Paul Marmet

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**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 M_{2} is equal to the
distance L between the point A on mirror M and point C on mirror
M_{1}.

** **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(ABA)
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) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

** 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 90^{o} because the mirror is at 45^{o}. 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 45^{o}, moving in the same downward direction as the
incoming light. The position of the mirror at time (t_{m} =1) is represented by
the narrow line between the pair of labels (t_{m}=1). At time t_{w}=0, (labeled with four
0’s in the wavefront) we see the incoming wave. We
consider light arriving progressively on mirror M. At time
t_{w}=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 t_{m}=1, t_{m}=2, t_{m}=3, and t_{m}=4.

Let us
now consider the motion of the wavefront. The labels on
each wavefront (t_{w}=0, 1, 2, 3 or 4) are repeated at each individual
quarter of wavefront. After the initial time t_{w}=0, that same
wavefront is shown at different later times at: t_{w}=1, t_{w}=2, t_{w}=3 and t_{w}=4, (inscribed on each
segment) during light propagation. All wavefronts (labeled
t_{w}=1, t_{w}=2, t_{w}=3 and t_{w}=4 ) drawn on figure 2
correspond to the same wavefront at different times.

** **Let us consider the progression of the
wavefront. At time t_{w}=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 t_{m}=1. Then, the
wavefront keeps moving down. At time t_{w}=2, the second quarter
of the same wavefront reaches the second quarter of the mirror,
(see bold segment at mirror location t_{m}=2), which has then
moved downward due to the velocity of the mirror.
Similarly, at time t_{w}=3, the third segment of the wavefront reaches the
third section of the mirror, (see bold segment at mirror
location t_{m}=3), which moved still further down during that
time. Finally, at time t_{w}=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 t_{m}=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 45^{o}. Since light is
moving downward at a velocity (c-v) with respect to the moving
frame, let us calculate the time interval T_{1} needed to reach the
opposite edge of the mirror. Since the mirror is at 45^{o}, the vertical
distance (of projection) P is the same. The time T_{1} taken by light to
travel the vertical distance P is:

(9) |

(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) |

(12) |

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 M_{2}, 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 M_{2}
(figure 3), independently of the location on the surface
of mirror M_{2}. 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 M_{2} is changing! The transit time is longer
because, in the M-M experiment, light traveling from mirrors M
to M_{2} 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 M_{2} 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 M_{1}, and the other half
is transmitted through mirror M, toward mirror M_{2}. 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 M_{2}, 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 M_{2}. 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) |

(14) |

(15) |

(16) |

(17) |

(18) |

(19) |

** 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 (t_{o}) 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 90^{o} 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 M_{1}. 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 45^{o}, but it is (45^{o}-q). Therefore, the angle of
reflection is also (45^{o}-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) |

(21) |

(22) |

(23) |

(24) |

(25) |

(26) |

(27) |

** 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) |

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 20

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.

**
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 (t_{m} =1) is represented on figure A by the narrow line
between the pair of labels (t_{m}=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 t_{m}=1, t_{m}=2, t_{m}=3, and t_{m}=4.

Let
us
now
consider
the motion of the wavefronts. The labels on each
wavefronts (t_{w}=0, 1, 2, 3, 4
and 5) are repeated at each individual quarter of
wavefront. After the initial time t_{w}=0, that same wavefront is shown at different later
times at: t_{w}=1, t_{w}=2, t_{w}=3, t_{w}=4 and t_{w}=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 t_{w}=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 t_{m}=1. Then, the wavefront keeps moving down.
At time t_{w}=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 t_{w}=3, the third segment of the wavefront reaches the
third section of the mirror, (see bold segment at mirror
location t_{m}=3), which moved
still further to the right hand side. Finally, at time t_{w}=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 t_{m}=4), which has
moved still further to the right due to the mirror
velocity.

Consequently, even if the mirror makes exactly an angle of 45^{o} 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 45^{o}.
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 45^{o} are equal to P.

We see that, since the angle of the moving mirror
is 45^{o}, the horizontal
distance (J-H) is equal to the vertical distance (H-K).

(1A) |

(2A) |

(3A) |

(F-G)=(H-K) | (4A) |

(5A) |

** 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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