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sa_electron.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 Electron</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"><img border="0" src="images/fleche_ag.gif" width="162" height="31"></a><a href="sa_plane.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 ELECTRON</font></p>
<P align=center><img border="0" src="images/electron.707.gif" width="480" height="400"></P>
<p align="center"><font face="Times New Roman" size="4">This wave is an
electron.</font></p>
<p align="center"><font face="Times New Roman" size="4">Mr. Jocelyn Marcotte's
equations below are fundamental.</font></p>
<p align="center"><font face="Times New Roman" size="4"><b> </b></font></p>
<p align="center"><font face="Times New Roman" size="4"> </font><img border="0" src="images/equations_Marcotte.jpg" width="795" height="223"></p>
<font face="Times New Roman" size="4">
<p align="center">x = 2 * pi * distance /
lambda</p>
<p align="center">y stands for amplitude.</p>
<p align="center">Please note that
amplitude is normalized to y = 1 at the center for phase and to y = 0 for
quadrature.</p>
<p align="center">Of course, those equations are well
known in the math literature.</p>
<p align="center">However, they had never been related to the electron.</p>
<p align="center"><b> </b></p>
</font>
<p align="center"><font size="4" face="Times New Roman"><b>ELECTRONS ARE WAVES</b></font></p>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>The Huygens Principle. </b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">I
have been fascinated by optics and wave phenomena since my early age. So I
know well that the Huygens Principle is always highly reliable.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Around
1995, personal computers finally became accessible, fast and practical. I
then elaborated
a new algorithm whose goal was to perform the summation of Huygens'
well known wavelets inside a 3-D space. I was working on the Airy
disk, which is the amazing interference pattern which is present at the
focal plane of any convergent lens or telescope mirror.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
program was a hit. The results below represent a very seldom shown
Airy disk. It should behave like this only for a very wide 180° aperture
angle. This means that instead of the usual narrow light
cone, the source is a full hemisphere. Look at this!</p>
</font> </td>
</tr>
</tbody>
</table>
</div>
<p align="center"><font face="Times New Roman" size="4"> </font></p>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6">
<tr>
<td>
<p align="center"><img border="0" src="images/airy180.gif" width="640" height="321"></td>
</tr>
</table>
</center>
</div>
<p align="center"><font face="Times New Roman" size="4">The Airy disk for a
180° aperture angle.</font></p>
<p align="center"><font face="Times New Roman" size="4">It can also be
considered as one half of an electron. Rightward waves only are present.</font></p>
<p align="center"><font face="Times New Roman" size="4">Mr. Marcotte's equations
above predict exactly the graphics shown in the lower right corner.</font></p>
<p align="center"><font face="Times New Roman" size="4"><b> </b></font></p>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>Discovering the electron.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">While
working on this, I already knew that matter and especially
electrons should be made of spherical standing waves. I was also aware
that such waves should undergo the Doppler effect, allowing them to
move freely at variable speeds. However, I did not reveal this major
discovery because I feared (I was wrong!) that a better knowledge of
matter, considering the amazing forces involved, would lead us to a
devastating Apocalypse. It is a well known fact that most discoveries such as
radioactivity were always followed by more and more powerful weapons.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">I
could never find any indication that this could be true for the wave
nature of matter, though. So, in 2002, I wrote a book which was exempt
of any mystery: Matter is made of Waves. It was not the case for
another book written in 2000: The Theory of Absolute. I had to make it
very evanescent about the wave nature of matter (it is not my
discovery, but I was the first and I am still the only person who can
explain all about it: electrons, matter, forces, mechanics). My goal
was simply to restore Lorentz's Relativity, whose concept is <b><i>absolute.</i></b>
Although this point of view leads to the same predictions as Einstein's,
it should be emphasized that his Relativity, while it proves to be true,
is nevertheless the result of our errors while recording phenomena.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">I
discovered Mr. Milo Wolff's site in July 2003. Many observations
appear to be correct, but I must strongly disapprove many of his ideas
here, and especially the WSM (wave structure of matter) ideology using
philosophy in order to make scientific discoveries. This is weird. But
Milo was right at least in one point: his
concentric spherical standing wave showed a full
wavelength core. Both static and Doppler models, which I presented in 2002, showed
only a
half-wavelength core. This may seem strange, but exploring a new world
is not obvious. I simply had not yet realized the similitude between
the electron and the Airy disk.
