Fermat's principle and curved spacetime
Albertito
between the source and observer. Einstein's GR predicts
gravitational lensing, claiming that it is caused by spacetime
curvature due to the presence of intermediary matter/energy.
Actually, both are the same phenomenon. All we have to do is
to rethink what we understand by vacuum and how is it that a
photon can travel through a vacuum.
If the speed of light is different in different media, does it mean
that
there is a massive body in the boundary of both media that causes
the spacetime to get curved?. The answer must be NO. the correct
answer is that atoms/molecules in a medium have to retransmit the
signal: if a medium is optically denser, the speed of light would be
lower. Therefore, the concept of spacetime curvature is only a pseudo-
phenomenon which implicitly refers to the variance of speed of light.
You can't claim both that a spacetime is curved and that there exists
a
locally variable speed of light. You have to choose either one or the
other, but not both. The problem with GR is that it still claims both,
so
that's a nonsense.
It is clear that if there exists an intermediary massive body between
source and observer, the vacuum (medium) becomes gradually dense
and inhomogenoeus, yielding different refractive indices, not only in
source and observer locations, but over the whole space. Thus,
another question arises. How could antimatter bend light?. If
ordinary
matter bend light towards the center of the intermediary body,
antimatter
should bend light in the opposite direction. Antimatter is then a
moniker
for a medium with inverse graded refractive indices. It is saying if a
massive
body of ordinary matter produces a graded refractive index n = N(r)
at
distance r, then an antimatter massive body of the same kind, would
produce n' = N'(r), such that n*n' = 1. If the function N(r) for the
former is
N(r) = exp( -2V_r/c^2),
with V_r the gravitational potential at r,
then the function N'(r) for the latter would be
N'(r) = exp( 2V_r/c^2).
We see that N(r)* N'(r) = 1.
Now, an interesting question arises as well. If a homogenoeus
medium, where the local speed of light is measured as being c,
is becoming denser towards a center, does it mean that a rarified
vacuum is being created in its exterior boundary, which behaves
as dark matter?.The answer must be YES. It can be observed in
any galaxy formation. The exterior region of any galaxy is filled
with dark matter. The exterior regions of galaxy clusters are also
filled with dark matter. Even our solar system has also a little
amount of dark matter in its exterior regions. dark matter is then
the moniker for a region where the local speed of light is higher
than the standard c.
Eric Gisse
> Fermat's principle states that light follows the path of least time,
> between the source and observer. Einstein's GR predicts
> gravitational lensing, claiming that it is caused by spacetime
> curvature due to the presence of intermediary matter/energy.
> Actually, both are the same phenomenon. All we have to do is
> to rethink what we understand by vacuum and how is it that a
> photon can travel through a vacuum.
>
> If the speed of light is different in different media, does it mean
> that
> there is a massive body in the boundary of both media that causes
> the spacetime to get curved?. The answer must be NO. the correct
> answer is that atoms/molecules in a medium have to retransmit the
> signal: if a medium is optically denser, the speed of light would be
> lower. Therefore, the concept of spacetime curvature is only a pseudo-
> phenomenon which implicitly refers to the variance of speed of light.
> You can't claim both that a spacetime is curved and that there exists
> a
> locally variable speed of light. You have to choose either one or the
> other, but not both. The problem with GR is that it still claims both,
> so
> that's a nonsense.
Since GR assumes a locally constant speed of light, your argument is
pointless.
It'd be sooo helpful if you learned some GR.
> It is clear that if there exists an intermediary massive body between
> source and observer, the vacuum (medium) becomes gradually dense
> and inhomogenoeus, yielding different refractive indices, not only in
> source and observer locations, but over the whole space. Thus,
> another question arises. How could antimatter bend light?. If
> ordinary
> matter bend light towards the center of the intermediary body,
> antimatter
> should bend light in the opposite direction. Antimatter is then a
Thanks for revealing you don't understand the subtleties of GR.
Antimatter is just oppositely charged matter. A cluster of matter and
antimatter cannot have different null geodesics in GR, otherwise
that'd be an equivalence principle violation.
> moniker
> for a medium with inverse graded refractive indices. It is saying if a
> massive
> body of ordinary matter produces a graded refractive index n = N(r)
> at
> distance r, then an antimatter massive body of the same kind, would
> produce n' = N'(r), such that n*n' = 1. If the function N(r) for the
> former is
>
> N(r) = exp( -2V_r/c^2),
> with V_r the gravitational potential at r,
Once again you pull this out of your ass, with no derivation or
support whatsoever.
>
> then the function N'(r) for the latter would be
>
> N'(r) = exp( 2V_r/c^2).
>
> We see that N(r)* N'(r) = 1.
Yea, whatever. Not like it is relevant to GR or physics in general.
>
> Now, an interesting question arises as well. If a homogenoeus
> medium, where the local speed of light is measured as being c,
> is becoming denser towards a center, does it mean that a rarified
> vacuum is being created in its exterior boundary, which behaves
> as dark matter?.The answer must be YES. It can be observed in
> any galaxy formation. The exterior region of any galaxy is filled
> with dark matter. The exterior regions of galaxy clusters are also
> filled with dark matter. Even our solar system has also a little
> amount of dark matter in its exterior regions. dark matter is then
> the moniker for a region where the local speed of light is higher
> than the standard c.
A different light speed has nothing to do with dark matter.
Albertito
Then, why did Einstein propose a local speed of light as
c'= c(1 + V/c^2)? or, are you suggesting Einstein firstly
shitted his GR and then abandoned it for you to frolic on
that bullshit, like dung beetles?.
>
> > It is clear that if there exists an intermediary massive body between
> > source and observer, the vacuum (medium) becomes gradually dense
> > and inhomogenoeus, yielding different refractive indices, not only in
> > source and observer locations, but over the whole space. Thus,
> > another question arises. How could antimatter bend light?. If
> > ordinary
> > matter bend light towards the center of the intermediary body,
> > antimatter
> > should bend light in the opposite direction. Antimatter is then a
>
> Thanks for revealing you don't understand the subtleties of GR.
>
> Antimatter is just oppositely charged matter. A cluster of matter and
> antimatter cannot have different null geodesics in GR, otherwise
> that'd be an equivalence principle violation.
>
Is the equivalence principle sacred?. Who says it can't be violated?
you?.
> > moniker
> > for a medium with inverse graded refractive indices. It is saying if a
> > massive
> > body of ordinary matter produces a graded refractive index n = N(r)
> > at
> > distance r, then an antimatter massive body of the same kind, would
> > produce n' = N'(r), such that n*n' = 1. If the function N(r) for the
> > former is
>
> > N(r) = exp( -2V_r/c^2),
> > with V_r the gravitational potential at r,
>
> Once again you pull this out of your ass, with no derivation or
> support whatsoever.
>
Fello, that equation can be easily deduced from newtonian gravity,
you only need some elementary notions on classical optics.
>
>
> > then the function N'(r) for the latter would be
>
> > N'(r) = exp( 2V_r/c^2).
>
> > We see that N(r)* N'(r) = 1.
>
> Yea, whatever. Not like it is relevant to GR or physics in general.
>
>
>
> > Now, an interesting question arises as well. If a homogenoeus
> > medium, where the local speed of light is measured as being c,
> > is becoming denser towards a center, does it mean that a rarified
> > vacuum is being created in its exterior boundary, which behaves
> > as dark matter?.The answer must be YES. It can be observed in
> > any galaxy formation. The exterior region of any galaxy is filled
> > with dark matter. The exterior regions of galaxy clusters are also
> > filled with dark matter. Even our solar system has also a little
> > amount of dark matter in its exterior regions. dark matter is then
> > the moniker for a region where the local speed of light is higher
> > than the standard c.
>
> A different light speed has nothing to do with dark matter.
Actually not. Dark matter is becoming the paradigm of gravitational
micro-lensings. How do you know that a micro-lensing is produced
by a MACHO, but it is not a lensing produced by a medium with less
refractive index?. By definition, dark matter is something that
can't be observed, so where is the dark matter's source located?.
You have two options, equally probable, either you localize the
source
in one point or you localize it in its mirror point. One of those
options will yield a refractive index n<1.
Dono
Eric Gisse
The answer to your question is irrelevant, as the theory is not a part
of general relativity.
>
>
>
>
>
> > > It is clear that if there exists an intermediary massive body between
> > > source and observer, the vacuum (medium) becomes gradually dense
> > > and inhomogenoeus, yielding different refractive indices, not only in
> > > source and observer locations, but over the whole space. Thus,
> > > another question arises. How could antimatter bend light?. If
> > > ordinary
> > > matter bend light towards the center of the intermediary body,
> > > antimatter
> > > should bend light in the opposite direction. Antimatter is then a
>
> > Thanks for revealing you don't understand the subtleties of GR.
>
> > Antimatter is just oppositely charged matter. A cluster of matter and
> > antimatter cannot have different null geodesics in GR, otherwise
> > that'd be an equivalence principle violation.
>
> Is the equivalence principle sacred?. Who says it can't be violated?
> you?.
It isn't my fault you are ignorant of that which you speak. The
equivalence principle is _the_ founding postulate of general
relativity, and your assumption that matter and antimatter deflect
light in different ways violates that founding postulate.
If you want to assume the EP is violated - sure, go ahead. Just don't
pretend you are talking about GR when you do so.
>
> > > moniker
> > > for a medium with inverse graded refractive indices. It is saying if a
> > > massive
> > > body of ordinary matter produces a graded refractive index n = N(r)
> > > at
> > > distance r, then an antimatter massive body of the same kind, would
> > > produce n' = N'(r), such that n*n' = 1. If the function N(r) for the
> > > former is
>
> > > N(r) = exp( -2V_r/c^2),
> > > with V_r the gravitational potential at r,
>
> > Once again you pull this out of your ass, with no derivation or
> > support whatsoever.
>
> Fello, that equation can be easily deduced from newtonian gravity,
> you only need some elementary notions on classical optics.
Since I have studied both Newtonian gravity and classical optics in
some detail and do not believe this to be true, I find this curious.
How about you present the derivation, or a reference to the
derivation?
Why are you even using Newtonian gravity? Newtonian gravity is well
known to be wrong when used to analyze deflection of light by massive
bodies.
What do you even think gravitational lensing is if not an observation
that light bends with respect to its' flat space trajectory?
Ken S. Tucker
...
> The
> equivalence principle is _the_ founding postulate of general
> relativity, and your assumption that matter and antimatter deflect
> light in different ways violates that founding postulate.
Hmmmmmmmmmmmmmm.
Suppose a light-ray passes an object that
is rotating CW or CWW, that's spin or ANTI-
spin, would the deflection of said light-ray
depend on spin?
Ken S. Tucker
...
Eric Gisse
As soon as you explain why you think the question is relevant.
Koobee Wublee
> Fermat's principle states that light follows the path of least
> time, between the source and observer. Einstein's GR predicts
> gravitational lensing, claiming that it is caused by spacetime
> curvature due to the presence of intermediary matter/energy.
> Actually, both are the same phenomenon. All we have to do is
> to rethink what we understand by vacuum and how is it that a
> photon can travel through a vacuum.
Actually, when an object or a photon travels from one point in space
or spacetime to another, it accumulates the following amount of
measurable parameters in doing so.
** Time elapsed
** Distance traversed
** Spacetime accumulated
Yes, Fermat's principle is the principle of least time where the time
elapsed is always minimized. Christoffel derived the geodesic
equations based on minimized distance traversed. The founding fathers
of GR being mostly mathematicians who were a little bit out of touch
with the physical world decided to have the geodesics follows the path
with the least spacetime accumulated. However, this model of
geodesics following the path with the least accumulated spacetime has
a very serious flaw. For a photon, whenever it propagates, it always
accumulates a spacetime of exactly zero. Thus, in this model of
geodesics, there is no particular path of travel that would allow a
minimized accumulated spacetime. So, from observations of the real
world, it is so obvious that the geodesics must follow the path with
the least amount of accumulated time in accordance with the principle
of least time or Fermat's principle.
> If the speed of light is different in different media, does it mean
> that
> there is a massive body in the boundary of both media that causes
> the spacetime to get curved?. The answer must be NO. the correct
> answer is that atoms/molecules in a medium have to retransmit the
> signal: if a medium is optically denser, the speed of light would be
> lower. Therefore, the concept of spacetime curvature is only a pseudo-
> phenomenon which implicitly refers to the variance of speed of light.
Yes.
> You can't claim both that a spacetime is curved and that there exists
> a locally variable speed of light. You have to choose either one or
> the other, but not both. The problem with GR is that it still claims
> both, so that's a nonsense.
