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From: BradGuth on 11 Sep 2009 08:48
On Sep 9, 10:15 pm, Pentcho Valev <pva...(a)yahoo.com> wrote:
> Premise: The wavelength is determined by the light source and cannot
> depend on the movements of the observer.
>
> Premise: (frequency)=(speed of light)/(wavelength)
>
> Conclusion: If the observer is initially at rest relative to but then
> starts moving towards the light source, the frequency (Doppler effect)
> and THE SPEED OF LIGHT INCREASE.
>
> Pentcho Valev
> pva...(a)yahoo.com

We're also headed towards The Great Attractor at <750 km/s (at times a
little faster when you toss in a little retrograde).

Ask these Einstein jokers; Where's the local SR distortions?

~ BG
From: Rock Brentwood on 12 Sep 2009 18:55
On Sep 10, 3:14 am, Don Stockbauer <donstockba...(a)hotmail.com> wrote:
> On Sep 10, 12:15 am, Pentcho Valev <pva...(a)yahoo.com> wrote:
>
> > Premise: The wavelength is determined by the light source and cannot
> > depend on the movements of the observer.
>
> > Premise: (frequency)=(speed of light)/(wavelength)
>
> > Conclusion: If the observer is initially at rest relative to but then
> > starts moving towards the light source, the frequency (Doppler effect)
> > and THE SPEED OF LIGHT INCREASE.
>
> > Pentcho Valev
> > pva...(a)yahoo.com
>
> The frequency increases, but the speed doesn't.
>
> What is the speed relative to?

One can also take the speed relative to the frame(s) of reference in
which the constitutive law (D,H) <- (E,B) is isotropic.

If the Lagrangian L governing the field (which yields D = @L/@E, H = -
@L/@B as the partial derivatives with respect to B, E) has an
isotropic frame, then it can be expressed as a function of the 3
isotropic invariants E^2/2, B^2/2, B.E.

So, the only question is whether such frames are unique or not. This
depends both on the spacetime signature and the nature of the
Lagrangian. ALL combinations are possible, and neither relativity/non-
relativity specifically includes or excludes either.

It bears pointing out, before going on any further, that the ACTUAL
form of the constitutive laws governing outer space are NOT boost-
invariant, but define a unique isotropic frame. Velocities can be
taken with respect to this frame. This remains true independently of
whether Relativity holds true or not. (The difference between what a
relativistic and non-relativistic theory say then boilds down to the
difference in the constitutive laws -- which is what I'm about to get
to).

For a boost non-invariant isotropic frame, the wave velocity is
relative to the isotropic frame -- again, true independent of whether
you're dealing with relativity or non-relativistic form of
electromagnetism. Again, this will be seen in more detail below.

One can, in fact, classify all the different types of constitutive
relations by which invariances they exhibit, along the following
lines:
"Vacuuon" -- translation invariant
"Quasi-Vacuum" -- rotation & boost invariant
"Vacuum" -- Vacuuon & Quasi-Vacuum
"Isotropic" -- rotation invariant
(the Vacuuon class corresponding to one of the 4 families of "irreps"
discussed by Wigner in his 1939 paper, but neither named by him nor by
successors -- the other 3 being Luxon, Tachyon and Tardion).

So, it would be of interest to see what the ACTUAL difference, or
contrast, between what a relativistic and non-relativistic signature
would give you, if there is indeed a unique isotropic frame.

In general, since L would be a function of the invariants, one can
define
epsilon = @L/@(E^2/2)
-1/mu = @L/@(B^2/2)
theta = @L/@(B.E)
in which case the constitutive laws become
D = epsilon E + theta B; H = B/mu - theta E.

This holds only in the isotropic frame. Maxwell believed that only one
such frame existed, for instance. Thus, he introduced a velocity G as
an extra letter in the Maxwell alphabet (A, B, C = total current, D,
E, F = force, G, H, I = magnetization, J; all of which Maxwell
introduced). In the Relativistic form of Maxwell's relations, G would
STILL be present. This was spelled out by the series of papers by
Einstein and Laub in 1908-1909 and also by Minkowski around the same
time.

These laws only hold in the isotropic frame. To answer the question of
what they look like in a general frame, one then needs to carry out a
boost. The definition of "boost" is also where the definition of
spacetime signature enters into play. So, first signature.

