-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathsa_Michelson.htm
1118 lines (980 loc) · 68.6 KB
/
sa_Michelson.htm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<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</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">Michelson's goal was to detect
the phase shift shown on the left.</font></P>
<P align=center><font face="Times New Roman" size="4">However, there is no phase shift because the interferometer contracts.</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="1000">
<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 tried to detect the speed of the Earth through
the aether by means of an interferometer. But his 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 transformations 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 reproduces a race
on a river between two swimmers. In 1887 planes
did not exist. Otherwise, he would certainly have spoken about a plane
race while a strong wind is blowing.</span>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Let
us consider two identical airplanes whose constant speed is 100 mph and
suppose that the wind is blowing at 50 mph. Then the beta normalized speed is given by v / c = 50 / 100 = .5. According to the rules, both
pilots must perform a round trip between two points 100 miles apart.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The first pilot prefers to fly in
the direction of the wind. But t</span></font><font face="Times New Roman" size="4"><span lang="FR-CA">he
second one chooses the transverse route and surprisingly, he easily wins the race.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
point is that those
planes behave exactly like the light waves. It is all about <a href="sa_Doppler.htm">the
Doppler effect</a>. Their speed may be compared
to the speed of light, and one may
consider that there is an aether wind because the emitter is moving.</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/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="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<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 on a go and return trip is given by Lorentz's contraction
factor g, which is the reciprocal of the gamma factor. In this
example, beta = .5 and g = .866:</span></p>
</font>
<p align="center"><img border="0" src="images/lorentz03a.gif" width="142" height="148"></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">Then
the relative speed on a round trip is: </font></p>
<font face="Times New Roman" size="4">
<P align=center>Along the wind : g<sup>2</sup> 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 face="Times New Roman" size="4">Across
the wind, planes (or waves) will be tilted to 30° according to the theta
angle:</font></p>
<P align=center><font face="Times New Roman" size="4">theta = arc sin (beta)</font>
</P>
<center>
<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 whatever the
direction. However, in the presence of wind, the duration increases more
severely in the direction of the wind according to g squared instead of
g in the transverse direction.</font></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font size="4" face="Times New Roman">1
- The
round-trip duration 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 duration 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. On
condition that there is no transverse contraction, the interferometer
must contract in accordance with
Lorentz's contraction factor. This is only one of the Lorentz
transformations because there is also a time effect:</font></p>
<font size="4" face="Times New Roman">
<p align="center"><img border="0" src="images/lorentz03b.gif" width="158" height="142"></p>
<p align="center">The Lorentz transformations.</p>
<p align="center">This equation set was simplified by Henri Poincaré
thanks to beta and g.</p>
<p align="center">Please note that x stands for distance to origin in
the contracted moving frame of reference.</p>
<p align="center">So it is smaller than x'. This was almost never
pointed out. </p>
<p align="center"> </p>
<p align="left"><b>The Michelson transformations.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Prior to the Lorentz transformations, Michelson
discovered a mechanical property of waves when they are observed in
a moving frame of reference. This could be called the Michelson
transformations but it is more simply the regular Doppler effect. A
wavelength contraction according to g occurs on both transverse y and z axes, but
a more
severe one according to g squared can be observed along the motion x axis.</p>
<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>
beta * </font></span></font>t) / g<sup> 2</sup></p>
<p align="center">y' = y /
g z' = z / g</p>
<p align="center">t' = t <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; letter-spacing: 0">+</span><font size="4"><span style="letter-spacing: 0"><font face="Times New Roman">
beta * </font></span></font>x</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">According
to our example, planes flying inside such an x, y and z contracted space would
always perform the round trip in two hours whatever the
speed of the wind or its direction. This explains why no abnormal time effect occurs.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">So
the main difference here is the time effect because both points of view
lead to a null result.</p>
<p align="left"><b>Galileo's transformation.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Galileo's
transformation is more simply a uniform translation motion. There
is no transverse contraction and the time is the same everywhere.</p>
<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>
beta * </font></span></font>t</p>
<p align="center">y' = y z' = z</p>
<p align="center">t' = t</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Here
too, x is the coordinate in the moving frame of reference. Thus: x
= x' + beta * t.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This
