the background frame at rest.
Therefore,
as in the Michelson-Morley apparatus, both, the source of light and the
interferometer move with respect to that background. On figure
4-A,
the emitted wavefront expands and form circles around the instantaneous
position where the light source is located at the moment of
emission.
On figure 4, half the light is reflected from location A on mirror M,
toward
mirror M1, and
the
other half is transmitted through mirror M, toward mirror M2.
Light paths are illustrated as bold dashes on a narrow line.
Figure
4 shows the moving interferometer and the wavefront as seen from the
rest
frame, at time t=0, at the instant light, emitted earlier, reaches the
mirror M of the interferometer. That light was previously
emitted
at time t=-1. On figure 4-A, the frame is moving downward.
It is moving upward on figure 4-B.
Figure
4-A illustrates light emitted from the source at time t(-1).
Later,
at time t(0) we see that the frame has moved down. Then, at time
t(0), the wavefront, which was emitted at t(-1), forms a circle just
reaching
location A on mirror M of the Michelson-Morley interferometer. As
illustrated
on figure 4-A, when light moves through mirror M toward location B on
mirror
M2, the
velocity of
the frame is parallel to the velocity of light. Light passes
directly
from A on mirror M toward point B on mirror M2.
We have seen above in equation (2) that when the moving frame moves
parallel
to the velocity of light, the time taken by light between mirrors is
equal
to:
 |
(13) |
However,
in the case of light reflected on mirror M toward mirror M1,
we have seen above on figure 2 that, due to the velocity of the mirror,
light is not reflected at 90o.
As
demonstrated in section 2, (equation 12), that light is reflected at an
additional angle q. Therefore light
is
not traveling from ACA.
Instead, due to the velocity of the mirror, light is traveling from A
to
C’ and return to A as shown on figure 4-A. Using figure 4, let us
calculate the extra time taken by light due to the extra distance at
the
angle
q instead of the horizonal path. The
relationship
between the distance ACA
and AC’A
is:
 |
(14) |
Using
a series expansion of Cos q, we get from
equation
(14)
 |
(15) |
Since the
times
t(AC’A)
and t(ACA)
for light to travel (at velocity c) is proportional to the distance, we
have from equation (14)
 |
(16) |
which is
equal
to:
 |
(17) |
Substituting
equation
(5) in equation (17) gives:
 |
(18) |
which is
equal
to:
 |
(19) |
Equation
(19) shows that the time for light to travel, in the transverse
direction
along AC’A,
is the same time as in the parallel direction given in equation
(13).
Therefore the number of wavelengths of light along the horizontal light
path is the same as the number along the transverse light path.
The
phenomenon of reflection on moving mirrors ignored by Michelson and
Morley
produce an effect, which is exactly equal to the difference of time,
and
which was erroneously interpreted as an agreement with relativity in
modern
physics.
Let
us also consider the case when light and the observer’s frame are
moving
in the opposite direction, as illustrated on figure 4-B.
Consequently,
as explained on figure 2, due to the proper upward velocity of mirror
M,
the angle q of the beam of light is in the
opposite
direction, with respect to the X-axis, compared with when the frame is
moving downward. As a consequence of this shift in light
direction
by the angle q, we get the same increase of
distance in the direction of q and the same
time interval as calculated in equation (19). Therefore, the
total
time interval t(AC’A)
is exactly the same as given in equation (19). There exists no
change
of transit time between the arms of the interferometer, contrary to the
Michelson-Morley oversimplified calculation.
5
– Moving Frame in the Transverse Direction to Incident Light.
We
now use figure 5 to see the trajectory of light entering the
interferometer
moving in a transverse direction, at velocity V, with respect to the
light
source.
On
figure
5-A, we see the light source at time t(-1), so that the
spherical
wavefront of light reaches the mirror M of the interferometer at time
t(0).
We see that, at the moment light reaches mirror M, the source of light
has now moved to location t(0). However, the new light just
emitted
at t=0 did not have the time to reach the interferometer yet.
