Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:IxJWe.253287$E95.87125@fed1read01...
....
... I'll keep my copy of "Spacetime Physics" open and ready.
...

Excellent, I have the paperback version so if
you have the hardback some page numbers may
differ. That can save me a lot of drawing :-)

What I have described above is shown in part on
page 112, exercise L-2 as the "Earth frame" but
take A as the bulb/detector and B as the lower
mirror. At event '2' the fist flash is received
and the second (later received at '4') is emitted.

I have the same book, and our pages line up exactly at this
point. I was moving rooms around all weekend, and just got my
computer reassembled. I will respond tomorrow night.

David A. Smith

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:PnqXe.253812$E95.156602@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

Agreed material trimmed again

At the centre, all our tools fail at the moment,
that's the problem.

Not really. The inifinte observer predicts an eternally expanding,
cooling Universe for the infaller.

The observer at infinity predicts sphagetification
for the infaller resulting in infinite compression
and temperature up to the centre but that is
irrelevant.

I disagree. Do you disagree that the infinite observer would attribute a
decreasing-speed-of-light-as-a-function-of-r as r decreases?

Yes, I disagree, because ...

So what is "falling faster than c", if not an assignment by
such an observer?

It is a description applicable to the observer
infinitely far away. The infaller sees himself
as not moving of course.

Or moving with whatever motion he had wrt other infalling "stuff".

No, he measures himself to be at rest and the stuff
to be moving relative to him. Remember "he" is the
instrument that is doing the measurement, the
anthropomorphic terminology can be misleading.

POV. I had to train myself to believe that the Earth is rotating, in my
heart of hearts.

From the POV of the infallingobserver, a small
patch of spacetime in his vicinity is always
Minkowski so has the speed of light equal to c.
There will be small effects due to tidal action
whiich are explored in the "bonus points" bit
of my other post.

I can believe that the matter infalling with me in toto, makes a frame I
can judge my relative motion wrt. Much as we judge our motion wrt the
CMBR (or the Universe at large).

You seem to have that backwards. All the nearby
galaxies are falling towards the Great Attractor
but I get stopped for speeding, the only measured
figure is my motion relative to the radar gun.
Relative to the observer, the speed of light is c.

What the infinite observer *should* expect, based on constant
local laws for the infaller, is an internal expanding Universe.

No, it should be tidal, expanding between the poles
but being compressed round the equator.

I disagree.

Look for "spaghetification" on any page about black
holes, it is a standard result.

It is the infinite observer that has "a singularity at the center" ...

No, curvature is a local value, basically a second
derivative at the location in question. The "curvature
at the oberver infinitely far away" is zero. The
"curvature at the centre" is infinite.

"Location", "curvature at the center". Outer-r ceases to be meaningful
inside the event horizon. So what does "location" mean in that context?

If you need to draw a distinction, it is what you
call inner-r because that is where the observer
lies, outer-r has no meaning for him in your view.

George

Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:IxJWe.253287$E95.87125@fed1read01...
Dear Geroge Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message newsUpWe.253218$E95.203645@fed1read01...
...
... I see no way for an infinte observer to make
a TWLS distance measurement.

Correct, it would take infinite time for the light
to even reach the area ;-)

Ditto for the infaller.

Ah, that's the interesting answer. Now suppose I
could show you how the infaller can make two-way
measurements over some region by sending light
to a mirror and back. With a little more detail,
would you be prepared to agree that the observer
and mirror are in the same universe during that
process?

That depends, George. Are we and the CMBRM in the
same Universe?

Whoa, slow down. One small step at a time.

OK.

We do send light between here and the Moon, with both
the initiation and reflection "in the past". But we cannot
bounce anything off of the CMBRM. We can't get "the
mirror" to be anything before/beyond "the singularity"
(regardless of its location).

I'll describe a simple one-dimensional experiment
but I want you to think of it as a subset of a
3D setup. That setup is as follows: An observer
is in a spherical lab of radius 3m which is fully
mirrored on the inside. In the centre there is a
flash bulb and an omni-directional photo-detector.
The detector will warn if light fails to return
from any direction and a stopwatch records then
time between a flash and its return (flashes are
tagged so they can be distinguished in some way).
this takes 20ns of course (to the nearest ns) so
gives a measurement of the radius.

OK.

The simplified version considers only two patches
of the spherical mirror 'above' and 'below' which
I will refer to as the upper and lower mirrors.
Left and right would be easier but we are going
to fall into the BH and the measurements need to
be radial. To match convention, in a spacetime
diagram space is usually shown horizontally so
I'll put the upper mirror on the left and the
lower on the right. Having written it, that sounds
confusing but it should be obvious when drawn.

OK.

... I'll keep my copy of "Spacetime Physics" open and ready.
...

Excellent, I have the paperback version so if
you have the hardback some page numbers may
differ. That can save me a lot of drawing :-)

What I have described above is shown in part on
page 112, exercise L-2 as the "Earth frame" but
take A as the bulb/detector and B as the lower
mirror. At event '2' the [first] flash is received
and the second (later received at '4') is emitted.

To complete it add another mirror C to the left
of A and add a light path from event 0 to C then
back to A at event '2' and so on, just an image
of the 0-1-2-3-4 path reflected in A's worldline.
A single flash at '0' produces a diamond shape
with the top at '2'.

