Spacetime curvature is the relativistic way of describing
gravity.
The best way of visualising this (without the benefit of mind-altering substances)
is to think a few dimensions down the ladder.
If spacetime were 2-D, then spacetime could be visualised as a elastic sheet.
If you place heavy objects on the sheet, it will bend under the weight, creating a
dip.
Passing objects will tend to move closer to the centre of this gravity well, which we
experience as gravitational attraction.
The more massive the object, the deeper the gravity well.
Planets orbit stars inside their gravitational fields, like stunt riders on a sloping
Wall of Death.
See those things that look like tubes leading straight down from the sheet?
Those are black holes, with their little singularity sulking in the centre.
Happy? Ok, now make the sheet 3-D.
(Most people can't do this).
Now make it 4-D.
(People who can do this don't tend to be allowed near
sharp objects.)
Of course, a curved 4-dimensional hypersurface needs a 5th dimension to curve in.
Luckily, math geeks like Riemann and Gauss found you
can calculate 4-D spacetime curvature
without needing to know anything about the 5th dimension itself
(which is handy, as we have no way of measuring that)
This works in the same way that Flatland inhabitants could calculate 3-d curvature
without being aware of a third dimension.
Hmmm. Ok, visualisation time again:
A. Square and T.Riangle live in a curved 2-D universe
(which to hyperdimensional superbeings like us looks like a sphere).
-
They both stand facing North on the equator: one at 0 degrees longitude,
one at 90 degrees longitude.
-
They both head due North
-
Time passses.
-
They bang heads together at the North Pole.
Now, (being 2-D), this seems quite odd.
As far as they are concerned, they both set off on a flat surface parallel to
each other.
Euclid (who was a Flatland kind of guy) says that
parallel lines never intersect.
So our Flatland pair think there must be some wierd force attracting them off course toward
s each other.
Once one of them has the trippy idea of curvature in a 3rd dimension,
they can not only explain this without the benefit of gravity,
but they can also figure out
exactly how curved the surface is.
The bigger the curve, the sooner their paths will cross.
And it's the same for us.
Just don't try to visualise it when you're sober, and you'll be
fine.