The Overlooked Phenomena in the
Michelson-Morley Experiment
Paul Marmet
( Last checked 2012/06/03 - The estate of 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
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 - W. M. Hicks, Phil. Mag. Vol. 3 , 9,
(1902)
3 - D. C. Miller "The Ether-Drift Experiment
and the Determination of the Absolute Motion of the Earth" Rev.
Mod. Phys. Vol 5, 203, (1933)
4 - E. W. Morley and D. C. Miller,
"Report on an Exp/riment to Detect the FitzGerald-Lorentz
Effect." Phil. Mag. 9, 669, (1905)
5 - M. Consoli and E. Costando, ”The Motion
of the Solar System and the Michelson-Morley Experiment”
in:
http://www.arxiv.org/pdf/astro-ph/0311576, 26 Nov 2003
6 - Raymond A. Serway, Clement J. Moses, and
Curt A. Moyer, Modern Physics, Saunders Golden Sunburst series,
Saunders College Publishing, London (1989), ISBN 0-03-004844-3
7 - Miller, D. C. Ether-drift experiments at Mount
Wilson, Proc. Nat. Acad. Sci. 11(1925) 306-314.
8 - Miller, D. C. The ether-drift experiment and
the determination of the absolute motion of the earth, Rev. Mod.
Phys. 5, (1933) 203-242.
9 - Piccard, A. and Stahel, E., Nouveaux
résultats obtenus par l’expérience de
Michelson, Compte rendus 184, (1927) 152.
10 - Kennedy, R. J., A Refinement of the
Michelson-Morley experiment, Proc. Nat. Acad. Sci. 12, (1926)
621-629.
11 - James
Bradley, “Aberration of light” at:
http://brandt.kurowski.net/projects/lsa/wiki/view.cgi?doc=563
(This web page does not seem to be available
anymore.)
12 - P. Marmet, Einstein's Theory
of Relativity Versus Classical Mechanics, 200 p. Ed. Newton
Physics Books, Ogilvie Road, Gloucester, Ontario, Canada, K1J
7N4
Also on the Web at: http://www.newtonphysics.on.ca/einstein/index.html
13 - P. Marmet, "Classical Description of the
Advance of the Perihelion of Mercury" in Physics Essays Volume 12, No:
3, 1999, P. 468-487. Also on the Web at:
http://www.newtonphysics.on.ca/mercury/index.html
14 - P. Marmet, “Natural Length Contraction
Mechanism Due to Kinetic Energy”, Journal of New Energy, ISSN
1086-8259, Vol. 6, No: 3, pp. 103-115, Winter 2002. Also
on the Web at:
http://www.newtonphysics.on.ca/kinetic/index.html
15 - P. Marmet, “Natural Physical Length
Contraction Due to Gravity”.
http://www.newtonphysics.on.ca/gravity/index.html
16 - P. Marmet, “Fundamental
Nature
of
Relativistic
Mass
and Magnetic Fields”.
Invited paper in: International IFNA-ANS Journal
"Problems of Nonlinear Analysis in Engineering Systems" No. 3
(19), Vol. 9, 2003 Kazan University, Kazan city, Russia.
17 - P. Marmet, Einstein’s Mercury Problem Solved
in Galileo’s Coordinates, Symposium “Galileo Back in Italy”
Bologna, Italy, P. 335-351, May 26-29,1999,
18 - Héctor Múnera,
Centro Internacional de Física, Michelson-Morley
Experiment Revisited: Systematic Errors, Consistency among
Different Experiments and Compatibility with Absolute
Space. A. A. 251955, Bogotá D.C. Columbia,
APEIRON, Vol 5, 37, (1998).
Also at: http://www.newtonphysics.on.ca/faq/michelson_morley.html
19 - P. Marmet, “The Collapse of the Lorentz
Transformation” P. Marmet, To be published.
On the Web at: http://www.newtonphysics.on.ca/lorentz/index.html
20 – A. Brillet, and J. L. Hall,
“Improved Laser Test on the Isotropy of Space”, Physical Review
Letters, Vol. 42, No: 9, (February 26, 1979).
21 – P. Marmet “Design
Error in the Brillet and Hall Experiment” to be published.
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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