Light
reaching the interferometer must always be emitted previously so that
light
has enough time to travel to the interferometer.
Figure
5 shows the moving interferometer and the wavefront as seen from the
rest
frame, at time t=0, at the instant light, emitted previously at (t-1),
reaches the mirror M of the interferometer. On figure 5-A,
the frame is moving toward the right hand side. That frame is
moving
toward the left hand side direction on figure 5-B. We notice that
at the instant t=0, the light source (to)
and mirror M, (at location A) are located exactly in a direction along
the Y-axis, just as explained on figure 4. This is necessary to
satisfy
the Michelson-Morley description that requires that the light source
must
be located at 90o
with respect to the frame velocity.
Consequently,
in that case, contrary to figure 4, due to the frame velocity, light
cannot
then move parallel to that Y-axis, due to the transverse motion of the
frame. On figure 5, we have now a new angle q,
with
respect
to the Y-axis, due to the velocity of the moving
frame.
Therefore, since light reaching the interferometer comes from a
transverse
direction, light necessarily arrives on the interferometer at the angle
q,
with respect to the Y-axis, as illustrated also on figure 3.
On figure 5-A, after reflection on the moving mirror M, light travels
in
the direction of M1.
Due to the velocity of the mirror explained on figure 2, and equation
(12),
light is reflected on mirror M, with an angle of incidence (with
respect
to the mirror surface) which is no longer 45o,
but it is (45o-q).
Therefore,
the
angle of reflection is also (45o-q).
This is illustrated on figure 5-A as the direction of the dashed line AK.
However, we have seen in the last paragraph of section 2 that due to
the
velocity of the mirror, the angle of reflection is reduced by the angle
q.
Consequently, the moving mirror reflects light in the direction of the
X-axis along the path ACA,
as shown on figure 5-A. Since the direction of light along ACA
is parallel to the X-axis, and that light moves parallel to the frame
velocity,
the time taken by light to travel between ACA
is given by equation (2).
We
must notice that due to the rotation of the apparatus, the notation
(label)
ABA
in equation 2 becomes ACA
after the rotation of the frame, as illustrated on figure 5.
Therefore,
the time t(ACA)
to move across the distance ACA
given by equation (2) becomes now:
 |
(20) |
Let us now
study
on figure 5-A, light moving through mirror M, between mirrors M and M2.
We have seen above that due to the transverse velocity of the moving
frame
with respect to light, light reaching mirror M makes angle q
with respect to the Y-axis.
That
angle q is needed, to be compatible with
the
Michelson-Morley description which has located the light source exactly
on the Y-axis. This is similar to figure 3 when the light
source
on the Y-axis produces a light beam making an angle q
with respect to the Y-axis. This is different of figure 4, in
which
case, a light source (at to)
on the Y-axis produces a light beam parallel to the Y-axis.
Therefore, light between mirrors M and M2
travels between AB’A.
Before calculating the time for light to travel between AB’A,
let us calculate first the time to travel between ABA.
We see on figure 5-A that light traveling between ABA
is in a transverse direction with respect to the frame velocity.
We have seen that in the case of a transverse direction between light
and
the moving frame, equation (5) gives the time taken by light to travel
the distance between ABA
along the Y-axis. We also must notice that due to the rotation of
the apparatus, the labels ACA
in equation (5) becomes ABA
in the rotated frame corresponding to figure 5. Therefore, the
time
t(ABA)
taken by light to travel along the path ABA
is:
 |
(21) |
However,
light does not travel exactly along direction ABA.
Instead due to the frame velocity, light travels between AB’A.
Therefore we must take into account that because light travels a longer
distance at the angle q, it takes a longer
time
to complete that new path. Let us calculate the time taken by
light,
between AB’A,
due to the angle q. Using figure 5,
we
find that the relationship between the distance ABA
and AB’A
is:
 |
(22) |
Using
a series expansion of Cos q, equation (22)
gives:
 |
(23) |
Since
the time t(ABA)
for light to travel across the distance ABA
is proportional to distance (at velocity c), equation (23) gives:
 |
(24) |
Equation
(24) gives:
 |
(25) |
Considering
the rotation, t(ACA)
in equation (5) becomes now t(ABA).
