 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 2 2017, 12:00 AM 
Of course, Einstein's special relativity & Maxwell's wave theory agree
that the speed of light, relative to its source, is, always,
equal to c, in vacuum.
But that is true, ONLY, in the case, in which the light source
is assumed to be at rest relative to Maxwell's aether!
Is that amazing or what?
Einstein's special theory says that there is no aether.
That is on one hand.
On the other hand, Maxwell's electromagnetic theory says that the speed of light,
relative to its emitting source, will be equal to 299792458 m/s,
if and only if the same emitting source is at absolute rest
relative to the aether.
In short, Maxwell's idea about the constant speed of light is quite different
from Einstein's idea about the constant speed of the same light.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 14 2017, 12:00 AM 
As pointed out already, the entire calculations, by Michelson & Morley,
for their experiment, have used nothing else beside the speed of light
relative to the light source, such as (c + v) & (c – v), and the speed
of light relative to the observer such as (c + v) & (c – v), as well.
Let's, now, take a closer look at the MichelsonMorley calculations of the total flight
time of light in the vertical direction of the earth's motion, from the light source
to the transversal mirror, and then from that mirror to the detector.
And once again, the math, here, is quite simple:
If the light beam travels with a speed, c, at right angles to the direction,
in which the earth is traveling at a speed, v, THEN, according to the
Maxwellian assumption, on the basis of which the speed of light is independent
of the speed of the light source, the speed of MichelsonMorley beam relative
to the transversal mirror is equal to
[c^{2}  v^{2}]^{0.5}.
And therefore, the total travel time of the transversal beam
is equal to T_3; i.e.,
T_3 = 2L / [c^{2}  v^{2}]^{0.5}
And that is the final result of the calculations, by Michelson & Morley,
in the case of all light beams traveling in the transversal direction.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 18 2017, 12:00 AM 
According to the assumption that, the speed of light is independent of the speed
of the light source, therefore, the MichelsonMorley beam of light takes an interval
of time T_3 to travel a total distance 2L from the light source
to the moving transversal mirror, and from that mirror
to the moving detector; i.e.,
T_3 = 2L / [c^{2}  v^{2}]^{0.5}
Nonetheless, if it's assumed that Earth is at rest, then the same light beam takes
an interval of time T_0 to travel a distance 2L from the light source
to the horizontal mirror, and from that mirror
to the moving detector; i.e.,
T_0 = 2L / c.
And so, the time interval T_3 is longer
than the time interval T_0; i.e.,
T_3 > T_0.
But why is T_3 is greater than T_0?
It's, clearly, because the speed of light relative to the moving
mirror, [c^{2}  v^{2}]^{0.5}
is less than c; i.e.,
[c^{2}  v^{2}]^{0.5} < c.
It's quite clear and simple.
NOTE:
In this equation:
T_3 = 2L / [c^{2}  v^{2}]^{0.5}
the Factor Gamma makes its first appearance, this way:
T_3 = 2L/c x [1  v^{2}/c^{2}]^{0.5}.
And by merely looking at the above equation, George Francis FitzGerald
stumbled upon his idea of length contraction:
https://en.wikipedia.org/wiki/George_Francis_FitzGerald

