Dear George Dishman:

"George Dishman" wrote in message
...

"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.

....
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.

OK.

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.

Can you prove that? I'm not trying to be a ball buster, but if
you cannot *ever* measure something, it is neither in your
future, nor your present, does it have any effect on you?

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.

OK.

....
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.

Note where I said "location of the process in curved space".
This means *not* local.

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.

Yes, in GR, and in QM. You cannot alter a photon, except by
absorbing or scattering it. "Position in a gravity well" is
meaningless to a photon. I don't know about what aether theory
would predict, and I don't claim to.

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.

.... and hence the apparent "frequency change".

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'.

Which is not altering the light, only acknowledging the variance
in curvature at the two *non-local* endpoints.

(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.

Adds or *subtracts*, yes.

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.

Yet the characteristic process indicates a different "time base"
at different altitudes. Hence Shapiro time delay.

Or type II supernovae spectra to supervonvae duration.

I think you mean type Ia.

Probably. But I have "6200 ly" down pat! ;)

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'.

"Motion" as Ned Wright has presented, OK. Yet it is still "only"
characteristic of the relative positions (and yes kinetic
velocities) of the emitters and receiver in curved space.

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.

Good point.

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.)

No issues.

It is not the fact
that 3m is small but that everything is exactly
reversed on the way back down.

More clear is to say the at the emitting clock is not affected by
the path the reflected photon took. Since the photon's frequency
is unaffected by the path (other than deflection of vector, and
possible boosting by frame dragging).

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

I disagree. I suspect, but don't know without doing the math,
that given sufficient resolution, the observer will appear to
simply "shift away from center" towards the "gravitational
source". Not really length contraction... since one axis should
"symmetrically" get longer.

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.

Nah! ;)

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.

In LET (I believe) as in SR/GR, it is still a system effect,
since both the emitter and receiver are immersed in aether that
controls "local" processes/measurements. I was not as clear as I
should have been. Sorry.

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.

.... as long as you aren't falling into a black hole, with a short
finite time before impacting at a "central singularity".
Pound-Rebka accumulated counts over a (relatively) long period of
time to achieve a measureable result.

....
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

Waaaaay, too much time on your hands! ;)

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.

And even if they were, they would still be red or blue shifted
when detected on that side.

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.

But something to consider carefully if one is to construct a
homogenous solution "from whole cloth".

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.

OK.

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).

Agreed.

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.

"The laws of physics are the same for all inertial observers."
Aether cannot be killed in any inertial frame.

....
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.

Sounds good. I've got to get to an "integration surface", which
hopefully is similar for sources near (eg. infalling matter
colliding with an accretion disk) and far.

David A. Smith

"Jeff Root" wrote in message
ups.com...
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.

No, the problem was that a line through Sussex and
Arizona rotates once a day while that through the
Milky Way to Andromeda is in a stable direction
hence David was concerned about "superluminal
scissors" since the rotation of the line can be
likened to the rotation of a blade.

http://math.ucr.edu/home/baez/physic.../scissors.html

The fact that the separation is reducing isn't a
problem, there can still be a hypothetical observer
for whom accelerating cosmological expansion gives
an event horizon half way between the galaxies.

George

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox wrote in
message news:jxoYe.261460$E95.141026@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
...

"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...

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.

Can you prove that?

Not without contacting an alien observer
and asking hime :-(

I'm not trying to be a ball buster, but if you cannot *ever* measure
something, it is neither in your future, nor your present, does it have
any effect on you?

That's not the point. We can measure light from
the Andromeda galaxy with no problem, and also
from other galaxies in the opposite direction.

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.

OK.

Well that is the meaning of "event horizon".
Events can happen in the same universe as us
but we may not be able to ever receive light
from them.

...
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.

Note where I said "location of the process in curved space". This means
*not* local.

I don't tread it that way, "location of the
process" refers to the one location where the
atom is situated when it was involved in the
process of emitting the photon. It's my turn
to say "This is very poor wording, IMO."

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.

Yes, in GR, and in QM. You cannot alter a photon, except by absorbing or
scattering it.

You don't "alter a photon" when receiving it
on a moving detector yet the Doppler effect
alters the frequency. However, I wasn't talking
about the photon. You said "the photon does not
change on the trip ... only the clocks" but
according to GR good clocks are not directly
affected as they would be in aether theory.

"Position in a gravity well" is meaningless to a photon. I don't know
about what aether theory would predict, and I don't claim to.

Lorentzian aether theory says clocks run slow
if they are in motion through the aether.

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.

