Re: "Tired" light
From: Bjoern Feuerbacher (feuerbac_at_thphys.uni-heidelberg.de)
Date: 06/30/04
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Date: Wed, 30 Jun 2004 12:49:18 +0200
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
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