Taking into account that change of label due to rotation, equation (5)
in equation (25) gives:
 |
(26) |
Equation
(26) gives:
 |
(27) |
Equation
(27) gives the time for light to travel between AB’A.
Using
a similar demonstration as above, we can see on figure 5-B, that, when
the direction of motion of the moving frame is reversed, the time for
light
to travel between AB’A,
is also the same, as given in equation (27). In a few words, we
see
that the angle of incidence with respect to the mirror is now (45o+q)
due to the velocity of the moving frame moving toward the left hand
side
direction. The light would be reflected along the direction AK
on figure 5-B. However, since the frame is moving toward
the
left hand side direction, we have seen in the last paragraph of section
2 that the angle of reflection is increased by the angle q.
Therefore, the reflected beam of light is reflected along the
X-axis.
This is similar to the problem calculated on figure 5-A.
In
the case of light moving downward on figure 5-B, the angle q
with respect to the Y-axis is similar to the problem in figure
5-A.
There is only a change of sign of the angle q.
Consequently,
the
time taken by light to travel the distance AB’A
is again similar to the case of figure 5-A.
Consequently
in
all
cases, the time taken by light to travel between mirrors is
always
the same.
6
- Analysis of the New Results.
We
have shown here that, in the Michelson-Morley experiment, using
classical
physics, the time for light to travel between any pair of mirrors, in
any
direction, is always the same, independently of the direction of the
moving
frame and also independently of having light moving either parallel or
transverse to the frame velocity. In any direction, that time
interval
Dt
between mirrors is always equal to:
 |
(28) |
More
specifically, in equations (20) and (27), when the velocity of the
frame
is perpendicular to the direction of light penetrating in the
instrument,
we have shown that the times for light to travel between the horizontal
and vertical mirrors are identical. We have shown that this is
always
true whether the frame is moving toward the right hand direction or the
left hand direction. Furthermore we have seen above in equations
(13) and (19), that when light penetrates into the instrument in a
direction
parallel to the frame velocity, the times for light to travel between
the
parallel or transverse arm of the interferometer are also always
identical.
We have also shown that this is always true, whether the frame is
moving
parallel or anti-parallel with respect to the velocity of light. We
must
conclude that the times taken by light to travel between any pair of
mirrors
are always the same, independently of any rotation of the
interferometer
in space.
Therefore,
according to classical physics, the rotation of the Michelson-Morley
apparatus
in space should never show any drift of interference lines. On
the
contrary, a positive shift of interference fringes with the amplitude
compatible
with the Michelson-Morley predictions is required in order to be
compatible
with Einstein’s relativity. Such a shift of interference fringes
due to a rotation has never been observed. The absence of an
observed
drift of interference fringes invalidates Einstein's relativity.
We
have
seen above that the prediction presented by Michelson and Morley are
based
on a model which ignores two important fundamental phenomena.
These
disregarded phenomena are the law of reflection of light on the moving
mirror and also the deviation of the observed direction of light coming
from a moving system.
Relativity
theory, astrophysics, and most of modern physics in the 20th
century has been based on the belief that a null result in the
Michelson-Morley
experiment is an argument in favor of relativity theory. We see
now
that the contrary is true. An enormous amount of human effort and
an unbelievable amount of money for research has been based on that
erroneous
prediction published in 1887. It is inconceivable that the
original
demonstration has never been seriously reconsidered. This is the
result of an extremely dogmatic attitude of the physics establishment
against
a few scientists whose status were threatened and even ruined because
they
dared to reconsider some fundamental principles of physics.
It
is also important to mention that the non-zero result observed in the
Michelson-Morley
experiment does not provide any proof of existence of ether. The
presence of ether appears totally useless, when an appropriate model is
used. Without matter nor radiation, space is nothing. Other
experiments(12-17)
have already shown that everything in physics can be explained using
classical
physics without the ether hypothesis.
