1) CLOCK 1 (longitudinal wave clock).
IT IS THE CLASSICAL ESTABLISHMENT OF TIME DILATION.
Text already published in the sci.physics.relativity newsgroup with the name: TIME DILATION, THE CLASSICAL ORIGIN !!!).
The original article may be retrieved using http://www.dejanews.com .
What you are going to read here is incredible, but true.
The fondamental hypothesis I am going to use is that ether is a gas of particules ABSOLUTELY NOT convected by matter but that the scalar hypersound-waves in ether reflect on matter or more exactly on the nucleus of frozen ether of the elementary particles and thus on matter (the way depending on frequency).
But it will be shown later that a nucleus of frozen ether of an elementary particle doesn't carry along ether, because it is continuously replaced by new ether particles by the standing hypersound-wave around it, while in motion in ether.
The name hypersound means a sound of very high frequency in the order of 1.23E(+20) Hz for the electron at rest.
For example, if you have an electromagnetic cavity in motion, the E.M. field produced by hypersound-waves propagates inside the cavity with the ether inside not carrying along at all by the walls, but these E.M. waves reflect on them (in my theory the E.M. field has an hypersound origin and the four Maxwell's equations are derived from the theory).
And obviously (incredibly), the formulas of the CLASSICAL Doppler effect must be used rigorously when there is a reflection.
I consider two mirrors A and B which form a resonator (for the hypersound-waves in ether of velocity c), separated by the distance L' (=B-A) and orthogonal to the X' axis of a Galileo's frame (x'= x-vt , t'=t) which will be considered at rest and in motion at the velocity v in ether in the purpose to compare the frequency detected inside.
-----------A----------------------------B------->>> K' frame
------------------------------------>>>> K rest frame
FIRST CASE: THE CAVITY AT REST.
An hypersound wave in ether is injected with a generator in the cavity and the frequency fo is chosen for a resonance. We consider now that no energy is lost by the cavity.
In this case, the standing wave is made of two travelling waves which travel in opposite directions which is A+ = sin[2.pi.fo(t-x/c)] in the positive way and A- = sin[2.pi.fo(t + x/c)] in the negative way.
The standing wave is obviously [A+]+[A-] = 2 sin[2.pi.fo.t].cos[2.pi.fo(x/c)].
As the wave length of each travelling wave is c/fo the round-trip of the sound-wave has an integer number n of wave-lengths (because the frequency fo has been chosen for a resonance of the cavity), that is to say: n =fo.L'/c.
The same way, the number of nodes (mirror's surfaces included) in the standing wave is n+1
SECOND CASE, CAVITY IN MOTION:
Now we are going to put the cavity in motion with its waves without oscillation of the cavity.
In this case, we must note here that the number of wavelengths along the round-trip (cyclic !) will not change if the cavity is not submitted to an oscillation. It is because we consider wave like sound-waves which may only be produced by an oscillation of the mirrors like a loudspeaker works.
But, now , obviously, due to the CLASSICAL DOPPLER EFFECT, the frequency in K (at rest) of the wave travelling in the positive way will be increased by the reflection on the left mirror (A) of the opposite wave (negative way), and the frequency of this opposite wave travelling in the negative way will decrease relatively to the positive travelling wave by the reflection of it on the right mirror (B).
I must remind here the rigorous formulas of the CLASSICAL DOPPLER EFFECT
teached in secondary school.
If a source of sound of frequency fo is in motion at velocity v, the frequency at the rear of it is fo.[c/(c+v)] and fo.[c/(c-v)] in front of it
If you are in motion at the velocity v relatively to a fix source of frequency fo, the frequency you detect is fo.[(c-v)/c] if you move away from it and fo.[(c+v)/c] if you approach it.
By combinaison of these formulas, you obtain immediately that if a wave of frequency fo falls on a mirror at velocity v, which move away from the wave, the frequency of the reflected wave decreases according to: f = fo.[(c-v)/(c+v)] (police radar !!!), and increases according to f = fo.[(c+v)/(c-v)] if the mirror is in motion in the opposite way as the incident travelling wave.
We go back to the resonator:
If we call f+ the increased frequency of the travelling wave in the positive way of the resonator and f- the one of the wave travelling in the negative way, we have: f- = f+.[(c-v)/(c+v)] because the right mirror is moving away from the incident wave.
But the reflected wave which reflect on the left mirror (which approches the reflected wave from the right mirror) is changed into F+ =[(c+v)/(c-v)].[f+].[(c-v)/(c+v)]=f+ and thus the phenomenon is cyclic.
Now, the travelling wave equations are A+ = sin[2.pi.(f+)(t-x/c)] in the positive way and A- = sin.[2.pi(f-)(t+x/c)]=sin.[2.pi(f+)[(c-v)/(c+v)](t+x/c)] in the negative way.
