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michelson_a.htm
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="GENERATOR" content="Microsoft FrontPage 4.0">
<meta name="ProgId" content="FrontPage.Editor.Document">
<title>The Michelson Interferometer</title>
<META NAME="description" CONTENT="Explanation of matter and physic laws by standing waves.">
<META NAME="keywords" CONTENT="physics, matter, standing waves, gravity, Relativity, Lorentz transformation, electron, atom, light, Doppler effect, fields, electricity, magnetism">
</head>
<body bgcolor="#E1E1E1">
<p align="center"><font size="4" face="Times New Roman"><a href="matter.htm"><img border="0" src="images/fleche_agg.gif" width="159" height="31"></a><a href="sa_aether.htm"><img border="0" src="images/fleche_ag.gif" width="162" height="31"></a><a href="sa_Lorentz.htm"><img border="0" src="images/fleche_ad.gif" width="133" height="31"></a><a href="sa_conclusion.htm"><img border="0" src="images/fleche_add.gif" width="146" height="31"></a></font></p>
<p align="center"><font face="Times New Roman" size="6">THE MICHELSON
INTERFEROMETER<a href="matiere.htm"><img border="0" src="images/quebecois.gif" width="60" height="40" align="left"><img border="0" src="images/francais.gif" width="60" height="40" align="right"></a></font></p>
<p align="center"><img border="0" src="images/michelson02.gif" width="334" height="334"><font size="4" face="Times New Roman">
</font><img border="0" src="images/michelson03.gif" width="321" height="334"></p>
<P align=center><font face="Times New Roman" size="4">Left: Michelson was
hoping to detect a phase shift. Right: The contraction yields a null
result.</font></P>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA"><b>A
GREAT IDEA</b></span></font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">In
1887, Albert A. Michelson and Edward Morley tried to measure the speed of the Earth through
aether using an interferometer. But this apparatus revealed nothing. It was a
"failure".</span>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Actually this experiment led to a
fantastic scientific discovery: the Lorentz transformation and the theory of
Relativity.</span>
<p align="left"><b>A race between two planes.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Michelson
explained to his children that his interferometer was simulating a race
on a river between two swimmers. In 1887 planes
did not exist. Otherwise he certainly would have spoken about a plane
race while a strong wind is blowing : </span>
</font>
</center>
</td>
</tr>
</table>
</div>
<P align=center> </P>
<P align=center><img border="0" src="images/michelson04_a.gif" width="706" height="399"></P>
<P align=center><font face="Times New Roman" size="4">The Michelson
interferometer works like a race between two planes.</font></P>
<P align=center><font size="4" face="Times New Roman"> </font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Let's
assume that
the two planes are identical. Their constant speed (c) is 100 mph. The wind
is blowing at 50 mph. According to Lorentz, the beta </font><font face="Symbol" size="4">b</font><font face="Times New Roman" size="4">
value (v / c) is then worth 0,5, </p>
<P align=left><b>Let's make it simple.</b>
</P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
relative speed of the planes may be found according to the Lorentz g value :</span></p>
</font>
<p align="center"><font face="Times New Roman" size="4"><font face="Times New Roman">g = (1 </font><span lang="FR-CA" style="font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">–</span><font face="Times New Roman"> </font></font><font face="Symbol" size="4">b</font><font face="Times New Roman"><sup>
2</sup> )<sup> (1 / 2)</sup></font></p>
<p align="center"><font face="Times New Roman" size="4">g =
.866
</font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">Then
the planes <b><i>round trip</i></b> relative speed will be : </font></p>
<font face="Times New Roman" size="4">
<P align=center>Along the wind : g<span lang="FR-CA"><sup>
2</sup></span> c g<span lang="FR-CA"><sup>
2</sup></span> = .75 c
75 mph
</P>
<P align=center>Across the wind : g
c g = .866 c
86.6 mph
</P>
</font>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify"><font size="4" face="Times New Roman"> </font></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify"><font face="Times New Roman" size="4">Across
the wind, the planes (or the waves) will be tilted to 30° according to
a theta </font><font face="Symbol" size="4">q</font><font face="Times New Roman" size="4">
angle:</font></p>
<P align=center><font face="Symbol" size="4">q</font><font face="Times New Roman" size="4">
= arc sin </font><font face="Symbol" size="4">b
q</font><font face="Times New Roman" size="4"> = 30°</font>
</P>
<center>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font size="4" face="Times New Roman">In
the absence of wind, the round-trip would last 2 hours.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font size="4" face="Times New Roman">1
- The
round-trip time along the wind: 2 hours / g<sup> 2</sup> = 2.6667
hours.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font size="4" face="Times New Roman">2
- The
round-trip time across the wind
: 2 hours / g = 2.3094 hours.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font size="4" face="Times New Roman">So
the plane flying across the wind will be: .357 hour = 21 minutes faster and the plane
flying along the wind will be defeated.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font size="4" face="Times New Roman">However
George F. FitzGerald and Hendrick Lorentz noted after Michelson's experiment that a
shorter circuit on the displacement axis would cancel the difference.
