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Empirically Refuted Superluminal Velocities.



 
 
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  #1  
Old October 29th 03, 04:24 AM
EL
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

[EL]
Randy wrote
{{{
[Randy]
I'm going to ask you again, politely, to please
look at my derivation, in which I took:

- one wave moving at speed v1
- another wave of higher frequency moving at speed 1.5*v1
- summed together they give a wave packet with peaks
wherever they are in phase (wavelength 3*lambda1 where
lambda1 = wavelength of first wave)

and showed
- the peaks of that wave packet propagate at 3*v1

This demonstrates that by taking a sum of waves with the
property that higher frequency wave move faster, I get
a wave packet that moves much faster than any individual
wave.

- Randy
}}}

And per his request I decided to include his example here to test its
physical validity while having confidence in Randy's mathematical
knowledge.
His example is included complete with his comments and my comments
would be interleaved.

{{{
[Randy]
Suppose we have a really simple wave composed of two
frequencies, f1 and f2. Let us suppose that f2 = 2f1.
Let us also suppose that the speed of propagation for
wave 1 is v, and for wave 2 is 1.5v. So the higher
frequency wave (wave 2) has 50% higher velocity.

The wave is described by
S(x,t) = cos(2*pi*f1*(x/v1 - t)) + cos(2*pi*f2*(x/v2 - t))

You should first make sure you believe that. Each term
describes a wave which is:
- constant for x - v*t = constant
- for fixed t, has spatial period (wavelength)
v/f = lambda
- for fixed x, has temporal period 1/f1
- has phase 0 at x = 0, t = 0.

The first wave has a wavelength of v1/f1 = lambda1, the
second has a wavelength of v2/f2 = (1.5*v1)/(2*f2)
= (3/4)*lambda1
}}}

[EL]
This is a very small glitch and here is the correction.
v2/f2 = (1.5*v1)/(2*f1)

{{{
[Randy]
So every 4 wavelengths of wave 2 corresponds to
3 wavelengths of wave 1, and the packet is in phase
every 4*lambda2 = 3*lambda1. If you fix time t, you
will see the waves add up constructively at x=0
and every 4*lambda1 afterward. These peaks will move
as the wave moves. The rate of advance of the peaks
will be the group velocity, as it is the motion of our
coherent pulse.

So let's analyze what happens as time evolves. Suppose
it is no longer time 0, but a little later, time T.
}}}

[EL]
Here I would like to emphasize on the word "later".
In fact, relativity did not screw anything else than the conception of
time and certainly every thing else consequently.
The classical calculation of wave modulation represented by Randy is
quite legitimate but the problem is in the interpretation of time
"what happens where".
Bare with me because this example should be a perfect example to see
what relativity destroyed, it destroyed the ability of quality minds
to distinguish between reckless sequencing and the impeccable
precision of logical event sequencing.

{{{
[Randy]
The phase of wave 1 is f1*(x/v1-T) and of wave 2 is
f2*(x/v2-T) = 2*f1*(x/(1.5*v1)-T)

These phases are equal where
f1*x/v1 - f1*T = 1.33*f1*x/v1 - 2*f1*T

or f1*T = 0.33*f1*x/v1

or x = 3*v1*T
}}}

[EL]
As you have noticed that I emphasized on the word "later", I would
like to drive the attention of the reader to some facts. When we draw
a graph representing a wave with time on the x-axis and amplitude on
the y-axis, we should pay attention to the meaning of zero time and
positive time more than zero where zero time comes first and more than
zero time comes "later".
This means that looking at the wave graph we should imagine the wave
evolving towards the left side and not to the right side as in
oscilloscopes where raster scanning begins at the left side of the
screen.
The implication of this fact is so great but quite overlooked by many
physicists and almost all mathematicians who take the hype O thesis
from physicists for granted.

Randy demonstrated that x = 3.v1.T, where the product of velocity and
time is a distance of course and that distance is where identifiable
group-wave-peaks may appear in LATER.

I shall not discuss the out-of-synchronisation artefacts of
oscilloscopes here again as you can read it up in this thread.
Now I shall focus on the paper graph and what the physical meaning of
wave modulation means.

It is quite easy to confuse the Time versus Amplitude chart with
velocity chart where Time is versus distance.
If you can avoid that confusion then that is precisely what we need
from the reader here.