was Galileo's point of view. However, according to Descartes, the x position
should definitely refer to the Cartesian frame
of reference, which is postulated to be at rest. After a given t time, because the rightward motion is a well
admitted convention, this procedure creates an artificial secondary
moving frame of reference. As a matter of fact, according to Descartes, the light propagates by means of the
aether, which is postulated to be at rest. So the aether is not only a preferred
frame of reference, it is the only admissible Cartesian frame of
reference. This should lead to this inversion: x' = x + beta * t.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">But
let us be honest: inside the moving frame of reference, the light
traveling forward clearly propagates slower and the Doppler effect
should be considered. The equation works for moving objects to a first
approximation, but what if matter is made of waves? </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">One
should bear in mind that Galileo's
transformation is wrong because matter actually transforms according to
the Lorentz transformations. Matter especially cannot reach the speed of
light for this reason.</p>
<p align="left"><b>A race between two waves.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Michelson
noticed that the relative speed of light on a go and return trip is slower in the direction
of motion. He realized that two orthogonal light beams could not produce the same interference fringes after a 90° rotation. He deduced from this that an interferometer could detect the
speed of the aether wind.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Here is a diagram showing Michelson's apparatus:
</font></p>
</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/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="1000">
<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">Only
one half of the
light beam emitted by the source is reflected 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 then reunifies them. </span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Finally,
both beams could be compared in 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 without any stress because the instrument was mounted
on a large stone floating on a mercury pond. The temperature was also
severely controlled.</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 show what is going on inside the interferometer
branches. I had to use a very high speed in order to obtain a clearly
visible phase shift: one
third of the speed of light. Then beta =</span> .3333 and g = .9428. <span lang="FR-CA">Such a speed
produces a 2 : 1 wavelength ratio R along the displacement axis,
according to: </span><p align="center">R
= (1 + beta)
/ (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> beta)</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
ratio indicates that on-axis planes crossing the starting
point each minute, one at a time, would be two times nearer while
flying against the wind.</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 shown below
represents a plane. The aether wind blows from the right. </span>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
diagram on the left displays exactly the same length for both branches.
This distance was calculated to obtain a full lambda / 2
phase shift. The wave fronts (or planes) along the motion axis are
pictured in red and 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"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<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. One of the branches (the horizontal one here)
underwent a contraction according to Lorentz's contraction
factor. In this example, it contracts to 94.28 % of its original
length.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
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"> </p>
<p align="center"><img border="0" src="images/exclam.gif" width="97" height="95"></p>
<p align="center"><b>A new fact in science history:</b></p>
<p align="center"><b>STANDING WAVE CONTRACTION</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This
web site shows that aether exists and that matter is made purely out of
spherical standing waves. Because moving standing waves undergo a contraction,
moving matter should also undergo a contraction. Lorentz was unaware of
this. It is a new fact. Now one can explain <b><i>why</i></b> the
Michelson interferometer contracts.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">I
will especially quote this page from Poincaré's book Electricity and
Optics (1901):
<p align="center"><img border="0" src="images/Poincare_coup_de_pouce.gif"></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Poincaré
is discussing Lorentz's opinion that matter should contract. In his
picture, this "strange property" is unthinkable because it
would seem some sort of "<i>coup de pouce</i>" (helpful hand)
from Nature in order to hide the way optical phenomena really work. He
very severely rejects this hypothesis without any valid reason. He says
that Lorentz's theory is near to be correct, but that it still needs
some adjustments. He finally proposes that optical phenomena should only
depend on the relative motion of sources, apparatus, etc.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Let
us be perfectly clear: Poincaré is definitely wrong here because
Lorentz's theory fully explains Relativity. Today, we are aware that
matter exhibits wave properties and that waves undergo the Lorentz
transformations. So the contraction is not a "helpful hand"
any more. It is rather an additional proof that Lorentz was right.</font> <p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4">It
should be emphasized that Albert Einstein could read French and that he
surely read this book. In all cases, his 1905 first edition about
Relativity was nothing but a "copy and paste" of Poincaré's
ideas. It is easily verifiable, and it is a shame that it is still
ignored today. Personally, I think that this is rather funny because
they were both wrong. So, who cares?