Now if the time from '0' to '2' is 20ns, the
measured distance from A to B is 3m as it that
from A to C.

Now add extra flashes, one emitted every ns, so
that toy get overlapping diamonds. My contention
is that within the region bounded by the future
light cone of event '0' (to event '1'), the
worldline of mirror B from event '1' to event '3'
and the past light cone of event '4' (from event
'3'), the B mirror must be in the same universe
as A.

It depends on how you want to simplify. If 3m is small enough to
be too small for your ability to detect curvature, then sure, you
get the same "diamond reflection" all the way in. But what you
cannot do, is extend that 3m beyond (for example) the
photosphere.

The same argument holds for mirror C on
the other side producing a hexagonal region of
spacetime which must all be within the same
universe. Thinking back to the 3D version, the
region is bounded by the future light cone of
the first pulse, the 4D world-surface of the
spherical mirror and the past light cone of the
final detection event. Do you agree with that?

I'm OK with this, given the proviso that a "small enough" volume
is chosen.

It's not quite rigorous if you want to nitpick
but I can make it so with a little more drawing
and it should be good enough for our purposes.
Please say if you spot that deliberate 'error,
or if not I will next time.

Now consider the similarity between "integration over all time"
for infall, and "the light emitted *at* the event horizon never
makes it out".

For bonus points [ ;-) ], you could consider the
effect of gravitational redshift remembering that
mirror C is at the top of the lab and mirror B at
the bottom (think Pound-Rebka) in three situations:

a) The lab is sitting on the surface of the
Earth and the lower mirror is level with
the surface of the Earth.

Parallel. Not as exciting as "falling at c"...

b) The lab is on a ship in deep space which
is undergoing constant acceleration as
measured by an accelerometer on the ship.

Parallel. Not as exciting as "falling at c"...

c) The lab is freefalling frame into a mine
having been dropped from a high crane and
event '2' occurs when the lower mirror is
level with the surface of the Earth.

The curvature is still present, and increasing slightly for some
distance down, before it levels out. The "curvature penalty" is
permanent. Clocks don't run faster deeper in.

.. "Skull on the spike", remember.

No way, just learning together! Hopefully we
will be playing Oz and Erk to Andrew Hamilton's
Wiz but without the chats, just his pages.

Actually "Oz" was Baez's themeline...

David A. Smith

Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:PnqXe.253812$E95.156602@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

Agreed material trimmed again

At the centre, all our tools fail at the moment,
that's the problem.

Not really. The inifinte observer predicts an eternally
expanding, cooling Universe for the infaller.

The observer at infinity predicts sphagetification
for the infaller resulting in infinite compression
and temperature up to the centre but that is
irrelevant.

I disagree. Do you disagree that the infinite observer
would attribute a decreasing-speed-of-light-as-a-
function-of-r as r decreases?

Yes, I disagree, because ...

Is it Shapiro time delay, or c_medium-as-a-function-of-density,
that you don't agree with? Or is it "double accounting"?

So what is "falling faster than c", if not an assignment
by
such an observer?

It is a description applicable to the observer
infinitely far away. The infaller sees himself
as not moving of course.

Or moving with whatever motion he had wrt other infalling
"stuff".

No, he measures himself to be at rest and the stuff
to be moving relative to him. Remember "he" is the
instrument that is doing the measurement, the
anthropomorphic terminology can be misleading.

POV. I had to train myself to believe that the Earth is
rotating, in my heart of hearts.

From the POV of the infallingobserver, a small
patch of spacetime in his vicinity is always
Minkowski so has the speed of light equal to c.
There will be small effects due to tidal action
whiich are explored in the "bonus points" bit
of my other post.

I can believe that the matter infalling with me in toto,
makes a frame I can judge my relative motion wrt.
Much as we judge our motion wrt the CMBR (or the
Universe at large).

You seem to have that backwards. All the nearby
galaxies are falling towards the Great Attractor
but I get stopped for speeding, the only measured
figure is my motion relative to the radar gun.
Relative to the observer, the speed of light is c.

I don't think it is backwards. We can only know our motion wrt
individual sources, and then only (usually) motion along line of
sight. I won't attribute the motion to the "other guy", unless
it is anomalous compared to other "other guys".

What the infinite observer *should* expect, based
on constant local laws for the infaller, is an internal
expanding Universe.

No, it should be tidal, expanding between the poles
but being compressed round the equator.

I disagree.

Look for "spaghetification" on any page about black
holes, it is a standard result.

A "result" that I believe ignores the facts, as I have pointed
out. A "result" of impressing an outer-r on inner-space, which
is clearly a mistake. A mistake that neither Schwarzchild,
Kruskal, nor Eddington can make.

It is the infinite observer that has "a singularity at the
center" ...

No, curvature is a local value, basically a second
derivative at the location in question. The "curvature
at the oberver infinitely far away" is zero. The
"curvature at the centre" is infinite.

"Location", "curvature at the center". Outer-r ceases to be
meaningful inside the event horizon. So what does "location"
mean in that context?

If you need to draw a distinction, it is what you
call inner-r because that is where the observer
lies, outer-r has no meaning for him in your view.

Sorry. I climbed back on my soapbox. I think I am being
consistent, at least... (hopefully not about the soapbox.)

David A. Smith

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:c4MXe.253961$E95.99377@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:PnqXe.253812$E95.156602@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

Agreed material trimmed again

At the centre, all our tools fail at the moment,
that's the problem.