</font> <font face="Times New Roman" size="4">So I immediately returned to my Airy disk
program and I found that Mr. Wolff was right. I obtained this:</p>
</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><img border="0" src="images/huygens00.gif" width="547" height="281"></p>
<p align="center"><font face="Times New Roman" size="4">Two opposite 180° Airy
disks adding themselves produce a spherical standing wave system.</font></p>
<p align="center"><font face="Times New Roman" size="4">The full lambda core
indicates that a pi phase shift (actually a wave acceleration) must occur
inside.</font></p>
<p align="center"><font face="Times New Roman" size="4">In order to achieve this, waves traveling through the core must behave in a very unusual way.</font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><img border="0" src="images/electron_statique.gif" width="340" height="256"></p>
<p align="center"><font face="Times New Roman" size="4">Mr. Milo Wolff's static
electron and its full lambda core, according to the Huygens Principle.</font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>LaFreniere's wave.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This Doppler moving electron is my
discovery. It was shown in my book and I called it LaFreniere's Wave when I uploaded my first
Internet web pages in September 2002. </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
electron can move at any speed from 0 to nearly the speed of light
through the aether because it undergoes the Doppler effect (or the
Lorentz transformations, which is the same). In spite of my desperate
attempts to make him recognize that, M.
Wolff never did. </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">I
also showed before anyone else the correct diagrams for it.
Unfortunately, Mr. Marcotte's formulas were missing, but I succeeded
anyway. As a matter of
fact, the Huygens Principle is far more important and relevant as a
tool. The results are a convincing proof that the system
should behave this way.</p>
<p align="left"><b>This wave shows all of the electron properties.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
electron's properties are well known. The list is astounding. It is so
small that it has no apparent dimension. Its electrostatic charge is
negative. There is
also a positive antiparticle, the positron, which exhibits exactly the
same properties except for the opposite charge. Its wave properties are now a well admitted fact. It can
accelerate, slow down and change its direction. It can act and react
as a result of an apparent contact, but also at a distance. It
contains intrinsic energy according to mc^2, and additional kinetic energy
according to m(gamma <font face="Times New Roman"><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>
1)c^2 while moving
as a result of Lorentz's mass increase. Except for the spin, which is
either <font face="Times New Roman"><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>1/2 or +1/2, all electrons are rigorously identical.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">In
addition, the electron is the main player for a lot of phenomena such
as magnetic and electric fields, light and radio waves emission, and
chemical reactions. It can stabilize itself around the nucleus to form
an atom, and it can bind molecules together. Finally, it is a well
known fact that electron and
positron collisions produce quarks and gluonic fields. This indicates that in
this case electrons and positrons
involved do
not really annihilate. They should most likely be hidden but still present inside
quarks and have their standing waves joined together as gluonic
fields. This
strongly suggests that matter (or any other particle) is solely made of electrons.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This
is a huge responsibility for so small a particle, but the electron
magnificently takes up the challenge. This web site explains how it is
possible.</p>
<P align=left><B>The moving spherical standing waves calculus.</B></P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">So
the electron appears to be the equivalent of a very
special Airy disk whose aperture angle is 360°. As seen above, just one hemisphere
becomes the source of traveling
waves, but adding the opposite one rather produces standing waves.