Yes. I am glad there is someone else besides me who has independently
identified this absurdity in GR. However, going through the
mathematics with the speed of light varying according to the Newtonian
limit, you will find it follows the Newtonian deflected amount or half
of GR claim.
Einstein that nitwit, plagiarist, and liar claimed time dilation will
contribute 0.87" and curved space will contribute an additional
0.87". Thus, the total amount is 1.7". Einstein did this without any
mathematics. Most of the physicists became the follower of Einstein.
Eddington's very liberal borderlining dishonest interpretations to the
data taken during a 1919 solar eclipse convinced every one. Einstein
became a messiah to the religion of SR and GR. However, there are a
few of us who understand both the mathematics involved and physical
model identified. We are laughing at those self-claimed physicists
ever since.
Ken S. Tucker
Does "E"ric NOT KNOW something??
I just felt a shutter in "THE FORCE",
Oop's I just farted, never mind.
Let Mr. Gisse speak!
Regards
Ken
Androcles
"Koobee Wublee" <koobee...@gmail.com> wrote in message
news:45cc3863-a701-4268...@i29g2000prf.googlegroups.com...
| Yes. I am glad there is someone else besides me who has independently
| identified this absurdity in GR.
I am way ahead of you but I do not hold the absurdity of aether, crank.
Tom Roberts
> Fermat's principle states that light follows the path of least time,
> between the source and observer. Einstein's GR predicts
> gravitational lensing, claiming that it is caused by spacetime
> curvature due to the presence of intermediary matter/energy.
Yes to both.
> Actually, both are the same phenomenon.
Sure. The null geodesic followed by light near "intermediary
matter/energy" is modeled well by the same variational principle Fermat
described much earlier, applied to the geometry of GR.
> All we have to do is
> to rethink what we understand by vacuum and how is it that a
> photon can travel through a vacuum.
Huh? No "rethink" is needed at all.
> If the speed of light is different in different media, does it mean
> that
> there is a massive body in the boundary of both media that causes
> the spacetime to get curved?. The answer must be NO.
Of course the answer is no! My eyeglasses bend light by many degrees,
but the entire mass of the sun can only bend light by a few arcseconds.
These are QUITE DIFFERENT phenomena!
> the correct
> answer is that atoms/molecules in a medium have to retransmit the
> signal: if a medium is optically denser, the speed of light would be
> lower. Therefore, the concept of spacetime curvature is only a pseudo-
> phenomenon which implicitly refers to the variance of speed of light.
No. Your attempt to use a common explanation for two very different
phenomena differing by factors of 10^20 or more is hopeless.
> You can't claim both that a spacetime is curved and that there exists
> a
> locally variable speed of light.
Why not? The presence of an optical medium has an ENORMOUSLY bigger
effect on the speed of light than does any mass. Two different phenomena
can both affect the speed of light.
> You have to choose either one or the
> other, but not both.
What God whispered in your ear and told you this? On what basis do you
think there can be only one influence on the speed of light?
> [...]
> Then, why did Einstein propose a local speed of light as
> c'= c(1 + V/c2)?
Because he was struggling to find General Relativity, but had not yet
figured out all the details. His intermediate formula is approximate,
but not correct. When he proposed it he did not fully understand the
difference between local and non-local phenomena.
Tom Roberts
N:dlzc D:aol T:com (dlzc)
"Albertito" <albert...@gmail.com> wrote in message
news:acc87498-7d1a-4bf8...@s8g2000prg.googlegroups.com...
...
> If the speed of light is different in different media, does
> it mean that there is a massive body in the boundary
> of both media that causes the spacetime to get
> curved?. The answer must be NO. the correct answer
> is that atoms/molecules in a medium have to retransmit
> the signal: if a medium is optically denser, the speed of
> light would be lower. Therefore, the concept of
> spacetime curvature is only a pseudo-phenomenon
> which implicitly refers to the variance of speed of light.
> You can't claim both that a spacetime is curved and
> that there exists a locally variable speed of light. You
> have to choose either one or the other, but not both.
> The problem with GR is that it still claims both, so
> that's a nonsense.
Your misunderstandings are legion.
Gamma radiation and x-rays propagate through all matter at c_0.
And these enegetic photons still "gravitationally lense".
The light that is lensed by matter, does so as a function of
frequency. Like a prism, different wavelengths bend different
amounts. This is called "chromatic aberration". Gravitational
lensing bends all wavelengths the same amount. No gas can do
this.
David A. Smith
Pentcho Valev
sci.physics.relativity:
> Albertito wrote:
> > Then, why did Einstein propose a local speed of light as
> > c'= c(1 + V/c2)?
>
> Because he was struggling to find General Relativity, but had not yet
> figured out all the details. His intermediate formula is approximate,
> but not correct. When he proposed it he did not fully understand the
> difference between local and non-local phenomena.
>
> Tom Roberts
Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent
with the gravitational redshift factor 1+V/c^2 confirmed
experimentally by Pound and Rebka. In other words Roberts Roberts, the
equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE: any different
equation (that may seem correct to you) would be inconsistent with the
redshift factor. For that reason Roberts Roberts superior brothers in
Einstein criminal cult have always been teaching that the speed of
light varies with the gravitational potential, in accordance with
Einstein's 1911 equation c'=c(1+V/c^2):
http://www.physlink.com/Education/AskExperts/ae13.cfm
"So, it is absolutely true that the speed of light is _not_ constant
in a gravitational field [which, by the equivalence principle, applies
as well to accelerating (non-inertial) frames of reference]. If this
were not so, there would be no bending of light by the gravitational
field of stars....Indeed, this is exactly how Einstein did the
calculation in: 'On the Influence of Gravitation on the Propagation of
Light,' Annalen der Physik, 35, 1911. which predated the full formal
development of general relativity by about four years. This paper is
widely available in English. You can find a copy beginning on page 99
of the Dover book 'The Principle of Relativity.' You will find in
section 3 of that paper, Einstein's derivation of the (variable) speed
of light in a gravitational potential, eqn (3). The result is,
c' = c0 ( 1 + V / c^2 )
where V is the gravitational potential relative to the point where the
speed of light c0 is measured."
http://www.blazelabs.com/f-g-gcont.asp "The first confirmation of a
long range variation in the speed of light travelling in space came in
1964. Irwin Shapiro, it seems, was the first to make use of a
previously forgotten facet of general relativity theory -- that the
speed of light is reduced when it passes through a gravitational
field....Faced with this evidence, Einstein stated:"In the second
place our result shows that, according to the general theory of
relativity, the law of the constancy of the velocity of light in
vacuo, which constitutes one of the two fundamental assumptions in the
special theory of relativity and to which we have already frequently
referred, cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position."......Today we find that since the Special
Theory of Relativity unfortunately became part of the so called
mainstream science, it is considered a sacrilege to even suggest that
the speed of light be anything other than a constant. This is somewhat
surprising since even Einstein himself suggested in a paper "On the
Influence of Gravitation on the Propagation of Light," Annalen der
Physik, 35, 1911, that the speed of light might vary with the
gravitational potential. Indeed, the variation of the speed of light
in a vacuum or space is explicitly shown in Einstein's calculation for
the angle at which light should bend upon the influence of gravity.
One can find his calculation in his paper. The result is c'=c(1+V/c^2)
where V is the gravitational potential relative to the point where the
measurement is taken. 1+V/c^2 is also known as the GRAVITATIONAL
REDSHIFT FACTOR."
Pentcho Valev
pva...@yahoo.com
Koobee Wublee
> "Koobee Wublee" wrote in message
> | Yes. I am glad there is someone else besides me who has independently
> | identified this absurdity in GR.
>
> I am way ahead of you but I do not hold the absurdity of aether, crank.
I am convinced that you are a wacko. Your denial of the Aether is not
wise. You are an Einstein Dingleberry by heart ranking in the same
league as moortel, Gisse, Jeckyl, Dono, and other Andro-phobic
Wackos. You all deserve each other. <shrug>
Koobee Wublee
> Albertito wrote:
> > Fermat's principle states that light follows the path of least time,
> > between the source and observer. Einstein's GR predicts
> > gravitational lensing, claiming that it is caused by spacetime
> > curvature due to the presence of intermediary matter/energy.
>
> Yes to both.
Other than my objection to "Einstein's GR", I have no objection to
your comment.
> > Actually, both are the same phenomenon.
>
> Sure. The null geodesic followed by light near "intermediary
> matter/energy" is modeled well by the same variational principle Fermat
> described much earlier, applied to the geometry of GR.
This is total nonsense. The geodesic model Fermat's principle clearly
has the trajectory following the path with the least amount of
accumulated time. The geodesic model under GR (which it does not have
to be) clearly chooses the path with the least accumulated spacetime.
The mathematical application for each model is very different with
drastically different results. Photon can propagate under Fermat's
principle but clearly cannot under the other one. This is all in the
mathematics. <shrug>
> > All we have to do is
> > to rethink what we understand by vacuum and how is it that a
> > photon can travel through a vacuum.
>
> Huh? No "rethink" is needed at all.
>
> > If the speed of light is different in different media, does it mean
> > that
> > there is a massive body in the boundary of both media that causes
> > the spacetime to get curved?. The answer must be NO.
>
> Of course the answer is no! My eyeglasses bend light by many degrees,
> but the entire mass of the sun can only bend light by a few arcseconds.
> These are QUITE DIFFERENT phenomena!
You miss the point. The geodesic model under GR if following Fermat's
principle has no problem of allowing photons to propagate through
space or spacetime. In the case of your glasses, you can directly
observe exactly how light bends. However in the case of a true
gravitational lens, you cannot directly observe how light bends. You
need to employ a more sophisticated method to do so. Any good
mathematical model would have no problem showing both cases under
Fermat's principle.
> > You can't claim both that a spacetime is curved and that there exists
> > a
> > locally variable speed of light.
>
> Why not? The presence of an optical medium has an ENORMOUSLY bigger
> effect on the speed of light than does any mass. Two different phenomena
> can both affect the speed of light.
>
> > You have to choose either one or the
> > other, but not both.
>
> What God whispered in your ear and told you this? On what basis do you
> think there can be only one influence on the speed of light?
If you take the time and conduct thought-experiments where the speed
of light all of a sudden changed dramatically, you will understand GR
cannot possibly allow a different value in the speed of light at each
point in space or spacetime. And believe me. This is not a spiritual
exercise. <shrug>
> > [...]
> > Then, why did Einstein propose a local speed of light as
> > c'= c(1 + V/c2)?
>
> Because he was struggling to find General Relativity, but had not yet
> figured out all the details. His intermediate formula is approximate,
> but not correct. When he proposed it he did not fully understand the
> difference between local and non-local phenomena.
First of all, Einstein certainly did not do that. It was more likely
his classmate Grossmann who proposed that. It is time for me to iron
out the timeline in the historic development of GR.
** In early 19th century, Gauss postulated the possibility of curved
space. This is just a conjecture.
** Gauss's student, Riemann, a generation later described the
mathematical foundation of what curved space is. This is still very
basic.
** In the 2nd half of the 19th century, Christoffel derived the
geodesic equations through curved space with the geodesic model of the
path with the shortest distance.
** In 1898, Gerber claimed the speed of gravity would affect
Mercury's observed orbital anomaly. However, his derivation was
merely a modification to the Newtonian gravitational potential where
it depends on both the radial displacement and the radial speed.
Gerber's result had a subtle mathematical error. However, his
mathematical method was ingenious and simple.
** Within the last decade of the 19th century, Ricci rewrote the
geodesic equations of as a mathematical operator operating on the
velocity term. Thus, the operator known as the covariant derivative
is constructed through Ricci's liking. There are actually many ways
to group the connection coefficients in the geodesic equations. This
means the covariant derivative is not unique. That did not prevent
Ricci to derive the Riemann curvature tensor which is merely a 3x3x3
matrix in 3-D or 4x4x4x4 matrix in 4-D by applying another covariant
derivative to the geodesic equations. There are also more than one
way to arrange the connection coefficients. However, Ricci only found
one. Thus, the Riemann curvature tensor is not unique.
** In 1908, Minkowski derived spacetime from the Lorentz transform
where spacetime is merely an extra dimension to space. The Goettingen
group of mathematicians which included Minkowski himself, Klein,
Hilbert, and Schwarzschild extrapolated Riemann's curved 3-dimensional
space into curved 4-dimensional spacetime. The geodesic equations of
Christoffel based on the shortest physical distance evolved into the
geodesic equations through spacetime based on the least accumulated
spacetime. They knew gravitation was the result of the curvature in
spacetime but were very clueless as what the metric should be into the
2nd order.