Not really. The inifinte observer predicts an eternally
expanding, cooling Universe for the infaller.

The observer at infinity predicts sphagetification
for the infaller resulting in infinite compression
and temperature up to the centre but that is
irrelevant.

I disagree. Do you disagree that the infinite observer
would attribute a decreasing-speed-of-light-as-a-
function-of-r as r decreases?

Yes, I disagree, because ...

Is it Shapiro time delay, or c_medium-as-a-function-of-density, that you
don't agree with? Or is it "double accounting"?

I guess it is what you mean by "double accounting".
I would assume any measurement of the speed of light
for comparison against c would be done in vacuo and
Shapiro delay is not local. In other words:

From the POV of the infallingobserver, a small
patch of spacetime in his vicinity is always
Minkowski so has the speed of light equal to c.
There will be small effects due to tidal action
whiich are explored in the "bonus points" bit
of my other post.


I can believe that the matter infalling with me in toto,
makes a frame I can judge my relative motion wrt.
Much as we judge our motion wrt the CMBR (or the
Universe at large).

You seem to have that backwards. All the nearby
galaxies are falling towards the Great Attractor
but I get stopped for speeding, the only measured
figure is my motion relative to the radar gun.
Relative to the observer, the speed of light is c.

I don't think it is backwards. We can only know our motion wrt individual
sources, and then only (usually) motion along line of sight.

No, what we _measure_ is red shift which tells us
radial speed relative to us because the instruments
are here, not there.

I won't attribute the motion to the "other guy", unless it is anomalous
compared to other "other guys".

Other way round. We notice that there is a general
trend in all the measurements of the "other guys"
so we switch that around and say we have some proper
motion relative to the general flow.

Look for "spaghetification" on any page about black
holes, it is a standard result.

A "result" that I believe ignores the facts, as I have pointed out. A
"result" of impressing an outer-r on inner-space, which is clearly a
mistake. A mistake that neither Schwarzchild, Kruskal, nor Eddington can
make.

So you are saying everyone who has ever studied GR has
got it wrong but you are right? I have to say I find
that out of character for you.

"Location", "curvature at the center". Outer-r ceases to be
meaningful inside the event horizon. So what does "location"
mean in that context?

If you need to draw a distinction, it is what you
call inner-r because that is where the observer
lies, outer-r has no meaning for him in your view.

Sorry. I climbed back on my soapbox. I think I am being consistent, at
least... (hopefully not about the soapbox.)

That's ok, I have just answered your question in terms
I think you might understand. It doesn't mean I agree
with your view but curvature goes to infinity at r=0
in either way of thinking.

George

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:3QKXe.253945$E95.216149@fed1read01...
"George Dishman" wrote in message
...
"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:IxJWe.253287$E95.87125@fed1read01...
"George Dishman" wrote in message
...

... suppose I
could show you how the infaller can make two-way
measurements over some region by sending light
to a mirror and back. With a little more detail,
would you be prepared to agree that the observer
and mirror are in the same universe during that
process?

That depends, George. ...
....
I'll describe a simple one-dimensional experiment
but I want you to think of it as a subset of a
3D setup. That setup is as follows: An observer
is in a spherical lab of radius 3m which is fully
mirrored on the inside. In the centre there is a
flash bulb and an omni-directional photo-detector.
The detector will warn if light fails to return
from any direction and a stopwatch records then
time between a flash and its return (flashes are
tagged so they can be distinguished in some way).
this takes 20ns of course (to the nearest ns) so
gives a measurement of the radius.

OK.

The simplified version considers only two patches
of the spherical mirror 'above' and 'below' which
I will refer to as the upper and lower mirrors.
Left and right would be easier but we are going
to fall into the BH and the measurements need to
be radial. To match convention, in a spacetime
diagram space is usually shown horizontally so
I'll put the upper mirror on the left and the
lower on the right. Having written it, that sounds
confusing but it should be obvious when drawn.

OK.

... I'll keep my copy of "Spacetime Physics" open and ready. ...

Excellent, I have the paperback version so if
you have the hardback some page numbers may
differ. That can save me a lot of drawing :-)

What I have described above is shown in part on
page 112, exercise L-2 as the "Earth frame" but
take A as the bulb/detector and B as the lower
mirror. At event '2' the [first] flash is received
and the second (later received at '4') is emitted.

To complete it add another mirror C to the left
of A and add a light path from event 0 to C then
back to A at event '2' and so on, just an image
of the 0-1-2-3-4 path reflected in A's worldline.
A single flash at '0' produces a diamond shape
with the top at '2'.

Now if the time from '0' to '2' is 20ns, the
measured distance from A to B is 3m as it that
from A to C.

Now add extra flashes, one emitted every ns, so
that toy get overlapping diamonds. My contention
is that within the region bounded by the future
light cone of event '0' (to event '1'), the
worldline of mirror B from event '1' to event '3'
and the past light cone of event '4' (from event
'3'), the B mirror must be in the same universe
as A.

It depends on how you want to simplify. If 3m is small enough to be too
small for your ability to detect curvature, then sure, you get the same
"diamond reflection" all the way in.

I am considering a supermassive black hole in which
the acceleration at r=2m is about 1g. That makes
r about half a light year I believe so 3m is a "small
lab" in comparison. In terms of tidal effects, that's
what the final questions were about.

