Re: Cosmology and Relativistic vector addition/subtraction of velocities

On Feb 21, 9:48 pm, Uncle Al <Uncle...@xxxxxxxxxxxxx> wrote:
"John (Liberty) Bell" wrote:

I have been giving this subject some further thought recently, given
that Chalky originally asked the SR question while some of us were
still struggling to define a simple inertial reference model of an
observable expanding universe, relative to which accelerating
expansion could be plotted (during a still eariler discussion over at
sci.astro.research). In practice, the Milne (empty) model of EFE is
used for that purpose by astronomers, and this can be tabulated for z
shift as a function of distance, simply by plugging Omega_Lamda = 0
and Omega_M =0 into, for example, Ned Wright's Cosmic calculator.
Admittedly, Chalky originally asked about z shift as a function of
dispersion angle, but this question could equally well have been asked
as a function of physical separation (or luminosity distance).

Now, if I understand the foundations of the theory correctly, when
Lambda and M are both set to zero, there should be no gravity and GR
thus approximates to SR, giving an inertial model of both the
expanding universe and, presumably, of exploding relativistic bombs
(when gravity is negligible), as the schrapnel velocity approaches c.

However, since I have arrived at this conclusion from a philosophical
perspective as opposed to rigorous mathematical analysis, informed
comments from others would be appreciated.

http://en.wikipedia.org/wiki/Redshift
Local redshift approximates Galilean (Doppler), cosmic redshfit is
relativistic (relativistic Doppler).

In the current context I imagine that you mean "special relativistic
Doppler" here, whereas there are many astrophysics sites which stress
that the cosmological redshift is a "different" general relativistic
effect. However, I am not completely convinced by this argument,
especially if one is considering the limiting case (Milne) general
relativistic solution, where the cosmological constant is zero, and
the mass is zero. This point is not totally academic as this is the
reference model against which astronomers plot the observable dynamics
of the accelerating expansion of the universe as well as the goodness
of fit of the various 'optimally tweaked' models of EFE.

If the source is moving at right angles to the observer's line of
sight the Galilean formula predicts *no* spectral shift while the
relativistic formula *does* predict a spectral shift.

This is very true.

This is
observed - transverse Doppler shift. This is why a Beckman
ultracentrifuge pulls a million gees but there are no associated
relativistic gravitational effects (e.g., slowing of radioactive decay
or radial Mossbauer redshift at the rotor's inner rim).

?? I don't get this. You SHOULD get slowing of clocks in a centrifuge,
precisely because the inner rim is moving fast relative to us. In
fact, Einstein used the rotating disc argument to derive a general
relativistic slowing of clocks in such a situation, special
relativistically. Whether you describe this as a special relativistic
effect relative to us, or a general relativistic effect relative to a
resident of the centrifuge would seem to be largely a question of
taste.

Gravitational redshift is GM/rc^2 where GM is Big G times the
gravitating body's mass, c is lightspeed and r is the radial climb up
or down the gravitational well.

This statement is not general enough. A linearly accelerating observer
also observes gravitational redshift, within his accelerating
reference frame, due entirely to that acceleration.

A million gees shrinks the Harvard
Tower experiment (Pound and Rebka)
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html
to 0.0226 mm climb (a hair is ~0.06 mm wide). There is no radial
redshift experimentally observed in an ultracentrifuge.

True. From within the centrifuge, it is observed as a gravitational
redshigt.

John.

.

Relevant Pages

  • Re: Lorentz Considerations on Gravitation
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  • Re: Redshift of Light Near a Black Hole
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  • Re: Redshift of Light Near a Black Hole
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  • Re: Gravitational redshift Query
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  • Re: Derivation of gravitational redshift from first principles proves GR is incorrect
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