# Re: johnreed take 14 - 2005

<randamajor@xxxxxxxxx> wrote in message
news:1116882081.569676.183890@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> What do we mean when we say spacetime is curved?

Simple - in flat space-time we can find a coordinate system such that ds^2 =
ct^2 - x^2 - y^2 - z^2 at each point. If not then not then it is curved.

> How do we conceptually
> grasp a curvature of spacetime? What do we mean when we say space is
> curved? How do we grasp a curvature of space?

By studying Riemanian geometry.

>
> Actually we don't.
>

So all the mathematicians since Riemann are fooling themselves?

Bill

> Instead we say, in such a space the motion of an
> object could be described in terms of the geometry of the space, rather
> than in terms of external forces.
>
> "The motion of an object" and "described in terms of the geometry of
> space". The motion of an object is one thing. The trajectory of an
> object is another. In any event, we are calling the space curved to
> describe the trajectory of the object and its motion. Kinda' like
> looking at a color photograph negative and trying to discern the
> picture.
>
> We are realy dealing with the trajectories of objects after all, and
> those trajectories are least action trajectories, so we have a least
> action, curved space, and spacetime.
>
> Newton's use of the least action property of stable systems was a
> little more crude. Einstein's use is attenuated to the max. I will
> continue with this theme later but for now,
>
> I say gravity does not exist. Mass operates within least action
> parameters. Mass does not follow the path of a least action space.
>
> johnreed
>

.