But what you cannot do, is extend that 3m beyond (for example) the
photosphere.

The same argument holds for mirror C on
the other side producing a hexagonal region of
spacetime which must all be within the same
universe. Thinking back to the 3D version, the
region is bounded by the future light cone of
the first pulse, the 4D world-surface of the
spherical mirror and the past light cone of the
final detection event. Do you agree with that?

I'm OK with this, given the proviso that a "small enough" volume is
chosen.

A 3m cubed volume some half light year from the
centre.

It's not quite rigorous if you want to nitpick
but I can make it so with a little more drawing
and it should be good enough for our purposes.
Please say if you spot that deliberate 'error,
or if not I will next time.

Now consider the similarity between "integration over all time" for
infall, and "the light emitted *at* the event horizon never makes it out".

It is my intention to move on to applying the
test described above to the spacetime diagram
for a black hole but first we need to do a bit
of SR to rotate axes. I'll get your comments on
tidal bits first and should find time to write
the next bit later.

In the meantime, think of this. I believe you are
in Arizona while I am in Sussex. If I draw a line
from me to you and project it some tens of billions
of light years, way off in the distance there is
an alien for whom you are moving slightly less than
c due to cosmological expansion while I am moving
slightly faster than c. Does that mean you and I
are in different universes? That is how two people
in my 3m radius lab would view the 'observer at
infinity' and his claim that a point half way
between them was "falling at c".

For bonus points [ ;-) ], you could consider the
effect of gravitational redshift remembering that
mirror C is at the top of the lab and mirror B at
the bottom (think Pound-Rebka) in three situations:

a) The lab is sitting on the surface of the
Earth and the lower mirror is level with
the surface of the Earth.

Parallel. Not as exciting as "falling at c"...

Light going from source to upper mirror will
be red shifted as in Pound-Rebka but after
reflection it is blue shifted by an equal
amount so a frequency change is not detected.
I think there would be a very slight Shapiro
delay hence the vertical height might not be
quite the same as the horizontal width but
I'm not sure if that too would cancel out.
The next question may shed some light on this.
The acceleration of gravity varies between
lower and upper as r^-2 from the centre of the
Earth but this is not evident as the profile
remains constant throughout the duration of
the experiment.

b) The lab is on a ship in deep space which
is undergoing constant acceleration as
measured by an accelerometer on the ship.

Parallel. Not as exciting as "falling at c"...

A comparison between vertical and horizontal
measurements might be thought of as the MMX
since the speed of the lab in any inertial
frame is not the same when the light return
as when it was emitted. However there are no
inertial frames in GR so would there be
measurable length contraction vertically? If
so could the observer attribute it to Shapiro
delay? BTW these aren't rhetorical questions,
I don't know the answers myself yet but I
intend to find out if I can.

Both the above could of course measure the
acceleration (of gravity or the ship) with a
something as simple as a mass on a spring.

c) The lab is freefalling frame into a mine
having been dropped from a high crane and
event '2' occurs when the lower mirror is
level with the surface of the Earth.

The curvature is still present, and increasing slightly for some distance
down, before it levels out. The "curvature penalty" is permanent. Clocks
don't run faster deeper in.

The light going from source to upper mirror is
red shifted as in Pound-Rebka. It is also blue
shifted while returning to the detector however
the lab has fallen some distance so on the
return the gravitational acceleration is
greater so there will be a net blue shift. This
allows the tidal force to be measured even in
a freefall condition. Do you agree?

This comes back to your comments a few posts ago
that even for a supermassive black hole the tidal
force can be measured with adequate instruments.
You are right, a sensitive spectrometer could do
that but it still produces only a minimal change
to the distance measurement (if any). IMHO I can
still claim the roof and floor are in the same
universe during the measurement.

.. "Skull on the spike", remember.

No way, just learning together! Hopefully we
will be playing Oz and Erk to Andrew Hamilton's
Wiz but without the chats, just his pages.

Actually "Oz" was Baez's themeline...

I thought he saw himself as the Wiz and Oz was
the handle used by a student who asked questions
in s.p.r. Anyway, I meant we were the students
trying to figure out what the experts are telling
us. I hope that's OK with you.

George

Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:c4MXe.253961$E95.99377@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:PnqXe.253812$E95.156602@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

Agreed material trimmed again

At the centre, all our tools fail at the moment,
that's the problem.

Not really. The inifinte observer predicts an eternally
expanding, cooling Universe for the infaller.

The observer at infinity predicts sphagetification
for the infaller resulting in infinite compression
and temperature up to the centre but that is
irrelevant.

I disagree. Do you disagree that the infinite observer
would attribute a decreasing-speed-of-light-as-a-
function-of-r as r decreases?

Yes, I disagree, because ...

Is it Shapiro time delay, or c_medium-as-a-function-
of-density, that you don't agree with? Or is it "double
accounting"?

I guess it is what you mean by "double accounting".
I would assume any measurement of the speed of light
for comparison against c would be done in vacuo and
Shapiro delay is not local. In other words:

From the POV of the infallingobserver, a small
patch of spacetime in his vicinity is always
Minkowski so has the speed of light equal to c.
There will be small effects due to tidal action
whiich are explored in the "bonus points" bit
of my other post.

OK.

I can believe that the matter infalling with me in toto,
makes a frame I can judge my relative motion wrt.
Much as we judge our motion wrt the CMBR (or the
Universe at large).

