Re: Steve Carlip on comoving coordinates



On Jul 18, 3:59 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
pmbwrote:
On Jul 18, 12:50 am, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
Note that if one interprets "gravitational field" as the
Christoffel symbols, they are not a field on the manifold; one has
a rather bad PUN on "field". Interpreting "gravitational field" as
any of the curvature tensors does give a field on the manifold.

I disagree. All that means is that the gravitational field isn't a
tensor field. It doesn't mean that it's not a field in the physicists
sense of the term.

Not true. A field ON THE MANIFOLD ...



So you claim. Since you didn't understand what I said I'll rephrase it
for you

“All that means is that the gravitational field isn't a tensor field -
on a manifold-.”

I left out “on a manifold” since I was speaking of a tensor field and
thus “on a manifold” is implied. I keep forgetting that this kind of
thing confuses you. Sorry.

Your claim about how physicists define fields is bogus since “most
physicists” don't know what a manifold is or even understand what a
tensor is, never mind them adhering to what your personal taste in
terminology.

A physicist understands "Field" as in http://en.wikipedia.org/wiki/Field_(physics)

Field - In physics, a field is a physical quantity associated to each
point of spacetime.

I already gave you an example, i.e. a uniform gravitational field. The
Christoffel
symbols for this field are

G^0_03 = 1/(1 + gz/c^2)
G^3_00 = g(1 + gz/c^2)

This holds for all values of t, x, and y. This means that a physical
quantity can be associated with each point in spacetime. A similar
situation holds for the electric and magnetic fields.

I think I see the problem that you’re having. I keep forgetting that
you never really understood the role of the observer as a geometrical
object in relativity. I explained to you a while back that when the
geometrical object “observer” has been chosen then the electric field
is well defined. In fact you can even construct an electric field 4-
vector as measured by observer. The “as measured by observer” is
redundant and can be left out since it’s implied. If you understood
that then perhaps you can understand that when you see the term
“Gravitational field” and understand it in terms of the components of
the affine connection then there is an observer implied. When you take
the observer into account this gives a unique quantity for each event.

But as Steve Carlip has so wisely said - I don't see why anyone should
be so interested in arguing over terminology. Isn't there some real
physics to do?

So feel free to drone on with your usual arguments rooted in
semantics. I’m sure some of your fans will love it.
.

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