** In 1908 after finally understood the Newtonian law of gravity
(Notice that I am being very generous here), Einstein reverse-
engineered the Newtonian law of gravity to re-discover the principle
of equivalence.
** Within the first decade of the 20th century, Ricci's student Levi-
Civita contracted his teacher's mathematical creation, the Riemann
curvature tensor, into a 3x3 matrix in 3-D or a 4x4 matrix in 4-D now
called the Ricci curvature tensor.
** From 1908 on to several years after, Einstein being so ignorant
even in the simplest of mathematics employed the help of his classmate
Grossmann to just do the mathematics. Grossmann's work is now called
the "entwurf" which is heavy in coordinate transformation because of
the equivalence principle re-discovered by Einstein. Newton
discovered the law of gravity by observing how an object such as that
apple behaved under gravity. These clowns tried to imagine themselves
as that falling apple in anticipation to describe gravitation. Of
course, Grossmann's work failed.
** In 1915 disgusted with Grossmann's lack of achievement, Einstein
came to Goettingen to enlist the help of the original folks who worked
on the curvature in spacetime. Through Einstein's credit, he was able
to convince Hilbert to re-continue to work on the hopeless problem.
From then on for unknown reasons, they became competitors rather than
working together.
** Towards that late summer of 1915, Einstein bragged about how he
had derived Mercury's orbital anomaly. What he did was to change the
Newtonian gravitational potential to be a function of only r. Copying
Gerber's mathematical method, Einstein was able to find the constant
to the 2nd order effect of the Newtonian gravitational potential that
suits the observed perihelion advance in Mercury.
** Hilbert thought the race to the field equations was lost to
Einstein. In a hail-Mary-pass (in American football), Hilbert
indulged a scalar to Einstein. This scalar is now the Lagrangian to
the Einstein-Hilbert action that has no physical meaning and
significance. There is even no justification that this so-called
Lagrangian is even a Lagrangian according to the mathematical method
of the calculus of variations. By taking the partial derivative of
this "Lagrangian" with respect to each element of the metric, Hilbert
came up with the field equations. Hilbert, then, promptly presented
his findings as a lecture on 11/20/1915 at Goettingen.
** Einstein now knew of Hilbert's work presented Hilbert's work as if
of his own on 11/25/1915 at Berlin.
** In early 1916, Schwarzschild found a static, spherically
symmetric, and asymptotically flat solution to the field equations.
In this metric, there exhibit no black holes. A few weeks later,
Schwarzschild would perish in the eastern front during WWI.
** In late 1916 or early 1917, Hilbert found another solution that is
also static, spherically symmetric, and asymptoticaly flat. Unlike
Schwarzschild's original solution, Hilbert's solution exhibits black
holes. Now, Hilbert's solution is called the Schwarzschild metric.
Confused? Don't be, for GR is utterly nonsense. It is merely a
series of mathematical manipulations. Only through very liberal
application of mathematics, humans can achieve godhood. <shrug>
Albertito
> How about you present the derivation, or a reference to the
> derivation?
>
> Why are you even using Newtonian gravity? Newtonian gravity is well
> known to be wrong when used to analyze deflection of light by massive
> bodies.
Dear Eric Gisse,
I will give you some clues to deduce that equation
for yourself. Some steps may not seem that obviuos,
but, I consider you're a smart guy, so take it easy,
because you might find the foundation of a correct
quantum gravity theory, here.
Consider a point-like body with mass M.
The newtonian gravitational potential at distance
r to the center is V = -GM/r. Define now, an
inverse distance s, such that r s = R_h l_p,
with R_h Hubble radius and l_p Planck length.
The gravitational potential can be expressed now
as
V = - GMs/R_h l_p,
where s can only take real values in the
range [l_p, R_h].
Consider now a refractive index N. What is the rate of
change of N as s runs from l_p to R_h, in that gravitational
field?. It is a differential equation
dN/ds = K N
where K is a constant.
The greater the mass M, the higher the value of K,
The solution to this simple differential equation is
N(s) = N_p exp(-s K),
where N_p is the refractive index at s=l_p.
(for practical proposes, you always can take the
approximation N_p=1, for small K).
For s=R_h, it yields N_h = N_p exp(- R_h K),
How can we know the value K?. We can expect it be
K = 2GM/(R_h l_p c^2). The gravitational potential is
indeed V = - (K/2) s c^2.
Therefore, we expect N(r) = N_p exp(-2V/c^2).
That's only for a point-like body with mass M. Consider
a two point-like bodies gravitational system, with
gravitational potentials V_1 and V_2, respectively. Then,
total refractive index at distance r would be
N(r) = N_1(r) N_2(r),
N(r) = N_p exp( - (2/c^2) ( V_1 + V_2) )
For a n-body system, you would get
N(r) = N_1(r) N_2(r) ... N_n(r),
N(r) = N_p exp( - (2/c^2) ( V_1 + V_2 + ... + V_n) )
Nevertheless , I can anticipate your arguments,
1. Where does the inverse distance definition r s = R_h l_p
come from?.
2, Where does the differential equation dN/ds = K N
come from?.
3. Why do I expect that K = 2GM/(R_h l_p c^2) be the correct
value?.
As I said above, I consider you're a smart guy, so there is no
doubt you can think deeply and correctly, although slowly. In
order to make your trance less dramatic, I'm glad to provide a
reference paper for you, where all the deduction steps turn out
in good agreement with GR,
http://arxiv.org/abs/0711.0633
Eric Gisse
[...]
The only useful piece of information was the arXiv reference - the
rest is crap.
I can't believe you are deluding yourself into believing you are onto
a quantum theory of gravity when you don't understand classical
gravity in either the Newtonian of General relativistic presentation.
Dirk Van de moortel
"Koobee Wublee" <koobee...@gmail.com> wrote in message news:586a73d1-15da-4278...@m34g2000hsb.googlegroups.com...
Most idiots seems be opponents of us, regular folks, *AND*,
when Androcles is around, of each other.
One should think they ought to stick together, but no, retired
engineers as they are, they tend to have this irresistible urge to
pull the last remaining hairs from each other's skulls.
Strange.
So far we have:
- Androcles - Savain
- Androcles - Henri Wilson
- Androcles - Koobee Wublee
Amusing but strange.
Dirk Vdm
NoEinstein
>
ATTENTION: Those of you who are interested in discussing the various
moot points of Einstein's theories, or the off-shoots of his
"reasoning", are invited to view the various posts of -- NoEinstein --
who has conclusively disproved Einstein both mathematically and
experimentally. Access may be gained via the following NoEinstein
post, and via the attached additional links following such. Those of
you wishing to reply to any point of science, are urged to do so in
the most recent post(s), because the earlier ones, though still quite
apt as to the science, are no longer being checked for comments. I
hope that you will find my links both interesting and educational! --
NoEinstein --
Matter from Thin Air
http://groups.google.com/group/sci.physics/browse_thread/thread/ee4fe3946dfc0c31/1f1872476bc6ca90?hl=en#1f1872476bc6ca90
Curing Einstein's Disease
http://groups.google.com/group/sci.physics/browse_thread/thread/4ff9e866e0d87562/f5f848ad8aba67da?hl=en#f5f848ad8aba67da
Dirk Van de moortel
"NoEinstein" <noein...@bellsouth.net> wrote in message news:b58a7fd6-bba0-4465...@d4g2000prg.googlegroups.com...
> On Jan 18, 2:03 am, Pentcho Valev <pva...@yahoo.com> wrote:
>>
> ATTENTION: Those of you who are interested in discussing the various
> moot points of Einstein's theories,
... in other words, those who are not hindered by any knowledge
of the subject at hand, can hereby nevertheless find out how Usenet's
most prominent retards tend to behave when confronted with points
of clarity:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/PompousPest.html
Dirk Vdm
JanPB
> On Jan 18, 6:37 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote in
> sci.physics.relativity:
>
> > Albertito wrote:
> > > Then, why did Einstein propose a local speed of light as
> > > c'= c(1 + V/c2)?
>
> > Because he was struggling to find General Relativity, but had not yet
> > figured out all the details. His intermediate formula is approximate,
> > but not correct. When he proposed it he did not fully understand the
> > difference between local and non-local phenomena.
>
> > Tom Roberts
>
> Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent
> with the gravitational redshift factor 1+V/c^2 confirmed
> experimentally by Pound and Rebka.
V=RI is also consistent with many experiments. It's also approximate.
So is F=kx, etc.
> In other words Roberts Roberts, the
> equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE:
In other words, it' doesn't follow.
--
Jan Bielawski
Dieter Heidorn
> On Jan 18, 6:37 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote in
> sci.physics.relativity:
>
>>Albertito wrote:
>>
>>>Then, why did Einstein propose a local speed of light as
>>>c'= c(1 + V/c2)?
>>
>>Because he was struggling to find General Relativity, but had not yet
>>figured out all the details. His intermediate formula is approximate,
>>but not correct. When he proposed it he did not fully understand the
>>difference between local and non-local phenomena.
>>
>>Tom Roberts
>
> Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent
> with the gravitational redshift factor 1+V/c^2 confirmed
> experimentally by Pound and Rebka.
>
In his 1911 work "Über den Einfluss der Schwerkraft auf die Ausbreitung
des Lichtes", Annalen der Physik 35 (1911); translated: "On the
Influence of Gravitation on the Propagation of Light" Einstein uses the
equivalence principle to derive the relation for gravitational red-shift
nu_1 = nu_2 (1 + V/c^2)
From this he concluded that the speed of light must vary according to
c = c_0 (1 + V/c^2)
Using this equation Einstein derives a relation for the deflection angle
for light passing the sun (1911):
alpha = 2 GM / (c^2 R)
This is wrong by a factor 2. Experimentally is found
alpha = 2 GM / (c^2 R)
> In other words Roberts Roberts, the
> equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE:
>
This equation is not correct, because it leads to a wrong prediction for
the deflection of light. The reason for the error was: In 1911 Einstein
used "curved time" and "flat space", not curved space-time.
> any different
> equation (that may seem correct to you) would be inconsistent with the
> redshift factor.
>
The gravitational red-shift is not caused by a variable speed of light.
In his 1916 work "Die Grundlage der allgemeinen Relativitätstheorie",
Annalen der Physik 49 (1916) Einstein shows:
* Space-time is described with the metric
ds^2 = g_mu,nu dx^mu dx^nu
* The gravitiational red-shift depends on the metric:
nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
* In weak fields the following approximation holds:
nu_B / nu_A = 1 + Delta V/c^2
* Speed of light:
- In a local inertial frame of reference the speed of light
is constant c
- In general, global coordinates the speed of light varies
(in weak fields) according to
c_A = c ( 1 + 2 V/c^2)
* This leads to the correct relation for the deflection angle
for light passing the sun:
alpha = 4 GM / (c^2 R)
> For that reason Roberts Roberts superior brothers in
> Einstein criminal cult have always been teaching that the speed of
> light varies with the gravitational potential, in accordance with
> Einstein's 1911 equation c'=c(1+V/c^2):
>
> http://www.physlink.com/Education/AskExperts/ae13.cfm
> [...]
> http://www.blazelabs.com/f-g-gcont.asp
> [...]
Probably these "superior brothers" have not read Einsteins 1916 work.
Dieter Heidorn
PS:
For those of you who understand a little german: Einsteins original
papers that were published in "Annalen der Physik" can be read and
downloaded here:
http://www.physik.uni-augsburg.de/annalen/history/Einstein-in-AdP.htm
Koobee Wublee
> Pentcho Valev schrieb:
> > Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent
> > with the gravitational redshift factor 1+V/c^2 confirmed
> > experimentally by Pound and Rebka.
>
> In his 1911 work "Über den Einfluss der Schwerkraft auf die Ausbreitung
> des Lichtes", Annalen der Physik 35 (1911); translated: "On the
> Influence of Gravitation on the Propagation of Light" Einstein uses the
> equivalence principle to derive the relation for gravitational red-shift
>
> nu_1 = nu_2 (1 + V/c^2)
>
> From this he concluded that the speed of light must vary according to
>
> c = c_0 (1 + V/c^2)
>
> Using this equation Einstein derives a relation for the deflection angle
> for light passing the sun (1911):
>
> alpha = 2 GM / (c^2 R)
>
> This is wrong by a factor 2. Experimentally is found
>
> alpha = 2 GM / (c^2 R)
You mean the very liberal interpretation of the data from the solar
eclipse of 1919. It was already decided to be the following even
before Eddington set out his quest.
alha = 4 G M / c^2 / R
> > In other words Roberts Roberts, the
> > equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE:
>
> This equation is not correct, because it leads to a wrong prediction for
> the deflection of light. The reason for the error was: In 1911 Einstein
> used "curved time" and "flat space", not curved space-time.
