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rotation

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  rotation RichD <r_delaney2001@yahoo.com> - 2016-02-09 12:34 -0800
    rotation David Fuller <fuller.david@hotmail.com> - 2016-02-09 14:37 -0800
      rotation David Fuller <fuller.david@hotmail.com> - 2016-02-09 14:46 -0800
        rotation David Fuller <fuller.david@hotmail.com> - 2016-02-09 15:18 -0800
      Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-10 07:23 +0100
        Re: rotation Heiðr Einherjar <einherjar@notformail.org> - 2016-02-10 16:01 +0000
          Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-10 09:40 -0800
            Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-10 09:46 -0800
          Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-10 09:42 -0800
            Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-10 10:29 -0800
              Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-14 08:13 -0800
                Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-14 08:25 -0800
          Re: rotation David Fuller <fuller.david@hotmail.com> - 2016-02-10 09:53 -0800
    Re: rotation jamesl51165@gmail.com - 2016-02-09 14:50 -0800
    Re: rotation jamesl51165@gmail.com - 2016-02-10 17:17 -0800
      Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-11 06:22 +0100
        Re: rotation Muddy Shoes <shoes@muddyshoes.org> - 2016-02-11 13:51 +0000
          Re: rotation Muddy Shoes <shoes@muddyshoes.org> - 2016-02-11 14:37 +0000
          Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-11 22:05 +0100
            Re: rotation Tom Roberts <tjroberts137@sbcglobal.net> - 2016-02-11 23:02 -0600
              Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-12 21:23 +0100
                Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-13 06:25 +0100
                  Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-14 05:03 +0100
                    Re: rotation benj <none@gmail.com> - 2016-02-13 23:57 -0500
                      Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-14 15:50 +0100
                      Re: rotation Thomas Heger <ttt_heg@web.de> - 2016-02-16 08:48 +0100
    Re: rotation Tom Roberts <tjroberts137@sbcglobal.net> - 2016-02-10 19:30 -0600
      Re: rotation RichD <r_delaney2001@yahoo.com> - 2016-02-12 22:34 -0800
        Re: rotation Tom Roberts <tjroberts137@sbcglobal.net> - 2016-02-13 21:25 -0600

Page 2 of 2 — ← Prev page 1 [2]

#376134

Am 12.02.2016 06:02, schrieb Tom Roberts:

> Everything you wrote is a complete fabrication and has NOTHING WHATEVER
> to do with rotation or light cones (ostensibly what you are attempting
> to write about).
>
> Why do you bother to just make stuff up and pretend it is true? What's
> the point?

I did not write about light-cones, but about black holes.

I assume a physical reality of spacetime, where the axis of time could 
turn in some regions into directions, which other observers regard as 
spatial.

See from the back a timeline points into the future and drags the 
observer and (everything else) with it.

This is a picture and similar to what the term 'black hole' means.

Seen from the other side (or: time-reverted) a black hole is similar to 
what we call 'big bang'.


TH

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#376150

Am 12.02.2016 21:23, schrieb Thomas Heger:
> Am 12.02.2016 06:02, schrieb Tom Roberts:
>
>> Everything you wrote is a complete fabrication and has NOTHING WHATEVER
>> to do with rotation or light cones (ostensibly what you are attempting
>> to write about).
>>
>> Why do you bother to just make stuff up and pretend it is true? What's
>> the point?
>
> I did not write about light-cones, but about black holes.
>
> I assume a physical reality of spacetime, where the axis of time could
> turn in some regions into directions, which other observers regard as
> spatial.
>
> See from the back a timeline points into the future and drags the
> observer and (everything else) with it.
>
> This is a picture and similar to what the term 'black hole' means.
>
> Seen from the other side (or: time-reverted) a black hole is similar to
> what we call 'big bang'.
>

https://en.wikipedia.org/wiki/Light_cone

It is this picture:

https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png

What we see (as observers) is what is happening along our own past light 
cone.

The cone itself is a reduction by one dimension, which we had to keep in 
mind.

The cone has 2+1 dimension, meaning actually 3+1.

So we need to multiply it with three, since there are there combinations 
of 2 out of 3 axis (xy, yz, xz).

Actually meant are nested spheres, which are nested in time (older the 
further away).

This is actually what we call 'universe'.

The point 'here and now' is actually the observer.

So to any observer belongs his own universe, since that is actually his 
view about a certain reality, we cannot see directly.

His view and his  now and his here are in fact comoving (with him/her).

This view is  - of course - not really real, but an impression someone 
has. But everybody has one, but about a different universe.

Also the axis of time is unique to any observer, since it is actually 
his own path through space and time, which is different for everybody.

Now we view upon regions, where time does not flow into the same 
direction as our own timeline points, than we would also see the 
corresponding space distorted.