You seem to have that backwards. All the nearby
galaxies are falling towards the Great Attractor
but I get stopped for speeding, the only measured
figure is my motion relative to the radar gun.
Relative to the observer, the speed of light is c.

I don't think it is backwards. We can only know our
motion wrt individual sources, and then only (usually)
motion along line of sight.

No, what we _measure_ is red shift which tells us
radial speed relative to us because the instruments
are here, not there.

Mox nix.

I won't attribute the motion to the "other guy", unless
it is anomalous compared to other "other guys".

Other way round. We notice that there is a general
trend in all the measurements of the "other guys"
so we switch that around and say we have some proper
motion relative to the general flow.

Look for "spaghetification" on any page about black
holes, it is a standard result.

A "result" that I believe ignores the facts, as I have
pointed out. A "result" of impressing an outer-r on
inner-space, which is clearly a mistake. A mistake
that neither Schwarzchild, Kruskal, nor Eddington can make.

So you are saying everyone who has ever studied GR has
got it wrong but you are right? I have to say I find
that out of character for you.

Did Schwarzchild, Kruskal, and Eddington never study GR? It is
their methods, and my interpretation of them, that we are
discussing.

It is really common for people to believe that the Sun moves
around the Earth, because they cannot "feel" that they are slowly
rotating "head over heels". Similarly, it is really easy for us
to naively map outer-r to the inside of a BH, and imagine all
sorts of "problems" as infalling matter approaches a "central
singularity". And they will do so even when it is clear that
outer-r is not a spatial distance measure inside the event
horizon, and ceased to be 1:1 even before that. It will be
eternity before we could ever be proved wrong in this provincial
attitude.

"Location", "curvature at the center". Outer-r ceases to be
meaningful inside the event horizon. So what does
"location"
mean in that context?

If you need to draw a distinction, it is what you
call inner-r because that is where the observer
lies, outer-r has no meaning for him in your view.

Sorry. I climbed back on my soapbox. I think I am being
consistent, at least... (hopefully not about the soapbox.)

That's ok, I have just answered your question in terms
I think you might understand. It doesn't mean I agree
with your view but curvature goes to infinity at r=0
in either way of thinking.

Cool.

David A. Smith

Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:3QKXe.253945$E95.216149@fed1read01...
"George Dishman" wrote in message
...

.... just snipping header a bit...
I'll describe a simple one-dimensional experiment
but I want you to think of it as a subset of a
3D setup. That setup is as follows: An observer
is in a spherical lab of radius 3m which is fully
mirrored on the inside. In the centre there is a
flash bulb and an omni-directional photo-detector.
The detector will warn if light fails to return
from any direction and a stopwatch records then
time between a flash and its return (flashes are
tagged so they can be distinguished in some way).
this takes 20ns of course (to the nearest ns) so
gives a measurement of the radius.

OK.

The simplified version considers only two patches
of the spherical mirror 'above' and 'below' which
I will refer to as the upper and lower mirrors.
Left and right would be easier but we are going
to fall into the BH and the measurements need to
be radial. To match convention, in a spacetime
diagram space is usually shown horizontally so
I'll put the upper mirror on the left and the
lower on the right. Having written it, that sounds
confusing but it should be obvious when drawn.

OK.

... I'll keep my copy of "Spacetime Physics" open and ready.
...

Excellent, I have the paperback version so if
you have the hardback some page numbers may
differ. That can save me a lot of drawing :-)

What I have described above is shown in part on
page 112, exercise L-2 as the "Earth frame" but
take A as the bulb/detector and B as the lower
mirror. At event '2' the [first] flash is received
and the second (later received at '4') is emitted.

To complete it add another mirror C to the left
of A and add a light path from event 0 to C then
back to A at event '2' and so on, just an image
of the 0-1-2-3-4 path reflected in A's worldline.
A single flash at '0' produces a diamond shape
with the top at '2'.

Now if the time from '0' to '2' is 20ns, the
measured distance from A to B is 3m as it that
from A to C.

Now add extra flashes, one emitted every ns, so
that toy get overlapping diamonds. My contention
is that within the region bounded by the future
light cone of event '0' (to event '1'), the
worldline of mirror B from event '1' to event '3'
and the past light cone of event '4' (from event
'3'), the B mirror must be in the same universe
as A.

It depends on how you want to simplify. If 3m is small
enough to be too small for your ability to detect curvature,
then sure, you get the same "diamond reflection" all the
way in.

I am considering a supermassive black hole in which
the acceleration at r=2m is about 1g. That makes
r about half a light year I believe so 3m is a "small
lab" in comparison. In terms of tidal effects, that's
what the final questions were about.

But what you cannot do, is extend that 3m beyond
(for example) the photosphere.

The same argument holds for mirror C on
the other side producing a hexagonal region of
spacetime which must all be within the same
universe. Thinking back to the 3D version, the
region is bounded by the future light cone of
the first pulse, the 4D world-surface of the
spherical mirror and the past light cone of the
final detection event. Do you agree with that?

I'm OK with this, given the proviso that a "small
enough" volume is chosen.

A 3m cubed volume some half light year from the
centre.

It's not quite rigorous if you want to nitpick
but I can make it so with a little more drawing
and it should be good enough for our purposes.
Please say if you spot that deliberate 'error,
or if not I will next time.

