Re: The relationship between meter, speed of light and c

In sci.physics.relativity, kenseto
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wrote
on Sun, 18 Feb 2007 17:14:49 -0500
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"The Ghost In The Machine" <ewill@xxxxxxxxxxxxxxxxxxxxxxx> wrote in message
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In sci.physics.relativity, kenseto
<kenseto@xxxxxxxxxx>
wrote
on Sun, 18 Feb 2007 09:42:22 -0500
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"The Ghost In The Machine" <ewill@xxxxxxxxxxxxxxxxxxxxxxx> wrote in
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In sci.physics.relativity, kenseto
<kenseto@xxxxxxxxxx>
wrote
on Sat, 17 Feb 2007 14:38:50 -0500
<45d75896$0$18891$4c368faf@xxxxxxxxxxxxxx>:


SR's frequency predictions for this scenario are as follows;
these are expressed as ratios. In IRT one might express
R(v_ab) = Fab/Faa, for example.

O A B C
O 1 R(v_a) R(v_b) R(v_c)
A R(v_a) 1 R(v_ab) R(v_ac)
B R(v_b) R(v_ba) 1 R(v_bc)
C R(v_c) R(v_ca) R(v_cb) 1

where R(v) = sqrt(1-v/c)/sqrt(1+v/c),
v_ab = v_ba = (v_b-v_a)/(1-v_b*v_a/c^2)
v_ac = v_ca = (v_c-v_a)/(1-v_c*v_a/c^2)
v_bc = v_cb = (v_c-v_b)/(1-v_c*v_b/c^2)

SR's wavelength predictions are:

O A B C
O 1 W(v_a) W(v_b) W(v_c)
A W(v_a) 1 W(v_ab) W(v_ac)
B W(v_b) W(v_ba) 1 W(v_bc)
C W(v_c) W(v_ca) W(v_cb) 1

where W(v) = sqrt(1+v/c)/sqrt(1-v/c).

I HAVE NO IDEA WHAT YOU ARE TALKING ABOUT.

Too bad. SR is fairly clear on this matter, although it takes some
massaging to get here from the Lorentz. Note that I'm using
light-defined (local) units throughout this system.

Regrettably, I forgot to expand(1) the above post, so that's screwed up
the formatting. I've corrected it in this post. (If your newsreader
is having problems switch to a font such as Courier.)

I have no idea what all these W(v), w(v_a), W(v_b), W(v_c) .....etc
means.
Also I have no idea what is your point.

The point is that I'm predicting the wavelengths (W(v)) and frequencies
(R(v)) using ad hoc notation, given the velocities. That's what a
theory *does*.

If you prefer I can restructure the problem so that I can predict the
velocity given wavelength and/or frequency.

In IRT relative velocity is predicted as follows:
Mean relative velocity = v = Lambda(Faa-Fab)
OR
Instantaneous relative velocity = v =Lambda(f_aa - f_ab)

OK. Hopefully I've defined sufficiently well my ad hoc notation W() and
R() for you. From section 3 of
http://www.geocities.com/kn_seto/2007IRT.pdf
f_aa is defined as "the instantaneous frequency measurement of a
standard light source in A's frame as measured by A".
f_ab = "the instantaneous frequency measurement of a standard
light source in B's frame as measured by A".
lambda = "the universal wave length". [*]

The interesting thing is that section 1 defines

F_aa = "The frequency of a standard light source in A's frame as
measured by A". [+]
F_ab = "The frequency of a standard light source in B's frame as
measured by A; if F_ab is not constant the mean value is used."

The sole difference is the word "instantaneous"; they are otherwise
identical. Are they? This quirk to me is a little weird.
But let's see how far I get.

The predicted velocity v_irt = Lambda * (F_aa - F_ab).
F_aa is a given, as is Lambda. F(SR)_ab, from SR's
predictions, is F_aa * sqrt(1-v/c)/sqrt(1+v/c)
and of course includes the Doppler effect.
Unfortunately, the paper stipulates F_ab = 1/gamma,
which is an interesting difference. How one can directly
measure this is far from clear, since v
is not initially known.

Also, c = Lambda * F_aa, as stated just below.

Therefore

v_irt/c = (F_aa - F_ab) / F_aa
= 1 - sqrt(1-v^2/c^2)

I for one would hope that v_irt = v; clearly, however, this is not the
case. If one, for instance, substitutes v/c = 7/25 (to make the math
somewhat easy), one gets

v_irt/c = 1 - 24/25 = 1/25 != 7/25 = v

It is of course possible to solve

v = 1 - sqrt(1-v^2/c^2)

which yields

(1 - v) = sqrt(1-v^2/c^2)
(1 - v)^2 = 1 - v^2/c^2
v^2 - 2v + 1 - 1 + v^2/c^2 = 0
v(-2 + v/c^2) = 0

so either v = 0 or v = 2*c^2, neither of which is a very
good value for general velocity.

In SR one can do a little juggling and come up with the
following formula:

v_sr = c * (1 - (F(SR)_ab/F_aa)^2) / (1 + (F(SR)_ab/F_aa)^2)

if one assumes F_aa and F(SR)_ab are measured using light-defined (local) units.

Since 1 + v_sr/c = 2/(1 + (F(SR)_ab/F_aa)^2) and
1 - v_sr/c = 2*(F(SR)_ab/F_aa)^2 / (1 + (F(SR)_ab/F_aa)^2),
sqrt(1-v_sr/c)/sqrt(1+v_sr/c) = F(SR)_ab/F_aa = sqrt(1-v/c)/sqrt(1+v/c);
this formula, at least, is mathematically consistent.

If you're very nice to me I might reply with a scathing review of the
rest of your mathematics. :-)



Ken Seto



[*] you have stated in the past that lambda is the same everywhere.

[+] presumably F_aa = Faa; the former is preferred by tools such as TeX.

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