Re: Fermat's principle and curved spacetime

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Topic:	Science > Physics
User:	"Pentcho Valev"
Date:	18 Jan 2008 01:03:25 AM
Object:	Re: Fermat's principle and curved spacetime

On Jan 18, 6:37=A0am, Tom Roberts <tjroberts...@sbcglobal.net> wrote in
sci.physics.relativity:

Albertito wrote:

Then, why did Einstein propose a local speed of light as
c'=3D 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'=3Dc(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'=3Dc(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'=3Dc(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' =3D 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'=3Dc(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
pvalev@yahoo.com
.

User: "JanPB"
Title: Re: Fermat's principle and curved spacetime	18 Jan 2008 02:46:38 PM

On Jan 17, 11:03 pm, Pentcho Valev <pva...@yahoo.com> wrote:

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)?

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
.

User: "NoEinstein"
Title: Re: Fermat's principle and curved spacetime	18 Jan 2008 12:12:58 PM

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, 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

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)?

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

User: "Dirk Van de moortel"
Title: Re: Fermat's principle and curved spacetime	18 Jan 2008 12:35:35 PM

"NoEinstein" <noeinstein@bellsouth.net> wrote in message news:b58a7fd6-bba0-4465-b1de-f17049ff644c@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
.

User: "Dieter Heidorn"
Title: Re: Fermat's principle and curved spacetime	18 Jan 2008 03:03:57 PM

Pentcho Valev schrieb:

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)?

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 "�ber 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 Relativit�tstheorie",
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
.

User: "Tom Roberts"
Title: Re: Fermat's principle and curved spacetime	19 Jan 2008 09:29:03 AM

Dieter Heidorn wrote:

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
.

User: "Koobee Wublee"
Title: Re: Fermat's principle and curved spacetime	20 Jan 2008 01:16:28 AM

On Jan 19, 7:29 am, Tom Roberts wrote:

Dieter Heidorn wrote:

In his 1911 work "=DCber den Einfluss der Schwerkraft auf die Ausbreitun=

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 =3D nu_2 (1 + V/c^2)
From this he concluded that the speed of light must vary according to
c =3D c_0 (1 + V/c^2)
Using this equation Einstein derives a relation for the deflection angle=
for light passing the sun (1911):
alpha =3D 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 =3D c0 (1 - U)
Where
** U =3D 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.
.

User: "Pentcho Valev"
Title: Re: Fermat's principle and curved spacetime	19 Jan 2008 01:31:24 AM

On Jan 18, 11:03=A0pm, Dieter Heidorn <d.heid...@t-online.de> wrote:

Pentcho Valev schrieb:

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'=3D c(1 + V/c2)?

Tom Roberts

Roberts Roberts, Einstein's 1911 equation c'=3Dc(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 "=DCber 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 =3D nu_2 (1 + V/c^2)

=A0From this he concluded that the speed of light must vary according to

c =3D c_0 (1 + V/c^2)

Using this equation Einstein derives a relation for the deflection angle
for light passing the sun (1911):

alpha =3D 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.
Pentcho Valev
pvalev@yahoo.com
.

User: "Dieter Heidorn"
Title: Re: Fermat's principle and curved spacetime	19 Jan 2008 07:33:52 AM

Pentcho Valev schrieb:

On Jan 18, 11:03 pm, Dieter Heidorn <d.heid...@t-online.de> wrote:

Pentcho Valev schrieb:

In his 1911 work "�ber 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
.

User: "Koobee Wublee"
Title: Re: Fermat's principle and curved spacetime	18 Jan 2008 04:35:18 PM

On Jan 18, 1:03 pm, Dieter Heidorn wrote:

Pentcho Valev schrieb:

Roberts Roberts, Einstein's 1911 equation c'=3Dc(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 "=DCber 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 =3D nu_2 (1 + V/c^2)

From this he concluded that the speed of light must vary according to

c =3D c_0 (1 + V/c^2)

Using this equation Einstein derives a relation for the deflection angle
for light passing the sun (1911):

alpha =3D 2 GM / (c^2 R)

This is wrong by a factor 2. Experimentally is found

alpha =3D 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 =3D 4 G M / c^2 / R

In other words Roberts Roberts, the
equation c'=3Dc(1+V/c^2) is CORRECT, NOT APPROXIMATE:

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 Relativit=E4tstheorie",
Annalen der Physik 49 (1916) Einstein shows:

* Space-time is described with the metric

ds^2 =3D g_mu,nu dx^mu dx^nu

* The gravitiational red-shift depends on the metric:

nu_B / nu_A =3D sqrt(g_00(r_A)/g_00(r_B))

* In weak fields the following approximation holds:

nu_B / nu_A =3D 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 =3D 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.
.