The equation is correct for gravitational redshift. <shrug>
> > any different
> > equation (that may seem correct to you) would be inconsistent with the
> > redshift factor.
>
> The gravitational red-shift is not caused by a variable speed of light.
>
> In his 1916 work "Die Grundlage der allgemeinen Relativitätstheorie",
> Annalen der Physik 49 (1916) Einstein shows:
>
> * Space-time is described with the metric
>
> ds^2 = g_mu,nu dx^mu dx^nu
>
> * The gravitiational red-shift depends on the metric:
>
> nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
>
> * In weak fields the following approximation holds:
>
> nu_B / nu_A = 1 + Delta V/c^2
>
> * Speed of light:
> - In a local inertial frame of reference the speed of light
> is constant c
> - In general, global coordinates the speed of light varies
> (in weak fields) according to
>
> c_A = c ( 1 + 2 V/c^2)
This equation will lead to a wrong value of the gravitational
redshift. This is another example where GR is contradictory of itself
because it does not agree with the metric derivation as you have shown
above.
Eric Gisse
Another assertion without proof. Do you really expect people to take
you at your word that what you say is true?
Pentcho Valev
Can you sleep well? If you are a clever Einsteinian, I guess you
cannot. Nightmares all night long.
Pentcho Valev
pva...@yahoo.com
Koobee Wublee
Anyone can do a little bit more research into Eddington's expedition
to find out the truth. <shrug>
> Do you really expect people to take
> you at your word that what you say is true?
I still do expect Einstein Dingleberries to deny facts and logic.
They continue to twist logic around and distort history so they can
proudly be Einstein Dingleberries. The question is that "does it get
old after a while?" After all, the study of physics demands the truth
and 100% logical reasoning that Einstein Dingleberries lack. <shrug>
Eric Gisse
Eddington's expedition is of historical interest only. He could have
made it all up and it still doesn't affect the more recent - more
accurate - measurements.
>
> > Do you really expect people to take
> > you at your word that what you say is true?
>
> I still do expect Einstein Dingleberries to deny facts and logic.
> They continue to twist logic around and distort history so they can
> proudly be Einstein Dingleberries. The question is that "does it get
> old after a while?" After all, the study of physics demands the truth
> and 100% logical reasoning that Einstein Dingleberries lack. <shrug>
...and when all is said and done, you are the one stuck posting on
USENET under a pseudonym because you are completely impotent in
effecting the change you believe is required.
Dieter Heidorn
> On Jan 18, 11:03 pm, Dieter Heidorn <d.heid...@t-online.de> wrote:
>
>>Pentcho Valev schrieb:
>>
>>In his 1911 work "Über den Einfluss der Schwerkraft auf die Ausbreitung
>>des Lichtes", Annalen der Physik 35 (1911); translated: "On the
>>Influence of Gravitation on the Propagation of Light" Einstein uses the
>>equivalence principle to derive the relation for gravitational red-shift
>>
>>nu_1 = nu_2 (1 + V/c^2)
>>
>> From this he concluded that the speed of light must vary according to
>>
>>c = c_0 (1 + V/c^2)
>>
>>Using this equation Einstein derives a relation for the deflection angle
>>for light passing the sun (1911):
>>
>>alpha = 2 GM / (c^2 R)
>>
>>This is wrong by a factor 2.
>
>
> Can you sleep well? If you are a clever Einsteinian, I guess you
> cannot. Nightmares all night long.
>
This is all you have to say?
I see: you have no arguments against the material in my previous
posting. Well, I half expected it...
Dieter Heidorn
Dieter Heidorn
> On Jan 18, 1:03 pm, Dieter Heidorn wrote:
>
>>Pentcho Valev schrieb:
>
>>>Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent
>>>with the gravitational redshift factor 1+V/c^2 confirmed
>>>experimentally by Pound and Rebka.
>>
>>In his 1911 work "Über den Einfluss der Schwerkraft auf die Ausbreitung
>>des Lichtes", Annalen der Physik 35 (1911); translated: "On the
>>Influence of Gravitation on the Propagation of Light" Einstein uses the
>>equivalence principle to derive the relation for gravitational red-shift
>>
>>nu_1 = nu_2 (1 + V/c^2)
>>
>> From this he concluded that the speed of light must vary according to
>>
>>c = c_0 (1 + V/c^2)
>>
>>Using this equation Einstein derives a relation for the deflection angle
>>for light passing the sun (1911):
>>
>>alpha = 2 GM / (c^2 R)
>>
>>This is wrong by a factor 2. Experimentally is found
>>
>>alpha = 2 GM / (c^2 R)
>
Sorry, here I meant to write
alpha = 4 GM / (c^2 R).
>>>In other words Roberts Roberts, the
>>>equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE:
>>
>>This equation is not correct, because it leads to a wrong prediction for
>>the deflection of light. The reason for the error was: In 1911 Einstein
>>used "curved time" and "flat space", not curved space-time.
>
> The equation is correct for gravitational redshift. <shrug>
>
Of course, because Einstein derived the c-equation in his 1911 work from
the correct equation for gravitational red-shift. The sequence of his
steps was:
equivalence principle
--> red-shift: nu_1 = nu_2 (1 + V/c^2)
--> varying speed of light: c = c_0 (1 + V/c^2)
--> deflection angle for bending of light: alpha = 2 GM / (c^2 R)
>>>any different
>>>equation (that may seem correct to you) would be inconsistent with the
>>>redshift factor.
>>
>>The gravitational red-shift is not caused by a variable speed of light.
>>
>>In his 1916 work "Die Grundlage der allgemeinen Relativitätstheorie",
>>Annalen der Physik 49 (1916) Einstein shows:
>>
>>* Space-time is described with the metric
>>
>> ds^2 = g_mu,nu dx^mu dx^nu
>>
>>* The gravitiational red-shift depends on the metric:
>>
>> nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
>>
>>* In weak fields the following approximation holds:
>>
>> nu_B / nu_A = 1 + Delta V/c^2
>>
>>* Speed of light:
>> - In a local inertial frame of reference the speed of light
>> is constant c
>> - In general, global coordinates the speed of light varies
>> (in weak fields) according to
>>
>> c_A = c ( 1 + 2 V/c^2)
>
> This equation will lead to a wrong value of the gravitational
> redshift. This is another example where GR is contradictory of itself
> because it does not agree with the metric derivation as you have shown
> above.
You can take this as contradiction only, if gravitational red-shift
would depend on a variable speed of light. In fact this is not correct
in GR. Gravitational red-shift depends on the metric, so I wrote a few
lines above:
The gravitiational red-shift depends on the metric:
nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
In weak fields the following approximation holds:
nu_B / nu_A = 1 + Delta V/c^2
You can find this in Einsteins 1916 work:
Die Grundlage der allgemeinen Relativitätstheorie.
AdP 49, 769 (1916)
(§22, pp 818 - 820)
http://www.physik.uni-augsburg.de/annalen/history/papers/1916_49_769-822.pdf
(Sorry, but I don't know where to find an english translation of this work.)
Dieter Heidorn
Tom Roberts
> On Jan 18, 6:37 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote in
> sci.physics.relativity:
>> Albertito wrote:
>>> Then, why did Einstein propose a local speed of light as
>>> c'= c(1 + V/c2)?
>> Because he was struggling to find General Relativity, but had not yet
>> figured out all the details. His intermediate formula is approximate,
>> but not correct. When he proposed it he did not fully understand the
>> difference between local and non-local phenomena.
>
> with the gravitational redshift factor 1+V/c^2 confirmed
> experimentally by Pound and Rebka.
Sure.
>In other words Roberts Roberts, the
> equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE: any different
> equation (that may seem correct to you) would be inconsistent with the
> redshift factor.
This is nonsense. You REALLY need to learn how mathematical physics
works. While that equation is CONSISTENT WITH CURRENT EXPERIMENTS, that
does not justify the word "correct". It was derived without any
consistent theoretical framework. Such a framework was presented in
1915, General Relativity. In GR the formula is DIFFERENT (and cannot be
written in closed form), but FOR THE SITUATIONS OF THE CURRENT
EXPERIMENTS THE GR EQUATION IS NOT DISTINGUISHABLE FROM THE ABOVE
EQUATION. That's what we mean when we say "it is an APPROXIMATION".
Indeed, contrary to your naive claim, the computations of GR are
consistent with the experiments.
> For that reason Roberts Roberts superior brothers in
> Einstein criminal cult have always been teaching that the speed of
> light varies with the gravitational potential, in accordance with
> Einstein's 1911 equation c'=c(1+V/c^2)
As I have said so often, your blind insistence on the validity of that
formula is wrong. In 1911 Einstein did not fully understand the
difference between local and global phenomena. With the advent of GR in
1915 Einstein (and anybody else with the wit to understand GR) learned
the distinction between local and global: that formula is valid only
when one uses standards of measure valid far from the location where the
measurement was made, which is NOT how we normally measure things.
Obviously YOU do not have the wit to understand this.
> http://www.physlink.com/Education/AskExperts/ae13.cfm
> [...]
You should read your own references. It includes the statement "You can
find a more sophisticated result derived later by Einstein from the full
general theory...". That is essentially what I have been trying to tell
you for a long time. That reference does not contradict what I have been
saying, as long as one considers its entire discussion.
[Do not expect me to respond further until you grow up and
stop acting like a spoiled 3-year-old.]
Tom Roberts
Tom Roberts
> In his 1911 work "Über den Einfluss der Schwerkraft auf die Ausbreitung
> des Lichtes", Annalen der Physik 35 (1911); translated: "On the
> Influence of Gravitation on the Propagation of Light" Einstein uses the
> equivalence principle to derive the relation for gravitational red-shift
> nu_1 = nu_2 (1 + V/c^2)
> From this he concluded that the speed of light must vary according to
> c = c_0 (1 + V/c^2)
> Using this equation Einstein derives a relation for the deflection angle
> for light passing the sun (1911):
> alpha = 2 GM / (c^2 R)
Yes. When I said the second equation above was approximately correct, I
meant only for measurements of speed using distant standards. I did not
consider the further elaboration of it to an invalid result for the
deflection of light by the sun. The approximation used for speeds is not
good enough for angles, because as you point out (and is well known),
spatial curvature enters into the latter.
Tom Roberts
Koobee Wublee
> Koobee Wublee schrieb:
> > The equation is correct for gravitational redshift. <shrug>
>
> Of course, because Einstein derived the c-equation in his 1911 work from
> the correct equation for gravitational red-shift. The sequence of his
> steps was:
>
> equivalence principle
>
> --> red-shift: nu_1 = nu_2 (1 + V/c^2)
>
> --> varying speed of light: c = c_0 (1 + V/c^2)
>
> --> deflection angle for bending of light: alpha = 2 GM / (c^2 R)
Einstein did not derive anything. In this case, he merely stated
them. <shrug>
There are at least two ways to state what the speed of light is as a
gradient.
** c = c_0 (1 - U)
** c = c_0 / (1 + U)
Where
** U = G M / c^2 / r
Both cases are the same if (1 >> U). However, at the extreme
boundaries, they are drastically different.
> > This equation will lead to a wrong value of the gravitational
> > redshift. This is another example where GR is contradictory of itself
> > because it does not agree with the metric derivation as you have shown
> > above.
>
> You can take this as contradiction only, if gravitational red-shift
> would depend on a variable speed of light. In fact this is not correct
> in GR. Gravitational red-shift depends on the metric, so I wrote a few
> lines above:
>
> The gravitiational red-shift depends on the metric:
>
> nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
>
> In weak fields the following approximation holds:
>
> nu_B / nu_A = 1 + Delta V/c^2
In physics in general, we have
C = nu lambda
Where
** nu = frequency
** lambda = wavelength
There is no way you can get away with the red-shift not dependent on
the speed if the speed does indeed vary. Thus, I stand by my
conclusion that the subject of gravitational redshift is one instance
where this interpretation to the field equations is contradicting
itself. <shrug>
> You can find this in Einsteins 1916 work:
>
> Die Grundlage der allgemeinen Relativitätstheorie.
> AdP 49, 769 (1916)
> (§22, pp 818 - 820)http://www.physik.uni-augsburg.de/annalen/history/papers/1916_49_769-...
>
> (Sorry, but I don't know where to find an english translation of this work.)
Sorry, ich lese nicht Deutsch.