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Michelson
and Lorentz strongly believed that aether should exist. So this page certainly matches
their thoughts.</font>
<font face="Times New Roman" size="4">
However,
this is not what scientists believe today, because they wrongly ruled out
the aether.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">So
this page does not submit to standard opinion, albeit it is consistent
with Lorentz's 1904 book. The science world
is rapidly evolving today because of the Internet. People familiar with Lorentz's researches generally
admit a privileged
frame of reference, which in most cases coincides with aether. Some of
them prefer the word "space", but this is obviously a
compromise because aether is a suspicious subject nowadays.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Only
people well aware of Lorentz's ideas can speak about Relativity, because
it is the result of the Lorentz transformations. Others should be less affirmative because they ignore how Relativity
was discovered.
<p align="left"><b> Lorentz's was right.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Most
web pages on the Michelson interferometer 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 undergoes a contraction in the
direction of motion. The first of Lorentz's three transformations is a length
contraction, which occurs only on the x axis.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">For example,
let us suppose a very high speed: 86.6% of the speed of
light. Then beta = .866 and Lorentz's contraction factor is .5. The gamma
factor equals 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 duration along any of the 4 possible paths inside the
interferometer's arms would be the same. This device can be seen as a <b><i>4
branch interferometer</i></b>. Here, the very high speed involves a severe
contraction to half of the original length, and the speed
difference becomes 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">The Doppler
effect.</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="1000">
<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 center O and using
a radar signal would find by timing the echoes that all A, B, C and D distances are the same.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">However,
he would not notice that the four radar echoes are two times longer because his
clock also runs two times slower according to the gamma factor.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Because
all forces are transmitted by means of waves, which undergo the Doppler
effect, all matter mechanisms are also slowed down in the same way. All
happens with a slower rate of time. Most often, one speaks about <b><i>time dilation</i></b>.
This is incorrect. Time is a concept, an idea; it does not
really exist. But a clock does exist, and it can tick slower. This does
not mean that time runs slower. </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Secondly, waves
(or planes) would reach the A point in the rear much more rapidly.
Because of the Doppler effect, the B point will be attained later. Henri
Poincare showed how, 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, A will be in
advance and B will be late. However, nobody would be able to notice
the resulting time shift. Inside such a moving frame of reference,
Poincare showed that such <b><i>local hours</i></b> lead to a sort of
virtual simultaneity. One cannot detect his actual speed any more. All happens as if the system was perfectly at rest inside aether.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">In
addition,
waves propagating forward contract 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>
beta while those moving backward expand according to 1 + beta.</font><font face="Times New Roman" size="4">
The </font><font face="Times New Roman" size="4"> backward </font><font face="Times New Roman" size="4">wavelength
expansion ranges only from 1 to 2 while waves can be infinitely
compressed forward. It turns out that the wave compression is much more
severe; it increases matter's energy according to the gamma factor. So
matter's mass/energy is doubled for .866 c and this was also discovered
by Lorentz. As a matter of fact, this phenomenon could be regarded as
Lorentz's fourth transformation:</p>
<p align="left">1 <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>
Distances along the displacement axis contract.</p>
<p align="left">2 <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>
All phenomena occur with a slower rate of time.</p>
<p align="left">3 <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>
A time shift appears between the front and the rear.</p>
<p align="left">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>
Matter is gaining in mass and the mass gain becomes kinetic energy.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This was the secret: matter is made of waves. 100
years were needed to solve this mystery. It was obvious,
though, because Lorentz's equations are almost a copy of the Woldemar
Voigt's ones on the Doppler effect (1887). Actually, the only difference
was an unknown constant whose k = 1 value was finally discovered by Lorentz
and Poincaré in 1904. It is that simple: matter behaves like waves.</p>
<p align="left"><b>Standing wave contraction.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Very
few people noticed that because light waves are reflected back on the
interferometer's mirrors, standing waves appear inside both of its branches.