... and hence the apparent "frequency change".

which is what I said next:

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'.

Which is not altering the light, only acknowledging the variance in
curvature at the two *non-local* endpoints.

That's right, GR says gravitational potential
doesn't influence the emitting or detecting
processes, it is the relationship between the
ends (integrated curvature if I have it right)
that produces the effects.

(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.

Adds or *subtracts*, yes.

I assumed you were happy with signed numbers ;-)

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.

Yet the characteristic process indicates a different "time base" at
different altitudes.

"time base" is not a standard term so I have
to guess what you mean. The "time bases" are
not different in that an atomic transition
gives the same frequency in terms of proper
time of the atom. It is the angle between one
and the other after parallel transport that
produces the effect.

Hence Shapiro time delay.

Or type II supernovae spectra to supervonvae duration.

I think you mean type Ia.

Probably. But I have "6200 ly" down pat! ;)

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'.

"Motion" as Ned Wright has presented, OK.

Yes, just "motion" in the normal sense.

Yet it is still "only" characteristic of the relative positions (and yes
kinetic velocities) of the emitters and receiver in curved space.

Right.

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.

Good point.

Just nitpicking again.

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.)

No issues.

It is not the fact
that 3m is small but that everything is exactly
reversed on the way back down.

More clear is to say the at the emitting clock is not affected by the path
the reflected photon took. Since the photon's frequency is unaffected by
the path (other than deflection of vector, and possible boosting by frame
dragging).

I think that's actually less clear. For example
"photon's frequency" sounds like some intrinsic
attribute but like kinetic energy frequency is
only meaningful so a specific observer.

Also, in later examples where the frequency is
affected, there is still no effect on "the
emitting clock". It is purely a path thing.

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

I disagree. I suspect, but don't know without doing the math, that given
sufficient resolution, the observer will appear to simply "shift away from
center" towards the "gravitational source". Not really length
contraction... since one axis should "symmetrically" get longer.

I was using 'centre' perhaps a little loosely
just to identify which observer, good nitpick.

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.

Nah! ;)

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.

In LET (I believe) as in SR/GR, it is still a system effect, since both
the emitter and receiver are immersed in aether that controls "local"
processes/measurements. I was not as clear as I should have been. Sorry.

No that is still wrong. In aether theory, the
emitter is slowed by speed relative to the aether
(characterised by the usual gamma function) due
to some unexplained interaction at the atomic
level. The same happens to any clock measuring it
but there is no change along the path. In SR there
is no interaction because there is no aether so
processes are unaltered and the effects are due
to curvature along the path. There is no curvature
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.

... as long as you aren't falling into a black hole, with a short finite
time before impacting at a "central singularity". Pound-Rebka accumulated
counts over a (relatively) long period of time to achieve a measureable
result.

We just need quicker tools which are always available
in thought experiments. However, perhaps you would
like to work out how long (proper time of course) it
takes from the event horizon to the centre for a black
hole large enough to have a 1g acceleration at the
horizon.

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

Waaaaay, too much time on your hands! ;)

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.

And even if they were, they would still be red or blue shifted when
detected on that side.

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.

But something to consider carefully if one is to construct a homogenous
solution "from whole cloth".

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.

OK.

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).

Agreed.

Good stuff, I think we are making progress so I'll
go straight to the hard part. Try taking the sketch
I drew above and distort it sideways as in the two
diagrams in T&W it so that the central source/
detector line is the worldline of the infalling
observer shown in the spacetime diagrams on this
page

http://www.phy.syr.edu/courses/modul...arzschild.html

Clearly a problem arises when the final detection
is at the singularity but I cannot see any reason
why the pattern should not extend across the event
horizon. Bear in mind the scale, the diamonds in my
sketch are 3m while the distance from the horizon
to the singularity is vastly larger.

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.

"The laws of physics are the same for all inertial observers."

"inertial observers" is problematic but I'll go
with the principle of equivalence.

Aether cannot be killed in any inertial frame.

True, since an aether doesn't exist in the first
place, at least not when we are learning GR.

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.

Sounds good. I've got to get to an "integration surface", which hopefully
is similar for sources near (eg. infalling matter colliding with an
accretion disk) and far.

Actually I've gone on the web page as we seem
to be agreeing the important stuff. I have no idea
why you keep referring to aether though.

George

Dear George Dishman:

"George Dishman" wrote in message
...

"N:dlzc D:aol T:com (dlzc)" N: dlzc1 D:cox
wrote in message news:jxoYe.261460$E95.141026@fed1read01...
Dear George Dishman:

"George Dishman" wrote in message
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"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
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"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...

