Re: Steve Carlip and Relativistic Mass

From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 01/03/05 

Date: 3 Jan 2005 15:05:21 -0800

carlip-nospam@physics.ucdavis.edu wrote:
> Ken S. Tucker <dynamics@vianet.on.ca> wrote:
>
> > carlip-nospam@physics.ucdavis.edu wrote:
> >> Ken S. Tucker <dynamics@vianet.on.ca> wrote:
>
> >> [...]
> >> > I hope Dr. Carlip et al, do find the time to clarify the
original
> >> > article perhaps including a statement about G_uv = T_uv,
> >> > instead of the G_uv=0.
>
> >> I don't understand the question. Of course, the general Einstein
> >> field equations are G=T. These are local equations -- they say
> >> that the Einstein tensor at point x at time t is equal to the
> >> stress-energy tensor at that same point at that same time.
>
> > To put a finer point on it, I would regard your "G"
> > as a relation between geodesics.
>
> It contains *some* information about the relationships among
> geodesics.
>
> > Math aside [...]
>
> That's a bad idea. If you put the math aside, you might be led
> to forget about the Weyl tensor, for example, and come to the
> mistaken conclusion that the Einstein tensor contains all of the
> information about relations among geodesics.

Ok,

> >> If you're talking about light traveling through a vacuum, then,
well,
> >> it's a vacuum -- there's nothing there, so T=0. So the relevant
> >> equation at the location you are interested in is G=0.
>
> > In the vicinity of the sun, what "volume" shall we use to
> > define a vacuum?
>
> None. As I said, it's a *local* equation.

That's a problem, you're allowing me to select a point
between the nucleus and the electron to be a vacuum.
Can we at least acknowledge there is an ambiguity in
defining the vacuum?

Why not consider a wave mechanical PoV, the energy density
T_uv has the same units as the Probablity density, (Psi*Psi),
it does hurt to look.

> > In the vicinity of the Sun, measurements will confirm
> > curvature (as I use above)
>
> Yes.
>
> > indicative of local matter.
>
> No. This is a basic error. Curvature at a point does *not* imply
> that the Einstein tensor at that point is nonzero. It implies that
> the Riemann curvature tensor is nonzero. It is perfectly possible
> to have R_{abcd} nonzero even if G_{ab}=0.

((Contradictions ignored)), Wow, I think so too.

It seems to me, Dr. Carlip suggests, G_uv = T_uv
provides an incomplete description of the relation
of spacetime and energy. His prescription above
requiring the Weyl tensor, and his acknowledgement
that G_uv=0=T_uv really doesn't contain sufficient
information to distinguish intergalatic space from
a point near the Sun.

I argue we can retain the Einstein Law, by defining
the T_uv as a wave-mechanical term, by equating
"Energy density" == "probablity density".

> Take the Schwarzschild solution. Compute the Einstein tensor --
> if you do the math right, you'll find that it is zero. Now compute
> the curvature tensor -- if you do the math right, you'll find that
> it is *not* zero. Now compute the null geodesics -- if you do the
> math right, you'll find that they match paths of light outside the
> Sun.

Sure, but aren't we supposed to find the geometry as
a function of the T_uv, and compute from there?
> Steve Carlip

Regards
Ken S. Tucker

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