"Tired" light

In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.

Mutatis mutandi, d = Ro * z/(1+z) = (c/Ho) * z/(1+z)

According to GR,

(1+z)^2 = (1+d/Ro)/(1-d/Ro).

But GR considers the frequency shifts of light from distant
sources in terms of special-relativistc Doppler shifts.
This is wrong, because expansion is symmetrical. In other words,
a clock situated on a galaxy moving at v from an observer
situated on Earth will show the same time as an Earth clock,
which moves at -v wrt the galaxy. The two relativistic effects
cancel each other.
On the other hand, GR ignores that the frequency of light is
affected by the gravitational field of the universe (cf. Steven
Weinberg, Gravitation and Cosmology, 1972, p. 417).

It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Let's consider a thought experiment:

A light ray is sent vertically from the bottom of the tower of Pisa.
For an observer situated at the top of the tower, the light will
redden in proportion to the height of the tower.

Assuming that the original wavelength is lambda, the wavelength
at the top is lambdaO, the height of the tower is d, and the
acceleration of gravity g is constant, the formula linking lambdaO,
lambda, d, and g is

lambdaO = lambda/(1-gd/c^2), thus

z = gd/(c^2-gd), and

d = (c^2/g) * z/(1+z)

In "Study of the anomalous acceleration of Pioneer 10 and 11",
John D. Anderson and al. wrote (arXiv: gr- qc/ 0104064 19 April 2001):
"As a number of people have noted, a_H = cH, or 8E-8 cm/s^2 if
H=82 km/s/Mpc."

Assuming that the observed acceleration cH is cosmological,
light should undergo a red shift in proportion to the distance
of its source.

By replacing g by cHo in the formula d = (c^2/g) * z/(1+z),
one gets

d = (c/Ho) * z/(1+z),

which is exactly the formula given above for an expanding
Euclidian universe.

Taking into account the existence of the "anomalous"
acceleration, the hypothesis of "tired" light should be preferred
to that of an expanding universe.

Marcel Luttgens

Marcel Luttgens wrote:
In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.

Where did you get this from?

Observations show that red shift z is proportional to distance d
(neglecting the accelerated expansion here - you also don't
mention it). Your formula contradicts that.


Mutatis mutandi, d = Ro * z/(1+z) = (c/Ho) * z/(1+z)

According to GR,

(1+z)^2 = (1+d/Ro)/(1-d/Ro).

But GR considers the frequency shifts of light from distant
sources in terms of special-relativistc Doppler shifts.

Wrong. Why do you think so?


This is wrong, because expansion is symmetrical. In other words,
a clock situated on a galaxy moving at v from an observer
situated on Earth will show the same time as an Earth clock,
which moves at -v wrt the galaxy. The two relativistic effects
cancel each other.

This makes no sense at all. How could the two effects cancel???

Try reading up on the "twin paradox".


On the other hand, GR ignores that the frequency of light is
affected by the gravitational field of the universe (cf. Steven
Weinberg, Gravitation and Cosmology, 1972, p. 417).

Quote, please.

And: What do you even mean by "gravitational field of the universe"? The
local gravitational acceleration? If yes: In a homogenous, isotropic
universe, the local gravitational acceleration is zero everywhere.


It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Let's consider a thought experiment:

A light ray is sent vertically from the bottom of the tower of Pisa.
For an observer situated at the top of the tower, the light will
redden in proportion to the height of the tower.

Assuming that the original wavelength is lambda, the wavelength
at the top is lambdaO, the height of the tower is d, and the
acceleration of gravity g is constant, the formula linking lambdaO,
lambda, d, and g is

lambdaO = lambda/(1-gd/c^2), thus

z = gd/(c^2-gd), and

d = (c^2/g) * z/(1+z)

In "Study of the anomalous acceleration of Pioneer 10 and 11",
John D. Anderson and al. wrote (arXiv: gr- qc/ 0104064 19 April 2001):
"As a number of people have noted, a_H = cH, or 8E-8 cm/s^2 if
H=82 km/s/Mpc."

Well, that value for H is now ruled out by observations.



Assuming that the observed acceleration cH is cosmological,
light should undergo a red shift in proportion to the distance
of its source.

How does this follow?


