Re: origin of inertia
From: Non Ame (noname_at_nospam.net)
Date: 03/22/05
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Date: Tue, 22 Mar 2005 15:24:48 +0000 (UTC)
Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> writes:
>Non Ame wrote:
>> Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> writes:
>>
>>
>>>Ken S. Tucker wrote:
>>>
>>>>>
>>>>>>Ok, go to Tolmans, (83.26).
>>>>>
>>>>>No book by Tolman on Relativity seems to be available in the local
>>>>>libraries here.
>>
>>
>> Tolman's Equation (83.26) is
>>
>> dr/dt = 1 - 2m/r,
>>
>> and Tolman specifies that this is the equation of the trajectory of light
>> originating near the surface of the spherically symmetric star, and
>> travelling radially outwards (with the Schwarzschild solution outside the
>> star).
>Thanks,
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."
>> Since not enough is left of the original context of the discussion in the
>> passage above,
>Thanks to Ken's persistent refusal to supply the reference...
>> I am uncertain about whether of not this was relevant to
>> the topic of discussion at the time.
>That's what Ken originally wrote:
>***quote***
>Would it be easier to agree the invariant
>ds2 = g_uv dx^u dx^v
>is true and then in SR simplify it to,
>ds2 = (cdt)2 - dx2
>When dx/dt = constant I think that will
>integrate to (c=1),
>s2 = t2 - x2 = t'^2 - x'^2.
>Anyway it's obvious when ds=0 then
>dx/dt = 1 = dx'/dt' .
>Suppose one were to set
>dt' = dt/g where g is a constant then
>dx' = dx/g .
>Anyway that's how it's done in GR, I have
>refs if anyone wants.
>***end quote***
>After asking several times, the only reference he
>gave was Tolman, (83.26).
>After your explanation above, I don't see what the
>two things have to do with each other.
>As suspected: yet another thing which Ken misunderstood.
Agreed. Ken's good at misunderstanding what he's reading.
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