This is Milo Wolff's unmoving electron. Now let's see how the Doppler effect
should transform it.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Using
the Huygens Principle, I submitted all
of Huygens' wavelets to a
Doppler effect. The algorithm then becomes a bit more complicated
because the wavelength must shorten regularly from 1<font face="Times New Roman"><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>beta
forward to 1+beta backward (beta = v/c). The
computer produced the following result, which is
correct only along the displacement axis:</p>
</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><img border="0" src="images/huygens01.gif" width="629" height="257"></p>
<p align="center"><font face="Times New Roman" size="4">The moving electron's axial waves, using
the Huygens Principle.</font></p>
<p align="center"><font face="Times New Roman" size="4">This was confirmed in
July 2006 by Mr. Jocelyn Marcotte thanks to his 3-D optimized wave algorithm.</font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>Marcotte's equations.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Mr.
Jocelyn Marcotte informed me in January 2006 that he had found a new
simpler algorithm for the aether. It is different from Mr. Philippe Delmotte's,
the first inventor, because square or sawtooth waves are propagating
normally, while Delmotte's produces some sort of heat, a local
vibration of the "aether granules". This does not mean that
it is better. It is simply different, but this suggests that many options
are possible for an ideal aether. However, in both cases, sine
waves behave normally, much like the sound propagates inside a solid
and homogeneous substance such as quartz. </p>
</font> <p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">Mr.
Marcotte graduated in 1989 as an electric engineer from É<span style="mso-fareast-font-family: Times New Roman; mso-ansi-language: FR; mso-fareast-language: FR; mso-bidi-language: AR-SA">cole Polytechnique,
Université de Montréal, Québec, Canada.</span> He is obviously a champion in
computer programming, because he firstly had to handle the new <a href="http://fbide.sourceforge.net/category/freebasic/">FreeBASIC</a>
programming language. He then immediately succeeded in testing my
moving electron inside his own 3-D Virtual Aether. Among
others, he also tested the evolution of a standard Gaussian impulse,
and he seemed to be the only person on Earth who understood my Airy
disk algorithm (up to now, just three people did).
By March 2006, he informed me that Milo Wolff's static electron could
be represented using the equation below where x stands for phase, distance
or delay in radians: x = 2 * pi * distance / lambda. Then
amplitude is given by:</font></p>
<p align="center"><font face="Times New Roman" size="4">y = sin(x) / x</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">This
is a well known equation in the math literature. It is also known as
the sinc(x) function, which is short for sinus cardinalis. But it had never been
related to the electron, albeit it is a solution of Bessel's spherical function. The
singularity for x = 0, y = 1 is also well established. I
was using the equivalent since the beginning: y = sin(2 * pi * distance / lambda) / distance. The distance
(x is more exactly the phase as a result of the delay) not being in radians, the wave shape for the electron
core was wrong, though.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">On
July 27, 2006, Mr. Marcotte finally found that the two wave sets
traveling in opposite directions and producing the electron could be
calculated according to the formula below, for quadrature (pi / 2
phase):</font></p>
<p align="center"><font face="Times New Roman" size="4">y = (1 <font face="Times New Roman"><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>
cos(x) ) / x</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">This
formula is also well known in the math literature. As far as I
know both equations were mainly used in order to find the
precalculus limits before performing trigonometric differential calculus.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">Those
formulas are awesome:</font></p>
</td>
</tr>
</tbody>
</table>
</div>
<p align="center"><img border="0" src="images/equations_Marcotte.jpg" width="795" height="223"></p>
<p align="center"><font face="Times New Roman" size="4"> Jocelyn Marcotte's
equations and the resulting graphics.</font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">It
should be pointed out that the cosine indicates quadrature (pi / 2
phase), which is normally the highest amplitude point. However,
the electron central antinode is an exception because it is a full
wavelength wide. A <a href="sa_phaseshift.htm">pi / 2 phase shift</a>
occurs in the center, and so the maximum amplitude there is indicated
by the sine function while the cosine indicates the zero level.
Anywhere else the normal amplitude level according to the distance
remains the rule, though.</p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">If
all happens like I presume, in the future, those equations will be recognized as the
first equations of all. They are fundamental.</p>
<p align="left"><b>Rotation.</b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">Mr.