By replacing g by cHo in the formula d = (c^2/g) * z/(1+z),

Why should one do that?


one gets

d = (c/Ho) * z/(1+z),

which is exactly the formula given above for an expanding
Euclidian universe.

And which contradicts observations, as pointed out above.
And your own remark above that red shift should be proportional
to the distance. Didn't you notice that you contradict yourself here?


Taking into account the existence of the "anomalous"
acceleration, the hypothesis of "tired" light should be preferred
to that of an expanding universe.

Suggestion: try comparing results of your formulas with what is actually
observed.


Bye,
Bjoern

Marcel Luttgens wrote:
In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.

Where did you get this from?

Observations show that red shift z is proportional to distance d
(neglecting the accelerated expansion here - you also don't
mention it). Your formula contradicts that.


Mutatis mutandi, d = Ro * z/(1+z) = (c/Ho) * z/(1+z)

According to GR,

(1+z)^2 = (1+d/Ro)/(1-d/Ro).

But GR considers the frequency shifts of light from distant
sources in terms of special-relativistc Doppler shifts.

Wrong. Why do you think so?


This is wrong, because expansion is symmetrical. In other words,
a clock situated on a galaxy moving at v from an observer
situated on Earth will show the same time as an Earth clock,
which moves at -v wrt the galaxy. The two relativistic effects
cancel each other.

This makes no sense at all. How could the two effects cancel???

Try reading up on the "twin paradox".


On the other hand, GR ignores that the frequency of light is
affected by the gravitational field of the universe (cf. Steven
Weinberg, Gravitation and Cosmology, 1972, p. 417).

Quote, please.

And: What do you even mean by "gravitational field of the universe"? The
local gravitational acceleration? If yes: In a homogenous, isotropic
universe, the local gravitational acceleration is zero everywhere.


It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Let's consider a thought experiment:

A light ray is sent vertically from the bottom of the tower of Pisa.
For an observer situated at the top of the tower, the light will
redden in proportion to the height of the tower.

Assuming that the original wavelength is lambda, the wavelength
at the top is lambdaO, the height of the tower is d, and the
acceleration of gravity g is constant, the formula linking lambdaO,
lambda, d, and g is

lambdaO = lambda/(1-gd/c^2), thus

z = gd/(c^2-gd), and

d = (c^2/g) * z/(1+z)

In "Study of the anomalous acceleration of Pioneer 10 and 11",
John D. Anderson and al. wrote (arXiv: gr- qc/ 0104064 19 April 2001):
"As a number of people have noted, a_H = cH, or 8E-8 cm/s^2 if
H=82 km/s/Mpc."

Well, that value for H is now ruled out by observations.



Assuming that the observed acceleration cH is cosmological,
light should undergo a red shift in proportion to the distance
of its source.

How does this follow?


By replacing g by cHo in the formula d = (c^2/g) * z/(1+z),

Why should one do that?


one gets

d = (c/Ho) * z/(1+z),

which is exactly the formula given above for an expanding
Euclidian universe.

And which contradicts observations, as pointed out above.
And your own remark above that red shift should be proportional
to the distance. Didn't you notice that you contradict yourself here?


Taking into account the existence of the "anomalous"
acceleration, the hypothesis of "tired" light should be preferred
to that of an expanding universe.

Suggestion: try comparing results of your formulas with what is actually
observed.


Bye,
Bjoern

Dear Marcel Luttgens:

"Marcel Luttgens" wrote in message
om...
....
It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Not by GR, it isn't. In your philosophy, apparently entering a gravity
well, the light does not blue shift, and red shift equally on its way out.
So you are removing energy and momentum through a mechanism you don't
describe, except by errors in formulation.

David A. Smith

Dear Marcel Luttgens:

"Marcel Luttgens" wrote in message
om...
....
It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Not by GR, it isn't. In your philosophy, apparently entering a gravity
well, the light does not blue shift, and red shift equally on its way out.
So you are removing energy and momentum through a mechanism you don't
describe, except by errors in formulation.

David A. Smith

Bjoern Feuerbacher wrote:
Marcel Luttgens wrote:

In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.


Where did you get this from?

Observations show that red shift z is proportional to distance d
(neglecting the accelerated expansion here - you also don't
mention it). Your formula contradicts that.

