That Black-Hole Space-Time Curvature Thing

John K Clark (
Sun, 14 Sep 1997 22:45:39 -0700 (PDT)


On Sun, 14 Sep 1997 "Eliezer S. Yudkowsky" <> Wrote:

>I disagree with your spatial visualization of divergence, though.
>It's tides, which derive from space*time* divergence.

You are unclear, tides was exactly what I was talking about.

>When "geodesic lines" diverge in spacetime, the result is different
>accelerations and tidal effects.

Exactly, and it's tidal effects on our astronaut that will kill him. The way
geodesic lines behave is a measure of the curvature of spacetime, a measure
of the curvature of anything for that matter.

>You make it sound like space is distorted,

It's not space, it's not time, it's spacetime that's curved. I don't use
"distorted", I make no value judgments in this matter. (:>)

>But the Flatlandish metaphor is incorrect,

I stole the metaphor from Kip Thorne, the Feynman professor of theoretical
physics at the California Institute of Technology, I highly recommend his
book. The point is that if the flatlanders lived on the surface of a sphere
they could still deduce that their world must be curved in the third
dimension even if they couldn't visualize it. We can't visualize the
curvature of 4 dimensional spacetime but we can deduce it must be happening.

>because Flattime is still flat.


>It's the spacetime divergence ("tide") that does it, not spatial

It's spacetime geometry that does it, and the spacetime geometry is
proportional to the density of mass (times c^2) in the vicinity plus 3 times
the pressure of matter in the same vicinity, although this last term only
becomes important when the pressure gets astronomical, like in the center of
a neutron star.

You make it sound like there is an absolute difference between space and time
and that's incorrect. If you and I are in different reference frames we would
disagree about the distance in space between two events and disagree about
the distance in time between two events but we would always agree on the
spacetime distance between two events. To quote Thorne "your space is a
mixture of my space and my time".

John K Clark

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