Pentcho Valev
Roberts Roberts your analysis of Einstein's 1911 equation c'=c(1+V/
c^2) is so silly and contradictory that I suspect you are just
experimenting with some new ad hoc camouflage. Perhaps 10 years ago
the experiment would have been more successful but now.....Look around
you Roberts Roberts - you are the only hypnotist in Einstein criminal
cult that still defends Einstein's idiocies. Even hypnotists as silly
as Steve Carlip and John Baez now know what is going on and do not
wish to take their heads out of the sand (lately you have not seen
messages from them defending or even mentioning Einstein's relativity
have you).
Pentcho Valev
pva...@yahoo.com
Koobee Wublee
> On Jan 18, 11:00 pm, Koobee Wublee wrote:
> > Anyone can do a little bit more research into Eddington's expedition
> > to find out the truth. <shrug>
>
> Eddington's expedition is of historical interest only. He could have
> made it all up and it still doesn't affect the more recent - more
> accurate - measurements.
Well, there is no other credible experiment on the bending of light
done since Eddington's dishonest deed. <shrug>
Try not to confuse bending light with Shapiro effect.
> > I still do expect Einstein Dingleberries to deny facts and logic.
> > They continue to twist logic around and distort history so they can
> > proudly be Einstein Dingleberries. The question is that "does it get
> > old after a while?" After all, the study of physics demands the truth
> > and 100% logical reasoning that Einstein Dingleberries lack. <shrug>
>
> ...and when all is said and done, you are the one stuck posting on
> USENET under a pseudonym because you are completely impotent in
> effecting the change you believe is required.
After so many years being a super senior, I would expect that getting
your BS degree is a priority rather than worrying about anyone else's
everyday lifestyle. <shrug>
Koobee Wublee
> Dieter Heidorn wrote:
> > In his 1911 work "Über den Einfluss der Schwerkraft auf die Ausbreitung
> > des Lichtes", Annalen der Physik 35 (1911); translated: "On the
> > Influence of Gravitation on the Propagation of Light" Einstein uses the
> > equivalence principle to derive the relation for gravitational red-shift
> > nu_1 = nu_2 (1 + V/c^2)
> > From this he concluded that the speed of light must vary according to
> > c = c_0 (1 + V/c^2)
> > Using this equation Einstein derives a relation for the deflection angle
> > for light passing the sun (1911):
> > alpha = 2 GM / (c^2 R)
> > This is wrong by a factor 2. [...]
>
> Yes. When I said the second equation above was approximately correct, I
> meant only for measurements of speed using distant standards.
Hmmm. It sounds like you are trying to retract your absurd
statement. If GR allows the speed of light to vary according to each
point in space, the following equation brought up by several
individuals is accurate to the first order effect. The second order
is at least 5 orders of magnitude smaller.
c = c0 (1 - U)
Where
** U = G M / c^2 / r
> I did not
> consider the further elaboration of it to an invalid result for the
> deflection of light by the sun.
As a professional experimental physicist, I would expect you to
qualify any experimental results thoroughly. Yet, you have chosen to
embrace Eddington's dishonest and very questionable interpretation to
the deflection angles during a solar eclipse.
> The approximation used for speeds is not
> good enough for angles, because as you point out (and is well known),
> spatial curvature enters into the latter.
Yes, modeling the speed of light accurate down to one in at least 5
orders of magnitude does not agree with the deflection angle
worshipped by the physicists since then. This should serve as an
alarm to establish a contradictory prediction within GR. Yet, it is
just swept under the rug. The physicists in the meantime just do a
lot of pretending.
Koobee Wublee
> Pentcho Valev wrote:
> > In other words Roberts Roberts, the
> > equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE: any different
> > equation (that may seem correct to you) would be inconsistent with the
> > redshift factor.
>
> This is nonsense. You REALLY need to learn how mathematical physics
> works. While that equation is CONSISTENT WITH CURRENT EXPERIMENTS, that
> does not justify the word "correct". It was derived without any
> consistent theoretical framework. Such a framework was presented in
> 1915, General Relativity. In GR the formula is DIFFERENT (and cannot be
> written in closed form), but FOR THE SITUATIONS OF THE CURRENT
> EXPERIMENTS THE GR EQUATION IS NOT DISTINGUISHABLE FROM THE ABOVE
> EQUATION. That's what we mean when we say "it is an APPROXIMATION".
In GR, there is no mathematics describing each point in space having
its own value of the speed of light. You are assuming too much.
<shrug>
> Indeed, contrary to your naive claim, the computations of GR are
> consistent with the experiments.
GR is only consistent with the experiments only if the outcome of
these experiments had already been decided before these experiments
were to take place.
> > For that reason Roberts Roberts superior brothers in
> > Einstein criminal cult have always been teaching that the speed of
> > light varies with the gravitational potential, in accordance with
> > Einstein's 1911 equation c'=c(1+V/c^2)
>
> As I have said so often, your blind insistence on the validity of that
> formula is wrong. In 1911 Einstein did not fully understand the
> difference between local and global phenomena.
Not just 1911, Einstein did not fully understand anything. PERIOD.
> With the advent of GR in
> 1915 Einstein (and anybody else with the wit to understand GR) learned
> the distinction between local and global: that formula is valid only
> when one uses standards of measure valid far from the location where the
> measurement was made, which is NOT how we normally measure things.
> Obviously YOU do not have the wit to understand this.
Given the spacetime below,
ds^2 = g_ij dq^i dq^j
Are you saying dq^i, dq^j are all local measurements? Well, you are
wrong. They are the measurements of an observer.
> >http://www.physlink.com/Education/AskExperts/ae13.cfm
> > [...]
>
> You should read your own references. It includes the statement "You can
> find a more sophisticated result derived later by Einstein from the full
> general theory...". That is essentially what I have been trying to tell
> you for a long time. That reference does not contradict what I have been
> saying, as long as one considers its entire discussion.
>
> [Do not expect me to respond further until you grow up and
> stop acting like a spoiled 3-year-old.]
So, after making all these silly statements, you just casually walk
away. Well, <shrug>
Eric Gisse
> On Jan 19, 12:51 am, Eric Gisse <jowr...@gmail.com> wrote:
>
> > On Jan 18, 11:00 pm, Koobee Wublee wrote:
> > > Anyone can do a little bit more research into Eddington's expedition
> > > to find out the truth. <shrug>
>
> > Eddington's expedition is of historical interest only. He could have
> > made it all up and it still doesn't affect the more recent - more
> > accurate - measurements.
>
> Well, there is no other credible experiment on the bending of light
> done since Eddington's dishonest deed. <shrug>
http://relativity.livingreviews.org/Articles/lrr-1998-12/
Now go away.
Dieter Heidorn
> On Jan 19, 5:46 am, Dieter Heidorn wrote:
>
>>Koobee Wublee schrieb:
>
>>
>>Of course, because Einstein derived the c-equation in his 1911 work from
>>the correct equation for gravitational red-shift.
>>
> them. <shrug>
>
A look in his 1911 work will show you that this is not correct. This
work is available in english (see the repeated postings of Pentcho Valev):
" 'On the Influence of Gravitation on the Propagation of
Light,' Annalen der Physik, 35, 1911. You can find a copy beginning on
page 99 of the Dover book 'The Principle of Relativity.' "
>>>> [variable speed of light in GR: c_A = c ( 1 + 2 V/c^2)]
>>>>
>>>This equation will lead to a wrong value of the gravitational
>>>redshift. This is another example where GR is contradictory of itself
>>>because it does not agree with the metric derivation as you have shown
>>>above.
>>
>>You can take this as contradiction only, if gravitational red-shift
>>would depend on a variable speed of light. In fact this is not correct
>>in GR.
>>The gravitational red-shift depends on the metric:
>>
>> nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
>>
>>In weak fields the following approximation holds:
>>
>> nu_B / nu_A = 1 + Delta V/c^2
>
>
> In physics in general, we have
>
> C = nu lambda
>
> Where
>
> ** nu = frequency
> ** lambda = wavelength
>
> There is no way you can get away with the red-shift not dependent on
> the speed if the speed does indeed vary. Thus, I stand by my
> conclusion that the subject of gravitational redshift is one instance
> where this interpretation to the field equations is contradicting
> itself. <shrug>
>
In local inertial frames of reference the speed of light is constant.
Thus local measurements always result in
c ~ 3e8 m/s
So a shifted frequency leads to a shifted wavelength and you have
c = nu lambda = const
The variability of the speed of light in GR is not to be understood in
the sense of Einstein's 1911 work. That was preliminary.
The meaning of the equation
c_A = c ( 1 + 2 V/c^2)
can be taken from Einstein's 1916 work:
>>Die Grundlage der allgemeinen Relativitätstheorie.
>>AdP 49, 769 (1916)
>
> Sorry, ich lese nicht Deutsch.
>
But you can write it - fine :-)
If you're interested, here's an english textbook containing Einstein's
four lectures given at Princeton University (1921) that gave an overview
of his main ideas in his 1916 work:
"The Meaning of Relativity (ISBN: 9780691120270)
University Presses of Ca."
I try to give a short overview of the part concerning the variable speed
of light in GR:
An observer at a point B outside the gravitational field of a mass M
(that means: in a sufficient great distance) uses a coordinate system CS
with coordinates (x^mu) = (ct, x^i). Using his coordinates he measures
the line element (or the metric)
ds^2 = g_mu,nu dx^mu dx^nu
In linear approximation for weak fields (V << c^2) the following
equation holds:
ds^2 = (1 + 2V/c^2) c^2dt^2 - (1 - 2V/c^2) dx^2
Another observer is located at a Point A near the mass M. He uses a
local frame of reference (at rest relative to CS) with coordinates
(X^alpha) = (cT, X^i). Using local coordinates he measures the line element
ds^2 = c^2 dT^2 - dX^2
The speed of light at A results as follows:
* measured by the observer at A:
ds^2 = 0
c^2 dT^2 = dX^2
c_A(measured at A) = dX/dT = c
That means as stated before:
In local inertial frames of reference the speed of light is constant,
and local measurements always result in
c ~ 3e8 m/s
* measured by the observer at B:
ds^2 = 0
(1 + 2V/c^2) c^2dt^2 = (1 - 2V/c^2) dx^2
c (1 + V/c^2) dt = (1 - V/c^2) dx
c_A(measured at B) = dx/dt = c (1 + V/c^2) / (1 - V/c^2)
c_A(measured at B) = c (1 + 2V/c^2)
Clearly the observer at A cannot use c_A = (1 + 2V/c^2), and of course
he will not measure a local variability of c in his local frame of
reference.
The difference between
c_A = c (1 + 2V/c^2) (1916)
and
c_A = c (1 + V/c^2) (1911)
is the factor 2 with the gravitational potential. Equation (1916) is
confirmed by experiment, for instance by:
* light deflection
(using eq.(1916) Einstein calculates the correct deflection angle
alpha = 4 GM / (c^2 R))
* radar time delay (Shapiro experiment)
So eq.(1911) is disproved by experiment. It's consistency with
gravitational redshift is based on the fact, that it was derived from
the correct equation for the frequency shift - however it's wrong
because it was derived using flat space instead of curved space-time.
The connections can (very) simplified be illustrated by the following
diagram:
equivalence principle
| |
| 1911 | 1916
| |
frequency shift <---------- metric ds^2
|
variable speed of light (non-local)
|
light deflection
Dieter Heidorn
Eric Gisse
[...]
You are wasting your time explaining anything to him, he is both
unwilling and unable to understand anything that disrupts his beliefs.
Ken S. Tucker
Dieter's answer is about as good as it gets.
We should have an FAQ for SP.relativity, and
put his post there, to save typing.
Regards
Ken S. Tucker
JanPB
So you have no arguments left. Why do you post?
--
Jan Bielawski
JanPB
>
> Not just 1911, Einstein did not fully understand anything. PERIOD.
The vehemence of your absurd claims of this sort is intriguing, BTW.
(Especially when spoken by a physics ignoramus.)
--
Jan Bielawski
Koobee Wublee
> Koobee Wublee schrieb:
> > Einstein did not derive anything. In this case, he merely stated
> > them. <shrug>
>
> A look in his 1911 work will show you that this is not correct. This
> work is available in english (see the repeated postings of Pentcho Valev):
> " 'On the Influence of Gravitation on the Propagation of
> Light,' Annalen der Physik, 35, 1911. You can find a copy beginning on
> page 99 of the Dover book 'The Principle of Relativity.' "
But, it is all Grossmann's work. <shrug>
> > In physics in general, we have
>
> > C = nu lambda
>
> > Where
>
> > ** nu = frequency
> > ** lambda = wavelength
>
> > There is no way you can get away with the red-shift not dependent on
> > the speed if the speed does indeed vary. Thus, I stand by my
> > conclusion that the subject of gravitational redshift is one instance
> > where this interpretation to the field equations is contradicting
> > itself. <shrug>
>
> In local inertial frames of reference the speed of light is constant.
