Re: origin of inertia
From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 03/24/05
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Date: 24 Mar 2005 14:23:29 -0800
Bjoern Feuerbacher wrote:
> Ken S. Tucker wrote:
> > Non Ame wrote:
> >
> >
> >>Tolman writes:
> >>
> >> "On the one hand, in accordance with the Schwarzschild line
> >> element (82.9) and the relation ds = 0 for the trajectory of
> >> light, we note that the velocity of light originating at the
> >> surface of the star would be given in terms of coordinates r
> >> and t by the expression
> >>
> >> dr/dt = 1 - 2m/r, (83.26)
> >>
> >> which is seen to be independent of the coordinate t. We may hence
> >> conclude that successive light impulses which are separated by the
> >> coordinate period delta t when they originate on the surface of
> >> the star would still be separated by this coordinate period on
> >> reaching a stationary observer.
> >>
> >> On the other hand, we note in accordance with the Schwarzschild
> >> line element that the proper period delta s for a stationary atom
> >> and its coordinate period delta t would be connected by
> >>
> >> delta s = sqrt(1 - 2m/r) delta t. (83.27)
> >>
> >> Hence since the proper period of an atom should be independent of
> >> its location, and since we have seen above that the coordinate
> >> period of light is in the present case unaltered by transmission,
> >> we can now write
> >>
> >> (lambda + delta lambda)/lambda = delta t/delta s
> >>
> >> = 1/sqrt(1 - 2m/r) approx 1 + m/r (83.28)
> >>
> >> for the ratio of the observed wavelengths of light corresponding
> >> to a given spectral line which originates in the one case at the
> >> surface of the star at r and in the other case at a great distance
> >> from the star where the observer himself is located.
> >>
> >> In the case of light originating on the surface of the sun this
> >> should lead to a very small shift towards the red to the extent
> >>
> >> delta lambda/lambda = 2.12 x 10^{-6}. (83.29)
> >>
> >> In the case of the very dense companion to Sirius, however, the
> >> shift should be about thirty times as great. In both cases the
> >> agreement between theory and observation is now satisfactory as a
> >> result of the work of St John and Adams."
> >
> >
> > Thanks Non Ame,
> > That's the page word for word, you certainly
> > are patient. There's alot of GR on the page,
> > that connects easily with reality.
>
> So you choose to ignore that what the page says is about a
> Schwarzschild metric, not a Minkowski metric (as the original post
> was!), and that a Schwarzschild metric is a special application of GR
> - not "how it is done in GR".
No that's incorrect read Non Ame's fine post,
I highly recommend it. After that explain to
us what you don't understand, and maybe someone
can help you.
Often a post is aimed to be of general interest
to MOST of the group, but I think it can be
simplified, if you can tell us what you don't
understand.
Hope that helps!
Ken S. Tucker
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