We are going to see now which are the frequencies f+' and f-' of the new wave equations in the moving frame K' in introducing the Galileo's transformations (x = x'+vt', t = t' ) in the original waves and we obtain: A+'= sin[2.pi.(f+)((c-v)/c)(t'-x'/(c-v))]
and A-' = sin.[2.pi.(f+)((c-v)/c)(t'+x'/(c+v))] and WE SEE that the FREQUENCY is UNIQUE for the two waves in K' and is: f'=(f+)[(c-v)/c)] .
We must express now the frequencies f+ and f- from the rest frame with the frequency f' inside the resonator (but don't forget that the resonator is in motion) and we have immediately:
f+ = f'[c/(c-v)] and f- = [(c-v)/(c+v)]f+ = f'[c/(c+v)]
and the wave equations are thus:
A+ = sin[2.pi.f'[c/(c-v)][t-x/c]]
A- = sin[2.pi.f'[c/(c+v)][t+x/c]] with the wave-lengths :
Lambda+ = (c-v)/f' and Lambda- = (c+v)/f'
Thus, the total number of wavelengths along the round-trip is :
n= L'[f'/(c-v) + f'/(c+v)] which according to what has been said must be the same as at rest: n.=.L'fo/c.
This yields the equation: L'[f'/(c-v) +f'/(c+v)]= L'fo/c which is the same as:
" f'=fo.(1-bb) " with b=v/c, a TIME DILATION !.
Now, if you agree with Lorentz (an intelligent man) that matter contracts
while in motion in ether according to L'1=L'.sqrt(1-bb) valid for the distance between the mirrors (made of matter), we have:
L'sqrt(1-bb)[f'/(c-v)+f'/(c+v)]=L'fo/c, that is to say:
" f' = fo.sqrt(1-bb) ", the CORRECT TIME DILATION.!!!!
I have to say here that the slight motion of one of the mirrors to Lorentz-contract the resonator, is without influence on the theory which remains true, because I need only the distance between the mirrors (resonator contracted) and to know the classical Doppler effect, nothing else !
Nevertheless, the slight motion of one mirror changes the frequencies of the waves and thus time dilation [1-bb to sqrt(1-bb) ].
In this case the wave equations are:
A+= sin[2.pi.fo.sqrt(1-bb)[c/(c-v)](t-x/c)] and
A-= sin[2.pi.fo.sqrt(1-bb)[c/(c+v)](t+x/c)] and the standing wave becomes:
which CONTAINS THE LORENTZ' TRANSFORMATIONS.
More, the first factor sinus is the DE BROGLIE WAVE, if fo is chosen of the following manner: fo= mcc/h where m is rest mass of the electron and h the Planck's constant.
More the frequency of the de Broglie wave: [mcc/h].[1/sqrt(1-bb)] increases with the velocity v, the same way as the mass of the electron in the Guye and Lavanchy experiment in 1915.
More, the Lorentz' contraction is a classical necessity in order to maintain an integer number of nodes between the mirrors equal to n+1 in the frame in motion K' like in the resonator at rest. To see that, we have to introduce the Galileo's transformations in the standing wave (obtained with the Lorentz' contraction):
2.sin[2.pi.fo[(t'(1-bb)-vx'/cc)/sqrt(1-bb)]]cos[2.pi.(fo/c)(x'/sqrt(1-bb))] where we see that the between nodes distance is [c/2.fo]sqrt(1-bb) contracted the same way as the distance between the mirrors and is thus invariable in the frame from rest to motion.
(To avoid a misunderstanding, I have to remind that the moving frame in which the calculations have been made is a Galileo's frame in which the Lorentz' contraction applies also).
A clear explanation of the origin of the Lorentz' contraction is given later when the wave structure of the electron will be established. It is also due to the classical Doppler effect.
THIS INCREDIBLE EXTREMELY SIMPLE CLASSICAL RESULTS have been the starting point of my electron theory made of hypersound waves which reflect on special surfaces and which is going to revolutionize the physics of this end of century, be sure !, even if a hard work remains to be done: to rebuild physics.
This is due to the fact, that the theory permits to demonstrate directly the Maxwell equations for vacuum, the Einsteinian equation E=Mcc (in the rest frame only), time dilation, length contraction, mass increase with velocity, permits to derive a new space-time theory in agreement with all the experiments in " agreement " with SR, like those not in agreement with it ether-wind detection), permits to understand the paradoxes of SR, and finally to build an explicative convincing theory of gravity.
The reader interested to see already an animation program about the wave structure of the electron on the computer screen has simply to send me an E-mail at:
firstname.lastname@example.org to ask it (free of any charge!,...except, may be, the Nobel Prize).
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