 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 22 2017, 12:00 AM 
As demonstrated earlier, the amount of time, T_3, is greater than the amount of time,T_0,
because the speed of light relative to the moving mirror,
[c^{2}  v^{2}]^{0.5} is less than c.
Now, if the moving mirror is replaced with a moving observer, will, in this case,
the moving observer measure [c^{2}  v^{2}]^{0.5},
as the speed of light relative to him/her; OR will he/she find out
the relative speed of light is equal to c?
According to Maxwell's theory of electromagnetic radiation, the moving observer,
in this case, must always find out that the speed of light relative to him/her is
always equal to [c^{2}  v^{2}]^{0.5},
and nothing else.
Does that conflict, directly or indirectly, with the Maxwellian assumption, which
states that, the speed of light is independent of the speed of the light source?
The short answer is no.
The speed of light, [c^{2}  v^{2}]^{0.5}, relative to the
moving transversal observer does not conflict, directly or indirectly, with the
Maxwellian assumption, according to which the speed of light is independent
of the speed of the light source.
To the contrary, the relative speed of light, [c^{2}  v^{2}]^{0.5},
is a direct and necessary consequence of the Maxwellian assumption that,
the speed of light is independent of the speed of the light source.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 24 2017, 12:00 AM 
So, the speed of light, [c^{2}  v^{2}]^{0.5},
relative to the moving transversal observer is, perfectly consistent with Maxwell's
theory of electromagnetic radiation, according to which the speed of light
is assumed to be, completely, independent of the speed of the light source.
And consequently, whenever a moving transversal observer measures the speed of light,
he/she must always obtain a speed value equal to
[c^{2}  v^{2}]^{0.5}.
Is the relative speed of light, [c^{2}  v^{2}]^{0.5},
as measured by moving transversal observers, equivalent, in every respect, to light speed,
in vacuum, equal to [c ^{2}  v ^{2}] ^{0.5}?
Yep!
As far as moving transversal observers are concerned, a relative speed of light equal
to [c^{2}  v^{2}]^{0.5} is equivalent, in every aspect
of it, to a speed of light, in vacuum, equal
to [c^{2}  v^{2}]^{0.5}.
Does that equivalence contradict, in any shape or form, the Maxwellian assumption that,
the speed of light is independent of the speed of the light source?
Not at all.
In fact, the exact opposite is true.
The equivalence between a relative speed of light equal to [c^{2}  v^{2}]^{0.5}
and a speed of light, in vacuum, equal to [c ^{2}  v ^{2}] ^{0.5} is,
simply, a direct consequence of the Maxwellian assumption, on the basis of which,
the speed of light is independent of the speed of the light source.
Important Note:
A relative speed of light equal to [c^{2}  v^{2}]^{0.5}
is equivalent to c divided by the Factor Gamma; i.e.,
[c^{2}  v^{2}]^{0.5} = c/Gamma = c[1  v^{2}/c^{2}]^{0.5}

 roger
 Re: On the Motion of the Earth Relative to the Aether  November 24 2017, 9:33 AM 
yes, relativists misrepresent Maxwell's theory 
 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 26 2017, 12:00 AM 
That is true.
The relativists do misrepresent Maxwell's theory.
...............................................................................................................................
The MichelsonMorley calculations, for their experiment, on the basis
of the Maxwellian assumption, according to which the speed of light
is independent of the speed of the light source, are extremely important,
because they are the true foundations, upon which the theories
of Albert Einstein & Hendrik Lorentz have been built.
To put it differently, nobody can, really, see, or claim to see, very clearly,
what Albert Einstein & Hendrik Lorentz have been trying to do, in their theories,
without taking the trouble, first, to understand & have a better handle
on the 'nitty gritty' details of the MichelsonMorley calculations,
for their experiment, on the basis of the fundamental assumption
of Maxwell's theory of electromagnetic radiation, according to which
the speed of light is independent of the speed of the light source.
That is because it's selfevident that the physical theories of Albert Einstein
& Hendrik Lorentz, & Henri Poincaré as well, have been designed, specifically,
as auxiliary hypotheses to deal with the null result of the MichelsonMorley
experiment, and to keep the Maxwellian assumption, according to which
the speed of light is independent of the speed of the light source,
in spite of it, and to save it from being,
experimentally, falsified by it.
Now, just pose, to yourself,
this simple question:
From where did Albert Einstein & Hendrik Lorentz import,
into their theories, the factor:
[1 – v^{2}/c^{2}]^{0.5}?
And, of course, the answer to the above question is:
Albert Einstein & Hendrik Lorentz have imported, into their theories,
the factor [1 – v^{2}/c^{2}]^{0.5},
directly, from the MichelsonMorley calculations.