{{{
[Randy]
The place where the waves are in phase has moved by a
distance 3*v1*T in time T.
}}}

As you can read in Randy's own statement, he used the expression "a
distance in time T".
We know that the velocity v1 is the distance per unit time traversed
by the wave W1.
We know that the velocity v2 is the distance per unit time traversed
by the wave W2.
To understand how the modulation proceeds we need a spatial reference
GATE through which the two waves propagate and modulate. That gate is
an infinite plane placed orthogonal to the waves' propagational
direction axis, assuming that they are coincident in direction.
T must be a multiple of time units in which a finite portion of each
wavelength is propagating through the medium and across our
referential gate.
Now that portion of the wave is what advances in one time unit.
So what does that distance [3.v1.T] mean?
Randy said that there is a periodically repeating event at which the
two waves become in phase once more and then go out of phase for some
time.
Here are Randy's own words again.
"So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave
1"
Naturally W2 is given to be faster than W1 such that every 4 cycles of
W2 correspond to 3 cycles of W1.
The resulting modulation IS a consequence of those two physical
velocities of wave propagation in Length over time dimensions.

{{{
[Randy]
Thus, the peak appears to
be moving forward at 3*v1, despite the fact that
one wave is moving at v1 and the other at 1.5*v1.
As the whole thing has a spatial periodicity of 3*lambda1,
you will find that all of the peaks, spaced 3*lambda1
apart, are similarly marching forward at 3*v1.
}}}

[EL]
This is the crux of the confusion.
Here we ask; what is it that is moving forward and relative to what?
In this particular case, as time advances, the difference in the two
velocities causes the in-phase event to show up at our referential
gate at regular time intervals when 3 cycles of W1 have passed through
the gate or 4 cycles of W2 have passed through the gate.

This means that the frequency of the in-phase event is a Third of the
frequency of W1 or a Quarter of the frequency of W2 if we assumed
proper time to dominate such frequencies.

Let us call this in-phase frequency F, then;

F = f1/3 = f2/4
Hence f2 = 4/3 f1, which contradicts our premise where we assumed that
f2 = 2 f1.

Something hidden must be screwed up here; can you guess what is it?

TIME.

Good guess!

If wave number one was 1000 Hz and wave number two was 2000 Hz then
our referential gate must be THE OBSERVER through which relative
velocities cause a frequency shift, such that 1000 complete cycles are
introduced less frequently than 2000 complete cycles being introduced
more frequently.

Here we propose a standard time window of one proper second in which
1000 complete cycles of wave number one happens and 2000 complete
cycles of wave number two happens concurrently.

By taking the proper time window during which W1 passes through the
gate of observation at its own velocity as our standard time frame we
realise that W2 introduces 3000 complete cycles rather than 2000
because the velocity of observation is 1.5 times faster. This means
that from the Observational gate's point of view the number of
complete cycles of W2 within one time window is 3 times greater than
the complete cycles encountered from W1 and it is not the velocity of
anything at all. When those two waves interfere the less frequent wave
becomes an envelope for the more frequent wave Such that each
composite wave is W1 subdivided into 3 cycles of W2.

This modulated wave becomes a moving reference envelope inside which
the other wave is moving and we end up with (v2/v1).(f2/f1) being a
dimensionless product of ratios that would yield the number 3 that
means nothing in physical essence.

You can see clearly that we could have taken the faster wave as the
reference to which modulation is happening less frequent rather than
more frequent.

So we have the observational freedom to see the faster wave slipping
forward inside the slower wave or to see the slower wave as a
peristaltic motion moving backwards over the faster wave as a
modulation of some constant peak amplitude.

Here I would like to make a historical declaration.
The observational gate that I have proposed does not observe any
velocities once both wavefronts have arrived and being observed, and
all that that gate could observe is the frequency of events because
the gate is stationary in the space of both wave velocities.

You could repeat this exercise by assuming a gate on a railway and let
one train be 1.5 times faster than the other train but both arrive at
the gate simultaneously. Let the size of the cars be twice longer on
the slow train and record your observations regarding the coincidence
of car-joints on both trains.
The gate-observer may have a clock but all he may observe is a
frequency of coincidences and no velocities are perceived at all. The
true velocities are what the trains' wheels make on the iron railway.

This in-phase frequency (car-joints on both trains coinciding) may be
(as in our example) the frequency of 3 cars on the slow train or 4
cars on the fast train.
Now we have two lambdas and one frequency so how can you decide on a
single velocity?