Marcotte soon found that these equations could show the wave rotation
step by step from 0 to 2*pi. He had to introduce a t time
(also in radians, from 0
pi to 2 * pi), and join them together like this:</p>
<p align="center"><span lang="FR-CA" style="COLOR: black; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">y
= (cos(t) * sin(x) </span><font face="Times New Roman"><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><span lang="FR-CA" style="COLOR: black; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">
sin(t) * (1 </span><font face="Times New Roman"><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><span lang="FR-CA" style="COLOR: black; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">
cos(x) ) ) / x</span></p>
<p align="center"><span lang="FR-CA" style="COLOR: black; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">y
= (cos(t) * sin(x) + sin(t) * (1 </span><font face="Times New Roman"><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><span lang="FR-CA" style="COLOR: black; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">
cos(x) ) ) / x (opposite direction)</span></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">Mr.
Philippe Delmotte found this simplification in September
2006 : </p>
<p align="center">
<span style="mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA" lang="FR-CA">y =
(sin(t + x) </span>
<font face="Times New Roman"><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><span lang="FR-CA" style="COLOR: black; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">
</span>
<span style="mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA" lang="FR-CA">sin(t)) / x</span>
</p>
<p align="center"><b> </b></p>
</font>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">I
made two programs showing all this:
<p align="center"><font face="Times New Roman" size="4"> <a href="programs/Aether06_Marcotte.exe">Aether06_Marcotte.exe</a>
Source code : <a href="programs/Aether06_Marcotte.bas">Aether06_Marcotte.bas</a></font></p>
<p align="center"><a href="programs/Aether06_Marcotte_Doppler.exe">Aether06_Marcotte_Doppler.exe</a>
Source Code: <a href="programs/Aether06_Marcotte_Doppler.bas">Aether06_Marcotte_Doppler.bas</a></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify"> You may freely copy, distribute and even modify
them. Please remember that the new 2008 <a href="http://www.freebasic.net/index.php/download">Compiler
for FreeBASIC</a> (<span lang="FR" style="mso-fareast-font-family: MS Mincho; color: black; mso-ansi-language: FR; mso-fareast-language: FR; mso-bidi-language: AR-SA">version
0.20.0b</span>) was released with some new requirements. Gosub keyword
is not allowed any more and variables including integer must be
declared. However, all previous programs will still work properly on
condition that they are edited as follows:
<p class="MsoNormal" align="center"><span lang="FR" style="color:black;mso-ansi-language:FR">#lang
"fblite"<o:p>
</o:p>
</span></p>
<p class="MsoNormal" align="center"><span lang="FR" style="color:black;mso-ansi-language:FR">Option
Gosub<o:p>
</span></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">The
FreeBASIC IDE editor is available here: <a href="http://fbide.freebasic.net/">http://fbide.freebasic.net/</a></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify"> Here
is a screenshot from the first program:
</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><img border="0" src="images/Aether06_Marcotte.jpg" width="800" height="600"></p>
<p align="center"><font face="Times New Roman" size="4">A screenshot from the program showing Marcotte's equations.</font></p>
<p align="center"><font face="Times New Roman" size="4">I also made an AVI
animation showing this: <a href="avi/Aether06_Marcotte.avi">Aether06_Marcotte.avi</a></font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>The Doppler effect.</b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">The
on-axis regular Doppler effect is quite simple: 1 <span lang="FR-CA" style="COLOR: black; 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"><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>
beta forward and 1 + beta backward (beta = v/c). In addition, the Lorentz
transformations indicate that the electron frequency should slow down,
producing a longer basic wavelength. I applied those modifications to
Marcotte's equations in order to show how its standing waves should behave
while the electron is moving. Surprisingly, the well known envelope
showing nodes and antinodes is still present.</p>
<p align="left"><b>The electron contraction.</b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">Despite
the longer basic wavelength, the envelope containing nodes and
