[TML] Is gravity backwards?

[Timothy Little]

On Thu, Jan 03, 2008 at 11:31:19AM -0700, Bruce Johnson wrote:
> The 'rubber sheet' model (Mass distorts space/time in its immediate
> vicinity in proportion to itself, things 'fall' down hill in gravity
> wells)

Gahhh :-(

The 'rubber sheet' model is quite a popular analogy for the curved
spacetime of general relativity, but one that is universally applied
incorrectly in a way that misses the whole point.

The central insight of general relativity is that all the known
effects of gravity can be modelled without invoking any extra type of
force at all.  The usual rubber sheet analogy has a 'supergravity'
that causes masses to fall into the wells (i.e. using gravity to
explain gravity), but nothing like this exists in GR.


In GR, all objects in free-fall move in the curved-space equivalent of
straight lines.  The 'force of attraction' is just an illusion caused
by the fact that in a curved space, lines that start out parallel do
not remain parallel.

By analogy, consider two lines drawn due north from the equator (of
the Earth, or an orange, whatever you find easier to think about).
They start off parallel, but will meet at the north pole.  To remain
at a constant distance, at least one of the lines would need to be
curved from its straight-ahead path.  In the analogy, the distance
along the line is time, the line itself is a path of motion, and
a curve in a line is an externally-imposed acceleration.

It is rather more complex in the case of gravity since matter
influences the local curvature, the curvature has its own laws, and
there are 3 space dimensions + 1 time instead of just 1+1.  However,
the underlying principles are almost identical.


- Tim