# Re: That black-hole space-time curvature thing

Eliezer S. Yudkowsky (sentience@pobox.com)
Thu, 11 Sep 1997 12:12:57 -0500

Sarah Marr wrote:
>
> When space-time distorts why do the objects around feel the effects of that
> distortion as forces acting on their undistorted state?
> [Deleted: "How would we know if everything got 100 times larger?"]
> So where does the force in a black-hole come from. It's
> perfectly understandable in terms of gravitational field theory, but I lose
> it when space-time distortion is used to explain it. It seems to me that
> space-time and the object are not separate, as the one distorts, so does
> the other, each of its points remaining in the same relative position to
> all its other points.
>
> Or does space-time distortion cause the creation of 'new' space-time?
>
> Confused of the UK.

Okay. Gravity does not just "stretch" space-time. It also "curves"
space-time. The rubber-sheet analogy is overused and does NOT give you a feel
for what gravity really is. The best explanation I know of is this: The
Earth moves in a straight line around the sun. If you toss a ball across a
room, it will move in a straight line. Newton says that everything moves in a
straight line unless a force acts on it. Since gravity isn't a force - it's
the curvature of space - objects under the free influence of gravity move in
straight lines.

How? Imagine an x-y graph, where y is space and x is time. If (the
graph)/(spacetime) isn't curved, then all particles move in straight lines
unless a force is acting on them. If a particle is drifting slowly "up" (in
1D space), then the graph of the particle's position is a straight line on a
flat 2D spacetime. If we introduce an acceleration towards "down", then a
particle which starts out by moving "up" will reach apogee, stop, and start
back "down" again. The spacetime trajectory, the picture on the graph, is a
parabola. (This even though space is only 1D; space AND time are 2D, so you
can graph a parabola in it.)

Now, if you have a curved surface - a 2D surface curved in 3D space - then a
"straight line" on that surface, a "geodesic", the shortest distance between
two points on that surface, can be a 3D curve. From the 2D perspective, it
looks like a straight line. From the 1D perspective, it looks like a
parabolic trajectory.

What looks like a parabolic trajectory to you (3D), is a straight line in
space-time (4D), which is curved. (Space-time does not necessarily require a
higher dimension to be curved "in"; by stretching and shrinking in particular
directions, you can get the isomorphic effect.) The ball is following a
geodesic; any other path between Event A (when it left your hand) and Event B
(when it hit the floor) would be a longer spacetime distance, by the
relativistic definition of distance.

(Confusing note: From the perspective of the ball, any other path would take
*less* time; for example, it could zoop off from your hand at .99c, then zoop
back to the floor. Since time slows down as c is approached, the ball would
think it made the trip in microseconds. In Special Relativity, the shortest
path always takes the most "proper time". "Distance" is arbitrary, depending
on your frame of reference. If distance were minimized, different observers
would disagree on what was a straight line, and would observe different laws
of physics.)

So what tears the astronaut apart is not stretched space or stretched time,
either of which would be undetectable, but curved spacetime, which from our
perspective is experienced as huge accelerations. Tidal forces, the
difference in accelerations between different points, are all that remains to
rip apart the astronaut like toilet paper.

For more, check out http://suhep.phy.syr.edu/courses/modules/LIGHTCONE/

```--
sentience@pobox.com      Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer:  Unless otherwise specified, I'm not telling you
everything I think I know.
```