We
acknowledge
that, the basic idea suggested by Michelson-Morley to test the variance
of space-time, using a comparison between the times taken by light to
travel
in the parallel direction with respect to a transverse direction is
very
attractive. However, this test is not valid, because there are
two
classical secondary phenomena, which have not been taken into
account.
Just one year before the commemoration of the 1905 Einstein’s paper, we
must realize that the relativity theory relies on a ghost
experiment.
The
calculations above do not include all the possible physical mechanisms
that can possibly perturb the light path in the Michelson-Morley
apparatus.
However, we strongly suspect that all other mechanisms produce effects,
which are enormously smaller than the phenomena overlooked by Michelson
and Morley. Of course, we have seen in this paper that there
exists
a fourth order term (v4/c4),
that
has
been neglected here. This high order term is much too
small
to be observed. We can also mention the Fizeau effect, which is
known
to drag light traveling in a moving medium as a function of the index
of
refraction. The empirical equation of the Fizeau effect is known
in the case of a medium moving parallel to the direction of
light.
We have verified that these other phenomena also make a negligible
contribution
to an assumed drift of fringes. However, that Fizeau drag
phenomenon
seems to be totally unknown when the medium moves perpendicular to
light
velocity. Finally, the misalignment of the mirrors of the
interferometer
might also have some effect on the fringes observed(18)
in the Michelson-Morley experiment.
It
is important to recall that the overlooked phenomena described here
also
have important implications in other fundamental experiments(19)
in relativity. For example, in the Lorentz transformation(19),
which usually predicts length contraction along the velocity axis of
moving
matter with respect to the transverse axis, it has been shown that the
predictions are also in error, due to a secondary phenomenon explained
in this present paper. We know also that the Brillet and Hall
experiment
(20)
is also a test for the anisotropy of space. The Brillet and Hall
experiment (20)
has also been carefully studied and similarly, it has been shown (21),
that a corresponding phenomenon is changing the light path inside a
Fabry-Pérot
etalon. Consequently, in that case again, the null change of
frequency
observed experimentally, corresponds to an absolute frame of reference,
while an anisotropic relativist space would require an observed shift
of
frequency.
-----------------------------------------
Appendix
Reflection
of Light on a Mirror Moving in a Transverse Direction.
On figure
A, let us consider the motion of mirror, moving horizontally when light
moves downward. The initial position of the mirror at time (tm
=1) is represented on figure A by the narrow line between the pair of
labels
(tm=1) at the moment the wavefront
reaches
the left hand side of the mirror. The continuous progression of
the
wavefront on the mirror, while the mirror is moving to the right hand
side,
is illustrated in four steps. During each step, the sideways
moving
mirror is shown moving toward the right hand side direction, between
each
pair of labels tm=1, tm=2,
tm=3, and tm=4.
Let
us
now consider the motion of the wavefronts. The labels on
each
wavefronts (tw=0, 1, 2, 3, 4 and 5)
are
repeated at each individual quarter of wavefront. After the
initial
time tw=0, that same wavefront is
shown
at different later times at: tw=1, tw=2,
tw=3, tw=4
and tw=5 during light
propagation.
All wavefronts on figure A correspond to the same wavefront at
different
times.
Let us
consider
the progression of a wavefront. At time tw=1,
(on figure A) the left hand side of the wavefront #1 of light just
reaches
the left hand side (bold segment) of mirror M. At that time, the
first segment (bold line) of the mirror is at mirror location tm=1.
Then, the wavefront keeps moving down. At time tw=2,
the mirror, is still moving to the right hand side, and the second
quarter
of the same wavefront reaches the second quarter of the mirror.
However, due
to the motion of the mirror toward the right hand side, the wavefront
is
reaching the mirror at an earlier time, as can be seen on figure
A.
Similarly, at time tw=3, the third
segment
of the wavefront reaches the third section of the mirror, (see bold
segment
at mirror location tm=3), which moved
still
further to the right hand side. Finally, at time tw=4,
the reflection of the wavefront on the mirror is completed after the
fourth
quarter of the wavefront is reflected on the fourth section of the
mirror
(bold segment at mirror location tm=4),
which
has
moved still further to the right due to the mirror
velocity.