3 cars take 3 times as much as one to pass on the slow train and 4
cars take 4 times as much as one to pass on the fast train. The static
length of 3 slow cars is equivalent to 6 fast cars not 4 and that is
what Lorentz Fitzgerald contraction is all about. Time dilation
follows if we compare times and fix the lengths.

So this idiotic game of juggling numbers makes no physics and makes no
science.

We can hybridize mathematics and physics and come up with negative
dispersion, time dilation, length contraction, black holes and big
bangs, but for what end is this clownish path taking us Randy?

What is so funny and pleasing in ****ing with innocent minds?
There are so many people out there that believe that such fiction is
true and real.
I am seriously asking why.
Why the academic establishment allows this comedy?
Are all scientists becoming incompetent to realise and figure out how
this modern wave of fiction is screwing with their sanity and sound
logic?

I see Lemmings, plenty of them, all the time and everywhere.
Rarely do I see like those men that made the solid foundations on
which we stand today.
Lemmings and clones are what the academic institutions are producing
today.

Perhaps it is time for humans to go extinct and rid nature from the
asshole species.

EL

{{{
[Randy]
The fact that their point of coincidence can move
forward faster than either wave alone is a consequence
of the shorter wave moving faster than the longer one.
In other words, of the longer wave having higher index
of refraction, or of dn/df being negative.

If the longer wave moved faster (had lower index of
refraction), you would not get this "superluminal"
effect.

You can do everything I just did in the more general
case of a complex, multi-frequency wave packet and
an arbitrary slope. You can further work out that
there is no information being propagated at speed v1.

This has nothing to do with relativity. It's pure
classical wave physics, analyzing sines and cosines.

- Randy
}}}
  #2  
Old October 29th 03, 06:56 AM
Minor Crank
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

"EL" wrote in message
om...

- one wave moving at speed v1
- another wave of higher frequency moving at speed 1.5*v1
- summed together they give a wave packet with peaks
wherever they are in phase (wavelength 3*lambda1 where
lambda1 = wavelength of first wave)

and showed
- the peaks of that wave packet propagate at 3*v1

This demonstrates that by taking a sum of waves with the
property that higher frequency wave move faster, I get
a wave packet that moves much faster than any individual
wave.


So what? This demonstrates absolutely nothing that is in violation of
relativity.

The superlimunal propagation of the wave packet depends on the prior
existence of its constituents that add to make it up. So, it can easily
race along at greater than c if those constituent trains are already in
existence.

But no information is being transferred, because all of the info encoded in
each train is already spread throughout all space, from the origin to the
target. The constituent trains need to reach the target first (at speed c),
in order to form the "red carpet" along which the wave packet can then
travel at any speed.

Minor Crank


  #3  
Old October 29th 03, 11:26 AM
EL
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

[EL]
Randy wrote
{{{
[Randy]
I'm going to ask you again, politely, to please
look at my derivation, in which I took:

- one wave moving at speed v1
- another wave of higher frequency moving at speed 1.5*v1
- summed together they give a wave packet with peaks
wherever they are in phase (wavelength 3*lambda1 where
lambda1 = wavelength of first wave)

and showed
- the peaks of that wave packet propagate at 3*v1

This demonstrates that by taking a sum of waves with the
property that higher frequency wave move faster, I get
a wave packet that moves much faster than any individual
wave.

- Randy
}}}

And per his request I decided to include his example here to test its
physical validity while having confidence in Randy's mathematical
knowledge.
His example is included complete with his comments and my comments
would be interleaved.

{{{
[Randy]
Suppose we have a really simple wave composed of two
frequencies, f1 and f2. Let us suppose that f2 = 2f1.
Let us also suppose that the speed of propagation for
wave 1 is v, and for wave 2 is 1.5v. So the higher
frequency wave (wave 2) has 50% higher velocity.

The wave is described by
S(x,t) = cos(2*pi*f1*(x/v1 - t)) + cos(2*pi*f2*(x/v2 - t))

You should first make sure you believe that. Each term
describes a wave which is:
- constant for x - v*t = constant
- for fixed t, has spatial period (wavelength)
v/f = lambda
- for fixed x, has temporal period 1/f1
- has phase 0 at x = 0, t = 0.