Addendum, before anyone makes a comment on this: I am well aware that
for d Ro, d/(R0 - d) is very close to d, i.e. that this
gives *approximately* a proportionality for small d. But the
relationship between z and d has not only been tested for
d Ro, but also for significantly larger d - and it would be
news to me that the formula above describes the observations
correctly.


[snip]

Bye,
Bjoern

Bjoern Feuerbacher wrote:
Marcel Luttgens wrote:

In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.


Where did you get this from?

Observations show that red shift z is proportional to distance d
(neglecting the accelerated expansion here - you also don't
mention it). Your formula contradicts that.

Addendum, before anyone makes a comment on this: I am well aware that
for d Ro, d/(R0 - d) is very close to d, i.e. that this
gives *approximately* a proportionality for small d. But the
relationship between z and d has not only been tested for
d Ro, but also for significantly larger d - and it would be
news to me that the formula above describes the observations
correctly.


[snip]

Bye,
Bjoern

Bjoern Feuerbacher wrote in message ...

Marcel Luttgens wrote:
In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.

Where did you get this from?

It is based on an observable universe of radius c/Ho
and the Gauss theorem.


Observations show that red shift z is proportional to distance d
(neglecting the accelerated expansion here - you also don't
mention it). Your formula contradicts that.


It is proportional to distance for small recession velocities.
As v = Ho*d, the above formula can be written z = v/(c-v), whose
results are close to those given by the classical formula
z = v/c when v is small.
But you recognize this (more or less) in your last message.
Otoh, the accelerated expansion is a mere hypothesis.


Mutatis mutandi, d = Ro * z/(1+z) = (c/Ho) * z/(1+z)

According to GR,

(1+z)^2 = (1+d/Ro)/(1-d/Ro).

But GR considers the frequency shifts of light from distant
sources in terms of special-relativistc Doppler shifts.

Wrong. Why do you think so?

Steve Weinberg claimed it.



This is wrong, because expansion is symmetrical. In other words,
a clock situated on a galaxy moving at v from an observer
situated on Earth will show the same time as an Earth clock,
which moves at -v wrt the galaxy. The two relativistic effects
cancel each other.

This makes no sense at all. How could the two effects cancel???

Try reading up on the "twin paradox".

This has nothing to do with the twin paradox. Try to visualize
an expanding universe (remember the expanding balloon analogy).

Excerpt rom the "Relativity FAQ":

"The Twin Paradox: Introduction

Our story stars two twins, sometimes unimaginatively named A and B;
we prefer the monikers Stella and Terence. Terence sits at home
on Earth. Stella flies off in a spaceship at nearly the speed of
light, turns around after a while, thrusters blazing, and returns.
(So Terence is the terrestrial sort; Stella sets her sights on
the stars.)
When our heroes meet again, what do they find? Did time slow
down for Stella, making her years younger than her home-bound
brother? Or can Stella declare that the Earth did the travelling,
so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short)
plumps unequivocally for the first answer: Stella ages less than
Terence between the departure and the reunion."

Thus Terence sits at home on Earth, Stella flies off at
some velocity v. Let's call some galaxy Stella, and some other
galaxy Terence (or Earth). Contrarily to the premises of the
twin paradox, in an expanding universe, Terence is not at rest
in the universe.
He and Stella are both moving at v/2 relatively to each other.
If SR claims that this is irrelevant, SR is simply physically
wrong, because Terence's clock and Stella's clock will tick at the
same rate.



On the other hand, GR ignores that the frequency of light is
affected by the gravitational field of the universe (cf. Steven
Weinberg, Gravitation and Cosmology, 1972, p. 417).

Quote, please.

"However, the frequency of light is also affected by the gravitational
field of the universe, and it is neither useful nor strictly
correct to interpret the frequency shifts of light from very
distant sources in terms of a special-relativistic Doppler effect
alone."

Let's appreciate the great insight of Weinberg.


And: What do you even mean by "gravitational field of the universe"? The
local gravitational acceleration? If yes: In a homogenous, isotropic
universe, the local gravitational acceleration is zero everywhere.


You should ask Steven Weinberg.


It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Let's consider a thought experiment:

A light ray is sent vertically from the bottom of the tower of Pisa.
For an observer situated at the top of the tower, the light will
redden in proportion to the height of the tower.