Moreover, in 1904, standing waves compression was not a well known phenomenon. As
far as I know it has been discovered by <a href="http://www.keelynet.com/spider/b-104e.htm">Mr.
Yuri Ivanov</a>, and only me and <a href="http://ondes-relativite.info/">Mr.
Serge Cabala</a> seem to have studied it in an acceptable manner. For
more details about moving standing waves (Ivanov's "lively standing
waves") see <a href="sa_plane.htm">standing waves</a>.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> <span lang="FR-CA">So,
in the animation, 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">The mean relative velocity of light in order to perform a
complete round-trip can be calculated as shown above. Let's repeat that waves behave in
exactly the same manner as planes in the presence of wind. So the compression
rate is also given by g and g squared:</span><p align="center">Relative
on-axis mean
wave velocity: v = c
g<sup> 2</sup></p>
<p align="center">On-axis standing wave compression: lambda' = lambda * g<sup> 2</sup></p>
<p align="center">Relative transverse constant
wave velocity: v = c g</p>
<p align="center">Transverse standing wave compression: lambda' = lambda * g</p>
<p align="center"> </p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Those
results can also be established according to the "relative" <a href="sa_Doppler.htm">Doppler
effect</a>. I elaborated the first equation below around 1998. It
derives from the regular Doppler effect 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>
beta * cos phi, but the number one gradually transforms to g until phi
reaches 90°.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> The
second formula yields the same results; I adapted it from <a href="http://www.keelynet.com/spider/b-108e.htm">Mr.
Ivanov's</a> web site.
<p align="center"><img border="0" src="images/Doppler_formula.gif" width="405" height="81"></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> It
should be pointed out that these equations also indicate the relative
wave velocity according to Michelson's calculus.
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Using
a 90° phi angle, one can easily note that transverse waves
undergo a compression according to Lorentz's g factor. Because the
relative transverse wave velocity is slowed down according to g, the time needed
to perform the transverse go and return trip is also longer according to 1/g. The
calculus for the on-axis whole round trip is a bit more complicated
because the go and return trips are different, but one
can use the simpler </span>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>
beta <span lang="FR-CA">formula forward and 1 + beta
backward.</span><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Finally,
the standing wave compression ratio equals the change in the relative velocity of
light on a go and return trip.
Both calculi yield the same results. Michelson preferred velocity and did not use
the standing wave method, which is simpler though, especially for studying the
Kennedy-Thorndyke experiment. Actually, Kennedy and Thorndyke did not
take the frequency reduction into account. The overall increased
wavelength cancels the transverse contraction and reduces the on-axis
contraction to g. So they were wrong.</span></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"><b>STANDING
WAVE CONTRACTION</b></font></p>
<p align="center"><font size="4" face="Times New Roman"> </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">beta
= 0 g = 1 Standard standing
waves. No contraction.</font></p>
<p align="center"><font face="Times New Roman" size="4"> </font></p>
<p align="center"><img border="0" src="images/stat.5a.gif" width="481" height="101"></p>
<p align="center"><font face="Times New Roman" size="4">Mr. Yuri Ivanov's "Lively standing
waves" showing nodes and antinodes <b><i>motion</i></b> and <b><i>contraction</i></b>.</font></p>
<p align="center"><font face="Times New Roman" size="4">beta = .5 g = .866
Same frequency, contraction to 75% according to g<sup>
2</sup>.</font></p>
<p align="center"><font face="Times New Roman" size="4">Here, the observer
is at rest with respect to the wave medium.</font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></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">beta = .5 g = .866
Same frequency, contraction to 75% according to g<sup>
2</sup>.</font></p>
<p align="center"><font face="Times New Roman" size="4">Here, the observer is
moving with the system's frame of reference.</font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<p align="center"><img border="0" src="images/stat.7.gif" width="321" height="101"></p>
<p align="center"><font face="Times New Roman" size="4">beta = .707 g = .707
Same frequency, contraction to 50% according to g<sup>
2</sup>.</font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<center>
<table border="4" width="600" cellpadding="20" cellspacing="6">
<tr>
<td width="100%">
<p align="center"><font face="Times New Roman" size="4">The Michelson
interferometer undergoes a length contraction in the direction of motion
according to Lorentz's contraction factor.</font></p>
</td>
</tr>
</table>
</center>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<P align=center><font face="Times New Roman" size="4"><b>THE LIGHT BEAM LENGTH</b></font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<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
animated diagrams shown above indicate that for one third of the
speed of light, the </span><span lang="FR-CA">
interferometer arm length must be 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 length using the
standing wave compression method. Theoretically, the calculus must take
the slower frequency into account. So, in the absence of contraction,
the formula for
obtaining two beams in phase opposition using the computer should be:</span></p>
<p align="center"><span style="letter-spacing: 0">According to the
absolute wavelength at rest: </span><span lang="FR-CA">L
= lambda /<span style="letter-spacing: 0">
4 g (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 class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">However,
Michelson was unaware of the Lorentz transformations, hence the
slower frequency</span><font face="Times New Roman" size="4"><span lang="FR-CA">.