The first wave has a wavelength of v1/f1 = lambda1, the
second has a wavelength of v2/f2 = (1.5*v1)/(2*f2)
= (3/4)*lambda1
}}}

[EL]
This is a very small glitch and here is the correction.
v2/f2 = (1.5*v1)/(2*f1)

{{{
[Randy]
So every 4 wavelengths of wave 2 corresponds to
3 wavelengths of wave 1, and the packet is in phase
every 4*lambda2 = 3*lambda1. If you fix time t, you
will see the waves add up constructively at x=0
and every 4*lambda1 afterward. These peaks will move
as the wave moves. The rate of advance of the peaks
will be the group velocity, as it is the motion of our
coherent pulse.

So let's analyze what happens as time evolves. Suppose
it is no longer time 0, but a little later, time T.
}}}

[EL]
Here I would like to emphasize on the word "later".
In fact, relativity did not screw anything else than the conception of
time and certainly every thing else consequently.
The classical calculation of wave modulation represented by Randy is
quite legitimate but the problem is in the interpretation of time
"what happens where".
Bare with me because this example should be a perfect example to see
what relativity destroyed, it destroyed the ability of quality minds
to distinguish between reckless sequencing and the impeccable
precision of logical event sequencing.

{{{
[Randy]
The phase of wave 1 is f1*(x/v1-T) and of wave 2 is
f2*(x/v2-T) = 2*f1*(x/(1.5*v1)-T)

These phases are equal where
f1*x/v1 - f1*T = 1.33*f1*x/v1 - 2*f1*T

or f1*T = 0.33*f1*x/v1

or x = 3*v1*T
}}}

[EL]
As you have noticed that I emphasized on the word "later", I would
like to drive the attention of the reader to some facts. When we draw
a graph representing a wave with time on the x-axis and amplitude on
the y-axis, we should pay attention to the meaning of zero time and
positive time more than zero where zero time comes first and more than
zero time comes "later".
This means that looking at the wave graph we should imagine the wave
evolving towards the left side and not to the right side as in
oscilloscopes where raster scanning begins at the left side of the
screen.
The implication of this fact is so great but quite overlooked by many
physicists and almost all mathematicians who take the hype O thesis
from physicists for granted.

Randy demonstrated that x = 3.v1.T, where the product of velocity and
time is a distance of course and that distance is where identifiable
group-wave-peaks may appear in LATER.

I shall not discuss the out-of-synchronisation artefacts of
oscilloscopes here again as you can read it up in this thread.
Now I shall focus on the paper graph and what the physical meaning of
wave modulation means.

It is quite easy to confuse the Time versus Amplitude chart with
velocity chart where Time is versus distance.
If you can avoid that confusion then that is precisely what we need
from the reader here.

{{{
[Randy]
The place where the waves are in phase has moved by a
distance 3*v1*T in time T.
}}}

As you can read in Randy's own statement, he used the expression "a
distance in time T".
We know that the velocity v1 is the distance per unit time traversed
by the wave W1.
We know that the velocity v2 is the distance per unit time traversed
by the wave W2.
To understand how the modulation proceeds we need a spatial reference
GATE through which the two waves propagate and modulate. That gate is
an infinite plane placed orthogonal to the waves' propagational
direction axis, assuming that they are coincident in direction.
T must be a multiple of time units in which a finite portion of each
wavelength is propagating through the medium and across our
referential gate.
Now that portion of the wave is what advances in one time unit.
So what does that distance [3.v1.T] mean?
Randy said that there is a periodically repeating event at which the
two waves become in phase once more and then go out of phase for some
time.
Here are Randy's own words again.
"So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave
1"
Naturally W2 is given to be faster than W1 such that every 4 cycles of
W2 correspond to 3 cycles of W1.
The resulting modulation IS a consequence of those two physical
velocities of wave propagation in Length over time dimensions.

{{{
[Randy]
Thus, the peak appears to
be moving forward at 3*v1, despite the fact that
one wave is moving at v1 and the other at 1.5*v1.
As the whole thing has a spatial periodicity of 3*lambda1,
you will find that all of the peaks, spaced 3*lambda1
apart, are similarly marching forward at 3*v1.
}}}

[EL]
This is the crux of the confusion.
Here we ask; what is it that is moving forward and relative to what?
In this particular case, as time advances, the difference in the two
velocities causes the in-phase event to show up at our referential
gate at regular time intervals when 3 cycles of W1 have passed through
the gate or 4 cycles of W2 have passed through the gate.

This means that the frequency of the in-phase event is a Third of the
frequency of W1 or a Quarter of the frequency of W2 if we assumed
proper time to dominate such frequencies.

