| I'm responding to this separately to reduce clutter. I'll post the rest of my response to your post after this one. I still don't know from this discussion how the argument in the blog
isn't sound. Sigh. Here are the basics boiled down as much as I can. I'll base my
comments on what you've said in this thread, since what you've said
here is a lot more coherent to me than the blog post itself is. I'll
give just bare statements, with no supporting argument; I've already
given the supporting arguments many, many times in this thread. - You have claimed that, within the astronaut LIF, the
directions "toward the singularity" and "toward infinity" are opposite
directions. That's wrong; they're not. - You have claimed that, since "toward r = 0" and "toward infinity" are
opposite directions in the skydiver LIF, they must also be opposite
directions in any LIF. (You made the claim about the astronaut LIF,
but the way you made the claim makes it clear that you would make the
same claim about any LIF whatsoever). That's wrong; see above. - You have claimed that, if we choose the mass of the black hole
appropriately, we can make it so that, if the two probes are initially
converging, the second will catch up to the first within the astronaut
LIF. That's wrong; we can't. - You have claimed that, if we can set up the skydiver LIF so that the second probe catches the first within that LIF, that somehow invalidates the equivalence principle, even if the second probe can't catch the first within the astronaut LIF. That's wrong; it doesn't. - You have claimed that, if the first probe has an increasing global r
coordinate while the second has a decreasing global r coordinate, the
two probes can't be converging within the astronaut LIF. That's wrong;
they can. - You have claimed that, since the two probes must be diverging in the
skydiver LIF if their r coordinates behave as above, they must also be
diverging in any LIF if their r coordinates behave as above. (Again,
you made the claim about the astronaut LIF, but the way you made the
claim makes it clear that you would make the same claim about any LIF
whatsoever). That's wrong; see above. And just for comparison, I'll briefly summarize what GR actually says
about the astronaut scenario; again, just bare statements since I've
already given the supporting arguments many times in this thread: - As the initial conditions are given, the two probes will converge
within the astronaut LIF. - Within the astronaut LIF, the black hole's horizon is a light ray
moving in the positive x direction, which passes the astronaut halfway
between him launching the first and second probes. So clearly the
second probe will remain below the horizon, even based on observations
solely within the LIF, since it starts out behind the light ray and is
moving slower. - Within the astronaut LIF, the horizon will (slowly) catch up to the
first probe. However, the distance it would take for the horizon to
catch up, based on its "closure rate" within the astronaut LIF, is
much, much larger than the size of the LIF. This holds regardless of
the mass of the black hole. And if the horizon can't catch the first
probe within the LIF, the second probe certainly can't either. - Once the probes and the horizon have exited the astronaut LIF, tidal
gravity can no longer be neglected; and tidal gravity will cause the
horizon to stop catching up with the first probe and start falling
behind it. Eventually, the first probe will escape to infinity. |