Re: GR1916 question about g=1?

On Nov 26, 9:49 pm, JanPB <film...@xxxxxxxxx> wrote:
On Nov 26, 12:04 am, Koobee Wublee <koobee.wub...@xxxxxxxxx> wrote:

On Nov 25, 10:09 pm, JanPB <film...@xxxxxxxxx> wrote:

On Nov 25, 9:16 pm, Koobee Wublee wrote:
Clearly, ds^2 is a scalar mathematically with rank-0. It is
impossible to fudge it into a ran-2 tensor or even a matrix.
Professor Roberts is very correct on this one. <shrug>

If ds^2 were a scalar then it would have a value at each point. So
tell us what is the value of ds^2 at (x,y,z,t) = (0,0,0,0) in the
Minkowski space? Remember, you've just said that it was a number -
what is it?

A scalar just means it is a number but no particular number. You are
confused with constants. <shrug>

But it must be a definite number - according to you - because ds^2 is
_given_ (the geometry has been specified). So in particular on the
Minkowski space what is ds^2 equal to at the origin?





Thanks for using my symbols to describe coordinate (not to be confused
with displacement).

Dream on :-)

No, it is no dream. It is reality. <shrug>

Have you taken calculus? After all, the mathematics involved is at
least 200 years old.

Infinitesimals are not well-defined mathematical objects (except in
certain esoteric mathematical contexts that so far have not been seen
in physics) and have status similar to that of the delta function
before Laurent Schwartz. Is this news to you?

Laurent Schwarz is news for you, yes. However, infinitesimals are the
essentials to understand the laws of physics. <shrug>

His name is spelled "Schwartz" not "Schwarz" (that's a different
fellow). I never said infinitesimals were not essential, I only said
that proper definition of infinitesimals on _manifolds_ is done by
limiting procedure of certain kind (Cauchy was the first to define
limits correctly) which results in tangent vectors, covectors, and
tensors or other ranks.

In mathematics/physics
the actual tool used whenever one talks about infinitesimals employs
various types of limiting processes (which are well-defined).

Yes, such as the mathematical methods of calculus.

It is
the notion of limit which is encapsulated in the concept of "tangent
vector" and "1-form" (aka. "tangent covector").

Yes, tangent vectors arise if you allow the mathematics to guide you
there. However, tangent covectors are nonsense or known in another
mathematical terms. They depend on very creative interpretations.
<shrug>

Covectors are not any "nonsense", they are gradients, just like
vectors are velocities.

It is so by definition. It has nothing to do with the curvature in
space or spacetime --- not the least with gamma whatever that is.

It is not so. Coordinates are not choice of ruler.

Coordinates are effectively a choice of ruler. They depend on the
observers. Hey, you don't dictate what coordinate has to be
utilized. The observer does. <shrug>

Choosing a ruler does not determine a coordinate system.

If you are passing coded messages to Professor Roberts, I'd appreciate
if you do so through your private mail. Thanks in advance.

Just refrain from posting if you don't know what to say.

You have been typing gibberish, and I was just too polite to tell you
so. Don't you have any decency?

Anyone can check who is "typing gibberish".

--
Jan Bielawski- Hide quoted text -

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