On 7/23/2020 7:56 PM, Alan Grayson wrote:
On Thursday, July 23, 2020 at 11:59:59 AM UTC-6, Brent wrote:
On 7/23/2020 4:41 AM, Lawrence Crowell wrote:
On Thursday, July 23, 2020 at 5:56:32 AM UTC-5
[email protected] wrote:
On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson
wrote:
On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence
Crowell wrote:
The tortoise coordinates is found from the
Schwarzschild metric
ds^2 = (1 - 2m/r)dt^2 - (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2
where for a signal leaving a point near the black
hole with ds = 0 (null path) and propagating radially
out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then
leads to
T = t - t0 - 2m ln|r - 2m|.
That is the tortoise coordinate. Please look this up
to read further. I can't spend beaucoup time going
over this for weeks to come.
LC
You don't have to. We're done. But you should IMO
address Brent's objection, maybe on another thread. AG
I don't know what objection you're referring to. LC is just
showing why it takes a distant observer forever to see an
infalling object reach the event horizon of a black hole.
Brent
Your words:
I wonder about the use of cicumlocutions like "from the perspective of
an outside observer". In special relativity it it is often said that
a moving object will looked shortened along the direction of motion.
But as Terrell pointed out that's not at all how they look. It is
more accurate to say that /measuring/ a moving a object will show that
it is shortened along the direction of motion; the difference being
that the measurement corrects for the fact that you want the
difference in arrival time of photons that left the ends of the object
at the same time (an ill defined concept), instead of the image formed
by photons that arrived at the same time. But then I think, why not
correct for the Lorentz contraction too in the measurement and arrive
at what we might call "the proper length". That's just as "measured"
as either of the other two.
By the same reasoning, you're really saying the visual impression of a
distant observer is that infalling stuff appears to be on the surface
of the event horizon. Which is because it takes forever for photons to
reach him. But why should he be so naive. He knows what he's seeing
is arbitrarily far in his past; so what he should be said to "measure"
or "calculate" is that the stuff has already been annihilated at the
"singularity" in his reference frame.
-----------------------------------------------------
I forget why LC brought up this particular coordinate system. He had
some point in response to a comment I made. I'll have to review my
comments; maybe that the gravitational field due to a BH, external to
the event horizon, has an objective reality. AG
LC is perfectly aware of what I wrote. I was just pointing that we have
no reason to privilege how things appear to distant observers, yet it's
seems to be a sort of convention in talking about relativity. It's like
discussing the refraction of light and saying, "See, the pencil in bent
when it's partly submerged."
Brent
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