Let us call this in-phase frequency F, then;

F = f1/3 = f2/4
Hence f2 = 4/3 f1, which contradicts our premise where we assumed that
f2 = 2 f1.

Something hidden must be screwed up here; can you guess what is it?

TIME.

Good guess!

If wave number one was 1000 Hz and wave number two was 2000 Hz then
our referential gate must be THE OBSERVER through which relative
velocities cause a frequency shift, such that 1000 complete cycles are
introduced less frequently than 2000 complete cycles being introduced
more frequently.

Here we propose a standard time window of one proper second in which
1000 complete cycles of wave number one happens and 2000 complete
cycles of wave number two happens concurrently.

By taking the proper time window during which W1 passes through the
gate of observation at its own velocity as our standard time frame we
realise that W2 introduces 3000 complete cycles rather than 2000
because the velocity of observation is 1.5 times faster. This means
that from the Observational gate's point of view the number of
complete cycles of W2 within one time window is 3 times greater than
the complete cycles encountered from W1 and it is not the velocity of
anything at all. When those two waves interfere the less frequent wave
becomes an envelope for the more frequent wave Such that each
composite wave is W1 subdivided into 3 cycles of W2.

This modulated wave becomes a moving reference envelope inside which
the other wave is moving and we end up with (v2/v1).(f2/f1) being a
dimensionless product of ratios that would yield the number 3 that
means nothing in physical essence.

You can see clearly that we could have taken the faster wave as the
reference to which modulation is happening less frequent rather than
more frequent.

So we have the observational freedom to see the faster wave slipping
forward inside the slower wave or to see the slower wave as a
peristaltic motion moving backwards over the faster wave as a
modulation of some constant peak amplitude.

Here I would like to make a historical declaration.
The observational gate that I have proposed does not observe any
velocities once both wavefronts have arrived and being observed, and
all that that gate could observe is the frequency of events because
the gate is stationary in the space of both wave velocities.

You could repeat this exercise by assuming a gate on a railway and let
one train be 1.5 times faster than the other train but both arrive at
the gate simultaneously. Let the size of the cars be twice longer on
the slow train and record your observations regarding the coincidence
of car-joints on both trains.
The gate-observer may have a clock but all he may observe is a
frequency of coincidences and no velocities are perceived at all. The
true velocities are what the trains' wheels make on the iron railway.

This in-phase frequency (car-joints on both trains coinciding) may be
(as in our example) the frequency of 3 cars on the slow train or 4
cars on the fast train.
Now we have two lambdas and one frequency so how can you decide on a
single velocity?

3 cars take 3 times as much as one to pass on the slow train and 4
cars take 4 times as much as one to pass on the fast train. The static
length of 3 slow cars is equivalent to 6 fast cars not 4 and that is
what Lorentz Fitzgerald contraction is all about. Time dilation
follows if we compare times and fix the lengths.

So this idiotic game of juggling numbers makes no physics and makes no
science.

We can hybridize mathematics and physics and come up with negative
dispersion, time dilation, length contraction, black holes and big
bangs, but for what end is this clownish path taking us Randy?

What is so funny and pleasing in ****ing with innocent minds?
There are so many people out there that believe that such fiction is
true and real.
I am seriously asking why.
Why the academic establishment allows this comedy?
Are all scientists becoming incompetent to realise and figure out how
this modern wave of fiction is screwing with their sanity and sound
logic?

I see Lemmings, plenty of them, all the time and everywhere.
Rarely do I see like those men that made the solid foundations on
which we stand today.
Lemmings and clones are what the academic institutions are producing
today.

Perhaps it is time for humans to go extinct and rid nature from the
asshole species.

EL

{{{
[Randy]
The fact that their point of coincidence can move
forward faster than either wave alone is a consequence
of the shorter wave moving faster than the longer one.
In other words, of the longer wave having higher index
of refraction, or of dn/df being negative.

If the longer wave moved faster (had lower index of
refraction), you would not get this "superluminal"
effect.

You can do everything I just did in the more general
case of a complex, multi-frequency wave packet and
an arbitrary slope. You can further work out that
there is no information being propagated at speed v1.

This has nothing to do with relativity. It's pure
classical wave physics, analyzing sines and cosines.

- Randy
}}}
  #4  
Old October 29th 03, 11:35 AM
Dirk Van de moortel
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.