antinodes rather contracts according to Lorentz's contraction factor.</p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">This
is consistent with Lorentz's first equation.</p>
<p align="left"><b>More energy means more mass for the accelerated electron.</b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify"> Lorentz
also predicted that the electron mass should increase according to the
gamma factor. This was soon verified by M. Kaufmann. The point is: if
the emitter accelerates, the
forward wave amplitude
increases much more severely then it is reduced backward.</p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">The
Doppler program (see below) shows that the electron amplitude indeed
increases at high speed. So its energy, hence its mass,
increases. This also indicates that the gain in mass according to the
gamma factor is pure kinetic energy: E = m(gamma<font face="Times New Roman"><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>1)c^2, as a consequence of the Doppler effect.</p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">However,
this gain in energy must be measured by an observer at rest. Any
instrument moving along with the electron would record wrong data
because the Doppler effect is unnoticeable inside the same frame of
reference. This was discovered in 1842 by Christian Doppler himself...</p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">Here
is a screen capture from the Doppler program:
</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><img border="0" src="images/Aether06_Marcotte_Doppler.jpg" width="800" height="600"></p>
<p align="center"><font face="Times New Roman" size="4"> A screenshot
from <a href="programs/Aether06_Marcotte_Doppler.exe">Aether06_Marcotte_Doppler.exe</a>
Source Code <a href="programs/Aether06_Marcotte_Doppler.bas">Aether06_Marcotte_Doppler.bas</a></font></p>
<p align="center"><font face="Times New Roman" size="4"> See also <a href="avi/Aether06_Marcotte_Doppler.avi">Aether06_Marcotte_Doppler.avi</a></font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><font face="Times New Roman" size="4"><b>THE ELECTRON DOPPLER
EFFECT</b></font></p>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
Lorentz transformations indicate that a "local time" takes
place inside any moving system. Actually, this means that the electron wave phase
should vary along the displacement axis. The phase is retarded forward according to
the distance to the center. Waves are rather pulsating in
advance at the rear.
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
effect on the moving electron is obvious. Its standing waves no longer
pulsate everywhere simultaneously. So a <b><i> phase wave</i></b> whose
velocity is 1 / beta (in wavelength per period units) becomes visible. The normalized beta speed equals v / c, hence
the speed of light in beta units becomes c = 1.
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">And
because the local time is the same everywhere on a transverse plane,
this phase wave is plane. It is clearly noticeable (see the
animations below) in the form of vertical stripes moving forward,
always faster then the speed of light (1 / beta).</font>
</p>
<p align="left"><font face="Times New Roman" size="4"><b>The electron
and the Lorentz transformations.</b></font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">The Lorentz transformations can be
simplified using a theta angle which equals arc sin(v / c):</font>
</p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<center>
<table border="4" cellpadding="20" cellspacing="6">
<tr>
<td>
<img border="0" src="images/lorentz03e.gif" width="203" height="145">
</td>
</tr>
</table>
</center>
</div>
<p align="center"><font size="4" face="Times New Roman">Lorentz's Doppler
trigonometric equations.</font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><span lang="FR-CA">For
example, lets suppose that a material body is moving at 86.6% of the
speed of light.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><span lang="FR-CA">Then
beta = .866 and theta = 60°. The first part of the first equation
above means that this material body will contract to one half
of its normal length (cos 60° = .5). Note that this occurs only along
the displacement axis. The second part indicates that this body will
have moved from x = 0 to x = .866 light-seconds (sin 60° = .866)
after a one second delay. This is quite obvious: a speed of .866
light-seconds per second surely means that it will move to .866 light
seconds after 1 second. One does not really need Lorentz's equation to
understand this!</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA"><font face="Times New Roman" size="4">It