The isotropic signatures for 4-dimensions are given by the invariants
beta dt^2 - alpha dr^2; beta del^2 - alpha (@/@t)^2.
The case alpha beta > 0 is the Lorentzian signature; alpha beta < 0
the Euclidean signature; alpha = 0 (beta non-0) the Galilean signature
of non-relativistic theory; and beta = 0 (alpha non-zero) the
Archimedean signature (of the Hellenistic Era).

The most general transformation respecting these invariants may be
deemed the "biorthogonal" transformation -- one orthogonal with
respect to the two metrics associated with the respective invariants
(the metric g <-> beta dt^2 - alpha dr^2 and dual metric g' <-> beta
del^2 - alpha (@/@t)^2). This is given in 3-vector form by
delta(dr) = omega x dr - beta upsilon dt
delta(dt) = -alpha upsilon.dr
delta(del) = omega x del + alpha upsilon (@/@t)
delta(@/@t) = beta upsilon.del
where omega generates rotations, and upsilon generates boost. From
this you can read off the transformations for the components
A.dr - phi dt
of the potential one form:
delta(A) = omega x A - alpha upsilon phi
delta(phi) = -beta upsilon.A

From this, one reads off the transformations for the components E and
B of the field 2-form:
F = dA = B.(dr x dr/2) + E.(dr dt)
are given by
delta(B)
= delta(del x A)
= (omega x del) x A + alpha upsilon x @A/@t + del x (omega x A) -
del x (alpha upsilon phi)
= omega x B - alpha upsilon x E
and
delta(E) = omega x E + beta upsilon x B.

In finite form, for a boost velocity v, a pure boost yields
Bp -> Bp
Bn -> (Bn - alpha v x E)/root(1 - alpha beta v^2)
Ep -> Ep
En -> (En + beta v x B)/root(1 - alpha beta v^2)
which holds for any boost velocity v where alpha beta v^2 < 1. Here ()
p and ()n are, respectively, the components parallel and perpendicular
to the boost.

For the components D and H of the dual 2-form
D.(dr x dr/2) - H.(dr dt)
one similarly derives
Dp -> Dp
Dn -> (Dn + alpha v x H)/root(1 - alpha beta v^2)
Hp -> Hp
Hn -> (Hn - beta v x D)/root(1 - alpha beta v^2).

Thus, under transformation by a boost velocity G, one obtains the
relations
Dp = epsilon Ep + theta Bp
Dn + alpha G x H = epsilon (En + beta G x B) + theta (Bn - alpha G
x E)
Hp = 1/mu Bp - theta Ep
Hn - beta G x D = 1/mu (Bn - alpha G x E) - theta (En + beta G x B)
which combine to yield the following:
D + alpha G x H = epsilon (E + beta G x B) + theta (B - alpha G x
E)
H - beta G x D = 1/mu (B - alpha G x E) - theta (E + beta G x B).

NOW ... it's at this point, you can ask whether there is a unique
isotropic frame or not; and what the contrast between the different
signatures looks like in all cases, whether it is unique or not).

Ignore the parity non-invariant parameter theta. In general all three
parameters, epsilon, theta, mu are functions of the 3 isotropic
invariants. For null fields or near null fields (ones where the 2
boost & rotation invariants are 0), these functions become nearly
constant. Theta can be arbitrarily changed by an additive constant, by
redefining D -> D + theta' B, H -> H - theta' E. So, for constant or
near-constant theta, it can be removed from the picture.

The equations reduce to
D + alpha G x H = epsilon (E + beta G x B)
B - alpha G x E = mu (H - beta G x D).

For a Lorentzian signature, one can take alpha = (1/c)^2, beta = 1,
and then one gets
D + (1/c)^2 G x H = epsilon (E + G x B)
B - (1/c)^2 G x E = mu (H - G x D).
This is the Einstein-Laub form of the constitutive law.

For a Galilean signature (alpha = 0, beta = 1), one has Maxwell's (and
Thomson's) form of the constitutive law:
D = epsilon (E + G x B), B = mu (H - G x D).