The interferometer would be contracted in accordance with
Lorentz's g value. This is the Lorentz transformation:</font></p>
<font size="4" face="Times New Roman">
<p align="center">x ' = (x <font size="4"><span style="letter-spacing: 0"><font face="Times New Roman"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
</font></span></font> v t) / g</p>
<p align="center">y ' = y z ' = z</p>
<p align="center">t ' = (t
<span style="letter-spacing: 0"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">–</span>
</span> v x / c<sup> 2 </sup>) / g</p>
</font><font size="4" face="Times New Roman">
<p align="left"><b>A race between two waves.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Michelson
discovered that the relative speed of light is slower in the direction
of motion. He deduced from this that an interferometer could detect the
speed of aether wind. He understood that two orthogonal light beams
would not produce the same interference fringes after a 90° rotation.
Here is a diagram showing Michelson's apparatus:</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> </font></p>
</center>
</td>
</tr>
</table>
</div>
<P align=center><img border="0" src="images/michelson04a_a.gif" width="584" height="374"></P>
<P align=center><font face="Times New Roman" size="4">The Michelson
interferometer.</font></P>
<P align=center><font size="4" face="Times New Roman"> </font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
light beam emitted by the source is separated into two halves by means
of a beam splitter containing a 45° partially reflecting mirror. Then
the beams are reflected on a flat mirror back to the beam splitter,
which now performs their reunification. </span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Finally
both beams could be compared inside a special scope. Michelson was
expecting a phase shift. Waves would add themselves constructively or
destructively, showing a characteristic interference pattern. <span lang="FR-CA">The
goal was to measure the fringes displacement after a 90° rotation. Such
a rotation could be performed easily because the instrument was mounted
on a large stone floating on a mercury pond.</span></p>
<p align="left"><b>The Michelson interferometer animated diagrams.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
animations below shows what is going on inside the interferometer
branches. In order to obtain a phase shift which is clearly visible, one
must use a very high speed. Here, the interferometer speed is worth one
third of the speed of light. Then </span> <font size="4" face="Symbol">b</font>
= .3333 and : g = .9428. <span lang="FR-CA">Such a speed
produces a 2 : 1 wavelength ratio R in the direction of motion,
according to: </span><p align="center">R
= (1 + <font face="Symbol" size="4">b</font>)
/ (1 <span lang="FR-CA" style="font-size:12.0pt;font-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-ansi-language:
FR-CA;mso-fareast-language:FR;mso-bidi-language:AR-SA">–</span> <font face="Symbol" size="4">b</font>)</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
ratio indicates that along the wind, planes crossing the start
point each minute and one at a time would not maintain the same distance
between them while returning. They would be two times nearer. </span><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">So
one can imagine that each small red or green line showed below
represents a plane. The wind is blowing from the right. Moreover, on the
transverse y axis, waves (or planes) are compressed
according to the Lorentz contraction g value, which is worth
.9428 here:</span><p align="center">
<font face="Symbol" size="4">
l</font>
' = g
<font face="Symbol" size="4">
l</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
diagram on the left indicates exactly the same length for both branches.
