Physics Banter - View Single Post - Empirically Refuted Superluminal Velocities.

**Randy Poe**

(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