 Bill Geist
 Re: On the Motion of the Earth Relative to the Aether  November 26 2017, 1:56 PM 
 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 28 2017, 12:00 AM 
Yes . . .
It is!
...............................................................................................................................................
Indeed, it's true that Albert Einstein & Hendrik Lorentz have imported,
into their theories, the factor [1 – v^{2}/c^{2}]^{0.5},
from no place else, beside the MichelsonMorley calculations,
for their widely publicized and very famous experiment.
And from where did Albert Einstein & Hendrik Lorentz import, into their theories,
the factor {1/[1 – v^{2}/c^{2}]^{0.5}}?
Once again, the correct answer
has to be this:
Albert Einstein & Hendrik Lorentz have imported, into their theories,
the factor 1/[1 – v^{2}/c^{2}]^{0.5}},
directly, from its original source; i.e, the MichelsonMorley calculations,
for their widely publicized and wellknown experiment.
Why did Albert Einstein & Hendrik Lorentz, in their theories, choose to shorten
the light path, in the forward direction of any sort of inertial motion by a factor
equal, always, to [1 – v^{2}/c^{2}]^{0.5}?
And, of course, the right answer,
once again, is this:
Albert Einstein & Hendrik Lorentz have chosen, in their theories, to shorten
the light path, in the forward direction of every uniformly linear motion by
a factor equal, always, to [1 – v^{2}/c^{2}]^{0.5},
because & only because of the MichelsonMorley calculations & the null result
of the MichelsonMorley experiment.
And so, the MichelsonMorley calculations, for their experiment, based on the Maxwellian
assumption, according to which the speed of light is independent of the speed
of the light source, are, within the present context, very important.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  November 30 2017, 12:00 AM 
Certainly, the MichelsonMorley calculations, for their experiment,
based on the Maxwellian assumption, according to which the speed
of light is independent of the speed of the light source, are an
important key for understanding the original motivation and making
sense of the bizarre and nonsensical things, which Albert Einstein
& Hendrik Lorentz have come up with, in their highly
counterintuitive and bizarre theories.
So, let's, now, examine the MichelsonMorley calculations, one more time,
in order to make sure those calculations are errorfree
and mathematically correct.
For beams of light traveling, in the longitudinal direction, the MichelsonMorley
calculations are quite intuitive and easy to fully understand
at first glance.
The MichelsonMorley light beam travels with a speed, c, in the same direction,
in which the earth is traveling at a speed, v; while, at the same time, the MichelsonMorley
horizontal mirror is traveling, away from that light beam, at a speed, v; and hence, if
the light beam takes an interval of time, T_1, to reach the horizontal mirror, that mirror
(itself) must move, during the same interval of time, a distance equal to vT_1; i.e.,
the light path becomes longer & equal
to (L + vT_1):
T_1 = [L + vT_1] / c = L / (c – v).
And since, according to Maxwell's theory, the mirror reflects the incident beam back
at the same speed c, the reflected beam takes an amount of time, T_2,
to reach a detector at a distance, L, away; and which is approaching
the reflected light with a speed, v,; i.e.,
the light path, in this case, becomes shorter & equal
to (L  vT_2):
T_2 = [L  vT_2] / c = L / (c + v).
And so, the total travel time of the light beam, in the longitudinal direction,
is equal to T:
T = T_1 + T_2 = 2L{ c / (c^{2} – v^{2})}.
And that is the final result of the calculations, by Michelson & Morley,
in the case of all light beams traveling in the longitudinal direction.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 2 2017, 12:02 AM 
As explained above, in the case of light beams traveling,
in the longitudinal direction, the MichelsonMorley
calculations are quite clear and easy
to understand right away.
For light beams traveling at right angles to the velocity vector
of Earth, the MichelsonMorley calculations, however,
are a little bit more complicated.
According to MichelsonMorley calculations, based on the assumption
that, the speed of light is independent of the speed of the light source,
the transversal beam of light takes an interval of time T_3 to travel
a total distance 2L from the light source to the moving transversal
mirror, and from that mirror to the moving detector:
T_3 = 2L / [c^{2}  v^{2}]^{0.5}
But why is the speed of the transversal beam, relative to the moving mirror,
equal to [c ^{2}  v ^{2}] ^{0.5}; and NOT equal,
for instance, to [c^{2} + v^{2}]^{0.5}?
Well, obviously, it's because, on the basis of the assumption,
according to which, the speed of light is independent of the speed
of the light source, the transversal beam is drifting in the backward
direction relative to the moving transversal mirror & relative
to the moving detector as well.
It is as simple as that!