This distance has been calculated in order to obtain a full lambda / 2
phase shift. The wave fronts (or planes) along the motion axis are
pictured in red. They are green crosswise.</span>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Michelson
was expecting the phase shift shown on the left:</span>
</font></center>
</td>
</tr>
</table>
</div>
<P align=center><font size="4" face="Times New Roman"> </font></P>
<p align="center"><img border="0" src="images/michelson02.gif" width="334" height="334"><font size="4" face="Times New Roman"> </font><font size="4" face="Times New Roman">
</font><img border="0" src="images/michelson03.gif" width="321" height="334"></p>
<p align="center"> </p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
diagram on the right shows what really occurred. This was against
Michelson's expectations. One of the branches (the horizontal one here)
underwent a contraction according to Lorentz's g value,
which is worth .9428. It was reduced to 94,28 % of its original
length.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
waves speed difference was cancelled and the wave fronts were still
perfectly in phase after a 90° rotation.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This
explains why the Michelson interferometer cannot reveal the aether wind.</p>
<p align="center"> </p>
<p align="center"><img border="0" src="images/ligne02.gif" width="559" height="10"></p>
<p align="center"><b> </b></p>
<p align="center"><img border="0" src="images/exclam.gif" width="97" height="95"></p>
<p align="center"><b>Warning</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This
web site shows that aether exists and that matter is purely made out of
standing waves. Such waves undergo a contraction while they are moving,
and so matter should also undergo a contraction. This is <b><i>a new
fact</i></b>: now we know the cause.
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Michelson
strongly believed that aether should exist. This page on his
interferometer certainly match his thoughts.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">However
this is not what scientists believe today, because they have wrongly ruled out aether.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">So
this page does not submit to standard opinion. However the science world
is rapidly evolving today because of the Internet. Most people who are
familiar with Lorentz's researches generally think that a privileged
frame of reference should exist, and this strongly supposes that aether
should also exist.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Such
people can speak about Relativity. Others who did not study Lorentz
should be more careful because they do not know what they are talking
about.
<p align="left"><b> Lorentz's explanation was the right one.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Most
web pages on the Michelson interferometer will explain that the null
result showed that aether does not exist. This is totally false.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Lorentz
explained that the interferometer would undergo a contraction in the
direction of motion. The Lorentz transformation is, firstly, a length
contraction, which occurs only in the direction of motion. For example,
let's suppose a very high speed: .866 c or 86.6% of the speed of
light. Then <font face="Symbol" size="4">b
</font>
= .866 and Lorentz's contraction g value is worth .5. The gamma
factor <font face="Symbol" size="4">g</font> is worth the
reciprocal: 1 / g = 2.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> The following animated diagram shows that the
round-trip time along any of the 4 possible directions inside the
interferometer's arms would be the same. This device can be seen as a <b><i>4
branches interferometer</i></b>. The very high speed involves a severe
contraction to half of the original length, and the waves speed
difference is then clearly visible:</font></center>
</td>
</tr>
</table>
</div>
<P align=center><font size="4" face="Times New Roman"> </font></P>
<font face="Times New Roman" size="4">
<div align="center">
<center>
<table border="4" cellspacing="6" width="137" height="257" cellpadding="4">
<tr>
<td width="100%">
<p align="center"><img border="0" src="images/relativite06.gif" width="135" height="255" align="center"></td>
</tr>
</table>
</center>
</div>
</font>
<P align=center>
<font face="Times New Roman" size="4">
The contraction cancels the relative speed difference.</font>
</P>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><img border="0" src="images/doppler00.gif" width="361" height="361"></p>
<p align="center"><font size="4" face="Times New Roman">Compare with the Doppler
effect.</font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">For
the same reason, any observer placed in the system's centre O, and using
a radar signal, would find that all A, B, C and D distance is the same.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">However
he would not notice that the signal round trip time is two times longer
because his clocks also run two times slower, according to the gamma
factor.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Because
matter is made of waves, all its mechanisms are also slowed down. It is
evolving slower. Most often, one speaks about <b><i>time dilation</i></b>.
This is a huge mistake. The time is a concept, an idea. It does not
really exist. A clock does, and it can tick two times slower. This does
not mean that the time runs slower. </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Secondly,
planes or waves would reach the A point on the rear much more rapidly.
Because of the Doppler effect, the B point will be attained later. Henri
Poincare showed that inside such a system, the central O observer must
use light or radio signals in order to synchronize A and B clocks.
