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From: Tom Roberts on 25 May 2010 22:54
Edward Green wrote:
> How would one go about operationally defining radial and
> circumferential distances in the vicinity of a black hole?

Let me only discuss Schwarzschild black holes. I'll also use the usual Schw.
coordinates.

One can determine that multiple locations are at the same altitude (value of r)
by measuring the gravitational attraction of a test particle toward the BH. One
can find such points all the way around that lie in a plane containing the BH.
One can lay rulers down between pairs of such points and measure the
circumference of the circle centered on the BH. We then DEFINE the Schw. r
coordinate of these points to be circumference/2pi. This of course is not the
distance of your question, but from it and knowledge of the form of the metric
one can compute radial distances. One can also lay out coplanar circles for
several different values of r, and lay down rulers radially between the circles,
and measure radial distance directly.

Obviously one must use rockets or some other method to remain at rest relative
to the BH. The above procedure requires stronger rockets for values of r nearer
to the horizon, becoming impossible as one gets very close (given the rockets
have finite thrust). It's also likely that near the horizon the strain involved
in keeping the ruler at rest (wrt the BH) will distort it (in principle one
needs a rocket at each point of a ruler lying radially).


> Does it
> mean something to be "1 cm above the horizon"?

No. Spatial distance along a path with constant {t,theta,phi} diverges
logarithmically as one approaches the horizon. That is, the radial distance from
r=2M to (say) r=3M is not well defined (loosely it is "infinite"). While a
dropped object requires only a finite proper time to cross the horizon, to an
observer remaining outside the horizon it never reaches the horizon (loosely, it
"requires an infinite time to reach the horizon").

One can discuss a value of r that is "1 cm above the horizon", but r is not
distance, it is merely a coordinate having the same units as length. r is well
defined near (but outside) and at the horizon; radial distance is not well
defined in the neighborhood of the horizon.


Eric Gisse said:
> Sure.

Not true - see above.


Tom Roberts
From: eric gisse on 26 May 2010 01:33
Tom Roberts wrote:

[...]

> One can discuss a value of r that is "1 cm above the horizon", but r is
> not distance, it is merely a coordinate having the same units as length. r
> is well defined near (but outside) and at the horizon; radial distance is
> not well defined in the neighborhood of the horizon.


If I integrate along a path of constant (t,theta,phi) from r_0 to r_1, that
isn't a distance?

When I say 'distance', I implicitly mean the result you would get it you
integrate g_uv dx^u dx^v along your particular worldline. Otherwise I could
mean the same thing for t/theta/phi, or u,v in parabolic coordinates, etc
which makes no physical sense.

I will agree that the meaning of distance gets physically 'fuzzy' around a
black hole but I still think it is well defined as long as you are on the
correct side of the event horizon and don't try to measure _across_ it.

>
>
> Eric Gisse said:
> > Sure.
>
> Not true - see above.
>
>
> Tom Roberts

From: Edward Green on 26 May 2010 19:55
On May 25, 10:54 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> Edward Green wrote:
> > How would one go about operationally defining radial and
> > circumferential distances in the vicinity of a black hole?
>
> Let me only discuss Schwarzschild black holes. I'll also use the usual Schw.
> coordinates.
>
> One can determine that multiple locations are at the same altitude (value of r)
> by measuring the gravitational attraction of a test particle toward the BH. One
> can find such points all the way around that lie in a plane containing the BH.
> One can lay rulers down between pairs of such points and measure the
> circumference of the circle centered on the BH. We then DEFINE the Schw. r
> coordinate of these points to be circumference/2pi. This of course is not the
> distance of your question, but from it and knowledge of the form of the metric
> one can compute radial distances. One can also lay out coplanar circles for
> several different values of r, and lay down rulers radially between the circles,
> and measure radial distance directly.
>
> Obviously one must use rockets or some other method to remain at rest relative
> to the BH. The above procedure requires stronger rockets for values of r nearer
> to the horizon, becoming impossible as one gets very close (given the rockets
> have finite thrust). It's also likely that near the horizon the strain involved
> in keeping the ruler at rest (wrt the BH) will distort it (in principle one
> needs a rocket at each point of a ruler lying radially).
>
> > Does it
> > mean something to be "1 cm above the horizon"?
>
> No. Spatial distance along a path with constant {t,theta,phi} diverges
> logarithmically as one approaches the horizon. That is, the radial distance from
> r=2M to (say) r=3M is not well defined (loosely it is "infinite"). While a
> dropped object requires only a finite proper time to cross the horizon, to an
> observer remaining outside the horizon it never reaches the horizon (loosely, it
> "requires an infinite time to reach the horizon").
>
> One can discuss a value of r that is "1 cm above the horizon", but r is not
> distance, it is merely a coordinate having the same units as length. r is well
> defined near (but outside) and at the horizon; radial distance is not well
> defined in the neighborhood of the horizon.