But surprisingly, his measurements for the yellow light wavelength would
remain unchanged at any speed. Because the frequency does change, the formula above
simplifies to:</span></font>
<p align="center"><font size="4"><font face="Times New Roman"><span style="letter-spacing: 0">L = lambda </span></font><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 align="left"><b>Example.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Let
us
suppose a g = .9 contraction. Then </span><font face="Times New Roman" size="4"><span lang="FR-CA">beta
= .4359 and </span></font><span lang="FR-CA">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. The formula </span><span style="letter-spacing: 0">yields </span><span lang="FR-CA">2.5
wavelengths, or 5 half-wavelengths. The plane mirror produces standing
waves and the distance between two
nodes is one half of a wavelength. The goal is to make a node coincide
with the nearest antinode. One may add that, from Michelson's point of
view, moving the mirror only a quarter of a wavelength produces a full
phase opposition because of the go and return trip. So only a quarter of a wavelength
difference is
needed:</span><p align="center"><img border="0" src="images/michelson08.gif" width="390" height="148"></p>
<p align="center">If g = .9, the first phase opposition occurs for 5 half-wavelengths.</p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<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 the sun through galaxies all around us has been estimated to be
about 300 km/sec. It could be its absolute speed through the aether, but it could
also be much faster. If beta is 300 / 300 000 = </span>
<font face="Times New Roman" size="4">
<span lang="FR-CA"> .001 </span></font><span lang="FR-CA">the Lorentz
contraction factor is .9999995 and the formula
yields 500,000 wavelengths. So 500,000 times .0006 (yellow light) is 300 mm or 30 cm (about
one foot). This suggests that a one foot tall interferometer should be
enough in most cases.</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 the Earth would still be 29 km/sec
(about 18 miles per second).
So he preferred a rather large interferometer according to the
following values:</span></p>
<ul>
<li>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">
<font face="Times New Roman" size="4">
<span lang="FR-CA">beta</span></font><span lang="FR-CA"><font face="Symbol" size="4">
</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">lambda
= .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">The
formula indicates 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. S</font><font face="Times New Roman" size="4">o
the arm length should be 32,000 mm or 32 meters (105 feet) in order to detect the
Earth's minimum 29 km/s speed through aether. 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
</span>
<font face="Times New Roman" size="4"><span lang="FR-CA"> arm length </span></font><span lang="FR-CA">for the 1887 experiment was 11 meters (36
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 (105 feet) interferometer and the null result was
confirmed.</span>
</p>
</font></center>
</td>
</tr>
</table>
</div>
<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>THE
KENNEDY-THORNDYKE EXPERIMENT WAS A MESS</b></span></font></P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<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, the second arm 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 simpler
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="1000">
<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">Planes
can be identified, but waves must be compared because they are all
identical. The comparison does not produce
an immediate result and Michelson had to rotate the apparatus in order to observe the difference in
the interference fringes. So the length
for the shorter arm is
optional because it is used only as a reference. </span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
<b><i>is not</i></b> what Kennedy and Thorndyke thought. They claimed that
different lengths would reveal the aether wind in spite of the contraction.
