Re: origin of inertia

From: Bjoern Feuerbacher (feuerbac_at_thphys.uni-heidelberg.de)
Date: 03/24/05 

Date: Thu, 24 Mar 2005 16:31:46 +0100

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".

As usual. No surprise.

Bye,
Bjoern

Relevant Pages

  • Re: origin of inertia
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