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 4 2017, 12:00 AM 
Of course, based on the assumption, according to which, the speed of light
is independent of the speed of the light source, the transversal beam is drifting
in the backward direction relative to the moving transversal mirror & relative
to the moving detector as well.
Here is a more detailed second method,
for calculating T_3:
The total path of the transversal beam, in the MichelsonMorley experiment,
forms an isosceles triangle, like this:
& whose height is equal to L; and whose base
is equal to vT_3;
where v is the orbital velocity of the earth.
And accordingly, T_3 can be computed
by using this equation:
T_3 = {2[(0.5vT_3)^{2} + L^{2}]^{0.5}} / c = 2L / [c^{2}  v^{2}]^{0.5}.
Q.E.D.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 6 2017, 12:00 AM 
So, the total path of the transversal beam, in the MichelsonMorley experiment,
forms an isosceles triangle, which looks like this one:
whose height is equal to L; and whose base is equal
to vT_3; & where v is the orbital velocity
of the earth.
But what is the main cause behind the inclination of the path of incident
light with respect to the transversal mirror?
The stationary path of the transversal beam is, of course, set,
by Michelson & Morley, to be at right angles to the reflecting
surface of the stationary transversal mirror.
However, due to the motion of the transversal mirror, the transversal
beam is drifting in the backward direction relative to the moving mirror;
i.e., the transversal mirror is receding away from the incident light beam.
And as a result, the direction of combined relative velocity of the mirror
and the incident light beam must coincide with the first side
of the above triangle.
And furthermore, according to the rules of reflections, as defined within
the framework of the Maxwellian theory, the transversal mirror must reflect
the incident light beam, towards the moving detector, along the second side
of the same isosceles triangle.
It follows, therefore, that the total path of the transversal beam is equal
to 2[(0.5vT_3)^{2} + L^{2}]^{0.5},
in accordance with the Pythagorean theorem as applied to the two
triangles, of which the above isosceles triangle,
for the total path, is composed.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 8 2017, 12:00 AM 
Is it possible, on the basis of the assumption, according to which,
the speed of light is independent of the speed of the light source,
to calculate the total travel time, T_3, for the MichelsonMorley
transversal beam, by dividing the light path:
2[(0.5vT_3)^{2} + L^{2}]^{0.5}
by the velocity of the transversal beam:
[c^{2}  v^{2}]^{0.5}
relative to the moving mirror?
No.
It's, mathematically, invalid to divide the path expression,
2[(0.5vT_3)^{2} + L^{2}]^{0.5},
by the relative velocity,
[c^{2}  v^{2}]^{0.5}.
The total path,
2[(0.5vT_3)^{2} + L^{2}]^{0.5},
must be divided by the velocity of, c, only.
That is because the velocity of the transversal mirror, v, is already
included in the equation, for calculating T_3;
i.e., this entire equation:
T_3 = {2[(0.5vT_3)^{2} + L^{2}]^{0.5}} / c = 2L / [c^{2}  v^{2}]^{0.5}
which has been, right from the start, constructed & built upon the fundamental
concept of relative velocity of light.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 10 2017, 12:00 AM 
Now, look, closely & very carefully, at these
two MichelsonMorley formulas:
1. Formula #1:
T = T_1 + T_2 = 2L*{ c / (c^{2} – v^{2})},
for calculating the total time of flight of the MichelsonMorley
horizontal light beam.
2. & Formula #2:
T_3 = 2L / [c^{2}  v^{2}]^{0.5},
for calculating the total time of flight of the MichelsonMorley
transversal light beam.
Believe it or not, the whole mathematics of the three physical theories,
by the three mathematical physicists, Albert Einstein, Hendrik Lorentz
& Henri Poincaré, has been, totally, designed and built, absolutely,
on nothing else beside the two MichelsonMorley
formulas listed above.
Is that amazing or what?

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 12 2017, 12:01 AM 
The fringe shift, which Michelson & Morley have been looking for, depends
on the phase difference between the longitudinal light beam and the transversal
light beam, in their experiment.
But that phase difference, itself, depends, necessarily, upon the numerical difference
between the total travel time of the longitudinal light beam, T,
and the total travel time of the transversal light beam, T_3,
in that experiment.
As demonstrated earlier, in the MichelsonMorley experiment, the total travel time
of the longitudinal light beam, T, is calculated
by using the following formula:
T = T_1 + T_2 = 2L*{ c / (c^{2} – v^{2})}.
& the total travel time of the transversal light beam, T_3, is computed
by using this formula:
T_3 = 2L / [c^{2}  v^{2}]^{0.5}.
And it follows, therefore, that the numerical difference, Delta_T,
between the total travel time of the longitudinal light beam & the total
travel time of the transversal light beam, in the MichelsonMorley experiment,
is equal to (T – T_3); i.e.,
Delta_T = T  T_3 = 2L*{c / (c^{2} – v^{2}  2L / [c^{2}  v^{2}]^{0.5}.
And accordingly, Delta_T, in the MichelsonMorley experiment,
must have this value:
Delta_T = {2L / c} *{(1  [1  v^{2}/c^{2}]^{0.5}) / (1  v^{2}//c^{2})} .