In case of a black hole this space would shrink and the bent axis of 
time would drag us with it, hence would let us see a different universe, 
which belongs to that now different axis of time.

In the opposite case the axis of time points towards us, hence there 
seem to pop things out of nowhere. There had been there before, but in 
this invisible space, which is not along our own past light cone.

And that is the same as a black hole, but only with the axis of time 
pointing towards us (a 'white hole').


TH

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#376193

Am 13.02.2016 06:25, schrieb Thomas Heger:

>>> Everything you wrote is a complete fabrication and has NOTHING WHATEVER
>>> to do with rotation or light cones (ostensibly what you are attempting
>>> to write about).
>>>
>>> Why do you bother to just make stuff up and pretend it is true? What's
>>> the point?
>>
>> I did not write about light-cones, but about black holes.
>>
>> I assume a physical reality of spacetime, where the axis of time could
>> turn in some regions into directions, which other observers regard as
>> spatial.
>>
>> See from the back a timeline points into the future and drags the
>> observer and (everything else) with it.
>>
>> This is a picture and similar to what the term 'black hole' means.
>>
>> Seen from the other side (or: time-reverted) a black hole is similar to
>> what we call 'big bang'.
>>
>
> https://en.wikipedia.org/wiki/Light_cone
>
> It is this picture:
>
> https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png
>
>
> What we see (as observers) is what is happening along our own past light
> cone.
>
> The cone itself is a reduction by one dimension, which we had to keep in
> mind.
>
> The cone has 2+1 dimension, meaning actually 3+1.
>
> So we need to multiply it with three, since there are there combinations
> of 2 out of 3 axis (xy, yz, xz).
>
> Actually meant are nested spheres, which are nested in time (older the
> further away).
>
> This is actually what we call 'universe'.
>
> The point 'here and now' is actually the observer.
>
> So to any observer belongs his own universe, since that is actually his
> view about a certain reality, we cannot see directly.
>
> His view and his now and his here are in fact comoving (with him/her).
>
> This view is - of course - not really real, but an impression someone
> has. But everybody has one, but about a different universe.
>
> Also the axis of time is unique to any observer, since it is actually
> his own path through space and time, which is different for everybody.
>
> Now we view upon regions, where time does not flow into the same
> direction as our own timeline points, than we would also see the
> corresponding space distorted.
>
> In case of a black hole this space would shrink and the bent axis of
> time would drag us with it, hence would let us see a different universe,
> which belongs to that now different axis of time.
>
> In the opposite case the axis of time points towards us, hence there
> seem to pop things out of nowhere. There had been there before, but in
> this invisible space, which is not along our own past light cone.
>
> And that is the same as a black hole, but only with the axis of time
> pointing towards us (a 'white hole').
>

Since I have made extensive use of this interpretation of relativity, I 
would like to add a link to my 'book' about this subject.

I regard it as important, since my interpretation would also allow a 
different understanding of matter and fields.

My 'book' is (still) not really a book, but a google.doc.presentation. 
You find it here:

https://docs.google.com/present/view?id=dd8jz2tx_3gfzvqgd6

I have stopped working on it in 2009, since nobody took any notice and I 
had failed to convince someone, even if I still believe, my ideas are 
actually correct.


TH

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#376194

On 02/13/2016 11:03 PM, Thomas Heger wrote:
> Am 13.02.2016 06:25, schrieb Thomas Heger:
>
>>>> Everything you wrote is a complete fabrication and has NOTHING WHATEVER
>>>> to do with rotation or light cones (ostensibly what you are attempting
>>>> to write about).
>>>>
>>>> Why do you bother to just make stuff up and pretend it is true? What's
>>>> the point?
>>>
>>> I did not write about light-cones, but about black holes.
>>>
>>> I assume a physical reality of spacetime, where the axis of time could
>>> turn in some regions into directions, which other observers regard as
>>> spatial.
>>>
>>> See from the back a timeline points into the future and drags the
>>> observer and (everything else) with it.
>>>
>>> This is a picture and similar to what the term 'black hole' means.
>>>
>>> Seen from the other side (or: time-reverted) a black hole is similar to
>>> what we call 'big bang'.
>>>
>>
>> https://en.wikipedia.org/wiki/Light_cone
>>
>> It is this picture:
>>
>> https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png
>>
>>
>>
>> What we see (as observers) is what is happening along our own past light
>> cone.
>>
>> The cone itself is a reduction by one dimension, which we had to keep in
>> mind.
>>
>> The cone has 2+1 dimension, meaning actually 3+1.
>>
>> So we need to multiply it with three, since there are there combinations
>> of 2 out of 3 axis (xy, yz, xz).
>>
>> Actually meant are nested spheres, which are nested in time (older the
>> further away).
>>
>> This is actually what we call 'universe'.
>>
>> The point 'here and now' is actually the observer.
>>
>> So to any observer belongs his own universe, since that is actually his
>> view about a certain reality, we cannot see directly.
>>
>> His view and his now and his here are in fact comoving (with him/her).
>>
>> This view is - of course - not really real, but an impression someone
>> has. But everybody has one, but about a different universe.
>>
>> Also the axis of time is unique to any observer, since it is actually
>> his own path through space and time, which is different for everybody.
>>
>> Now we view upon regions, where time does not flow into the same
>> direction as our own timeline points, than we would also see the
>> corresponding space distorted.
>>
>> In case of a black hole this space would shrink and the bent axis of
>> time would drag us with it, hence would let us see a different universe,
>> which belongs to that now different axis of time.
>>
>> In the opposite case the axis of time points towards us, hence there
>> seem to pop things out of nowhere. There had been there before, but in
>> this invisible space, which is not along our own past light cone.
>>
>> And that is the same as a black hole, but only with the axis of time
>> pointing towards us (a 'white hole').
>>
>
> Since I have made extensive use of this interpretation of relativity, I
> would like to add a link to my 'book' about this subject.
>
> I regard it as important, since my interpretation would also allow a
> different understanding of matter and fields.
>
> My 'book' is (still) not really a book, but a google.doc.presentation.
> You find it here:
>
> https://docs.google.com/present/view?id=dd8jz2tx_3gfzvqgd6
>
> I have stopped working on it in 2009, since nobody took any notice and I
> had failed to convince someone, even if I still believe, my ideas are
> actually correct.