So, because the Kennedy-Thorndyke experiment still ended with a null result, scientists deduced from it that aether does not
exist. This is weird: believe it or not, nobody could correctly calculate
this in accordance with the Lorentz transformations!</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA"> It should be pointed out that
the Lorentz transformations do not solely involve a contraction. The time equation also predicts that any periodic phenomenon should be slowed down in
accordance with Lorentz's contraction factor. This means that the
basic wavelength<b><i> becomes longer</i></b>. Then, whatever the
shorter arm length, the correct length formula for the longer one 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="Times New Roman" size="4">lambda /</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 its standing waves do. The consequence is that <b><i>any
length</i></b> yields 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"><b><font face="Times New Roman" size="4">LORENTZ'S
ANGULAR ABERRATION</font></b></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Some
authors noticed that the 45° angle for the beam splitter cannot be constant because of
the Lorentz transformations. Any contraction would cause it to be tilted in
accordance with: arc tan (1 / g). Then, because of the well known
opticians' equal
angle law, the beam could not be reflected along the orthogonal axis according to a
90° angle any more.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
truth is that this equal angle law is false inside a moving frame of
reference. Lorentz himself discovered that a special "angular
aberration" should occur. So he wrote to Michelson, who agreed and
changed his calculus. Lorentz probably applied Huygens' Principle, which
postulates that any wave can be seen as billions of "wavelets".</p>
<p align="left"><b>Huygens' Principle.</b></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
web site does explain light by such wavelets, but this detail is not
relevant here. However, one must admit that those wavelets should be
spherical. Obviously, their center of curvature should remain at rest
inside the aether. </span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Lorentz
noticed that any abnormal deviation could invalidate Michelson's calculus.
Some authors are misleading because they speak about Bradley's stellar
aberration. This phenomenon occurs when the emitter and the receptor speed
<b><i>
is not</i></b> the same. The aberration is different here because
the light source moves at the same speed.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">One
should observe carefully how those wavelets behave in the animation below.
According to the Huygens Principle, they reinforce themselves along their
common envelope, and this produces a wave front. The absolute speed is half of the speed of light: </span><font face="Times New Roman"><span lang="FR-CA"><font size="4">
</font></span></font><span lang="FR-CA">beta = 0.5 and g = .866. The mirror angle is increased to:
</span><span lang="FR-CA"> arc
tan (1 / g) = 49.1066° </span><span lang="FR-CA"> because of Lorentz's
contraction, but surprisingly the wave front is still deviated according
to a 90° angle. The Doppler effect accounts for Lorentz's 30°
theta</span></font><span lang="FR-CA"><font face="Times New Roman" size="4">
angle. This means that waves traveling crosswise are tilted according
to this angle, the same way the planes studied above are.</font></span></p>
</td>
</tr>
</table>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<P align=center><img border="0" src="images/michelson07.gif" width="232" height="224"></P>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA">The
49° mirror angle still produces a 90° deviation.</span></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="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Additionally,
one can now experiment such phenomena in Philippe Delmotte's amazing Virtual Aether. Using my
Ether19 program, I made several mpeg-4 videos showing how the light waves
behave in the vicinity of the beam splitter:</p>
<p align="center"><a href="avi/Michelson_axial_forward_51_angle.avi">Michelson_axial_forward_51_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_axial_forward_45_angle.avi">Michelson_axial_forward_45_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_axial_backward_51_angle.avi">Michelson_axial_backward_51_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_axial_backward_45_angle.avi">Michelson_axial_backward_45_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_orthogonal_forward_51_angle.avi">Michelson_orthogonal_forward_51_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_orthogonal_forward_45_angle.avi">Michelson_orthogonal_forward_45_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_orthogonal_backward_51_angle.avi">Michelson_orthogonal_backward_51_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_orthogonal_backward_45_angle.avi">Michelson_orthogonal_backward_45_angle.avi</a></p>