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 14 2017, 12:00 AM 
So, on the basis of of the assumption, according to which, the speed of light is independent
of the speed of the light source, the numerical difference, Delta_T, between the total travel
time of the longitudinal light beam & the total travel time of the transversal light beam,
in the MichelsonMorley experiment, is calculated by using this MichelsonMorley formula:
Delta_T = {2L / c} *{(1  [1  v^{2}//c^{2}]^{0.5}) / (1  v^{2}//c^{2})} .
Now, take a closer look at this mathematical term,
in the above equation:
[1  v^{2}/c^{2}]^{0.5}.
Relativists call it the reciprocal of the 'Lorentz Factor'.
But they should have, properly, called it the 'MichelsonMorley Factor;
shouldn't they?
This very special MichelsonMorley term can be found everywhere, within the theoretical
framework of each one of the three physical theories, which have been put forward,
by the three theoretical physicists, Albert Einstein & Hendrik Lorentz
& Henri Poincaré, in order to explain away the null result
of the MichelsonMorley experiment.
Why is it everywhere, in those three theories?
Well, it's, mainly, because that mathematical term plays a central role
in each and every one of the MichelsonMorley formulas.

 Bill Geist
 Re: On the Motion of the Earth Relative to the Aether  December 15 2017, 5:50 AM 
 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 16 2017, 12:00 AM 
Hello, Bill Geist:
Thomas J. Roberts says that: "In short, this is every experimenter’s nightmare:
he was unknowingly looking at statistically insignificant patterns in his systematic
drift that mimicked the appearance of a real signal":
https://arxiv.org/ftp/physics/papers/0608/0608238.pdf
.................................................................................................................................................................................
Let's look, closely, once again, at This MichelsonMorley equation, for computing
the numerical difference, Delta_T, between the total travel time of
the longitudinal light beam & the total travel time
of the transversal light beam:
Delta_T = {2L / c} *{(1  [1  v^{2}/c^{2}]^{0.5}) / (1  v^{2}/c^{2})} .
In the 'good old' days, many physics textbooks, on the three physical theories
of Albert Einstein & Hendrik Lorentz & Henri Poincaré, used to call the above
MichelsonMorley mathematical term; i.e.,
[1  v^{2}/c^{2}]^{0.5},
the 'Lorentz factor'.
Nowadays, however, it's called, by those textbooks, the reciprocal
of the 'Lorentz factor'.
So, keep that in mind!
And, now, let's rewrite the aforementioned mentioned MichelsonMorley equation
in this form:
Delta_T = {2L / c} *{([1  v^{2}/c^{2}]^{0.5}  1) / [1  v^{2}/c^{2}]^{0.5}} .
What do the physics textbooks, on the three physical theories of Albert Einstein
& Hendrik Lorentz & Henri Poincaré, now, label or call this new MichelsonMorley
mathematical term:
[1  v^{2}/c^{2}]^{0.5}?
Those physics textbooks, on the three physical theories of Albert Einstein & Hendrik Lorentz
& Henri Poincaré, now, call the new MichelsonMorley mathematical term;
the 'Gamma factor', and, of course, more often than not,
the 'Lorentz factor'.
And it follows, therefore, that the Gamma factor is nothing more than the reciprocal
of the 'goodold' Lorentz factor.
But, clearly, those two mathematical factors should have been named, in all physics textbooks,
after Michelson & Morley, & not after Hendrik Lorentz or anybody else.

 AAF
 Re: On the Motion of the Earth Relative to the Aether  December 18 2017, 12:00 AM 
It's very clear that the reciprocal Lorentz factor,
[1  v^{2}/c^{2}]^{0.5},
as well as the Gamma factor,
[1  v^{2}/c^{2}]^{0.5},
are all over the place, mentioned over and over again, & used a lot
and so many times, throughout the three physical theories of
Albert Einstein & Hendrik Lorentz & Henri Poincaré.
But, here, the big question, once again,
is this:
Why do the three physical theories, by the three mathematical physicists 
Albert Einstein & Hendrik Lorentz & Henri Poincaré –
employ & apply & use, over and over again, the reciprocal
Lorentz factor & the Gamma factor?
It's, certainly, because those three physical theories are, in fact, helper hypotheses
that have been designed, by Albert Einstein & Hendrik Lorentz & Henri Poincaré,
for one main purpose & one main purpose only; i.e., for saving the assumption,
according to which, "light is propagated in vacant space, with a velocity
c which is independent of the nature of motion of the emitting body"
from the null result of the MichelsonMorley experiment.
And so, the reciprocal Lorentz factor & the Gamma factor are two important tools,
for getting rid of the MichelsonMorley difference, Delta_T, between
the total travel time of the longitudinal light beam & the total travel time
of the transversal light beam:
Delta_T = {2L / c} *{([1  v^{2}/c^{2}]^{0.5}  1) / [1  v^{2}/c^{2}]^{0.5}} .
 
   