Thank you for your thorough operational definition and discussion.
From: xxein on 27 May 2010 19:47
On May 26, 7:55 pm, Edward Green <spamspamsp...(a)netzero.com> wrote:
> On May 25, 10:54 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
>
>
>
>
>
> > Edward Green wrote:
> > > How would one go about operationally defining radial and
> > > circumferential distances in the vicinity of a black hole?
>
> > Let me only discuss Schwarzschild black holes. I'll also use the usual Schw.
> > coordinates.
>
> > One can determine that multiple locations are at the same altitude (value of r)
> > by measuring the gravitational attraction of a test particle toward the BH. One
> > can find such points all the way around that lie in a plane containing the BH.
> > One can lay rulers down between pairs of such points and measure the
> > circumference of the circle centered on the BH. We then DEFINE the Schw.. r
> > coordinate of these points to be circumference/2pi. This of course is not the
> > distance of your question, but from it and knowledge of the form of the metric
> > one can compute radial distances. One can also lay out coplanar circles for
> > several different values of r, and lay down rulers radially between the circles,
> > and measure radial distance directly.
>
> > Obviously one must use rockets or some other method to remain at rest relative
> > to the BH. The above procedure requires stronger rockets for values of r nearer
> > to the horizon, becoming impossible as one gets very close (given the rockets
> > have finite thrust). It's also likely that near the horizon the strain involved
> > in keeping the ruler at rest (wrt the BH) will distort it (in principle one
> > needs a rocket at each point of a ruler lying radially).
>
> > > Does it
> > > mean something to be "1 cm above the horizon"?
>
> > No. Spatial distance along a path with constant {t,theta,phi} diverges
> > logarithmically as one approaches the horizon. That is, the radial distance from
> > r=2M to (say) r=3M is not well defined (loosely it is "infinite"). While a
> > dropped object requires only a finite proper time to cross the horizon, to an
> > observer remaining outside the horizon it never reaches the horizon (loosely, it
> > "requires an infinite time to reach the horizon").
>
> > One can discuss a value of r that is "1 cm above the horizon", but r is not
> > distance, it is merely a coordinate having the same units as length. r is well
> > defined near (but outside) and at the horizon; radial distance is not well
> > defined in the neighborhood of the horizon.
>
> Thank you for your thorough operational definition and discussion.- Hide quoted text -
>
> - Show quoted text -

xxein: It's only a theory. Don't get your panties in an uproar by
thinking you have learned a truth. Notice that r is NOT 'well
defined' around and inside 2M. It takes another theory and a
different 'take' of the physic to explain that.

Iow, there is something missing in our (so far) best 'and want to
believe' theories. I don't have to tell you that Einstein was an
'armchair' physicist, do I? I mean, after all, he was just a
mathematician with an imaginary way to describe the physic. And just
because a real physist designed an experiment, it does not mean his
interpretation of the result is the valid interpretation of the real
physic.

Tread all of this lightly and don't step into the deep end of a
favorite belief (as well as it may seem to work in the mundane). When
you read of a 'result', just think of it as the latest 'guess' of a
part of how all things really work. With all the mumbo-jumbo we can
come up with, don't think anything is solved. It all has holes in
it. Plugging up those holes is just patchwork.