VERY interesting model! I love the development of cones, white holes, 
zero point and the rest. However the chances of discussing a model of 
complex valued four-vector quaternions with anyone posting here is 
well....ZERO.

Your assumption of a GR continuum is I believe only an approximation. 
Math is not more real than reality.

Hey, never give up.



-- 

       ___           ___           ___            ___
      /\  \         /\  \         /\__\          /\  \
     /::\  \       /::\  \       /::|  |         \:\  \
    /:/\:\  \     /:/\:\  \     /:|:|  |     ___ /::\__\
   /::\~\:\__\   /::\~\:\  \   /:/|:|  |__  /\  /:/\/__/
  /:/\:\ \:|__| /:/\:\ \:\__\ /:/ |:| /\__\ \:\/:/  /
  \:\~\:\/:/  / \:\~\:\ \/__/ \/__|:|/:/  /  \::/  /
   \:\ \::/  /   \:\ \:\__\       |:/:/  /    \/__/
    \:\/:/  /     \:\ \/__/       |::/  /
     \::/__/       \:\__\         /:/  /
      ~~            \/__/         \/__/

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#376211

Am 14.02.2016 05:57, schrieb benj:

>>>>> Everything you wrote is a complete fabrication and has NOTHING
>>>>> WHATEVER
>>>>> to do with rotation or light cones (ostensibly what you are attempting
>>>>> to write about).
>>>>>
>>>>> Why do you bother to just make stuff up and pretend it is true? What's
>>>>> the point?
>>>>
>>>> I did not write about light-cones, but about black holes.
>>>>
>>>> I assume a physical reality of spacetime, where the axis of time could
>>>> turn in some regions into directions, which other observers regard as
>>>> spatial.
>>>>
>>>> See from the back a timeline points into the future and drags the
>>>> observer and (everything else) with it.
>>>>
>>>> This is a picture and similar to what the term 'black hole' means.
>>>>
>>>> Seen from the other side (or: time-reverted) a black hole is similar to
>>>> what we call 'big bang'.
>>>>
>>>
>>> https://en.wikipedia.org/wiki/Light_cone
>>>
>>> It is this picture:
>>>
>>> https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png
>>>
>>>
>>>
>>>
>>> What we see (as observers) is what is happening along our own past light
>>> cone.
>>>
>>> The cone itself is a reduction by one dimension, which we had to keep in
>>> mind.
>>>
>>> The cone has 2+1 dimension, meaning actually 3+1.
>>>
>>> So we need to multiply it with three, since there are there combinations
>>> of 2 out of 3 axis (xy, yz, xz).
>>>
>>> Actually meant are nested spheres, which are nested in time (older the
>>> further away).
>>>
>>> This is actually what we call 'universe'.
>>>
>>> The point 'here and now' is actually the observer.
>>>
>>> So to any observer belongs his own universe, since that is actually his
>>> view about a certain reality, we cannot see directly.
>>>
>>> His view and his now and his here are in fact comoving (with him/her).
>>>
>>> This view is - of course - not really real, but an impression someone
>>> has. But everybody has one, but about a different universe.
>>>
>>> Also the axis of time is unique to any observer, since it is actually
>>> his own path through space and time, which is different for everybody.
>>>
>>> Now we view upon regions, where time does not flow into the same
>>> direction as our own timeline points, than we would also see the
>>> corresponding space distorted.
>>>
>>> In case of a black hole this space would shrink and the bent axis of
>>> time would drag us with it, hence would let us see a different universe,
>>> which belongs to that now different axis of time.
>>>
>>> In the opposite case the axis of time points towards us, hence there
>>> seem to pop things out of nowhere. There had been there before, but in
>>> this invisible space, which is not along our own past light cone.
>>>
>>> And that is the same as a black hole, but only with the axis of time
>>> pointing towards us (a 'white hole').
>>>
>>
>> Since I have made extensive use of this interpretation of relativity, I
>> would like to add a link to my 'book' about this subject.
>>
>> I regard it as important, since my interpretation would also allow a
>> different understanding of matter and fields.
>>
>> My 'book' is (still) not really a book, but a google.doc.presentation.
>> You find it here:
>>
>> https://docs.google.com/present/view?id=dd8jz2tx_3gfzvqgd6
>>
>> I have stopped working on it in 2009, since nobody took any notice and I
>> had failed to convince someone, even if I still believe, my ideas are
>> actually correct.
>
> VERY interesting model! I love the development of cones, white holes,
> zero point and the rest. However the chances of discussing a model of
> complex valued four-vector quaternions with anyone posting here is
> well....ZERO.
>
> Your assumption of a GR continuum is I believe only an approximation.
> Math is not more real than reality.
>
> Hey, never give up.
>