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.

Can you prove that?

Not without contacting an alien observer
and asking [him] :-(

... which we stated cannot occur. I caution you in analogies
involving expansion with the EH of a black hole. Note that
light-based information can go one way across the event horizon
of a black hole, but *neither way* across the entire span between
source and emitter once over an "expansion horizon".

I'm not trying to be a ball buster, but if you cannot *ever*
measure something, it is neither in your future, nor your
present, does it have any effect on you?

That's not the point. We can measure light from
the Andromeda galaxy with no problem, and also
from other galaxies in the opposite direction.

So the Andromeda galaxy is in our Universe, but the question is,
is the alien? Light from the CMBRM is in our Universe, but
likely, some/most of the corresponding substance is no longer
within our "horizon".

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.

OK.

Well that is the meaning of "event horizon".
Events can happen in the same universe as us
but we may not be able to ever receive light
from them.

The reason the term was coined, is because those events are *not*
part of our experience. In other words "event" is "coordinate",
and "coordinate" defines spacetime. No events, no ability to
define spacetime, no effect on spacetime, not *in* spacetime...
except as a "boundary condition". The boundary being the event
horizon.

...
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.

Note where I said "location of the process in curved
space". This means *not* local.

I don't [read] it that way, "location of the
process" refers to the one location where the
atom is situated when it was involved in the
process of emitting the photon. It's my turn
to say "This is very poor wording, IMO."

Let's put the context back in...

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.

I then brought up the GPS. *I* think I was clear, in the context
I wrote. But of course the context was disassembled. So one
sentence chewed on twice, loses some of its flavor. I'll try not
to do that to you.

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.

Yes, in GR, and in QM. You cannot alter a photon, except
by absorbing or scattering it.

You don't "alter a photon" when receiving it
on a moving detector yet the Doppler effect
alters the frequency.

The Doppler effect describes one component of a frequency shift,
yes. Nothing is altered between the observer and the photon by
motion, since it arrives at c regardless. What is altered by
proper or kinetic motion is your relationship with the emitter
(and the underlying process).

However, I wasn't talking
about the photon. You said "the photon does not
change on the trip ... only the clocks" but
according to GR good clocks are not directly
affected as they would be in aether theory.

GPS has "two components"... the dice roll again? Even good
clocks *are* directly affected by their position in curved space,
compared to a different clock at a different "elevation". They
are however only reporting/recording the correct passage of time
in that location/position.

"Position in a gravity well" is meaningless to a photon. I
don't
know about what aether theory would predict, and I don't claim
to.

Lorentzian aether theory says clocks run slow
if they are in motion through the aether.

And Ilja would likely also have the relationship to collections
of mass similarly affect "local clock rate". But I cannot get my
head around it, which is why I did not know what its predictions
would be where gravity was concerned.

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.

... and hence the apparent "frequency change".

which is what I said next:

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'.

Which is not altering the light, only acknowledging the
variance in curvature at the two *non-local* endpoints.

That's right, GR says gravitational potential
doesn't influence the emitting or detecting
processes, it is the relationship between the
ends (integrated curvature if I have it right)
that produces the effects.

Sounds right.

(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.

Adds or *subtracts*, yes.

I assumed you were happy with signed numbers ;-)

Well, with "vector", I'd have to be, now wouldn't I? Vector
subtraction isn't really defined directly... Well duh!

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.

Yet the characteristic process indicates a different "time
base" at different altitudes.

"time base" is not a standard term so I have
to guess what you mean. The "time bases" are
not different in that an atomic transition
gives the same frequency in terms of proper
time of the atom. It is the angle between one
and the other after parallel transport that
produces the effect.

Right. My intention was not the velocity-term of GPS, but the
"elevation in a gravity field".

Hence Shapiro time delay.

Or type II supernovae spectra to supervonvae duration.

I think you mean type Ia.

Probably. But I have "6200 ly" down pat! ;)

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'.

"Motion" as Ned Wright has presented, OK.

Yes, just "motion" in the normal sense.

Not just motion in the normal sense. In the normal sense, we
have motion wrt the Universe of about 300 km/sec. Expansion of
space did not involve thrusters, or changing kinetic energy (of
us or other objects) to acheive recession velocities of nearly c.
"Normal" perhaps because you consider it everyday, but not
"normal" to the average Joe.

Yet it is still "only" characteristic of the relative
positions
(and yes kinetic velocities) of the emitters and receiver in
curved space.

Right.

We are spending a lot of time talking past each other. Lets move
on, unless you have quibbles with what I've said up to here.

