On Feb 20, 7:17 pm, Edward Green wrote:
On Feb 20, 1:15 am, Koobee Wublee wrote:

Kinetic energy is observer dependent, and so is the momentum. This is
also true for the observed mass. Thus, the energy-momentum tensor
must be observer dependent as well. Since it is the energy-momentum
tensor that equates with the Einstein tensor, the field equations
allow an observer dependent quantity to shape the curvature of
spacetime that is supposed to be observer independent or invariant.
Please give me a date when you personally will be in peace with this
particular self-inconsistency.

Even I can answer that like an establishment pro!

The _components_ of the tensor may be observer dependent, but the
abstract tensor itself is independent of any coordinate system.

Can you prove that mathematically? Proof by faith does not count.

That's just how tensors are.

Well, in that case, the metric cannot be a tensor. shrug

Are you saying the whole machinery was
put together wrong?

Yes.

It is less contradictory if you allow an invariant quantity to decide
how spacetime should be curved. shrug

I'm still unsatisfied with this one. It doesn't seem to me to be
"contradictory" as much as "insuifficiently specified".

A relativistic ideal gas has, even in its rest frame, a pressure and a
an energy density, the latter including an increment to the rest
energy. Both of these terms happen to involve the motion of the
molecules, but they are observationally distinct, and don't require us
to know anything about any damn molecules. In treating such a gas in
field equations which include energy and pressure, if we can't simply
plug both the observable values in, but invoke extra accounting
principles -- that's cheating.

You need to think about this scenario more carefully. The pressure as
you describe still is relative. shrug.

Either we can blindly plug in both terms, in or there is something
imperfect about the formulation.- Hide quoted text -

Just a misunderstanding on your part. shrug