Darren New <dne### [at] sanrrcom> wrote:
> > Thus, in the observer's reference frame (I'm deliberately avoiding the phrase
> > "as seen from the observer", because the formula doesn't say anything about
> > perception, but plain hard facts), as soon as the "victim" would hit the EH,
> > its time would come to a standstill, so it couldn't move *any* distance in
> > finite time.
>
> I'm not sure that follows. Photons move as fast as possible, and in their
> own reference frame, time has come to a standstill. Why does the victim's
> clock influence the velocity of the victim in the observer's timeframe?

That's a misconception here: Time for photons has not come to a standstill in
their *own* frame of reference, but at their location in the *observer's* frame
of reference (i.e. in the spacetime co-ordinate system where the observer is not
moving in space, and time flows at "normal speed" at his location).

Time is not universal, even in a single frame of reference.

> This is like saying I stick a giant engine on a spaceship, turn it on, and
> just go, and after a while you see me slowing down, because my clock is
> getting asymptotically close to stopped from your reference frame.

It's a bit different here I guess, because this is not about GR, but just about
SR, with a different underlying mechanism for time dilation.

In SR, which ignores gravitation and acceleration and just deals with constant
relative motion, all time dilation effects are just due to a change in frame of
reference, and can in fact be applied *mutually*: If you zoom by me at near
lightspeed, it seems to me that *your* clock is slower, while at the same time
it seems to you that *my* clock is slower. These are really just illusions due
to the peculiar nature of the question what "now" and "here" actually is.

This apparent paradoxon, however, only leads to problems when we meet once
again, which can only happen if at least one of us accelerates. Enter GR, which
deals with accelerated motion and gravitation; here, *real* time delation
effects happen, that are independent of the frame of reference, with the only
difference that in the "here" frame of reference, time "over there" slows down,
while in the "over there" frame of reference, it is time "here" that speeds up.
The relative effect is the same: Time "over there" runs slower than "here"

> > (Note however that time slows down so dramatically already very
> > close to the EH that the "victim" will not even *reach* EH in finite time.)
>
> *That* is why I think the victim will not find himself inside the EH - the
> universe (including himself) will have decayed to nothingness or some such
> before he gets there.

Yesss!

> > So, the equation does *not* state that the EH has a radius of r[s] = 2GM/c^2
> > after all. Instead, it states that it has a *surface* of 4 pi (2GM/c^2)^2.
>
> That difference is exactly the warped space. It happens with the sun and the
> earth, too, because of their gravity.
>
> IIRC, I read where the circumference of the (ideal) earth is something like
> a cm shorter than what it should be given the radius, and the sun is a
> kilometer or ten kilometers or some such different.

The order of magnitude is right, but someone messed up the sign; see
http://www.johnstonsarchive.net/relativity/stcurve.pdf (emphasis added):

"The true diameters of the Sun and Earth are 4.1 km and 4.4 mm GREATER,
respectively, than one would expect from applying Euclidean geometry (C = pi d)
to the observed surface of these bodies"

(Duh - took quite a while to google that one up. Looks like this is a topic not
so frequently tackled.)


> > Given that spacetime is notoriously distorted at the EH, this makes *no*
> > statement whatsoever about its radial distance from the singularity. It could
> > be - ta-ding! - zero after all...
>
> More like infinity, methinks.

(*scratches head*)
Doesn't make sense to me: We get closer to the black hole's center, and when we
have reached the EH this distance becomes *infinite*?

Now *that* would be *really* warped spacetime! :)


> > (Good enough to quality for a world-class crackpot this time, huh? =B))
>
> I don't think real crackpots go "Mwa ha ha ha!"

Darn. Lost again, hm?

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