Because the signal speed is much faster backward, the A clock will be in
advance and B clock will be late. However nobody would be able to notice
the resulting time shift. Inside such a moving frame of reference,
Poincaré showed that <b><i>local hours</i></b> lead to a sort of
virtual simultaneity. Nobody can measure the frame's actual speed. It
all happens as if the system was perfectly at rest inside aether.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Finally,
waves moving frontward are contracted according to 1 <span lang="FR-CA" style="font-size:12.0pt;font-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-ansi-language:
FR-CA;mso-fareast-language:FR;mso-bidi-language:AR-SA">–</span>
</font>
<font face="Symbol" size="4">
b
</font>
<font face="Times New Roman" size="4">
while those moving backward are dilated according to 1 +
</font><font face="Symbol" size="4">b</font><font face="Times New Roman" size="4">.
The wavelength ranges from 1 to 2 backward while it can be infinitely
compressed frontward. The waves compression is much more severe. On the
other hand energy is proportional to frequency. Because waves contain
energy, and because matter as waves also contains energy as mass, moving
matter must increase its energy according to the gamma factor. So
matter's mass is doubled for .866 c.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">So
this was the Lorentz transformation secret: matter is made of waves. 100
years were needed in order to solve this mystery. This was obvious,
though, because Lorentz established his equations while working on
Maxwell's equations. The Lorentz transformation is linked to the Doppler
effect.</p>
<p align="left"><b>The standing waves contraction.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Very
few people noticed that because the light waves are reflected back on
flat mirrors, this produces standing waves inside both branches.
Moreover standing waves compression is not a well known phenomenon. As
far as I know it seems to have been discovered by <a href="http://www.keelynet.com/spider/b-104e.htm">Mr.
Yuri Ivanov</a> in 1990, and nobody else (except for me and <a href="http://members.aol.com/scabala25/index.htm">Mr.
Serge Cabala</a>) seems to have studied it in an acceptable manner. For
more details about pseudo-standing waves or "lively standing
waves" see the page on <a href="sa_plane.htm">standing waves</a>.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> <span lang="FR-CA">So
I managed to add some reference marks along both branches in order to
locate the nodes position. It should be pointed out that such nodes are
still present in the direction of motion, notwithstanding the fact that
the wavelength is two times longer while the waves are traveling
backward. This is possible because those waves also seem to travel two
times faster. One needs a little concentration to observe this, but it
finally becomes obvious.</span><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> <span lang="FR-CA">On
the other hand the mean relative velocity of light in order to perform a
complete round-trip can be calculated as shown above. The waves behave
exactly in the same manner as planes while the wind is blowing. So the
calculus is very simple:</span><p align="center">Mean velocity along the
motion x axis: v = c
g<sup> 2</sup>
Transverse velocity: v = c g</p>
<p align="center">Waves compression along the x axis: <font face="Symbol" size="4">l</font>'
= </font><font face="Symbol" size="4">l
</font><font face="Times New Roman" size="4"> g<sup> 2</sup>
Transverse compression: <font face="Symbol" size="4">l</font>' = </font><font face="Symbol" size="4">l
</font><font face="Times New Roman" size="4"> g</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Finally,
the standing waves compression is worth the relative velocity or light.
