Re: Equivalence: inertial and gravitational mass

brad wrote:
On Jun 26, 4:00 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
brad wrote:
From whence doth arise the Einstein Tensor?
It is the only tensor that can be constructed from first and second
derivatives of the metric such that its covariant divergence is

Covariance is a puzzling concept (for me) and it may be the key to my
*language* difficulties.

While the word is similar, the covariant derivative is far removed from covariance.

The covariant derivative is a derivative operator that has a
tensor argument and which returns another tensor. the details are
complicated enough to require a textbook, not a post like this.

A set of equations are said to be covariant when a change of
coordinates leaves their form unchanged. Invariably such
equations are between components of tensors, and when the
coordinates are changed the equations intermix among themselves
(i.e. there is not in general a precise correspondence between
individual equations, but the entire set is unchanged).


I thought the stress energy tensor was the source of attraction(?) and
the
Einstein Tensor was just his definition locally (the Solar System).

The stress-energy tensor, aka the energy-momentum tensor, aka the stress-energy-momentum tensor, is the "source" of gravitation in GR. The Einstein tensor in a measure of the curvature of the manifold. The Einstein field equation equates them (plus an optional cosmological-constant term).


It seems incomplete to just say "matter gives rise to the
stress-energy tensor".
Why? The energy-momentum tensor has the property that all dynamics can
be obtained from it.

Because it seems to me that it implies an incomplete genesis. Sort of
like
'the field is centered on the matter' as in magnetism. It does not say
how or
why the matter can have this influence.

The "influence" known as gravity comes from its effect on the geometry of the manifold.


It seems to be more an
explanation
based in mathematics. It works! It just seems that it doesn't give a
physical
explanation.

One of the major lessons of modern physics is that "physical explanations" are generally not possible at all. There is no "physical explanation" for any quantum phenomenon, probably because of the difference between humans' mental environment and the real world. "Explanations" are the domain of theology and people who have not thought very deeply about physics and its relationship to the world; science can only make models of the world, and test them experimentally.


But choice of coordinates is an arbitrary human choice,
and no physical phenomenon can depend on such a choice.

Not in GR.


There has to be physical reason.

Why do you think your rather naive opinions and mental outlook have the power to put requirements on nature? How could ANY human have such a capability?


Tom Roberts
.

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