> Thus local measurements always result in
>
> c ~ 3e8 m/s
>
> So a shifted frequency leads to a shifted wavelength and you have
>
> c = nu lambda = const
Well, if each point in space measures the speed of light to be 3e8m/
Sec, there would be serious problems in principle, but that is another
chapter of discussion.
> The variability of the speed of light in GR is not to be understood in
> the sense of Einstein's 1911 work. That was preliminary.
> The meaning of the equation
>
> c_A = c ( 1 + 2 V/c^2)
>
> can be taken from Einstein's 1916 work:
We shall see.
> >>Die Grundlage der allgemeinen Relativitätstheorie.
> >>AdP 49, 769 (1916)
>
> > Sorry, ich lese nicht Deutsch.
>
> But you can write it - fine :-)
Danke. Ich schreibe nicht zehr gut in Deutsch.
There is no mathematics that says c should be 3e8m/Sec. <shrug>
Your exercise was already claimed by Poincare that the speed of light
must be a scalar and constant to an observer.
> * measured by the observer at B:
>
> ds^2 = 0
>
> (1 + 2V/c^2) c^2dt^2 = (1 - 2V/c^2) dx^2
>
> c (1 + V/c^2) dt = (1 - V/c^2) dx
>
> c_A(measured at B) = dx/dt = c (1 + V/c^2) / (1 - V/c^2)
>
> c_A(measured at B) = c (1 + 2V/c^2)
>
> Clearly the observer at A cannot use c_A = (1 + 2V/c^2), and of course
> he will not measure a local variability of c in his local frame of
> reference.
OK, but since an observer always observe the speed of light to be c
whatever the square root of the product of the permeability and the
permittivity in free space happens to be, the speed of light as a
function of the Newtonian gravitational potential does not reflect the
observed. What you have written down represents the actual speed of
light at that point in space even if you have observed the speed of
light in accordance to c.
> The difference between
>
> c_A = c (1 + 2V/c^2) (1916)
>
> and
>
> c_A = c (1 + V/c^2) (1911)
>
> is the factor 2 with the gravitational potential. Equation (1916) is
> confirmed by experiment, for instance by:
>
> * light deflection
> (using eq.(1916) Einstein calculates the correct deflection angle
> alpha = 4 GM / (c^2 R))
Theoretically, yes. However, the only experiment (the 1919 expedition
of Eddington) on is flawed. <shrug>
> * radar time delay (Shapiro experiment)
If you have followed through the mathematics, this actually supports
the 1911 result after establishing the following relationship.
dt / c = dTau / C
Where
** dt = Observer's own flow of time
** dTau = Flow of time at a particular point in space
** c = Observer's own speed of light
** C = Speed of light at that particular point in space
> So eq.(1911) is disproved by experiment.
No, not really. There has been no experiment that disproves the 1911
equation. In fact, the 1916 equation is very absurd, for it does not
agree with the gravitational redshift or with the gravitational time
delay.
Koobee Wublee
> On Jan 19, 10:03 pm, Koobee Wublee wrote:
> > Well, there is no other credible experiment on the bending of light
> > done since Eddington's dishonest deed. <shrug>
>
> http://relativity.livingreviews.org/Articles/lrr-1998-12/
>
> Now go away.
Apparently, you do not understand anything, and that is why you are
still a multi-year super-senior today. Your mom and dad must be very
disappointed of you.
The article does not give any other credible experiment after
Eddington's 1919 expedition. You smell Einstein Dingleberry even
before encountering one when you read about the gravitational lens
must prove the validity of GR. Lord Cavendish and a generation later
Soldner had already predicted the gravitational lens based on the
Newtonian law of gravity.
> > After so many years being a super senior, I would expect that getting
> > your BS degree is a priority rather than worrying about anyone else's
> > everyday lifestyle. <shrug>
Now, get lost.
JanPB
> You smell Einstein Dingleberry even
> before encountering one when you read about the gravitational lens
> must prove the validity of GR. Lord Cavendish and a generation later
> Soldner had already predicted the gravitational lens based on the
> Newtonian law of gravity.
Hahahahaha!
--
Jan Bielawski
The TimeLord
> On 17 ene, 12:27, Eric Gisse <jowr...@gmail.com> wrote:
>> On Jan 17, 3:05 am, Albertito <albertito1...@gmail.com> wrote:
[...]
>> It'd be sooo helpful if you learned some GR.
>
> Then, why did Einstein propose a local speed of light as
> shitted his GR and then abandoned it for you to frolic on
> that bullshit, like dung beetles?.
Why is it that people like you keep quoting Einstein out of context.
If you read what Einstein actually wrote in deriving that equation, it
is not the local speed of light, but the _apparent_ speed of light due
time lapse in a gravitational field.
If you're going to quote Einstein's equations, then at least try to
quote them correctly and in context.
[...]
> Is the equivalence principle sacred?. Who says it can't be violated?
> you?.
Yes the Equivalence Principle is sacred. The reason is that all
_experiments_ have shown it to be correct.
[...]
>>> N(r) = exp( -2V_r/c^2),
>>> with V_r the gravitational potential at r,
>> Once again you pull this out of your ass, with no derivation or
>> support whatsoever.
>>
>
> Fello, that equation can be easily deduced from newtonian gravity,
> you only need some elementary notions on classical optics.
Optics? Photons have mass=0 (as shown by experiment), which makes the
Newtonian version invalid for light.
[...]
--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!
Eric Gisse
> On Jan 20, 5:07 am, Eric Gisse <jowr...@gmail.com> wrote:
>
> > On Jan 19, 10:03 pm, Koobee Wublee wrote:
> > > Well, there is no other credible experiment on the bending of light
> > > done since Eddington's dishonest deed. <shrug>
>
> >http://relativity.livingreviews.org/Articles/lrr-1998-12/
>
> > Now go away.
>
> Apparently, you do not understand anything, and that is why you are
> still a multi-year super-senior today. Your mom and dad must be very
> disappointed of you.
>
> The article does not give any other credible experiment after
> Eddington's 1919 expedition. You smell Einstein Dingleberry even
> before encountering one when you read about the gravitational lens
> must prove the validity of GR. Lord Cavendish and a generation later
> Soldner had already predicted the gravitational lens based on the
> Newtonian law of gravity.
You are not qualified to determine if an observation is credible.
Dieter Heidorn
> On Jan 20, 9:11 am, Dieter Heidorn <d.heid...@t-online.de> wrote:
>
>>Koobee Wublee schrieb:
>
>>>Einstein did not derive anything. In this case, he merely stated
>>>them. <shrug>
>>
>>A look in his 1911 work will show you that this is not correct. This
>>work is available in english (see the repeated postings of Pentcho Valev):
>>" 'On the Influence of Gravitation on the Propagation of
>>Light,' Annalen der Physik, 35, 1911. You can find a copy beginning on
>>page 99 of the Dover book 'The Principle of Relativity.' "
>
> But, it is all Grossmann's work. <shrug>
>
The 1911 work is based on an article Einstein published 1907 in
"Jahrbuch der Radioaktivität und Elektronik" 4,411(1907)
Here the relation
c' = c(1 + V/c^2)
is derived for the first time.
Einstein and Grossmann worked together in 1912/1913. In their common
work, Grossmann contributed Riemannian Geometry and tensor calculus as
convenient mathematical frame for the development of GR. The physical
part is completely due to Einstein. For historical details see for
instance A.Pais: " 'Subtle is the Lord...' The Science and the Life of
Albert Einstein".
>> In local inertial frames of reference the speed of light is constant,
>> and local measurements always result in
>>
>> c ~ 3e8 m/s
>
> There is no mathematics that says c should be 3e8m/Sec. <shrug>
>
I didn't claim that the value of c could be derived mathematically... I
just mentioned that local measurements always result in this value.
>>* [speed of light at A] measured by the observer at B:
>>
>> ds^2 = 0
>>
>> (1 + 2V/c^2) c^2dt^2 = (1 - 2V/c^2) dx^2
>>
>> c (1 + V/c^2) dt = (1 - V/c^2) dx
>>
>> c_A(measured at B) = dx/dt = c (1 + V/c^2) / (1 - V/c^2)
>>
>> c_A(measured at B) = c (1 + 2V/c^2)
>>
>>Clearly the observer at A cannot use c_A = (1 + 2V/c^2), and of course
>>he will not measure a local variability of c in his local frame of
>>reference.
>
> OK, but since an observer always observe the speed of light to be c
>
...locally...
> whatever the square root of the product of the permeability and the
> permittivity in free space happens to be, the speed of light as a
> function of the Newtonian gravitational potential does not reflect the
> observed. What you have written down represents the
>
non-local
> actual speed of
> light at that point in space even if you have observed the
local
> speed of
> light in accordance to c.
>
The difference between local and non-local must always be kept in mind.
>>The difference between
>>
>>c_A = c (1 + 2V/c^2) (1916)
>>
>>and
>>
>>c_A = c (1 + V/c^2) (1911)
>>
>>is the factor 2 with the gravitational potential. Equation (1916) is
>>confirmed by experiment, for instance by:
>>
>>* light deflection
>> (using eq.(1916) Einstein calculates the correct deflection angle
>> alpha = 4 GM / (c^2 R))
>
> Theoretically, yes. However, the only experiment (the 1919 expedition
> of Eddington) on is flawed. <shrug>
>
"Eddington" was just the first experiment. Further experiments with
improved accuracy were carried out, for instance:
* measurements using radio-interferometery
* VLBI measurements on quasistellar radio sources
* observations made by the Hipparcos optical astrometry satellite
VLBI light deflection measurements have reached agreement with GR to
0.02 percent.
For references see
http://arxiv.org/abs/gr-qc/0510072
>>* radar time delay (Shapiro experiment)
>
> If you have followed through the mathematics, this actually supports
> the 1911 result after establishing the following relationship.
>
> dt / c = dTau / C
>
> Where
>
> ** dt = Observer's own flow of time
> ** dTau = Flow of time at a particular point in space
> ** c = Observer's own speed of light
> ** C = Speed of light at that particular point in space
>
Let's see.
c' = c (1 + kV/c^2)
k = 1: 1911
k = 2: 1916
Round-trip travel time for a light-ray started on earth (position -a_E),
passing near the sun (position 0, radius R), reaching Venus (position
a_V) and returning to earth:
t = 2 int dx/c' (from -a_E to a_V)
~ 2 int (1 - kV/c^2) dx/c
= 2 int dx/c - 2 int kV/c^3 dx
= t_N + delta t
The first term is the Newtonian travel time, the second term is the
relativistic deviation from the Newtonian result.
delta t = 2 kGM/c^3 int dx/r
= 2 kGM/c^3 int dx/sqrt(R^2 + x^2)
delta t ~ 2 kGM/c^3 ln(4 a_E a_V / R^2)
~ k * 120e-6 s
This agrees with the experimental value delta t ~ 240e-6 s only if
k = 2
Thus eq.(1916) c' = c (1 + 2V/c^2) is confirmed.
>>So eq.(1911) is disproved by experiment.
>
> No, not really. There has been no experiment that disproves the 1911
> equation.
>
* All time delay measurements like the Shapiro-experiment (Venus)
disprove the 1911 equation:
- Mercury
- Mariner 6 and 7
- Viking Mars landers and orbiters
- Cassini spacecraft to Saturn
For references see http://arxiv.org/abs/gr-qc/0510072
* All experiments on the deflection of light disprove the 1911
equation, because this equation leads to the wrong deflection angle
alpha = 2 GM / (c^2 R) (1911)
> In fact, the 1916 equation is very absurd, for it does not
> agree with the gravitational redshift or with the gravitational time
> delay.
>
There's no reason why eq.(1916) should agree with gravitational
redshift, because in GR gravitational redshift depends on the curved
space-time, not on variable speed of light. The agreement with
gravitational time delay was just shown.
Dieter Heidorn
Koobee Wublee
> Koobee Wublee schrieb:
> > But, it is all Grossmann's work. <shrug>
>
> The 1911 work is based on an article Einstein published 1907 in
> "Jahrbuch der Radioaktivität und Elektronik" 4,411(1907)
> Here the relation
>
> c' = c(1 + V/c^2)
>
> is derived for the first time.
Do you have a link to this article in the yearbook of radio and
electronics even if it is in German?
> Einstein and Grossmann worked together in 1912/1913. In their common
> work, Grossmann contributed Riemannian Geometry and tensor calculus as
> convenient mathematical frame for the development of GR. The physical
> part is completely due to Einstein. For historical details see for
> instance A.Pais: " 'Subtle is the Lord...' The Science and the Life of
> Albert Einstein".