should be emphasized that Lorentz established that transverse distances
never change: y'=y; z'=z. This indicates that the electron
wavelength along those axes should be constant. Because a transverse
Doppler contraction
according to g normally occurs, the electron frequency must slow down according to the same g
factor. I wrote a
program showing that this produces a longer basic wavelength which cancels the
transverse wavelength contraction:</font></span>
</p>
<font face="Times New Roman" size="4">
<p align="center"><a href="programs/Electron_Doppler_effect.bas">Electron_Doppler_effect.bas</a>
<a href="programs/Electron_Doppler_effect.exe">Electron_Doppler_effect.exe</a></p>
<p align="center"><b> </b></p>
<div align="center">
<center>
<table border="4" cellpadding="20" cellspacing="6" width="500">
<tr>
<td>
<p align="center"><span lang="FR-CA"><font face="Times New Roman" size="4"><b>Remember
this !</b></font></span></p>
<p align="center"><span lang="FR-CA"><font face="Times New Roman" size="4">Relativity
</font></span><font face="Times New Roman" size="4"><span lang="FR-CA">is true simply because </span></font><span lang="FR-CA"><font face="Times New Roman" size="4">the
electron frequency slows down according to Lorentz's
contraction factor.</font></span> </td>
</tr>
</table>
</center>
</div>
<p align="center"><b> </b></p>
<p align="left"><b>Relativity.</b></p>
</font> <p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><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><span lang="FR-CA">
Moving clocks are ticking slower because they are made out of electrons
whose frequency is slower.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><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">–
Matter does not contract on transverse y and z axes because the electron
transverse wavelength does not change in spite of the Doppler effect.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><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">–
Matter contracts along the displacement axis because the electron
axial standing waves contract according to g. Standing wave contraction
is still not so well known, yet it is undisputable. Now, the Michelson interferometer
absolute contraction (which was wrongly ruled out by Poincaré and
Einstein) must be reconsidered because the electron really binds molecules
according to its wavelength. </span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><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">–
Any moving observer cannot detect this Doppler effect because it is
perfectly symmetrical.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><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">The
electron forward wavelength for beta = .5 is (1 – beta) / g = .577 * lambda
while the backward wavelength is (1 + beta) / g = 1.732 *
lambda. Note that 1 / .577 = 1.732. This is not the case for the normal
Doppler effect. But here, the slower frequency and the resulting reciprocity will fool any
moving observer trying to detect the Doppler effect.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><span lang="FR-CA"> I know that you will seriously
doubt this. So I wrote the <a href="programmes/Ether14.exe">Ether14.exe</a>
program (source code <a href="programmes/Ether14.bas">Ether14.bas</a>)
in order to prove it. This program is highly consistent and reliable.
It shows that any observer moving with the system at the same speed will
be unable to measure his absolute speed through the aether. He will
always think that he is at rest. He will rather think that a system
which is truly at
rest is moving.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><span lang="FR-CA">This
is what Relativity is all about. No more mystery. No more tricky
reasoning. So forget about inane ideas such as space contraction and
time dilation.</span></font>
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><span lang="FR-CA">This
is indeed a great discovery, and it is undisputable: the Lorentz transformations are <b><i>nothing
else</i></b> but the mathematical expression of electron's very
special Doppler effect. Please examine my
program <a href="programmes/Ether17.exe">Ether17.exe</a> (source code <a href="programmes/Ether17.bas">Ether17.bas</a>): the Doppler effect is
really generated
by the modified Lorentz equations shown
above.</span></font>
</p>
<p align="left"><font face="Times New Roman" size="4"><b>The phase wave.</b></font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">So
the phase wave is a consequence of the t' time in the Lorentz transformations. Look at
those animated diagrams showing the moving electron at different speeds.