Now consider the similarity between "integration over
all time" for infall, and "the light emitted *at* the event
horizon never makes it out".

It is my intention to move on to applying the
test described above to the spacetime diagram
for a black hole but first we need to do a bit
of SR to rotate axes. I'll get your comments on
tidal bits first and should find time to write
the next bit later.

OK.

In the meantime, think of this. I believe you are
in Arizona while I am in Sussex.

Si, Senior.

If I draw a line
from me to you and project it some tens of billions
of light years, way off in the distance there is
an alien for whom you are moving slightly less than
c due to cosmological expansion while I am moving
slightly faster than c. Does that mean you and I
are in different universes?

Superlumenal scissors. No.

That is how two people
in my 3m radius lab would view the 'observer at
infinity' and his claim that a point half way
between them was "falling at c".

Yet said alien would receive light from us, and we could receive
from him (given sufficent time). So clearly the analogy is as
flawed as it is for "superlumenal jets".

For bonus points [ ;-) ], you could consider the
effect of gravitational redshift remembering that
mirror C is at the top of the lab and mirror B at
the bottom (think Pound-Rebka) in three situations:

a) The lab is sitting on the surface of the
Earth and the lower mirror is level with
the surface of the Earth.

Parallel. Not as exciting as "falling at c"...

Light going from source to upper mirror will
be red shifted as in Pound-Rebka but after
reflection it is blue shifted by an equal
amount so a frequency change is not detected.

This is very poor wording, IMO. The light emitted is
characeristic of the process that emitted it and the location of
the process in curved space at the time of emission. Since we
cannot steal some energy from a photon, then the photon does not
change on the trip "up and down"... only the clocks, that decide
what the frequency is, change. (Neglecting differential motion
between the emitting process and the observer's instruments, of
course.) Just correlate the observations with GPS-vs-ground
clocks to light emitting processes. Or type II supernovae
spectra to supervonvae duration.

I think there would be a very slight Shapiro
delay hence the vertical height might not be
quite the same as the horizontal width but
I'm not sure if that too would cancel out.

It is exactly equal to the detected red shift.

The next question may shed some light on this.
The acceleration of gravity varies between
lower and upper as r^-2 from the centre of the
Earth but this is not evident as the profile
remains constant throughout the duration of
the experiment.

3m is still pretty small.

b) The lab is on a ship in deep space which
is undergoing constant acceleration as
measured by an accelerometer on the ship.

Parallel. Not as exciting as "falling at c"...

A comparison between vertical and horizontal
measurements might be thought of as the MMX
since the speed of the lab in any inertial
frame is not the same when the light return
as when it was emitted. However there are

.... in general ...

no
inertial frames in GR so would there be
measurable length contraction vertically?

Yes. But not for our "too small to detect system".

If
so could the observer attribute it to Shapiro
delay?

Yes, and correctly so, I believe. For a different observer.

BTW these aren't rhetorical questions,
I don't know the answers myself yet but I
intend to find out if I can.

OK.

Both the above could of course measure the
acceleration (of gravity or the ship) with a
something as simple as a mass on a spring.

c) The lab is freefalling frame into a mine
having been dropped from a high crane and
event '2' occurs when the lower mirror is
level with the surface of the Earth.

The curvature is still present, and increasing slightly for
some
distance down, before it levels out. The "curvature penalty"
is
permanent. Clocks don't run faster deeper in.

The light going from source to upper mirror is
red shifted as in Pound-Rebka.

The base process is "red shifted", rather.

It is also blue
shifted while returning to the detector however
the lab has fallen some distance so on the
return the gravitational acceleration is
greater so there will be a net blue shift. This
allows the tidal force to be measured even in
a freefall condition. Do you agree?

Not if 3m is "too small to detect". In general, our motion will
have increased, and light travelling "radially outwards" should
appear net red shifted. It was emitted from a source that had
lower radial velocity, bounced off a mirror with only slightly
higher radial velocity (assuming the system was intact) and
received by an observer that is moving increasingly fast radially
inwards. Otherwise, no, you cannot measure freefall "tidal
force" without access to an "infinite frame".

This comes back to your comments a few posts ago
that even for a supermassive black hole the tidal
force can be measured with adequate instruments.

I don't recall that. It doesn't matter. It is incorrect, as I
consider it now. "Accelerating wrt what?", doesn't work for a
"too small" system. Perhaps we need to drop the Earth and Moon
into a BH, and use LLR? Or simply assert that 1m is our
detection limit.

You are right, a sensitive spectrometer could do
that but it still produces only a minimal change
to the distance measurement (if any). IMHO I can
still claim the roof and floor are in the same
universe during the measurement.

As long as the roof and floor are interchanging light, this would
be a valid claim. Keep in mind that aether cannot be killed, so
dual interchange of light will be required "to be in the same
Universe".

.. "Skull on the spike", remember.

No way, just learning together! Hopefully we
will be playing Oz and Erk to Andrew Hamilton's
Wiz but without the chats, just his pages.

Actually "Oz" was Baez's themeline...

I thought he saw himself as the Wiz and Oz was
the handle used by a student who asked questions
in s.p.r.

You attributed it to Hamilton, when it was Baez, was my point.

Anyway, I meant we were the students
trying to figure out what the experts are telling
us. I hope that's OK with you.

Absolutely. I never got into D&D, but role playing can be
instructive. Press on. Two students, and the professor has
simply left clues in "strange" places.