"Minor Crank" wrote in message news:IEInb.53464$Fm2.33079@attbi_s04...
"EL" wrote in message
om...


Troll alert. Look at bottom of
http://users.pandora.be/vdmoortel/di...rsenLogic.html

Dirk Vdm


  #5  
Old October 29th 03, 01:11 PM
Minor Crank
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

"Dirk Van de moortel" wrote
in message ...

"Minor Crank" wrote in message

news:IEInb.53464$Fm2.33079@attbi_s04...
"EL" wrote in message
om...


Troll alert. Look at bottom of

http://users.pandora.be/vdmoortel/di...rsenLogic.html

Understood.

I don't have the whole thread visible from this server, but I was responding
to the wrong person, because of EL's confusing posting habits.

Sorry, Randy.

Minor Crank


  #6  
Old October 29th 03, 04:33 PM
Randy Poe
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

"Minor Crank" wrote in message news:IEInb.53464$Fm2.33079@attbi_s04...
"EL" wrote in message
om...

- one wave moving at speed v1
- another wave of higher frequency moving at speed 1.5*v1
- summed together they give a wave packet with peaks
wherever they are in phase (wavelength 3*lambda1 where
lambda1 = wavelength of first wave)

and showed
- the peaks of that wave packet propagate at 3*v1

This demonstrates that by taking a sum of waves with the
property that higher frequency wave move faster, I get
a wave packet that moves much faster than any individual
wave.


So what? This demonstrates absolutely nothing that is in violation of
relativity.


The words above are mine, before EL's comments. I agree
of course. That was the point of my calculation: To show
that if dv/df is positive (dn/df is negative), then you
can get superluminal group velocities.

It rapidly devolved into rants about the evils of the
term "negative dispersion", which eventually highlighted
that EL could not maintain any consistent view of what is
meant by dn/df, dispersion, or the slope of a curve. My
favorite part in this discussion is where he gives data
from one dispersion curve and announces that because
the delta-n's between his irregularly-spaced tabulated
values are not constant, "there is no ****ing slope".

So I recommended getting away from all discussion of
derivatives and slopes entirely and just concentrating
on what happens when the shorter wave moves faster.

I can't make sense of the resulting rant. It still seems
to be something about relativity and time. As far as
I can tell, he's upset that the wavelengths of my two
waves are in a 4/3 relationship rather than a 2/1
relationship as the frequencies are, and suspects this
is some product of the evil modern physicists.

It is really a product, of course, of the fact that in
my hypothetical medium, the two waves do not have the
same velocity. Therefore wavelength is not inversely
proportional to frequency.

- Randy
  #7  
Old October 29th 03, 04:44 PM
Uncle Al
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

EL wrote:

[EL]
Randy wrote
{{{
[Randy]
I'm going to ask you again, politely, to please
look at my derivation, in which I took:

- one wave moving at speed v1
- another wave of higher frequency moving at speed 1.5*v1
- summed together they give a wave packet with peaks
wherever they are in phase (wavelength 3*lambda1 where
lambda1 = wavelength of first wave)

and showed
- the peaks of that wave packet propagate at 3*v1

This demonstrates that by taking a sum of waves with the
property that higher frequency wave move faster, I get
a wave packet that moves much faster than any individual
wave.


http://gregegan.customer.netspace.ne...ETS/20/20.html

[snip]

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
  #8  
Old October 29th 03, 05:23 PM
Randy Poe
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

(EL) wrote in message . com...

{{{
[Randy]
The place where the waves are in phase has moved by a
distance 3*v1*T in time T.
}}}

As you can read in Randy's own statement, he used the expression "a
distance in time T".


Is there something wrong with that phrase?

We know that the velocity v1 is the distance per unit time traversed
by the wave W1.
We know that the velocity v2 is the distance per unit time traversed
by the wave W2.
To understand how the modulation proceeds we need a spatial reference
GATE through which the two waves propagate and modulate. That gate is
an infinite plane placed orthogonal to the waves' propagational
direction axis, assuming that they are coincident in direction.
T must be a multiple of time units in which a finite portion of each
wavelength is propagating through the medium and across our
referential gate.
Now that portion of the wave is what advances in one time unit.
So what does that distance [3.v1.T] mean?


It means that if you have two such gates separated
by a distance 3*v1*T, then the second gate will
record a pulse T seconds after the first gate records
one. For every value of T you choose.