I'll leave you with that instead of asking you the reason you think
gravity exists. Oops! I just did.
From: BURT on 27 May 2010 22:39
On May 27, 4:47 pm, xxein <xx...(a)comcast.net> wrote:
> On May 26, 7:55 pm, Edward Green <spamspamsp...(a)netzero.com> wrote:
>
>
>
>
>
> > On May 25, 10:54 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
>
> > > Edward Green wrote:
> > > > How would one go about operationally defining radial and
> > > > circumferential distances in the vicinity of a black hole?
>
> > > Let me only discuss Schwarzschild black holes. I'll also use the usual Schw.
> > > coordinates.
>
> > > One can determine that multiple locations are at the same altitude (value of r)
> > > by measuring the gravitational attraction of a test particle toward the BH. One
> > > can find such points all the way around that lie in a plane containing the BH.
> > > One can lay rulers down between pairs of such points and measure the
> > > circumference of the circle centered on the BH. We then DEFINE the Schw. r
> > > coordinate of these points to be circumference/2pi. This of course is not the
> > > distance of your question, but from it and knowledge of the form of the metric
> > > one can compute radial distances. One can also lay out coplanar circles for
> > > several different values of r, and lay down rulers radially between the circles,
> > > and measure radial distance directly.
>
> > > Obviously one must use rockets or some other method to remain at rest relative
> > > to the BH. The above procedure requires stronger rockets for values of r nearer
> > > to the horizon, becoming impossible as one gets very close (given the rockets
> > > have finite thrust). It's also likely that near the horizon the strain involved
> > > in keeping the ruler at rest (wrt the BH) will distort it (in principle one
> > > needs a rocket at each point of a ruler lying radially).
>
> > > > Does it
> > > > mean something to be "1 cm above the horizon"?
>
> > > No. Spatial distance along a path with constant {t,theta,phi} diverges
> > > logarithmically as one approaches the horizon. That is, the radial distance from
> > > r=2M to (say) r=3M is not well defined (loosely it is "infinite").. While a
> > > dropped object requires only a finite proper time to cross the horizon, to an
> > > observer remaining outside the horizon it never reaches the horizon (loosely, it
> > > "requires an infinite time to reach the horizon").
>
> > > One can discuss a value of r that is "1 cm above the horizon", but r is not
> > > distance, it is merely a coordinate having the same units as length. r is well
> > > defined near (but outside) and at the horizon; radial distance is not well
> > > defined in the neighborhood of the horizon.
>
> > Thank you for your thorough operational definition and discussion.- Hide quoted text -
>
> > - Show quoted text -
>
> xxein:  It's only a theory.  Don't get your panties in an uproar by
> thinking you have learned a truth.  Notice that r is NOT 'well
> defined' around and inside 2M.  It takes another theory and a
> different 'take' of the physic to explain that.
>
> Iow, there is something missing in our (so far) best 'and want to
> believe' theories.  I don't have to tell you that Einstein was an
> 'armchair' physicist, do I?  I mean, after all, he was just a
> mathematician with an imaginary way to describe the physic.  And just
> because a real physist designed an experiment, it does not mean his
> interpretation of the result is the valid interpretation of the real
> physic.
>
> Tread all of this lightly and don't step into the deep end of a
> favorite belief (as well as it may seem to work in the mundane).  When
> you read of a 'result', just think of it as the latest 'guess' of a
> part of how all things really work.  With all the mumbo-jumbo we can
> come up with, don't think anything is solved.  It all has holes in
> it.  Plugging up those holes is just patchwork.
>
> I'll leave you with that instead of asking you the reason you think
> gravity exists.  Oops!  I just did.- Hide quoted text -
>
> - Show quoted text -

Where time ends physics ends. Proper time ends with the ending of time
at the event horizon. When time ends it ends.

Mitch Raemsch
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