Assuming that the original wavelength is lambda, the wavelength
at the top is lambdaO, the height of the tower is d, and the
acceleration of gravity g is constant, the formula linking lambdaO,
lambda, d, and g is

lambdaO = lambda/(1-gd/c^2), thus

z = gd/(c^2-gd), and

d = (c^2/g) * z/(1+z)

In "Study of the anomalous acceleration of Pioneer 10 and 11",
John D. Anderson and al. wrote (arXiv: gr- qc/ 0104064 19 April 2001):
"As a number of people have noted, a_H = cH, or 8E-8 cm/s^2 if
H=82 km/s/Mpc."

Well, that value for H is now ruled out by observations.


Note that some of your buddies call now H a parameter, implying that
it is no more a constant. As for me, it is still a cosmological
constant.



Assuming that the observed acceleration cH is cosmological,
light should undergo a red shift in proportion to the distance
of its source.

How does this follow?

From z = gd/(c^2-gd).



By replacing g by cHo in the formula d = (c^2/g) * z/(1+z),

Why should one do that?


The light sent vertically from the ground reddens according
to z = gd/(c^2-gd), where g is a negative acceleration.
a_H is also a negative acceleration. The formula is general,
hence it can be rightly used with a_H = cHo.


one gets

d = (c/Ho) * z/(1+z),

which is exactly the formula given above for an expanding
Euclidian universe.

And which contradicts observations, as pointed out above.
And your own remark above that red shift should be proportional
to the distance. Didn't you notice that you contradict yourself here?


Imo, "In proportion to" doesn't mean "proportional to". But yes,
saying that red shift is a function of the distance is a clearer
formulation.


Taking into account the existence of the "anomalous"
acceleration, the hypothesis of "tired" light should be preferred
to that of an expanding universe.

Suggestion: try comparing results of your formulas with what is
actually observed.


I did. The SNe Ia data can be analysed in terms of my formula.
My suggestion is that you should think by yourself, instead of
blindly espousing classical doctrine.


Bye,
Bjoern

Marcel Luttgens

Bjoern Feuerbacher wrote in message ...

Marcel Luttgens wrote:
In an expanding Euclidian universe, the reddening of light
emitted at a distance d is given by

z = d/(Ro - d), with Ro = c/Ho.

Where did you get this from?

It is based on an observable universe of radius c/Ho
and the Gauss theorem.


Observations show that red shift z is proportional to distance d
(neglecting the accelerated expansion here - you also don't
mention it). Your formula contradicts that.


It is proportional to distance for small recession velocities.
As v = Ho*d, the above formula can be written z = v/(c-v), whose
results are close to those given by the classical formula
z = v/c when v is small.
But you recognize this (more or less) in your last message.
Otoh, the accelerated expansion is a mere hypothesis.


Mutatis mutandi, d = Ro * z/(1+z) = (c/Ho) * z/(1+z)

According to GR,

(1+z)^2 = (1+d/Ro)/(1-d/Ro).

But GR considers the frequency shifts of light from distant
sources in terms of special-relativistc Doppler shifts.

Wrong. Why do you think so?

Steve Weinberg claimed it.



This is wrong, because expansion is symmetrical. In other words,
a clock situated on a galaxy moving at v from an observer
situated on Earth will show the same time as an Earth clock,
which moves at -v wrt the galaxy. The two relativistic effects
cancel each other.

This makes no sense at all. How could the two effects cancel???

Try reading up on the "twin paradox".

This has nothing to do with the twin paradox. Try to visualize
an expanding universe (remember the expanding balloon analogy).

Excerpt rom the "Relativity FAQ":

"The Twin Paradox: Introduction

Our story stars two twins, sometimes unimaginatively named A and B;
we prefer the monikers Stella and Terence. Terence sits at home
on Earth. Stella flies off in a spaceship at nearly the speed of
light, turns around after a while, thrusters blazing, and returns.
(So Terence is the terrestrial sort; Stella sets her sights on
the stars.)
When our heroes meet again, what do they find? Did time slow
down for Stella, making her years younger than her home-bound
brother? Or can Stella declare that the Earth did the travelling,
so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short)
plumps unequivocally for the first answer: Stella ages less than
Terence between the departure and the reunion."

