On May 13, 2:48 pm, Koobee Wublee wrote:
On May 12, 11:51 pm, JanPB wrote:

On May 12, 11:24 pm, Koobee Wublee wrote:
The Schwarzschild metric only applies to the spherically symmetric
polar coordinate system and nothing else.

No, that's false. It's exactly like saying "the vector pointing to the
North Star applies only to the spherically symmetric polar coordinate
system and nothing else".

The spacetime described by the Schwarzschild metric only applied to
the spherically symmetric polar coordinate.

Not _spacetime_, the _coordinate representation of the metric_. There
is no such thing as "spacetime" that can be "applied" to a coordinate
system. The concept doesn't exist.

I notice that you didn't comment on the North Star vector example. You
always evade points that disprove your claims and then you post semi-
responses on a slightly altered topic. (A standard strategy around
these parts - it won't work with me as I've been posting to this NG
since its inception and have seen it all (by definition :-) ).

You are welcome to
transform to another coordinate system with a different metric.

Metric is like that vector pointing to the North Star - a coordinate-
independent entity. Here I'm standing, here is the North Star, here is
my finger pointing to it. This is a vector. No coordinate system
involved. [No answer, right?] Metric is the same way except it needs
more data to describe it than just magnitude and direction as in the
vector case.

The
segment of spacetime remains the same and thus invariant while the
coordinate is your choice as well as the metric associated with this
coordinate

....there is no such thing as "metric associated with this coordinate"
just like there is no "vector pointing to the North Star associated
with this coordinate".

to describe the invariant segment of spacetime. shrug
This concept is so basic, but you have a lot of trouble understanding
that. There is no point to go through the north star nonsense.

But it's the crux of the matter. For months now you have been avoiding
answering this question: why is vector coordinate independent and
metric suddenly _isn't_?

--
Jan Bielawski