Pais declared Poincare to be a vegetable that could not even
understand the basics of special relativity. Pais' account cannot be
any accurate.
> > There is no mathematics that says c should be 3e8m/Sec. <shrug>
>
> I didn't claim that the value of c could be derived mathematically... I
> just mentioned that local measurements always result in this value.
Why would any one measure this value in the speed of light? Have any
experiments been attempted to do just so at various places?
> * light deflection
> (using eq.(1916) Einstein calculates the correct deflection angle
> alpha = 4 GM / (c^2 R))
>
> > Theoretically, yes. However, the only experiment (the 1919 expedition
> > of Eddington) on is flawed. <shrug>
>
> "Eddington" was just the first experiment. Further experiments with
> improved accuracy were carried out, for instance:
>
> * measurements using radio-interferometery
> * VLBI measurements on quasistellar radio sources
> * observations made by the Hipparcos optical astrometry satellite
>
> VLBI light deflection measurements have reached agreement with GR to
> 0.02 percent.
>
> For references see
>
> http://arxiv.org/abs/gr-qc/0510072
These are not experimentations on deflection but measurements in speed
delay or rather gravitational time delay. <shrug>
> > If you have followed through the mathematics, this actually supports
> > the 1911 result after establishing the following relationship.
>
> > dt / c = dTau / C
>
> > Where
>
> > ** dt = Observer's own flow of time
> > ** dTau = Flow of time at a particular point in space
> > ** c = Observer's own speed of light
> > ** C = Speed of light at that particular point in space
>
> Let's see.
>
> c' = c (1 + kV/c^2)
>
> k = 1: 1911
> k = 2: 1916
>
> Round-trip travel time for a light-ray started on earth (position -a_E),
> passing near the sun (position 0, radius R), reaching Venus (position
> a_V) and returning to earth:
>
> t = 2 int dx/c' (from -a_E to a_V)
>
> ~ 2 int (1 - kV/c^2) dx/c
>
> = 2 int dx/c - 2 int kV/c^3 dx
>
> = t_N + delta t
Please note the constant '2' arises due to the round trip condition.
> The first term is the Newtonian travel time, the second term is the
> relativistic deviation from the Newtonian result.
>
> delta t = 2 kGM/c^3 int dx/r
>
> = 2 kGM/c^3 int dx/sqrt(R^2 + x^2)
>
> delta t ~ 2 kGM/c^3 ln(4 a_E a_V / R^2)
>
> ~ k * 120e-6 s
G = 6.7e-11 in MKS system
M = Mass of the sun = 2.0e30 Kg
R = Radius of the sun = 1.4e9 m
c = 3.0e8 m/Sec
a_E = 1.5e11 m
a_V = 1.1e11 m
delta t (round trip) = 100 k uSec
> This agrees with the experimental value delta t ~ 240e-6 s only if
>
> k = 2
>
> Thus eq.(1916) c' = c (1 + 2V/c^2) is confirmed.
I don't know where you get 240uSec of delay time from. With k = 1, it
agrees with all the calculations. One example is discussed below.
http://en.wikipedia.org/wiki/Shapiro_effect
Thus, the 1916 equation is wrong. As I mentioned below, this 1916
equation fails the necessary condition for the observed gravitational
time dilation and thus gravitational red shift.
By the way, this type of measurement on the delay time requires you to
know the accuracy of the distance involved. You'd better know this
accuracy from the earth to the Venus with a few centimeters or
better. Without an interferometer, how can you accept any
experimental results on this subject without any question?
> > No, not really. There has been no experiment that disproves the 1911
> > equation.
>
> * All time delay measurements like the Shapiro-experiment (Venus)
> disprove the 1911 equation:
>
> - Mercury
> - Mariner 6 and 7
> - Viking Mars landers and orbiters
> - Cassini spacecraft to Saturn
>
> For references seehttp://arxiv.org/abs/gr-qc/0510072
All of these involve the gravitational time dilation which is
basically the Shaprio delay as you have derived.
> * All experiments on the deflection of light disprove the 1911
> equation, because this equation leads to the wrong deflection angle
>
> alpha = 2 GM / (c^2 R) (1911)
Only 1911 equation would predict the above quantity. See the link I
gave you above.
> > In fact, the 1916 equation is very absurd, for it does not
> > agree with the gravitational redshift or with the gravitational time
> > delay.
>
> There's no reason why eq.(1916) should agree with gravitational
> redshift, because in GR gravitational redshift depends on the curved
> space-time, not on variable speed of light. The agreement with
> gravitational time delay was just shown.
To derive the Shapiro time delay through gravitational time dilation,
we have
T = 2 int[ds / c] (from -a_E to a_V)
= 2 int[dx / sqrt(1 - 2 U)] / c
~ 2 int[dx (1 + U)] / c
= 2 x / c + (G M / c^3) sinh^-1(x / R)
~ 2 (a_E + a_V) / c + 2 (G M / c^3) ln(4 a_E a_V / R^2)
Where
** U = G M / c^2 / r
** a_E >> R
** a_V >> R
This is the same derivation when we have the following 1911 equation
C(r) = c (1 - U)
The deflection must agree with time delay. Since in GR, the
deflection does not agree with time delay, GR has internal conflict.
This is not the only instance where an internal self-conflict occurs.
Thus, GR is a lousy interpretation to the very faulty set of field
equations, but this is not Einstein's fault because Einstein really
had nothing to do with the field equations and GR in general.
Would you accept this as the 'weltmaennisch' checkmate?
Dieter Heidorn
> On Jan 22, 8:38 am, Dieter Heidorn wrote:
>
>>Koobee Wublee schrieb:
>
>>>But, it is all Grossmann's work. <shrug>
>>
>>The 1911 work is based on an article Einstein published 1907 in
>>"Jahrbuch der Radioaktivität und Elektronik" 4,411(1907)
>>Here the relation
>>
>>c' = c(1 + V/c^2)
>>
>>is derived for the first time.
>
> Do you have a link to this article in the yearbook of radio and
> electronics even if it is in German?
>
I only know where to find the original work - also leider auf Deutsch:
http://www.soso.ch/wissen/hist/SRT/E-1907.pdf
>>Einstein and Grossmann worked together in 1912/1913. In their common
>>work, Grossmann contributed Riemannian Geometry and tensor calculus as
>>convenient mathematical frame for the development of GR. The physical
>>part is completely due to Einstein. For historical details see for
>>instance A.Pais: " 'Subtle is the Lord...' The Science and the Life of
>>Albert Einstein".
>
> Pais declared Poincare to be a vegetable that could not even
> understand the basics of special relativity. Pais' account cannot be
> any accurate.
>
It's not a question of account but a question of historical sources, for
instance:
* the correspondence between Einstein and Grossmann before 1912,
when Einstein returned to Zürich and started working with Grossmann,
* the papers published by Einstein before 1912.
Grossmann has nothing to do with Einstein's works before 1912.
>>* light deflection
>> (using eq.(1916) Einstein calculates the correct deflection angle
>> alpha = 4 GM / (c^2 R))
>>
>>>Theoretically, yes. However, the only experiment (the 1919 expedition
>>>of Eddington) on is flawed. <shrug>
>>
>>"Eddington" was just the first experiment. Further experiments with
>>improved accuracy were carried out, for instance:
>>
>>* measurements using radio-interferometery
>>* VLBI measurements on quasistellar radio sources
>>* observations made by the Hipparcos optical astrometry satellite
>>
>>VLBI light deflection measurements have reached agreement with GR to
>>0.02 percent.
>>
>>For references see
>>
>>http://arxiv.org/abs/gr-qc/0510072
>
> These are not experimentations on deflection but measurements in speed
> delay or rather gravitational time delay. <shrug>
>
These _are_ experiments on light deflection. Please have a look at
http://arxiv.org/abs/gr-qc/0510072
pages 33 - 35.
>>c' = c (1 + kV/c^2)
>>
>> k = 1: 1911
>> k = 2: 1916
>>
>>Round-trip travel time for a light-ray started on earth (position -a_E),
>>passing near the sun (position 0, radius R), reaching Venus (position
>>a_V) and returning to earth:
>>
>>t = 2 int dx/c' (from -a_E to a_V)
>>
>> ~ 2 int (1 - kV/c^2) dx/c
>>
>> = 2 int dx/c - 2 int kV/c^3 dx
>>
>> = t_N + delta t
>
> Please note the constant '2' arises due to the round trip condition.
>
That's why I wrote "round-trip travel time".
>>The first term is the Newtonian travel time, the second term is the
>>relativistic deviation from the Newtonian result.
>>
>>delta t = 2 kGM/c^3 int dx/r
>>
>> = 2 kGM/c^3 int dx/sqrt(R^2 + x^2)
>>
>>delta t ~ 2 kGM/c^3 ln(4 a_E a_V / R^2)
>>
>> ~ k * 120e-6 s
>
> G = 6.7e-11 in MKS system
> M = Mass of the sun = 2.0e30 Kg
> R = Radius of the sun = 1.4e9 m
>
In Europe we are told that the radius of the sun is
R = 6.96e8 m :-)
> c = 3.0e8 m/Sec
> a_E = 1.5e11 m
> a_V = 1.1e11 m
>
> delta t (round trip) = 100 k uSec
>
Using the sun's european radius ;-) we obtain using the above equation
for delta t:
delta t (round trip) = k * 120 uSec
This agrees with the experimental value delta t ~ 240 uSec only if
k = 2
Thus eq.(1916) c' = c (1 + 2V/c^2) is confirmed.
> I don't know where you get 240uSec of delay time from. With k = 1, it
> agrees with all the calculations.
>
Obviously not: for k = 1 you get
delta t (round trip) = 1 * 120 uSec
> http://en.wikipedia.org/wiki/Shapiro_effect
>
The equation given there:
delta t = -2 (GM / c^3) ln(1 - R.x)
is valid for one half of the round-trip. The factor in this equation is
due to eq.(1916) - it's the k = 2.
> By the way, this type of measurement on the delay time requires you to
> know the accuracy of the distance involved. You'd better know this
> accuracy from the earth to the Venus with a few centimeters or
> better. Without an interferometer, how can you accept any
> experimental results on this subject without any question?
>
The delta t (round trip) is equivalent to a seeming (virtual?
apparent?) increase of the distance between Earth and Venus of
c delta t / 2 = 36 km
It's not necessary to know the distance with an accuracy of centimeters.
The distance Earth - Venus when Venus stands between Earth and
Sun can be measured by measuring the travel time of reflected radar
signals. In combination with the data of Venus' orbit you get the
distance needed for the Shapiro-Experiment.
>>* All time delay measurements like the Shapiro-experiment (Venus)
>> disprove the 1911 equation:
>>
>> - Mercury
>> - Mariner 6 and 7
>> - Viking Mars landers and orbiters
>> - Cassini spacecraft to Saturn
>>
>> For references see http://arxiv.org/abs/gr-qc/0510072
>
>>* All experiments on the deflection of light disprove the 1911
>> equation, because this equation leads to the wrong deflection angle
>>
>> alpha = 2 GM / (c^2 R) (1911)
>
Your calculation concerning time delay:
> To derive the Shapiro time delay through gravitational time dilation,
> we have
>
> T = 2 int[ds / c] (from -a_E to a_V)
> = 2 int[dx / sqrt(1 - 2 U)] / c
> ~ 2 int[dx (1 + U)] / c
> = 2 x / c + (G M / c^3) sinh^-1(x / R)
> ~ 2 (a_E + a_V) / c + 2 (G M / c^3) ln(4 a_E a_V / R^2)
>
> Where
>
> ** U = G M / c^2 / r
> ** a_E >> R
> ** a_V >> R
>
> This is the same derivation when we have the following 1911 equation
>
> C(r) = c (1 - U)
>
Your calculation is the same calculation as I have given - with a little
meaningful difference. Please compare:
[KW] T = 2 int[dx (1 + U)] / c or:
T = (2/c) int dx (1 - V/c^2)
[DH] T = (2/c) int dx (1 - kV/c^2)
For the round trip we get:
[KW] delta t (round trip) = 2 (G M / c^3) ln(4 a_E a_V / R^2)
[DH] delta t (round trip) = 2 k (G M / c^3) ln(4 a_E a_V / R^2)
The values are as mentioned above:
[KW] delta t (round trip) ~ 120 uSec
[DH] delta t (round trip) ~ 240 uSec
240 uSec is in agreement with experimental data.
> The deflection must agree with time delay.