David A. Smith

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:4p2Ye.256955$E95.192022@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:3QKXe.253945$E95.216149@fed1read01...
"George Dishman" wrote in message
...

... just snipping header a bit...

I'll snip the experiment, we can always look back.

In the meantime, think of this. I believe you are
in Arizona while I am in Sussex.

Si, Senior.

If I draw a line
from me to you and project it some tens of billions
of light years, way off in the distance there is
an alien for whom you are moving slightly less than
c due to cosmological expansion while I am moving
slightly faster than c. Does that mean you and I
are in different universes?

Superlumenal scissors. No.

No, superluminal scissors is not related, this
was an alien in a fixed distant galaxy. Perhaps
if I had used the Andromeda galaxy and our it
would have been clearer. I am talking simply of
the observed expansion of the universe.

A distant observer look back at our region and
sees a red patch in the CMBR which will later
become the Virgo cluster. The Andromeda galaxy
is sufficiently close to his location that
light emitted 'now' will reach that observer
billions of years from now. It will take a long
time because initially he sees that galaxy moving
away from him at nearly the speed of light.

However light from our galaxy will never reach
him because we are a little farther away and
hence we are moving "faster than c" relative to
him. Okay, it's loose wording to talk of movement,
really the space between Andromeda and him is
expanding at the rates I indicate but I'm sure
you get the point, that we and the Andromeda
galaxy are not in separate universes just because
some distant alien sees an event horizon between
us.

That is how two people
in my 3m radius lab would view the 'observer at
infinity' and his claim that a point half way
between them was "falling at c".

Yet said alien would receive light from us, and we could receive from him
(given sufficent time).

He would receive light from you but space is
expanding so fast that he can never receive
light from me, I'm just that little bit farther
away.

So clearly the analogy is as flawed as it is for "superlumenal jets".

For bonus points [ ;-) ], you could consider the
effect of gravitational redshift remembering that
mirror C is at the top of the lab and mirror B at
the bottom (think Pound-Rebka) in three situations:

a) The lab is sitting on the surface of the
Earth and the lower mirror is level with
the surface of the Earth.

Parallel. Not as exciting as "falling at c"...

Light going from source to upper mirror will
be red shifted as in Pound-Rebka but after
reflection it is blue shifted by an equal
amount so a frequency change is not detected.

This is very poor wording, IMO.

It was phenomenologically worded. We observe a
frequency shift without assuming a specific
mechanism. However, I'll correct that below!

The light emitted is characeristic of the process that emitted it and the
location of the process in curved space at the time of emission.

Oh dear. No, frequency of the light measured
locally is characteristic of the process, period.
See next.

Since we cannot steal some energy from a photon, then the photon does not
change on the trip "up and down"... only the clocks, that decide what the
frequency is, change.

Not in SR or GR, you are describing aether theory.

Let's correct the wording in relation to
Pound-Rebka. An atom at the bottom of their
tower produced light of a characteristic
frequency. Considering one cycle, it has a
well defined period. The atom's proper time
is measured as always along the tangent to its
worldline (4-velocity) so consider a vector in
that direction of length equal to the period.
Now parallel-transport that along a null
(light-like) geodesic to the mirror or in the
case of Pound-Rebka to the reference atom at the
top of the tower. Because of the curvature,
this transported vector is not parallel to the
4-velocity of the upper atom. Project the
transported vector onto the worldline of the
atom and it does not match the period of the
local atom, in other words it exhibits a
'red shift'.

(Neglecting differential motion between the emitting process and the
observer's instruments, of course.)

Any differential motion adds to the angle
between the transported vector from the
lower atom and the tangent to the worldline
of the upper atom.

Just correlate the observations with GPS-vs-ground clocks to light
emitting processes.

Two factors, one due to gravity and one due to
the orbital speed, exactly as described above.

Or type II supernovae spectra to supervonvae duration.

I think you mean type Ia. This is more
interesting. If you parallel transport a unit
time vector *v*/|v| where *v* is the 4-velocity
of the CoM from the source to the observer along
a light-like path, the result is at a significant
angle to our local 4-velocity due to curvature
hence is 'gravitational red shift'. However over
short distances one can extend the local
coordinate patch to nearby SNe and the angle can
then be thought of as 'motion of the SNe'.

I think there would be a very slight Shapiro
delay hence the vertical height might not be
quite the same as the horizontal width but
I'm not sure if that too would cancel out.

It is exactly equal to the detected red shift.

The delay would need be the integral of the
shift over the path to get the units right.

The next question may shed some light on this.
The acceleration of gravity varies between
lower and upper as r^-2 from the centre of the
Earth but this is not evident as the profile
remains constant throughout the duration of
the experiment.

3m is still pretty small.

Send a signal to the altitude of GPS and
transpond it back (without an onboard shift)
and you get the same frequency you sent. The
gravitational effects cancel. (I'm glossing
over the speed effect.) It is not the fact
that 3m is small but that everything is exactly
reversed on the way back down.

b) The lab is on a ship in deep space which
is undergoing constant acceleration as
measured by an accelerometer on the ship.

Parallel. Not as exciting as "falling at c"...

A comparison between vertical and horizontal
measurements might be thought of as the MMX
since the speed of the lab in any inertial
frame is not the same when the light return
as when it was emitted. However there are

... in general ...

no
inertial frames in GR so would there be
measurable length contraction vertically?