Assuming that the electron accelerates, intervals between vertical stripes (which
indicate a phase shift)
become more and more narrow, and the stripe speed slows down until it is
finally very near to c:</font>
</p>
</td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6" bordercolorlight="#FFFFFF">
<tr>
<td align="center"><img border="0" src="images/electron.1.gif" width="335" height="272"></td>
<td align="center"><img border="0" src="images/electron.5.gif" width="335" height="272"></td>
</tr>
<tr>
<td align="center">
<font face="Times New Roman" size="4">
v = 0,1 c
</font>
</td>
<td align="center">
<font face="Times New Roman" size="4">
v = 0,5 c
</font>
</td>
</tr>
</table>
</center>
</div>
<P align=center>The moving vertical stripes indicate a phase shift as a result
of Lorentz's "local time".</P>
<p align="center"><b> </b></p>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6">
<tr>
<td>
<p align="center"><img border="0" src="images/electron_variable.gif" width="335" height="286"></td>
</tr>
</table>
</center>
</div>
<p align="center">The accelerating electron also shows the nodes and
antinodes contraction.</p>
<p align="center">The phase shifts occur on vertical planes regularly spaced
according to g * lambda / beta wavelengths.</p>
<p align="center">This is a consequence of Lorentz's second equation..</p>
<p align="center">The result is a "phase wave" moving at 1 /
beta wavelengths per period, or light-seconds per second.</p>
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">It
should be pointed out that my "<a href="sa_scanner.htm">Time
Scanner</a>" conveniently exploits this phase wave in order to
reproduce the Lorentz transformations. For example, scanning concentric
waves moving inwards or outwards will add a Doppler effect to them.
Surprisingly, it will also transform Milo Wolff's static electron into
my moving electron.
</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This Time Scanner is
another invention of
mine. It proves
that the Lorentz transformations are simply a Doppler effect involving a
slower frequency.
</p>
</font>
</td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><font face="Times New Roman" size="4"><b>THE VIRTUAL AETHER
TO THE RESCUE</b></font></p>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>Mr. Philippe Delmotte.</b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">The
Virtual Aether is Mr. Philippe Delmotte's brilliant invention (June
2005). It is a computerized virtual medium capable of reproducing any
wave phenomenon. Its algorithm supposes that the aether is made of an
infinite number of "granules", which can vibrate in
accordance with Hooke's law. Thus those granules must initially
contain kinetic energy, and also inertia, which can be seen as a memory of its
precedent energy. In addition, this energy can be transmitted to the
nearest neighbors.<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">The
program algorithm is remarkably simple. Believe it or not, this pure
jewel needs only three program lines!
<p align="left"><b>M. Jocelyn Marcotte.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">On
July 10, 2006, Mr. Jocelyn Marcotte
succeeded in experimenting my Doppler moving electron. Even better, he used the Lorentz transformations
in order to reproduce the Doppler effect. Those
transformations are not about a space-time distortion. They more
simply predict the way on-axis waves contract and exhibit local phases producing a
"phase wave". Mr. Marcotte used his own
Virtual Aether algorithm (see <a href="programs/WaveMechanics04.bas">WaveMechanics04.bas</a>), which is different from Mr.
Delmotte's, in a 3-D space.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">In
my opinion, this experiment will be related in the future as a
memorable achievement. It was the ultimate proof, showing that this
amazing wave can exist. Because today's science is afflicted with <a href="sa_errors.htm">so
many
errors</a>, this new discovery will launch a severe revolution in the world of physics. </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Mr.