Consequently,
even if the mirror makes exactly an angle of 45o
with respect to the incoming wave, that wave is reflected by a mirror
making
effectively a different angle, because the mirror has the time to move
to the right hand side, during the total time of reflection on the
whole
surface of the mirror.
The
“effective mirror” is illustrated on figure A as the sum of the four
bold
segments of the mirror, which makes an affective angle q.
The effective angle of that moving mirror is illustrated on figure A,
by
the wide set of narrow lines (crossed by three parallel lines),
covering
the average location of the four bold sections of the mirror.
The angle
a
between the real and the effective angle of the mirror is shown
separately
on figure A (bottom left). It can be shown that this angle a,
represents half of the increase of the angle q of
reflection
of
light due to the mirror velocity. However here, the
angle of reflection of light is calculated using the Huygens’ principle
as seen in section 2 above.
Let us
calculate
the angle of the reflected wavefront, taking into account the velocity
of the moving mirror. The projected width of the wavefront on
mirror
M is equal to P (see fig. A). The “instantaneous” angle of the
mirror
with respect to the wavefront is exactly 45o.
However, since the mirror is moving to the right hand side, while the
wavefront
moves downward, light will not reach the opposite side at the same time
as when the mirror is stationary. In fact, since the mirror is
moving,
we see on figure A that, compared with a stationary mirror, light
reaches
the mirror at an earlier time, at location H. Light travels only
from G to H.
At rest, the
vertical and horizontal components of the mirror at 45o
are equal to P.
We see that, since the angle of the moving mirror is
45o, the horizontal distance (J-H) is
equal
to the vertical distance (H-K).
 |
(1A) |
The time
interval
T1 is equal to the time for light to
travel
the distance P. During that time interval, the mirror M travels
the
distance J-H. Therefore, using equation (1A), we have:
 |
(2A) |
Equation
(2A)
gives:
 |
(3A) |
Equation
(3A)
shows that the distance traveled by light is shorter, before hitting
the
mirror at location H, when the mirror is moving. Let us compare
this
time interval for light travel, with the distance A-G, after a Huygens
reflection on point A). Using the Huygens principle again, the
wavefront
re-emitted at location A cannot reach location G (after traveling
distance
P) during the same time interval light reaches the mirror at H.
Due
to the mirror motion, (G-H) is now shorter than (A-G). After the
Huygens reflection on point A, light travels only the shorter distance
(A-F). Therefore we have:
Therefore
after
reflection, at the moment light is finally reflected at location H
(forming
the wavefront #4), the reflected wavefront makes an angle q
with respect to the vertical axis. This gives:
 |
(5A) |
A moment
later,
the wavefront #5 escapes from the surface of the mirror at the angle q.
One must conclude that light reflected on a moving mirror makes an
extra
angle of reflection q, as given in equation
(5A). Using the same demonstration, we see that changing the
direction
of the velocity v of the mirror also changes the sign of the angle q.
This demonstration explains the behavior of light on figure 5.
7
- References
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2 - W. M. Hicks, Phil. Mag. Vol. 3 , 9, (1902)
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on an Exp/riment to Detect the FitzGerald-Lorentz Effect." Phil.
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5 - M. Consoli and E. Costando, ”The Motion of
the Solar System and the Michelson-Morley Experiment”
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http://www.arxiv.org/pdf/astro-ph/0311576,
26 Nov 2003
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with Absolute Space. A. A. 251955, Bogotá D.C.
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Collapse of the Lorentz Transformation” P. Marmet, To be
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20 – A. Brillet, and J. L. Hall,
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21 – P. Marmet “Design Error in
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On the Web at: http://www.newtonphysics.on.ca/brillet_hall/index.html
-----
To be published in Galilean Electrodynamics.
Ottawa, Original paper May 30, 2004
Updated Nov. 30, 2004.
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