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.

Good point.

Just nitpicking again.

Necessary.

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.)

No issues.

It is not the fact
that 3m is small but that everything is exactly
reversed on the way back down.

More clear is to say the at the emitting clock is not
affected by the path the reflected photon took. Since
the photon's frequency is unaffected by the path (other
than deflection of vector, and possible boosting by frame
dragging).

I think that's actually less clear. For example
"photon's frequency" sounds like some intrinsic
attribute but like kinetic energy frequency is
only meaningful so a specific observer.

Yet "everything is reversed on the way back down" is clearly
wrong, since nothing intrinsic to the photon is altered by simply
moving through on a short two-way path through curved space.
Only a choice of "endpoints" yields "redshift" or "blueshift".

Also, in later examples where the frequency is
affected, there is still no effect on "the
emitting clock". It is purely a path thing.

The "end points on the path" thing yes. A path thing alone, no.
Witness Einstein rings. Quite a different path, and through
highly curved space, yet the endpoints are the same, so the
observation is unsurprising.

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

I disagree. I suspect, but don't know without doing the
math, that given sufficient resolution, the observer will
appear to simply "shift away from center" towards the
"gravitational source". Not really length contraction...
since one axis should "symmetrically" get longer.

I was using 'centre' perhaps a little loosely
just to identify which observer, good nitpick.

I think that the heart of the matter lies in what, and how, this
is modelled. I think your finger is on the pulse. Good
thinking!

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.

Nah! ;)

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.

In LET (I believe) as in SR/GR, it is still a system effect,
since both the emitter and receiver are immersed in
aether that controls "local" processes/measurements.
I was not as clear as I should have been. Sorry.

No that is still wrong. In aether theory, the
emitter is slowed by speed relative to the aether
(characterised by the usual gamma function) due
to some unexplained interaction at the atomic
level. The same happens to any clock measuring it
but there is no change along the path. In SR there
is no interaction because there is no aether so
processes are unaltered and the effects are due
to curvature along the path. There is no curvature
in LET.

Both emitter and observer are immersed in aether, and neither can
be counted on to be at rest wrt to it. It *is* a system effect.
And LET is indifferentiable from SR (so there is curvature since
both time and space are its product). LET's not talk about this
any further. ;)

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.

... as long as you aren't falling into a black hole, with a
short
finite time before impacting at a "central singularity".
Pound-Rebka accumulated counts over a (relatively) long
period of time to achieve a measureable result.

We just need quicker tools which are always available
in thought experiments. However, perhaps you would
like to work out how long (proper time of course) it
takes from the event horizon to the centre for a black
hole large enough to have a 1g acceleration at the
horizon.

Since there is no center (other than in outer geometry), and
since I already know how long in this Unvierse from Big Bang to
"infinitely diffuse future" with "no particle in any other
particle's future" (125 billion years, give or take tens of
billion years), all that remains is to find out what size BH the
Big Bang was.

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

....
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).

Agreed.

Good stuff, I think we are making progress so I'll
go straight to the hard part. Try taking the sketch
I drew above and distort it sideways as in the two
diagrams in T&W it so that the central source/
detector line is the worldline of the infalling
observer shown in the spacetime diagrams on this
page

http://www.phy.syr.edu/courses/modul...arzschild.html

Clearly a problem arises when the final detection
is at the singularity but I cannot see any reason
why the pattern should not extend across the event
horizon. Bear in mind the scale, the diamonds in my
sketch are 3m while the distance from the horizon
to the singularity is vastly larger.

At the event horizon, light cannot go outwards to *infinity*
because escape velocity is exactly c. I see problems with this,
but I need to cogitate a bit more.

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.

"The laws of physics are the same for all inertial observers."

"inertial observers" is problematic but I'll go
with the principle of equivalence.

Aether cannot be killed in any inertial frame.

True, since an aether doesn't exist in the first
place, at least not when we are learning GR.

"Double entry bookkeeping". It is always good to know your
limitations.

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.

Sounds good. I've got to get to an "integration surface",
which hopefully is similar for sources near (eg. infalling
matter colliding with an accretion disk) and far.

Actually I've gone on the web page as we seem
to be agreeing the important stuff. I have no idea
why you keep referring to aether though.

As a double-check. The rules of this Universe do not disallow a
Lorentz-class aether for any "macroscopic model". I don't expect
anything we do will disallow it either. I don't depend on aether
for answers, or for (for me) a workable model of how things work,
but it has certain limitations on how things *can't* be, that are
useful in first pass modelling.

David A. Smith