User: "Dieter Heidorn"
Title: Re: Fermat's principle and curved spacetime	19 Jan 2008 07:46:41 AM

Koobee Wublee schrieb:

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 "�ber 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:

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 Relativit�tstheorie",
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)

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 Relativit�tstheorie.
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
.

User: "Koobee Wublee"
Title: Re: Fermat's principle and curved spacetime	19 Jan 2008 10:34:08 PM

On Jan 19, 5:46 am, Dieter Heidorn wrote:

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 =3D nu_2 (1 + V/c^2)

--> varying speed of light: c =3D c_0 (1 + V/c^2)

--> deflection angle for bending of light: alpha =3D 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 =3D c_0 (1 - U)
** c =3D c_0 / (1 + U)
Where
** U =3D G M / c^2 / r
Both cases are the same if (1 >> U). However, at the extreme
boundaries, they are drastically different.

In physics in general, we have
C =3D nu lambda
Where
** nu =3D frequency
** lambda =3D 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 Relativit=E4tstheorie.
AdP 49, 769 (1916)
(=A722, pp 818 - 820)http://www.physik.uni-augsburg.de/annalen/history/pap=

ers/1916_49_769-...

(Sorry, but I don't know where to find an english translation of this work=

..)
Sorry, ich lese nicht Deutsch.
.

User: "Dieter Heidorn"
Title: Re: Fermat's principle and curved spacetime	20 Jan 2008 11:11:42 AM

Koobee Wublee schrieb:

On Jan 19, 5:46 am, Dieter Heidorn wrote:

Koobee Wublee schrieb:

The equation [c = c_0 (1 + V/c^2)] is correct for gravitational redshift.

Of course, because Einstein derived the c-equation in his 1911 work from
the correct equation for gravitational red-shift.

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.' "

[variable speed of light in GR: c_A = c ( 1 + 2 V/c^2)]

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 Relativit�tstheorie.
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
.

User: "Eric Gisse"
Title: Re: Fermat's principle and curved spacetime	20 Jan 2008 11:52:47 AM

On Jan 20, 8:11 am, Dieter Heidorn <d.heid...@t-online.de> wrote:
[...]
You are wasting your time explaining anything to him, he is both
unwilling and unable to understand anything that disrupts his beliefs.
.

User: "Ken S. Tucker"
Title: Re: Fermat's principle and curved spacetime	20 Jan 2008 12:54:04 PM

On Jan 20, 9:11 am, Dieter Heidorn <d.heid...@t-online.de> wrote:

Koobee Wublee schrieb:

On Jan 19, 5:46 am, Dieter Heidorn wrote:

Koobee Wublee schrieb:

The equation [c =3D c_0 (1 + V/c^2)] is correct for gravitational redsh=

ift.

Of course, because Einstein derived the c-equation in his 1911 work from=
the correct equation for gravitational red-shift.

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.' "

[variable speed of light in GR: c_A =3D c ( 1 + 2 V/c^2)]

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 =3D sqrt(g_00(r_A)/g_00(r_B))

In weak fields the following approximation holds:

nu_B / nu_A =3D 1 + Delta V/c^2

In physics in general, we have

C =3D nu lambda

Where

** nu =3D frequency
** lambda =3D 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 =3D nu lambda =3D 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 =3D c ( 1 + 2 V/c^2)

can be taken from Einstein's 1916 work:

Die Grundlage der allgemeinen Relativit=E4tstheorie.
AdP 49, 769 (1916)

Sorry, ich lese nicht Deutsch.

ent

ds^2 =3D c^2 dT^2 - dX^2

The speed of light at A results as follows:

* measured by the observer at A:

ds^2 =3D 0

c^2 dT^2 =3D dX^2

c_A(measured at A) =3D dX/dT =3D 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 =3D 0

(1 + 2V/c^2) c^2dt^2 =3D (1 - 2V/c^2) dx^2

c (1 + V/c^2) dt =3D (1 - V/c^2) dx

c_A(measured at B) =3D dx/dt =3D c (1 + V/c^2) / (1 - V/c^2)

c_A(measured at B) =3D c (1 + 2V/c^2)

Clearly the observer at A cannot use c_A =3D (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 =3D c (1 + 2V/c^2) (1916)

and

c_A =3D 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 =3D 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

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
.