Both calculus yield the same results. Michelson did not use this method,
but it is indeed a much preferable one. </span>
</font></center>
</td>
</tr>
</table>
</div>
<p align="center"><font size="4" face="Times New Roman"><b><center> </center></b></font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><font size="4" face="Times New Roman"><b>THE
STANDING WAVES CONTRACTION</b></font></p>
<p align="center"><font size="4" face="Times New Roman"><b> </b></font></p>
<p align="center"><img border="0" src="images/stat.0.gif" width="640" height="101"></p>
<p align="center"><font size="4" face="Times New Roman">Standard standing
waves. </font><font size="4" face="Symbol">b</font><font size="4" face="Times New Roman">
= 0</font></p>
<p align="center"><center><font face="Times New Roman" size="4"> </font></center></p>
<p align="center"><img border="0" src="images/stat.5.gif" width="481" height="101"></p>
<p align="center"><font face="Times New Roman" size="4">"Lively standing
waves".</font></p>
<p align="center"><font size="4" face="Symbol">b</font><font face="Times New Roman" size="4">
= 0,5 g =
0,866 Contraction to 75% according to g<sup> 2</sup>.</font></p>
<p align="center"><center><font face="Times New Roman" size="4"> </font></center></p>
<p align="center"><img border="0" src="images/stat.7.gif" width="321" height="101"></p>
<p align="center"><font size="4" face="Symbol">b</font><font face="Times New Roman" size="4">
= 0,707 g =
0,707 Contraction to 50% according to g<sup> 2</sup>.</font></p>
<p align="center"><center><font face="Times New Roman" size="4"> </center></font></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p align="left"><b>At last, a plausible explanation.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">In
1892, </span> George F. FitzGerald postulated that Michelson's
interferometer should contract in order to cancel the phase shift. He
also tried to explain this phenomenon by aether's pressure. His
discovery was never published (FitzGerald was not sure) and Hendrik A. Lorentz
also independently discovered that matter should contract. He also
discovered a time effect.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">FitzGerald
and Lorentz were unaware of matter's wave properties, but it is a well
known fact since de Broglie's discovery. From this very moment
scientists could establish the relationship with standing waves
contraction.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Today
one can postulate that matter is purely made out of standing waves. Then
Michelson's interferometer should indeed contract and cancel the phase
shift because the light waves behave exactly the same way as matter
waves do.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">In
1904, Lorentz et Henri Poincaré finally found the correct g
contraction value. There is no transverse contraction. They also showed
that a time shift should occur, and that moving clocks should slow down.
This is the Lorentz transformation. Lorentz's equations are famous today
because they led to Relativity.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Matter
is made of standing waves. Without any frequency change, it should
contract according to Michelson's calculations:<p align="center">Standing
waves contraction in the direction of motion: according to g<sup> 2</sup>.</p>
<p align="center">Standing waves contraction in transverse directions:
according to g.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">However,
because matter waves frequency should slow down according to g,
the wavelength is increased according to 1 / g. One obtains: g / g = 1
and finally there is no transverse contraction any more. In the
direction of motion, the g<sup> 2</sup> contraction is reduced
according to: g<sup> 2</sup> / g = g:<p align="center">Matter contraction
in the direction of motion: according to g.</p>
<p align="center">Matter contraction in transverse directions: none.</p>
</font></center>
</td>
</tr>
</table>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<center>
<table border="4" width="60%" cellpadding="20" cellspacing="6">
<tr>
<td width="100%"><font face="Times New Roman" size="4">This explains why a
length contraction according to g occurred in Michelson's
interferometer, and only in the direction of motion.</font></td>
</tr>
</table>
</center>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<P align=center><font face="Times New Roman" size="4"><b>THE ARMS
LENGTH CALCULUS</b></font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
interferometer diagrams shown above indicate that for one third of the
speed of light, the arms length must be worth about 4 wavelengths in
order to obtain the phase opposition. This length must be greater for
smaller speeds. So Michelson had to build a very large interferometer.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Michelson's
calculus was rather complex because he considered the relative speed of
light. One can more easily obtain the same arms length using the
standing waves compression method. Then the correct formulas for
obtaining two beams in phase opposition are:</span></p>
<p align="center"><span style="letter-spacing: 0">According to absolute
wavelength: </span><span lang="FR-CA">L
= g <font size="4" face="Symbol"> l</font> /<span style="letter-spacing: 0">
4 ( 1 <span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
g )</span></span></p>
<p align="center"><font size="4"><font face="Times New Roman"><span style="letter-spacing: 0">According
to actual wavelength measurements: L = </span></font><font face="Times New Roman" size="4"><span style="letter-spacing: 0">
</span></font><span lang="FR-CA"><font face="Symbol">l</font></span><font face="Times New Roman" size="4"><span lang="FR-CA">
/</span></font><span style="letter-spacing: 0"><font face="Times New Roman">
4 ( 1 <span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
g )</font></span></font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
first formula is the right one for the computer. The Doppler effect
formulas need absolute values. However Michelson did not know his
absolute speed through aether. He had to measure the wavelength from his
own point of view.</span>
<p align="left"><b>One must use transformed values.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman"><span lang="FR-CA"><font size="4">On
the one hand standing waves are compressed according to Lorentz's
g value along a transverse axis. On the other hand the wave
frequency is slowed down according to the same g value. This
means that the wavelength is increased according to the reciprocal,
which is worth: 1 / g. Finally the wavelength <b><i>never</i></b>
changes along the y transverse axis. Moreover Lorentz showed
that there is no length contraction along this axis, and so transverse
wavelength measurements never change. They are constant and
absolute. </font></span></font><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Secondly,
the wavelength is compressed according to <span lang="FR-CA">g<sup> 2</sup></span>
along the displacement x axis. However, as shown above, the
frequency is slowed down. Then the wavelength is increased according to
1 / g. Finally the standing waves nodes and antinodes are compressed
according to Lorentz's g value along the displacement axis.
