## On the Motion of the Earth Relative to the Aether

AAF
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

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
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

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 Michelson-Morley 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 Michelson-Morley beam relative
to the transversal mirror is equal to
[c2 - v2]0.5.

And therefore, the total travel time of the transversal beam
is equal to T_3; i.e.,

<font size="4">T_3 = 2L / [c2 - v2]0.5</font>

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
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

According to the assumption that, the speed of light is independent of the speed
of the light source, therefore, the Michelson-Morley 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 / [c2 - v2]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, [c2 - v2]0.5
is less than c; i.e.,

[c2 - v2]0.5 < c.

It's quite clear and simple.

NOTE:

In this equation:

T_3 = 2L / [c2 - v2]0.5

the Factor Gamma makes its first appearance, this way:

T_3 = 2L/c x [1 - v2/c2]-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
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

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,
[c2 - v2]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 [c2 - v2]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 [c2 - v2]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 speed of light, [c2 - v2]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, [c2 - v2]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
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

So, the speed of light, [c2 - v2]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
[c2 - v2]0.5.

Is the relative speed of light, [c2 - v2]0.5,
as measured by moving transversal observers, equivalent, in every respect, to light speed,
in vacuum, equal to [c2 - v2]0.5?

Yep!

As far as moving transversal observers are concerned, a relative speed of light equal
to [c2 - v2]0.5 is equivalent, in every aspect
of it, to a speed of light, in vacuum, equal
to [c2 - v2]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 [c2 - v2]0.5
and a speed of light, in vacuum, equal to [c2 - v2]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 [c2 - v2]0.5
is equivalent to c divided by the Factor Gamma; i.e.,

[c2 - v2]0.5 = c/Gamma = c[1 - v2/c2]0.5

roger
roger

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

yes, relativists misrepresent Maxwell's theory

AAF
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

That is true.

The relativists do misrepresent Maxwell's theory.

...............................................................................................................................

The Michelson-Morley 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 Michelson-Morley 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 self-evident 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 Michelson-Morley
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 – v2/c2]0.5?

And, of course, the answer to the above question is:

Albert Einstein & Hendrik Lorentz have imported, into their theories,
the factor [1 – v2/c2]0.5,
directly, from the Michelson-Morley calculations.

Bill Geist
Bill Geist

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

See
http://www.network54.com/Forum/304711/t ... of+science

AAF
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

Yes . . .

It is!

...............................................................................................................................................

Indeed, it's true that Albert Einstein & Hendrik Lorentz have imported,
into their theories, the factor [1 – v2/c2]0.5,
from no place else, beside the Michelson-Morley 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 – v2/c2]0.5}?

has to be this:

Albert Einstein & Hendrik Lorentz have imported, into their theories,
the factor 1/[1 – v2/c2]0.5},
directly, from its original source; i.e, the Michelson-Morley calculations,
for their widely publicized and well-known 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 – v2/c2]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 – v2/c2]0.5,
because & only because of the Michelson-Morley calculations & the null result
of the Michelson-Morley experiment.

And so, the Michelson-Morley 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
AAF

<font size="5">On the Motion
of the Earth Relative to the Aether
</font>

"Examples of a similar kind such as the unsuccessful attempt to substantiate the motion of the earth relative to the "Light-medium" lead us to the supposition that not only in mechanics, but also in electrodynamics, no properties of observed facts correspond to a concept of absolute rest; but that for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also, as has already been shown for magnitudes of the first order. In the following we make these assumptions (which we shall subsequently call the Principle of Relativity) and introduce the further assumption, —an assumption which is at the first sight quite irreconcilable with the former one— that light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body. These two assumptions are quite sufficient to give us a simple and consistent theory of electrodynamics of moving bodies on the basis of the Maxwellian theory for bodies at rest. The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place":

https://en.wikisource.org/wiki/On_the_E ... ing_Bodies_(1920_edition)

Yep . . .

Back to Einstein!

And that is because Colleague Ufonaut99; after 15 consecutive
months of defending Einstein's false notion of relative axial rotation and,
rigorously & vigorously, arguing for it, apparently, his case has, at last
& finally, run out of gas, completely:

http://www.network54.com/Forum/304711/t ... instein%21

Certainly, the Michelson-Morley 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
counter-intuitive and bizarre theories.

So, let's, now, examine the Michelson-Morley calculations, one more time,
in order to make sure those calculations are error-free
and mathematically correct.

For beams of light traveling, in the longitudinal direction, the Michelson-Morley
calculations are quite intuitive and easy to fully understand
at first glance.

The Michelson-Morley 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 Michelson-Morley
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 / (c2 – v2)}<i></i>.

And that is the final result of the calculations, by Michelson & Morley,
in the case of all light beams traveling in the longitudinal direction.