Thus spake Juan R. GonzГЎlez-ГЃlvarez
canonicalscience.com>>Oh No wrote on Tue, 06 May 2008 05:38:53 -0600:
>
>>>I have discussed this part of my work with an expert on curved spacetime
>>>equations of motion, Eric Poisson [1]. Eric confirms that a = 0 in the
>>>linear regime of GR:
>>>
>>>(\blockquote
>>> Since the energy-momentum tensor is already of first-order, in the
>>> linearized theory the conservation equations must be written down with
>>> the Minkowski metric, and this implies that the matter cannot have
>>> gravitational interactions. Or as you point out, particles would have
>>> to
>>> move on straight lines.
>>>)
>>
>> I am not sure what you mean by a=0,
>
>Do not know that zero acceleration mean?
a can stand for anything you want it to. If you want it to stand for
acceleration, you have to say so.
>
>> but it seems that the expert is
>> explaining to you that that the Newtonian limit is not the same as the
>> linear limit. Rather than claim that the text books have got it wrong,
>> you study what the Newtonian limit actually is.
>
>He had no problem to accept my finding about weak fields. Why do you have
>one?
Perhaps you did not make clear to him that you were confusing the linear
limit with the weak field limit.
>
>Poisson is simply confirming i said in my start message.
He is not confirming that the text books have it wrong.
>E.g. I said
>
>(\blockquote
> Another way to see this is deriving motion from D{T_ab} = 0.
> In the linear regime, it reduces to \partial{T_ab} = 0, and like in the
> special relativity case, this implies bodies move in straight lines.
>)
>
>Textbooks state that in the weak field limit (linear regime) bodies move
>according to equation
>
>a = -\grad \phi
>
>But that is not true,
It is true in the weak field limit. The weak field limit is *defined* as
the regime in which this is true.
> because the *correct* weak field equation (linear
>regime) is
>
and it is not the same as your linear regime.
>
>The mistake in usual textbook 'derivations' has been traced and
>discussed. E.g. if one check details of Carroll lecture notes one can
>notice he is computing
>
>Z[a] = L[\Gamma] Z[vv]
>
>and this gives the equation of motion
>
>a = -\grad \phi
>
>But Carroll would compute instead the linear limit of the geodesic
>
>L[a] = L[\Gamma] Z[vv]
>
>and then would really obtain
>
>a = 0
>
>by *geometrical* requirements.
>
>Or, in words, in the linearized theory particles would have to move on
>straight lines.