Yes. But not for our "too small to detect system".

If
so could the observer attribute it to Shapiro
delay?

Yes, and correctly so, I believe. For a different observer.

For the observer at the centre. The effect
applies in his frame when the photon is
at some distance from him. It is very slight
but integrated over the path could be
comparable to any length effect.

BTW these aren't rhetorical questions,
I don't know the answers myself yet but I
intend to find out if I can.

OK.

I think we agree, but we might both be wrong.

Both the above could of course measure the
acceleration (of gravity or the ship) with a
something as simple as a mass on a spring.

c) The lab is freefalling frame into a mine
having been dropped from a high crane and
event '2' occurs when the lower mirror is
level with the surface of the Earth.

The curvature is still present, and increasing slightly for some
distance down, before it levels out. The "curvature penalty" is
permanent. Clocks don't run faster deeper in.

The light going from source to upper mirror is
red shifted as in Pound-Rebka.

The base process is "red shifted", rather.

Not according to SR/GR, it is a system effect
rather than local to either end. The base
process is changed by an interaction with the
aether in LET.

It is also blue
shifted while returning to the detector however
the lab has fallen some distance so on the
return the gravitational acceleration is
greater so there will be a net blue shift. This
allows the tidal force to be measured even in
a freefall condition. Do you agree?

Not if 3m is "too small to detect".

Well yes, I am saying that there is a blue shift
in question c) where there is none in questions
a) and b) which allows it to be distinguished
assuming your can measure such a small quantity.
Pound-Rebka used 22.5m so my 3m isn't unreasonable.

In general, our motion will have increased, and light travelling "radially
outwards" should appear net red shifted. It was emitted from a source
that had lower radial velocity, bounced off a mirror with only slightly
higher radial velocity (assuming the system was intact) and received by an
observer that is moving increasingly fast radially inwards.

Right.

Otherwise, no, you cannot measure freefall "tidal force" without access
to an "infinite frame".

This comes back to your comments a few posts ago
that even for a supermassive black hole the tidal
force can be measured with adequate instruments.

I don't recall that. It doesn't matter. It is incorrect, as I consider
it now. "Accelerating wrt what?",

"Tidal" therefore 'does the acceleration at the
top of my lab differ from that at the bottom'.
Obviously the size of lab required is related to
the sensitivity of the instruments.

doesn't work for a "too small" system.

Exactly.

Perhaps we need to drop the Earth and Moon into a BH, and use LLR? Or
simply assert that 1m is our detection limit.

You are right, a sensitive spectrometer could do
that but it still produces only a minimal change
to the distance measurement (if any). IMHO I can
still claim the roof and floor are in the same
universe during the measurement.

As long as the roof and floor are interchanging light, this would be a
valid claim.

OK, that was where I wanted to get to. I finally
did the diagram for an inertial lab, just SR:

http://www.georgedishman.f2s.com/david/in_the_lab.png

I have also shown a couple of past/future light
cones in green. The colours just let you
distinguish the light going to the upper (red)
and lower (blue) mirrors. They mimic the shift
that would be observed at the mirrors but aren't
intended to mean anything, just to clarify that
the beams aren't crossing the centre.

The 'deliberate mistake I mentioned was that
strictly it would be better to bound the
region classed as 'in the same universe' by the
past lightcone of the first reception and the
future lightcone of the final transmission so
that it includes only the crosshatched area
where we have two-way light propagation at
every event but that is academic for our
purposes.

If this was plotted by an observer moving at
constant speed past the lab, it should be clear
that you would get a picture like the "Rocket
Frame" diagram on the same page (112) of T&W.

Now consider what happens if that is drawn for
a free falling lab as in my question c). Since
curvature cannot be removed, the central line
for the observer must become curved and if
the lab structure is rigid in the sense of no
measurable strain due to the tidal forces then
the mirror worldlines would run almost parallel
to that of the observer (not quite parallel due
to rotation of the spatial axis - at a constant
distance).

Keep in mind that aether cannot be killed, so dual interchange of light
will be required "to be in the same Universe".

What aether? I am talking GR and I thought you
were too, I have no interest in aether theories.

.. "Skull on the spike", remember.

No way, just learning together! Hopefully we
will be playing Oz and Erk to Andrew Hamilton's
Wiz but without the chats, just his pages.

Actually "Oz" was Baez's themeline...

I thought he saw himself as the Wiz and Oz was
the handle used by a student who asked questions
in s.p.r.

You attributed it to Hamilton, when it was Baez, was my point.

Ah, I meant Hamilton in our discussion was the
counterpart of Baez in the web pages as we are
the counterparts of Oz and Erk.

Anyway, I meant we were the students
trying to figure out what the experts are telling
us. I hope that's OK with you.

Absolutely. I never got into D&D, but role playing can be instructive.
Press on. Two students, and the professor has simply left clues in
"strange" places.

Ok, the next instalment is applying our agreement
on the 'same universe' test to a free-falling lab
and the next will be that as seen by an observer
falling at constant speed in the gravitational
field. The step after that should get us back to
the web pages.

George

Seems to me the analogy using Andromeda has the same problem
as that using two points on Earth, because Andromeda and the
Milky Way are moving closer together, not moving apart. I
certainly agree with the point, though.

-- Jeff, in Minneapolis