User: "Koobee Wublee"
Title: Re: Fermat's principle and curved spacetime	20 Jan 2008 11:26:05 PM

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>

But, it is all Grossmann's work. <shrug>

In physics in general, we have

C =3D nu lambda

Where

** nu =3D frequency
** lambda =3D wavelength

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 =3D c ( 1 + 2 V/c^2)

can be taken from Einstein's 1916 work:

We shall see.

Die Grundlage der allgemeinen Relativit=E4tstheorie.
AdP 49, 769 (1916)

Sorry, ich lese nicht Deutsch.

But you can write it - fine :-)

Danke. Ich schreibe nicht zehr gut in Deutsch.

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) =3D (ct, x^i). Using his coordinates he measures
the line element (or the metric)

ds^2 =3D g_mu,nu dx^mu dx^nu

In linear approximation for weak fields (V << c^2) the following
equation holds:

ds^2 =3D (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) =3D (cT, X^i). Using local coordinates he measures the line elem=

ent

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 =3D 0

(1 + 2V/c^2) c^2dt^2 =3D (1 - 2V/c^2) dx^2

c (1 + V/c^2) dt =3D (1 - V/c^2) dx

c_A(measured at B) =3D dx/dt =3D c (1 + V/c^2) / (1 - V/c^2)

c_A(measured at B) =3D c (1 + 2V/c^2)

Clearly the observer at A cannot use c_A =3D (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 =3D c (1 + 2V/c^2) (1916)

and

c_A =3D 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 =3D 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 =3D dTau / C
Where
** dt =3D Observer's own flow of time
** dTau =3D Flow of time at a particular point in space
** c =3D Observer's own speed of light
** C =3D 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.
.

User: "Dieter Heidorn"
Title: Re: Fermat's principle and curved spacetime	22 Jan 2008 10:38:25 AM

Koobee Wublee schrieb:

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>

But, it is all Grossmann's work. <shrug>

The 1911 work is based on an article Einstein published 1907 in
"Jahrbuch der Radioaktivit�t 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
.

User: "Koobee Wublee"
Title: Re: Fermat's principle and curved spacetime	22 Jan 2008 02:29:29 PM

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 Radioaktivit=E4t und Elektronik" 4,411(1907)
Here the relation

c' =3D 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 =3D 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 =3D dTau / C

Where

** dt =3D Observer's own flow of time
** dTau =3D Flow of time at a particular point in space
** c =3D Observer's own speed of light
** C =3D Speed of light at that particular point in space

Let's see.

c' =3D c (1 + kV/c^2)

k =3D 1: 1911
k =3D 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 =3D 2 int dx/c' (from -a_E to a_V)

~ 2 int (1 - kV/c^2) dx/c

=3D 2 int dx/c - 2 int kV/c^3 dx

=3D 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 =3D 2 kGM/c^3 int dx/r

=3D 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 =3D 6.7e-11 in MKS system
M =3D Mass of the sun =3D 2.0e30 Kg
R =3D Radius of the sun =3D 1.4e9 m
c =3D 3.0e8 m/Sec
a_E =3D 1.5e11 m
a_V =3D 1.1e11 m
delta t (round trip) =3D 100 k uSec

This agrees with the experimental value delta t ~ 240e-6 s only if

k =3D 2

Thus eq.(1916) c' =3D c (1 + 2V/c^2) is confirmed.

I don't know where you get 240uSec of delay time from. With k =3D 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 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 =3D 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.

To derive the Shapiro time delay through gravitational time dilation,
we have
T =3D 2 int[ds / c] (from -a_E to a_V)
=3D 2 int[dx / (1 - 2 U)] / c
~ 2 int[dx (1 + U)] / c
=3D 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 =3D 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) =3D 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?
.

User: "Koobee Wublee"
Title: Re: Fermat's principle and curved spacetime	22 Jan 2008 02:39:44 PM