<p align="center"><a href="avi/Michelson_orthogonal_unmoving_45_angle.avi">Michelson_orthogonal_unmoving_45_angle.avi</a></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Those experiences are much better then Michelson's
because one can truly see what is going on inside the interferometer. The
Virtual Aether shows that Lorentz was right: the angle can no longer be 45° at high speed. But surprisingly an angular aberration occurs which
maintains the light beam reflected to a 90° angle. It is absolutely amazing!</p>
</font>
</td>
</tr>
</table>
</div>
<font face="Times New Roman" size="4">
<p align="center"> </p>
<p align="center"><img border="0" src="images/michelson12.jpg" width="520" height="219"></p>
</font><P align=center><font face="Times New Roman" size="4"><span lang="FR-CA">On
the right, the unchanged 45° mirror angle produces an incorrect reflection
angle.</span></font></P>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA"> On
the left, the contraction according to Lorentz works perfectly.</span></font></P>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA">Note
that upward transverse waves are tilted according to the theta angle like the planes shown above.</span></font></P>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA">Moreover,
the transverse light beam also contracts according to Lorentz.</span></font></P>
<P align=center><font face="Times New Roman" size="4"><span lang="FR-CA">Clearly,
Lorentz was right!</span></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="1000">
<tr>
<td width="100%">
<center>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><font face="Times New Roman" size="4"><span lang="FR-CA">The
Lorentz transformations are decidedly a fantastic phenomenon. They always
prove to be correct.</span></font></p>
<font face="Times New Roman" size="4">
<p align="left"><b>A dramatic argument.</b>
</p>
</font>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">So
the 45° aberration is no longer an objection. It is rather a spectacular confirmation.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">On
the one hand, the apparatus undergoes a contraction which cancels the
waves' speed difference. On the other hand, the beam splitter angle is
increased in order to deviate the light beam in the correct direction.
Finally, waves arrive in the scope without any phase difference.</span></p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This
explains the null result.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Many
authors, even sometimes highly respectable and well known scientists,
still think that Michelson's experience ruled out aether. Such people
are "Panurge's sheep". They studied physics but just memorized
and repeated
what their professor said. They did not verify. They forgot Descartes' maxim: doubt is the
origin of wisdom.</span></p>
<p align="center"><span lang="FR-CA">"Dubium sapientiae initium"</span>
</p>
<p align="center"><span lang="FR-CA"> </span>
</p>
</font>
</center>
</td>
</tr>
</table>
</div>
<p align="center"><img border="0" src="images/ligne02.gif" width="559" height="10"></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>
<p align="center"><b><font face="Times New Roman" size="4">LORENTZ
WAS RIGHT</font></b></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">The
interferometer really undergoes a contraction in the direction of
motion. Lorentz's explanation was the right one, but nobody believed
him. All scientists preferred Poincare's version and Einstein's special theory of Relativity,
which predict the same effects but negate the absolute point of view.</span><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">This
was an enormous mistake. There <b><i>is</i></b> a mechanical explanation for all
phenomena. This includes gravity, light, magnetic and electrostatic
fields, nuclear forces, etc. The absolute point of view is important
because the goal is to explain what is really going on.</span></font>
</td>
</tr>
</table>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<center>
<table border="4" width="800" cellpadding="20" cellspacing="6">
<tr>
<td width="100%">
<p align="center"><font face="Times New Roman" size="4"><span lang="FR-CA">One
must firstly postulate that aether exists and that matter really
transforms according to its absolute speed the way Lorentz showed. Then
the goal is to establish carefully how a moving observer sees
phenomena from his own
frame of reference. The result is Lorentz's Relativity.</span></font>
</td>
</tr>
</table>
</center>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"><span lang="FR-CA">Relativity
is not complicated. It is not a mysterious theory any more. It is a law
of nature. The next pages show that it can be deduced from elementary
calculus, especially the Lorentz transformations and the Doppler effect.</span><p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
main difference from Einstein's concept is that any moving observer is
wrong about his situation, while one at rest sees phenomena the way
they really occur. The moving observer also thinks
that he is at rest because he sees the observer at rest undergoing the Lorentz