To ask the general question of what combinations yields boost-
invariant constitutive laws, solve for (D,H).
D = epsilon E + (beta mu epsilon - alpha)/(mu (1 - alpha beta G^2))
G x (B - alpha G x E)
H = mu B + (beta mu epsilon - alpha)/(mu(1 - alpha beta G^2)) G x
(E + beta G x B)

The case alpha beta G^2 = 1 (the "Casimir Threshold") stands out as a
singular case. Here, there remains a semblance of boost non-invariance
EVEN IN the Relativistic domain. This is unknown in the literature, as
of yet.

Away from the Casimir Threshold, boost invariance reduces to the
condition that
alpha = beta mu epsilon.

For the Lorentzian signature, this means that the wave velocity, which
is given by (1/V)^2 = mu epsilon, will match the invariant velocity c,
which is given by (1/c)^2 = alpha, where beta = 1.

More generally, for boost non-invariant fields in the Lorentz
signature, the formulae reduce to the following expressions in terms
of the wave speed V:
D = epsilon E + epsilon (c^2 - V^2)/(c^2 - G^2) G x (B - (1/c)^2 G
x E)
H = mu B + epsilon (c^2 - V^2)/(c^2 - G^2) G x (E + G x B)

Here, you can also see what happens at the Casimir Threshold, V = G:
D = epsilon E + epsilon G x (B - (1/c)^2 G x E)
H = mu B + epsilon G x (E + G x B)

This relation holds true EVEN WHEN |G| = c! Hence, among other things,
we can answer Einstein's own question "what is it like to travel
alongside a lightr beam?"

But that isn't the end of it! One can solve for other combinations,
e.g. (E,H) in terms of (D,B); (D,B) in terms of (E,H) or (E,B) in
terms (D,H). Two solutions yields REGULAR transitions across the
Casimir threshold and singular thresholds on the causal barrier, |G| -
> c.

One, however, yields a regular transition across BOTH the Casimir and
causal threshold, only going singular as |G| -> c^2/V.

So, we can actually go further, and answer Einstein's unasked
question: "what's it then like to overtake the light beam?"

Note: that the picture presented gets far more complex when
generalizing to gauge fields ("gauge field" does NOT mean Yang-Mills
field, which it is often confused with in the literature, but is far
more general; but yet conforms to what are essentially non-linear
generalizations of Maxwell's equations). .Here, there are two families
of fields (E^a, B^a) one for each degree of symmetry (a) of the gauge
field, two dual familiar (D_a, H_a), and the isotropic invariants now
become 7 FAMILIES in place of the 3 invariants for electromagnetism:
E^a.E^b/2, E^a.B^b, B^a.B^b/2,
E^a x E^b . E^c/6, E^a x E^b . B^c/2,
E^a . B^b x B^c/2, B^a x B^b . B^c/6.

So, there are now 7 families of coefficients in place of epsilon, mu
and theta. Correspondingly, the conditrions for determining which
field configurations and constitutive laws are both isotropic and
boost invariants generalize. Now, it's no longer just a single extra
velocity V = 1/root(mu epsilon), but a huge number of coefficient
combinations that define boost-invariance.
From: Pentcho Valev on 13 Sep 2009 07:32
Premise: Einstein's equivalence principle

Conclusions:
If the speed of light varies with the gravitational potential V in
accordance with Einstein's 1911 equation c'=c(1+V/c^2) given by
Newton's emission theory of light, then the speed of light varies with
the speed of the light source v in accordance with the equation c'=c+v
given again by Newton's emission theory of light, that is, Einstein's
1905 light postulate is false.

If the speed of light varies with the gravitational potential V in
accordance with Einstein's 1915 equation c'=c(1+2V/c^2), then the
speed of light varies with the speed of the light source v in
accordance with the equation c'=c+2v, that is, Einstein's 1905 light
postulate is false.

If the speed of light does not vary with the gravitational potential V
(Einstein would not agree but nowadays silly Einsteinians do teach
so), then the speed of light does not vary with the speed of the light
source v either, that is, Einstein's 1905 light postulate is true.

Pentcho Valev wrote:

Premise: The wavelength is determined by the light source and cannot
depend on the movements of the observer.

Premise: (frequency)=(speed of light)/(wavelength)

Conclusion: If the observer is initially at rest relative to but then
starts moving towards the light source, the frequency (Doppler effect)
and THE SPEED OF LIGHT INCREASE.