Exactly the way matter is. <p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman"><span lang="FR-CA"><font size="4">This
indicates that the calculus goes like this: just compare the constant
transverse wavelength with the g-contracted wavelength along the
displacement axis.</font></span></font><p align="left"><b>Example.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Let's
suppose a 10% contraction. Then 1 </span><font size="4"><span style="letter-spacing: 0"><font face="Times New Roman"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
</font></span></font><span lang="FR-CA"> g = .1, g = .9 and <font face="Symbol" size="4">b
</font>
= .4359. The second formula:</span><span lang="FR-CA"> 1 </span><font size="4"><font face="Times New Roman" size="4"><span lang="FR-CA">/</span></font><span style="letter-spacing: 0"><font face="Times New Roman">
4 (1 <span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
0,9) </font></span></font><span style="letter-spacing: 0">yields </span><span lang="FR-CA">2,5
wavelengths, or 5 half-wavelengths. Because the distance between two
nodes is worth a half-wavelength, only a quarter-wavelength shift is
needed in order to obtain the full phase opposition:</span><p align="center"><img border="0" src="images/michelson08.gif" width="390" height="148"></p>
<p align="center">Phase opposition is attained for 5 half-wavelengths
and 10% contraction.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">
<p align="left"><b>The worst of scenarios.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
speed of Sun through galaxies all around us has been estimated to be
about 300 km/sec. It could be its absolute speed through aether. It
could even be much faster. While the beta value is worth .001 (300 / 300
000) the Lorentz g value is worth .9999995 and the formula
yields 500,000 wavelengths. So 500,000 times .0006 are 300 mm or 30 cm
(one foot). This suggests that a one foot tall interferometer should be
enough.</span><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">However
Michelson preferred to play safe. The Sun being perfectly at rest, which
is highly improbable, the speed of Earth would still be worth 29 km/sec.
So he managed to build a rather large apparatus, according to the
following values:</span></p>
<ul>
<li>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">
<font face="Symbol" size="4">
b
</font>
= .0000966667
</span></li>
<li>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">
<span lang="FR-CA">g
= .9999999953</span>
</li>
<li>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Symbol" size="4">
l</font>
= .0006 mm yellow light.
</li>
</ul>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA"><font size="4"><font face="Times New Roman">According
to: 1 / 4 (1 <span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> – </span>
g), 53,419,000 times the wavelength </font><font face="Symbol" size="4">l</font><font face="Times New Roman" size="4">,
the arms length should be worth 32,000 mm or 32 meters. The
interferometer arms must be about 100 feet long in order to detect the
minimum 29 km/s speed through aether. So Michelson added many mirrors in
order to elongate the total light trip. </font></font></span>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
1887 Michelson-Morley experiment arms length was 11 meters (about 35
feet). This should have been enough because one does not really need a
full half-wavelength phase shift. Edward W. Morley tried again in 1902
with a longer 32 meters/100 feet apparatus. The null result was
confirmed.</span>
</p>
</font></center>
</td>
</tr>
</table>
</div>
<p align="center"> </p>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA"><b>THE
KENNEDY-THORNDYKE EXPERIMENT WAS A MESS</b></span></font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Believe
it or not, one
arm of the interferometer is useless.</span>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">It
can be omitted like this:</span>
</font>
</center>
</td>
</tr>
</table>
</div>
<p align="center"><img border="0" src="images/michelson04b_a.gif" width="608" height="150"></p>
<p align="center"><font face="Times New Roman" size="4">A more simple
interferometer.</font></p>
<p align="center"><font face="Times New Roman" size="4"> </font></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="80%">
<tr>
<td width="100%">
<center>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
model seems to be totally unknown. It would be quite useless to build it
because we already know that the Michelson interferometer cannot reveal
the aether wind. However it shows that the shorter arm length is
optional, because this arm can only be used as a reference. This is
possible because Michelson had to rotate his apparatus (its main stone
was floating on a mercury pond) in order to observe the difference in
the interference fringes.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Surprisingly,
the formula which yields the correct length for the lambda / 2 phase
shift remains the same for any shorter arm length, assuming that the
lambda distance is measured inside a frame of reference <b><i>at rest</i></b>:</p>
<p align="center"><span lang="FR-CA">L</span><font size="4"><span lang="FR-CA"><font face="Times New Roman">
= </font><font face="Symbol">l</font><font face="Times New Roman" size="4"> g /</font><span style="letter-spacing: 0"><font face="Times New Roman">
4 ( 1 <span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
g )</font></span></span></font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
<b>IS NOT</b> what Kennedy and Thorndyke said. They claimed that
different lengths would reveal the aether wind in spite of the contraction.