Thus you conclude that the pulse propagates at 3*v1.

Randy said that there is a periodically repeating event at which the
two waves become in phase once more and then go out of phase for some
time.


If you fixed in space, e.g. monitoring one of your gates,
then this is what you will see.

Here are Randy's own words again.
"So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave
1"
Naturally W2 is given to be faster than W1 such that every 4 cycles of
W2 correspond to 3 cycles of W1.
The resulting modulation IS a consequence of those two physical
velocities of wave propagation in Length over time dimensions.


I'm not sure what point you're making other than to repeat
what I said. Wavelength = velocity/frequency. The velocities
are in a ratio of 3/2, the frequencies are in a ratio of
2/1, thus the wavelengths are in a ratio of (3/2)/(2/1) = 3/4.

[Randy]
Thus, the peak appears to
be moving forward at 3*v1, despite the fact that
one wave is moving at v1 and the other at 1.5*v1.
As the whole thing has a spatial periodicity of 3*lambda1,
you will find that all of the peaks, spaced 3*lambda1
apart, are similarly marching forward at 3*v1.



[EL]
This is the crux of the confusion.


What confusion? What's confused?

Here we ask; what is it that is moving forward and relative to what?
In this particular case, as time advances, the difference in the two
velocities causes the in-phase event to show up at our referential
gate at regular time intervals when 3 cycles of W1 have passed through
the gate or 4 cycles of W2 have passed through the gate.

This means that the frequency of the in-phase event is a Third of the
frequency of W1 or a Quarter of the frequency of W2 if we assumed
proper time to dominate such frequencies.


Why use relativistic terms like "proper time"? All of this
analysis would have been clearly understandable to a
contemporary of Galileo.


Let us call this in-phase frequency F, then;

F = f1/3 = f2/4


Incorrect. These waves are not propagating at the
same speed, so you can not draw this conclusion.

OK, I see what you meant by "crux of the confusion". The
confusion is yours, again.

Understandable, as I slipped something under the rug. I
made a subtle point which was easy to miss: The thing
propagating at 3*v1 is NOT a peak of either wave. Your
calculation assumes that the peak of the wave packet
is always at the place where the waves have phase 0,
corresponding to their individual peaks.

It's not. I calculated the place where the phases are
the same. But those phases are not zero. They oscillate
through the whole range of phases, and as a result the
packet is an oscillating thing. It has a nice constant
envelope, but within that envelope it wiggles. If you
read the Wikipedia article I cited (the one you claimed
I never read, the one you claim doesn't exist) you will
see that group velocity is the rate at which some defined
ENVELOPE propagates. That's what I'm calculating.

Hence f2 = 4/3 f1, which contradicts our premise where we assumed that
f2 = 2 f1.


Right. Because your equation F = f1/3 is wrong, and so
is your equation F = f2/4.

Something hidden must be screwed up here; can you guess what is it?


Your ability to draw a picture and reason from it.

Your ability to follow a simple algebraic argument.

- Randy
  #9  
Old October 29th 03, 09:58 PM
EL
external usenet poster
 
Posts: n/a
Default Empirically Refuted Superluminal Velocities.

Uncle Al wrote in message ...


http://gregegan.customer.netspace.ne...ETS/20/20.html

[snip]


[EL]
Al,
How can you post while being in coma!
Man you are a comatose for so long that I began to believe that you
descended from a vegetable.
You just reposted a link to an applet that was completely and
legitimately refuted by exposing the out-of-synch trick being used to
fool idiots of your high calibre, sir.
Go look at your picture and take your head out of your arse.


EL
  #10  
Old October 29th 03, 10:11 PM
Bill Hobba
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Posts: n/a
Default Empirically Refuted Superluminal Velocities.

Minor Crank correctly wrote:
So what? This demonstrates absolutely nothing that is in violation of
relativity.

The superlimunal propagation of the wave packet depends on the prior
existence of its constituents that add to make it up. So, it can easily
race along at greater than c if those constituent trains are already in
existence.

But no information is being transferred, because all of the info encoded

in
each train is already spread throughout all space, from the origin to the
target. The constituent trains need to reach the target first (at speed

c),
in order to form the "red carpet" along which the wave packet can then
travel at any speed.


Exactly. SR does not say that things (effects - whatever you like) can not
happen faster than light. It says information can not be sent faster than
light - it is only be being able to send information you run into the
causality problems of FTL.

Thanks
Bill


 




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