Marcotte's program displays an electron moving as predicted,
but alas inside a limited 500^3 granules aether cube. In a few years, computers will
run faster using multiple core processors and more memory. Then new programs
using advanced code and powerful graphic cards will deliver much better results.</p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">Clearly,
the Virtual Aether results are consistent with those using the Huygens
Principle. The graphics below is a screenshot from Mr. Marcotte's 3-D
program. Please note that the on-axis wave structure is identical to that obtained
with the Aether06_Marcotte_Doppler.exe program shown above. The
overall wave structure is also identical to that obtained with the <a href="programs/Aether10_Marcotte.exe">Aether_10_Marcotte.exe</a>
program, which shows that Mr. Marcotte's equations can reproduce the
whole electron structure:</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6">
<tr>
<td>
<p align="center"><img border="0" src="images/Ether09_3D_Marcotte.jpg" width="441" height="316"></td>
</tr>
</table>
</center>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<p align="center"><font face="Times New Roman" size="4">This is a screen capture
from Mr. Jocelyn Marcotte's 3-D (cubic) Virtual Aether program.</font></p>
<p align="center"><font face="Times New Roman" size="4">And here is a 500 images
<a href="avi/electron_in_virtual_aether.avi">AVI animation</a> produced thanks
to Mr. Marcotte's program.</font></p>
<p align="center"><font face="Times New Roman" size="4">See the electron moving
freely to the right without any mathematical intervention.</font></p>
<p align="center"><font face="Times New Roman" size="4">Unfortunately, without
aether waves traveling through it, no amplification can occur and it vanishes rapidly.</font></p>
<p align="center"><font face="Times New Roman" size="4">We will need a much larger
aether in order to produce a more satisfying experience.</font></p>
<p align="center"><font face="Times New Roman" size="4">However, this is a
flawless demonstration: this wave system is possible.</font></p>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>The electron is not infinite.</b></p>
<p class="MsoTitle" style="text-indent: 35.4pt; text-align: justify">Without
incoming energy, the electron would still emit spherical outgoing
waves. So it would rapidly fade out. Obviously, it needs
replenishment. This is accomplished by powerful and constant
aether waves. Traveling waves penetrating through standing wave
antinodes are deviated because of a
lens effect. A small part of the energy is transferred to the
standing waves. This constantly refilled energy allows the electron to exist
forever. </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Outgoing spherical waves
weaken according to the square of
the distance law. In spite of this, the light from a star, for instance, can travel for
billions of years, almost infinitely. It never totally disappears.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The electron too
produces outgoing spherical waves. Those are regular traveling waves.
Because the electron is rather made of standing waves, amplitude
can
no longer be the same everywhere in both directions, making them "partially
standing waves". Finally, even farther, just outgoing traveling waves
remain.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
diagram below shows how the transition between those three states is
possible:</p>
</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6">
<tr>
<td>
<p align="center"><img border="0" src="images/proton08.gif" width="640" height="258"></td>
</tr>
</table>
</center>
</div>
<p align="center">The electron is not made of pure standing waves.</p>
<p align="center">Far from the center, standing waves are progressively
replaced by traveling waves.</p>
<p align="center"><b> </b></p>
</font>
<div align="center">
<table cellSpacing="0" cellPadding="0" width="1000" border="0">
<tbody>
<tr>
<td width="100%"><font face="Times New Roman" size="4">
<p align="left"><b>Radiation pressure.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Obviously,
while it is accelerating, slowing down or changing its direction, the
electron cannot use its incoming waves any more. Its focal
point is not compatible with their future position any more.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">However,
the radiation pressure mechanism can overcome this problem. Waves
emitted by an electron will inevitably encounter those incoming from
all other electrons, especially on the axis joining them. This will
produce a very special set of standing waves, a <a href="sa_fields.htm">field
of force</a>, which will also be amplified by aether waves. Half of
the resulting energy is then returned and focused directly towards
both electrons which created the field.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Programs
to come will show
clearly how and why this phenomenon is possible. Those fields of force
are emitting focused and powerful traveling waves towards the
electron. And because their phase and wavelength do not
necessarily coincide, the electron will progressively change its
position according to them.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Because
the wave's amplitude is higher near the center, it turns out that half
of the electron energy may be present inside a very small
sphere, maybe the size of an atom. There is enough space for thousands
and even millions of wavelengths, though. The other half may expand
inside a much wider sphere.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
amplification process can be seen as the production of an infinite
number of Huygens' wavelets. According to Huygens, the wavelets'
addition must create a wave front wherever their phases coincide.
Clearly, incoming wavelets can produce standing waves, but outgoing
ones can only produce outgoing wavefronts.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">It
turns out that the wavelets' summation, hence new energy, is far greater
near the center. It does not obey the square of the distance law. This
indicates that very far from the electron, permanent standing waves
compatible with the core phase cannot exist any more.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The Virtual Aether is a new tool which can show how a
limited number of wavelets will behave. The diagram below is a good
example:</p>
</font> </td>
</tr>
</tbody>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"><b> </b></p>
</font>
<div align="center">