Compare with John Norton's reasoning (the TEXT IN CAPITALS is wrong):

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang/index.html
John Norton: "Here's a light wave and an observer. If the observer
were to hurry towards the source of the light, the observer would now
pass wavecrests more frequently than the resting observer. That would
mean that moving observer would find the frequency of the light to
have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE
BETWEEN CRESTS - TO HAVE DECREASED)."

Pentcho Valev
pvalev(a)yahoo.com
From: Peter Webb on 13 Sep 2009 07:40

"Pentcho Valev" <pvalev(a)yahoo.com> wrote in message
news:591919d7-ea36-47fa-9665-baa18671fe6d(a)37g2000yqm.googlegroups.com...
> Premise: Einstein's equivalence principle
>
> Conclusions:
> If the speed of light varies with the gravitational potential V in
> accordance with Einstein's 1911 equation c'=c(1+V/c^2) given by
> Newton's emission theory of light, then the speed of light varies with
> the speed of the light source v in accordance with the equation c'=c+v
> given again by Newton's emission theory of light, that is, Einstein's
> 1905 light postulate is false.
>

No, you have made two different errors:

1. You use V as a gravitaional potential, the confuse it with v being a
velocity.

2. Einsteins 1905 postulate only applied to inertial reference frames.

HTH



> If the speed of light varies with the gravitational potential V in
> accordance with Einstein's 1915 equation c'=c(1+2V/c^2), then the
> speed of light varies with the speed of the light source v in
> accordance with the equation c'=c+2v, that is, Einstein's 1905 light
> postulate is false.
>
> If the speed of light does not vary with the gravitational potential V
> (Einstein would not agree but nowadays silly Einsteinians do teach
> so), then the speed of light does not vary with the speed of the light
> source v either, that is, Einstein's 1905 light postulate is true.
>
> Pentcho Valev wrote:
>
> Premise: The wavelength is determined by the light source and cannot
> depend on the movements of the observer.
>
> Premise: (frequency)=(speed of light)/(wavelength)
>
> Conclusion: If the observer is initially at rest relative to but then
> starts moving towards the light source, the frequency (Doppler effect)
> and THE SPEED OF LIGHT INCREASE.
>
> Compare with John Norton's reasoning (the TEXT IN CAPITALS is wrong):
>
> http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang/index.html
> John Norton: "Here's a light wave and an observer. If the observer
> were to hurry towards the source of the light, the observer would now
> pass wavecrests more frequently than the resting observer. That would
> mean that moving observer would find the frequency of the light to
> have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE
> BETWEEN CRESTS - TO HAVE DECREASED)."
>
> Pentcho Valev
> pvalev(a)yahoo.com

From: BradGuth on 13 Sep 2009 12:37
On Sep 10, 12:43 am, Pentcho Valev <pva...(a)yahoo.com> wrote:
> On Sep 10, 8:10 am, Pentcho Valev <pva...(a)yahoo.com> wrote:
>
> > Premise: The wavelength is determined by the light source and cannot
> > depend on the movements of the observer.
>
> > Premise: (frequency)=(speed of light)/(wavelength)
>
> > Conclusion: If the observer is initially at rest relative to but then
> > starts moving towards the light source, the frequency (Doppler effect)
> > and THE SPEED OF LIGHT INCREASE.
>
> Compare with John Norton's reasoning (the TEXT IN CAPITALS is wrong):
>
> http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang/ind...
> John Norton: "Here's a light wave and an observer. If the observer
> were to hurry towards the source of the light, the observer would now
> pass wavecrests more frequently than the resting observer. That would
> mean that moving observer would find the frequency of the light to
> have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE
> BETWEEN CRESTS - TO HAVE DECREASED)."
>
> Pentcho Valev
> pva...(a)yahoo.com

Correct, whereas the merging or closing velocity of two individual
photon wave-fronts, each arriving at exactly 180 degrees from one
another is 2c. The speed of light is therefore directly relative to
the velocity of the observer (regardless of the original transmitted
monochromatic spectrum of either photon). A Doppler demodulation of
this proof should confirm this kind of dipolar merging event.

~ BG
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