Thus Terence sits at home on Earth, Stella flies off at
some velocity v. Let's call some galaxy Stella, and some other
galaxy Terence (or Earth). Contrarily to the premises of the
twin paradox, in an expanding universe, Terence is not at rest
in the universe.
He and Stella are both moving at v/2 relatively to each other.
If SR claims that this is irrelevant, SR is simply physically
wrong, because Terence's clock and Stella's clock will tick at the
same rate.



On the other hand, GR ignores that the frequency of light is
affected by the gravitational field of the universe (cf. Steven
Weinberg, Gravitation and Cosmology, 1972, p. 417).

Quote, please.

"However, the frequency of light is also affected by the gravitational
field of the universe, and it is neither useful nor strictly
correct to interpret the frequency shifts of light from very
distant sources in terms of a special-relativistic Doppler effect
alone."

Let's appreciate the great insight of Weinberg.


And: What do you even mean by "gravitational field of the universe"? The
local gravitational acceleration? If yes: In a homogenous, isotropic
universe, the local gravitational acceleration is zero everywhere.


You should ask Steven Weinberg.


It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Let's consider a thought experiment:

A light ray is sent vertically from the bottom of the tower of Pisa.
For an observer situated at the top of the tower, the light will
redden in proportion to the height of the tower.

Assuming that the original wavelength is lambda, the wavelength
at the top is lambdaO, the height of the tower is d, and the
acceleration of gravity g is constant, the formula linking lambdaO,
lambda, d, and g is

lambdaO = lambda/(1-gd/c^2), thus

z = gd/(c^2-gd), and

d = (c^2/g) * z/(1+z)

In "Study of the anomalous acceleration of Pioneer 10 and 11",
John D. Anderson and al. wrote (arXiv: gr- qc/ 0104064 19 April 2001):
"As a number of people have noted, a_H = cH, or 8E-8 cm/s^2 if
H=82 km/s/Mpc."

Well, that value for H is now ruled out by observations.


Note that some of your buddies call now H a parameter, implying that
it is no more a constant. As for me, it is still a cosmological
constant.



Assuming that the observed acceleration cH is cosmological,
light should undergo a red shift in proportion to the distance
of its source.

How does this follow?

From z = gd/(c^2-gd).



By replacing g by cHo in the formula d = (c^2/g) * z/(1+z),

Why should one do that?


The light sent vertically from the ground reddens according
to z = gd/(c^2-gd), where g is a negative acceleration.
a_H is also a negative acceleration. The formula is general,
hence it can be rightly used with a_H = cHo.


one gets

d = (c/Ho) * z/(1+z),

which is exactly the formula given above for an expanding
Euclidian universe.

And which contradicts observations, as pointed out above.
And your own remark above that red shift should be proportional
to the distance. Didn't you notice that you contradict yourself here?


Imo, "In proportion to" doesn't mean "proportional to". But yes,
saying that red shift is a function of the distance is a clearer
formulation.


Taking into account the existence of the "anomalous"
acceleration, the hypothesis of "tired" light should be preferred
to that of an expanding universe.

Suggestion: try comparing results of your formulas with what is
actually observed.


I did. The SNe Ia data can be analysed in terms of my formula.
My suggestion is that you should think by yourself, instead of
blindly espousing classical doctrine.


Bye,
Bjoern

Marcel Luttgens

"N:dlzc D:aol T:com \(dlzc\)" N: dlzc1 D:cox wrote in message news:TxzEc.3577$nc.1280@fed1read03...
Dear Marcel Luttgens:

"Marcel Luttgens" wrote in message
om...
...
It is claimed that the whole redshift can be explained by the
gravitational field of a stable universe.

Not by GR, it isn't.

It is claimed by me ;-)

In your philosophy, apparently entering a gravity
well, the light does not blue shift, and red shift equally on its way out.
So you are removing energy and momentum through a mechanism you don't
describe, except by errors in formulation.

In the case of a negative acceleration, light is redshifted, meaning that
it loses energy, like a stone thrown vertically from the ground
(where g is the negative acceleration). In the universe, a_H plays the
role of g.


David A. Smith

Marcel Luttgens