>
Starting with the equation
c' = c (1 + kV/c^2)
k = 1: 1911
k = 2: 1916
you can derive
1. light deflection angle:
alpha = k * 2 GM / (c^2 R)
Experiments show: k = 2.
2. time delay:
delta t (round trip) = k * (2 G M / c^3) ln(4 a_E a_V / R^2)
Experiments show: k = 2
So eq.(1911) is disproved by experiment.
Dieter Heidorn
Dono
> You are an Einstein Dingleberry by heart ranking in the same
> league as moortel, Gisse, Jeckyl, Dono, and other Andro-phobic
> Wackos. You all deserve each other. <shrug>
Dono
>
> The article does not give any other credible experiment after
> Eddington's 1919 expedition.
How can be so a denying asshole? Wait, don't answer that, look at
this:
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Koobee Wublee
> Koobee Wublee schrieb:
> > Do you have a link to this article in the yearbook of radio and
> > electronics even if it is in German?
>
> I only know where to find the original work - also leider auf Deutsch:
>
> http://www.soso.ch/wissen/hist/SRT/E-1907.pdf
Danke. It is going to take some time for me to sort through it.
> > Pais declared Poincare to be a vegetable that could not even
> > understand the basics of special relativity. Pais' account cannot be
> > any accurate.
>
> It's not a question of account but a question of historical sources, for
> instance:
Yes, indeed. However, the modern historic sources are from the
usurpers like Pais who tried to write his own account of history.
<shrug>
> * the correspondence between Einstein and Grossmann before 1912,
> when Einstein returned to Zürich and started working with Grossmann,
>
> * the papers published by Einstein before 1912.
> Grossmann has nothing to do with Einstein's works before 1912.
OK, from all the references I have uncovered all have claimed Einstein-
Grossmann cooperation began in 1912.
> > These are not experimentations on deflection but measurements in speed
> > delay or rather gravitational time delay. <shrug>
>
> These _are_ experiments on light deflection. Please have a look at
>
> http://arxiv.org/abs/gr-qc/0510072
>
> pages 33 - 35.
Have you not noticed that there are all claims and no specific
experiments shown with analyzable data given?
> > G = 6.7e-11 in MKS system
> > M = Mass of the sun = 2.0e30 Kg
> > R = Radius of the sun = 1.4e9 m
>
> In Europe we are told that the radius of the sun is
>
> R = 6.96e8 m :-)
OK, it is my mistake to use the diameter instead of the radius.
> > By the way, this type of measurement on the delay time requires you to
> > know the accuracy of the distance involved. You'd better know this
> > accuracy from the earth to the Venus with a few centimeters or
> > better. Without an interferometer, how can you accept any
> > experimental results on this subject without any question?
>
> The delta t (round trip) is equivalent to a seeming (virtual?
> apparent?) increase of the distance between Earth and Venus of
>
> c delta t / 2 = 36 km
What does this 36Km have anything to do with anything?
> It's not necessary to know the distance with an accuracy of centimeters.
Why?
> The distance Earth - Venus when Venus stands between Earth and
> Sun can be measured by measuring the travel time of reflected radar
> signals. In combination with the data of Venus' orbit you get the
> distance needed for the Shapiro-Experiment.
I am still not convinced this 240uSec is qualified. There is no
interferometer to detect such a minute difference in signal. There is
no way to nail down the distance from the earth to Venus to an
accuracy of mere centimeters. There is no reference signal to be
compared with.
> > To derive the Shapiro time delay through gravitational time dilation,
> > we have
>
> > T = 2 int[ds / c] (from -a_E to a_V)
> > = 2 int[dx / sqrt(1 - 2 U)] / c
> > ~ 2 int[dx (1 + U)] / c
> > = 2 x / c + (G M / c^3) sinh^-1(x / R)
> > ~ 2 (a_E + a_V) / c + 2 (G M / c^3) ln(4 a_E a_V / R^2)
>
> > Where
>
> > ** U = G M / c^2 / r
> > ** a_E >> R
> > ** a_V >> R
>
> > This is the same derivation when we have the following 1911 equation
>
> > C(r) = c (1 - U)
>
> Your calculation is the same calculation as I have given - with a little
> meaningful difference.
Well, I see my mistake. Thank you for pointing that out. There is an
extra curvature in the r direction. Thus, according to the
Schwarzschild metric, we have the round trip time derived as the
following.
T = 2 int[ds / sqrt(1 - 2 U) / sqrt(1 - 2 U)] (from -a_E to a_V)
= 2 int[dx / (1 - 2 U)] / c
~ 2 int[dx (1 + 2 U)] / c
= 2 x / c + (4 G M / c^3) sinh^-1(x / R)
~ 2 (a_E + a_V) / c + (4 G M / c^3) ln(4 a_E a_V / R^2)
Thus, the delay time is
dt = (4 G M / c^3) ln(4 a_E a_V / R^2)
> Starting with the equation
>
> c' = c (1 + kV/c^2)
>
> k = 1: 1911
> k = 2: 1916
However, this does not mean
C(r) = c (1 + 2 U), k = 2
Or
C(r) = c (1 + U), k = 1
Under the concept of GR, the speed of light must be the same
everywhere. That is
C(r) = c
It is the gravitational time dilation and the curvature in space that
seems to affect the speed of light in an experiment.
Eric Gisse
No, persistent idiot, the local speed of light is the same everywhere.
GR makes no claims about the global speed.
Dieter Heidorn
> On Jan 23, 1:09 pm, Dieter Heidorn schrieb:
>
>>Koobee Wublee schrieb:
>
>>>delay or rather gravitational time delay. <shrug>
>>
>>These _are_ experiments on light deflection. Please have a look at
>>
>>http://arxiv.org/abs/gr-qc/0510072
>>
>>pages 33 - 35.
>
> Have you not noticed that there are all claims and no specific
> experiments shown with analyzable data given?
>
See page 1:
"Abstract
The status of experimental tests of general relativity and of
theoretical frameworks for analysing them is
_reviewed_."
To all listed experiments are given references, for instance concerning
light deflection:
[165] Lebach, D.E., Corey, B.E., Shapiro, I.I., Ratner, M.I., Webber,
J.C., Rogers, A.E.E., Davis, J.L., and Herring, T.A., “Measurement of
the solar gravitational deflection of radio waves using
very-long-baseline interferometry”, Phys. Rev. Lett., 75, 1439–1442, (1995).
[241] Shapiro, S.S., Davis, J.L., Lebach, D.E., and Gregory, J.S.,
“Measurement of the solar gravitational deflection of radio waves using
geodetic very-long-baseline interferometry data, 1979–1999”, Phys. Rev.
Lett., 92, 121101, (2004).
[116] Froeschl´e, M., Mignard, F., and Arenou, F., “Determination of the
PPN parameter gamma with the Hipparcos data”, in Proceedings from the
Hipparcos Venice ’97 Symposium, Proceedings of the symposium held on
13-16May 1997, (ESA, Noordwijk, Netherlands, 1997).
...and so on.
>>The distance Earth - Venus when Venus stands between Earth and
>>Sun can be measured by measuring the travel time of reflected radar
>>signals. In combination with the data of Venus' orbit you get the
>>distance needed for the Shapiro-Experiment.
>
> I am still not convinced this 240uSec is qualified.
>
Irwin I. Shapiro et al.: Fourth Test of General Relativity: New Radar
Result. In: Physical Review Letters 26, 1971, S. 1132 - 1135
> Thus, the delay time is
>
> dt = (4 G M / c^3) ln(4 a_E a_V / R^2)
>
Agreed :-)
>>Starting with the equation
>>
>>c' = c (1 + kV/c^2)
>>
>> k = 1: 1911
>> k = 2: 1916
>
> However, this does not mean
>
> C(r) = c (1 + 2 U), k = 2
>
> Or
>
> C(r) = c (1 + U), k = 1
>
> Under the concept of GR, the speed of light must be the same
> everywhere. That is
>
> C(r) = c
>
The difference between local and non-local must be considered - but we
had that discussed already. I think we can end here.
Thanks for the discussion.
-----
I have collected my remarks concerning variable speed of light in GR on
my homepage. Maybe you're interested to take a look:
http://www.d1heidorn.homepage.t-online.de/Physik/VSL/VSL.html
Dieter Heidorn
Ockham
"Dieter Heidorn" <d.he...@t-online.de> wrote in message
news:fng2ih$88t$02$1...@news.t-online.com...
"The variability of the speed of light in GR is not to be understood"
Do you often write in Irish?|
Odysseus
<70d76ea7-ff98-4c90...@d21g2000prf.googlegroups.com>,
Koobee Wublee <koobee...@gmail.com> wrote:
> On Jan 23, 1:09 pm, Dieter Heidorn schrieb:
> > Koobee Wublee schrieb:
>
<snip>
> > > R = Radius of the sun = 1.4e9 m
> >
> > In Europe we are told that the radius of the sun is
> >
> > R = 6.96e8 m :-)
>
> OK, it is my mistake to use the diameter instead of the radius.
<LOL> Incroyable!
--
Odysseus
Dono
>
> I have collected my remarks concerning variable speed of light in GR on
> my homepage. Maybe you're interested to take a look:
>
> http://www.d1heidorn.homepage.t-online.de/Physik/VSL/VSL.html
>
> Dieter Heidorn
Very nice, it is great to see some real physics for a change.
Koobee Wublee
> On Jan 26, 11:44 am, Dieter Heidorn wrote:
> > I have collected my remarks concerning variable speed of light in
> > GR on my homepage. Maybe you're interested to take a look:
>
> >http://www.d1heidorn.homepage.t-online.de/Physik/VSL/VSL.html
>
> Very nice, it is great to see some real physics for a change.
Now, I am very convinced that you do not know anything. You are
embracing a renegade GR hypothesis, and you don't know.
Koobee Wublee
> Koobee Wublee schrieb:
> > Have you not noticed that there are all claims and no specific
> > experiments shown with analyzable data given?
>
> See page 1:
>
> "Abstract
> The status of experimental tests of general relativity and of
> theoretical frameworks for analysing them is
> _reviewed_."
>
> To all listed experiments are given references, for instance concerning
> light deflection:
>
> [165] Lebach, D.E., Corey, B.E., Shapiro, I.I., Ratner, M.I., Webber,
> J.C., Rogers, A.E.E., Davis, J.L., and Herring, T.A., "Measurement of
> the solar gravitational deflection of radio waves using
> very-long-baseline interferometry", Phys. Rev. Lett., 75, 1439-1442, (1995).
>
> [241] Shapiro, S.S., Davis, J.L., Lebach, D.E., and Gregory, J.S.,
> "Measurement of the solar gravitational deflection of radio waves using
> geodetic very-long-baseline interferometry data, 1979-1999", Phys. Rev.
> Lett., 92, 121101, (2004).
>
> [116] Froeschl´e, M., Mignard, F., and Arenou, F., "Determination of the
> PPN parameter gamma with the Hipparcos data", in Proceedings from the
> Hipparcos Venice '97 Symposium, Proceedings of the symposium held on
> 13-16May 1997, (ESA, Noordwijk, Netherlands, 1997).
>
> ...and so on.
Well, all these are talking about the interferometry of signals.
There is only one signal involved. How do you get the signal to
interfere with itself and get meaningful data?
> > I am still not convinced this 240uSec is qualified.
>
> Irwin I. Shapiro et al.: Fourth Test of General Relativity: New Radar
> Result. In: Physical Review Letters 26, 1971, S. 1132 - 1135
If you understand what he did, please explain how he qualified his
data.
> > Thus, the delay time is
>
> > dt = (4 G M / c^3) ln(4 a_E a_V / R^2)
>
> Agreed :-)
Yes, once again, thanks for your correction.
> > However, this does not mean
>
> > C(r) = c (1 + 2 U), k = 2
>
> > Or
>
> > C(r) = c (1 + U), k = 1
>
> > Under the concept of GR, the speed of light must be the same
> > everywhere. That is
>
> > C(r) = c
>
> The difference between local and non-local must be considered - but we
> had that discussed already. I think we can end here.
If you have time, please explain how Shapiro qualified his data.
Otherwise, let's end here if you don't know either but choose to
embrace how one can pull a very small meaningful signal out of a sea
of incoherence.
> Thanks for the discussion.
Likewise, the pleasure is mine.
> I have collected my remarks concerning variable speed of light in GR on
> my homepage. Maybe you're interested to take a look:
>
> http://www.d1heidorn.homepage.t-online.de/Physik/VSL/VSL.html
I think it would be better if you also explain how one is able to
actually determine this delay time.
Dono
No , imbecile. You wouldn't know, pompous pretender.