So, because the Kennedy-Thorndyke experiment
gave a null result too, scientists deduced from it that aether does not
exist. This means that nobody could correctly calculate the arms lengths,
or waves relative speed and compression. All scientists were deceivingly mislead by Kennedy
and Thorndyke.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Moreover,
because they did not know their true speed through aether, they had to manage
with their distorted view of the wavelength. It should be pointed out that
the Lorentz transformation <b><i>does not solely involve a contraction.</i></b>
It also predicts that any periodic phenomenon should be slowed down in
accordance with the Lorentz g value. This means that <b><i> the
wavelength will be increased</i></b>. Then, and whatever the
shorter arm's length is, the correct length formula for the longer arm
remains:</span></p>
<p align="center"><span lang="FR-CA">L </span><font size="4"><span lang="FR-CA"><font face="Times New Roman">
= </font><font face="Symbol">l</font><font face="Times New Roman" size="4"> /</font><span style="letter-spacing: 0"><font face="Times New Roman">
4 ( 1 </font></span></span></font><font size="4"><span style="letter-spacing: 0"><font face="Times New Roman">
<span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA"> –</span>
</font></span></font><font size="4"><span style="letter-spacing: 0"><font face="Times New Roman">
g )</font></span></font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Quite
simply, because it is made of standing waves, matter must contract exactly the
way all standing waves do. The inevitable consequence of this is that <b><i>any
length</i></b> for both interferometer's arms will <b><i>always</i></b>
yield a null result. Today,
scientists still think that the Kennedy-Thorndyke experiment ruled out
matter contraction.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Once
again, this
is totally false.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Clearly,
Kennedy and Thorndyke were wrong.</span></p>
</font></center>
</td>
</tr>
</table>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><font size="4" face="Times New Roman"><a href="matter.htm"><img border="0" src="images/fleche_agg.gif" width="159" height="31"></a><a href="sa_aether.htm"><img border="0" src="images/fleche_ag.gif" width="162" height="31"></a><a href="sa_Lorentz.htm"><img border="0" src="images/fleche_ad.gif" width="133" height="31"></a><a href="sa_conclusion.htm"><img border="0" src="images/fleche_add.gif" width="146" height="31"></a></font></p>
<p align="center"> </p>
<p align="center"><font face="Times New Roman" size="4"><a href="./matter.htm">01</a><span class="white">
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| </span><a href="./sa_plane.htm">03</a><span class="white">
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| </span><a href="./sa_relativity.htm">10</a><span class="white">
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| </span><a href="./sa_quarks.htm">17</a><span class="white">
| </span><a href="./sa_wavetheory.htm">18</a><span class="white">
| </span><a href="./sa_postulates.htm">19</a><span class="white">
| </span><a href="./sa_Genesis.htm">20</a><span class="white">
| </span><a href="./sa_conclusion.htm">21</a></font></p>
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Gabriel LaFreniere,</font>
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Bois-des-Filion in Québec. <a href="mailto:absolu2000@hotmail.com">absolu2000@hotmail.com</a></font>
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<p style="text-indent: 35.4pt" align="left"><font face="Times New Roman" size="4"> On the Internet since September
2002.
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<font face="Times New Roman" size="4">Last
update May 13, 2004.
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