Well, in a way I do not want to continue to work on this subject. It is 
a problem to maintain the ability, if you have no feedback or support.

So I have changed my 'research' and do other stuff now. Mainly I try to 
learn some more electronics and develop 'conspiracy theories'.

But maybe you like to continue to develop the concept a little further. 
You may, if you like.

Thanks anyhow, since I didn't had many readers so far.


TH

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#376312

Am 14.02.2016 05:57, schrieb benj:
...
>>> Now we view upon regions, where time does not flow into the same
>>> direction as our own timeline points, than we would also see the
>>> corresponding space distorted.
>>>
>>> In case of a black hole this space would shrink and the bent axis of
>>> time would drag us with it, hence would let us see a different universe,
>>> which belongs to that now different axis of time.
>>>
>>> In the opposite case the axis of time points towards us, hence there
>>> seem to pop things out of nowhere. There had been there before, but in
>>> this invisible space, which is not along our own past light cone.
>>>
>>> And that is the same as a black hole, but only with the axis of time
>>> pointing towards us (a 'white hole').
>>>
>>
>> Since I have made extensive use of this interpretation of relativity, I
>> would like to add a link to my 'book' about this subject.
>>
>> I regard it as important, since my interpretation would also allow a
>> different understanding of matter and fields.
>>
>> My 'book' is (still) not really a book, but a google.doc.presentation.
>> You find it here:
>>
>> https://docs.google.com/present/view?id=dd8jz2tx_3gfzvqgd6
>>
>> I have stopped working on it in 2009, since nobody took any notice and I
>> had failed to convince someone, even if I still believe, my ideas are
>> actually correct.
>
> VERY interesting model! I love the development of cones, white holes,
> zero point and the rest. However the chances of discussing a model of
> complex valued four-vector quaternions with anyone posting here is
> well....ZERO.
>

The electrical engineers use complex numbers to model waves.

You could think about a wave as something spinning in the complex plane.

But, apparently, our world is not flat. So how do we model spherical waves?

Well: the trick is, to 'multiply by three'. This means, you need to 
multiply the complex plane by three and have three pointers rotating 
over three interlocking planes.

Now: how does THAT look like.

Answer: depends on the wave.

One wave could be kind of fixed in place. Such waves are candidates for 
what we call 'matter'.

Such a wave could be turned into other waves, which behave more like 
radiation, by external forces.

If we apply relativity to such radiation and base the FoR on that wave, 
the wave seems to stand still and is matter again.

With this change of the FoR we also change the timeline, since in one 
FoR the movement is in space, while in the other in time.

Now apply this concept to black holes, than the black hole is a region, 
where time 'points away' (into the future).

Now that arrow of time is reverted, hence we see something in the past, 
coming towards us. This would be a 'white hole' and similar to the big bang.


To really model this behaviour mathematically we need a certain type of 
quaternions: so called bi-quaternions, (also called complex 
valued-four-vectors).

To actually use these things I'm a little too lazy. But I can draw quite 
well, so I have made a lot of illustrations, which show how these things 
work.

A very good paper in a more mathematical fashion stems from Jonathan Scott:

http://pws.prserv.net/jonathan_scott/physics/diraceqn.pdf


TH

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#376001

On 2/9/16 2/9/16   2:34 PM, RichD wrote:
> A black hole has angular momentum as one of its characteristic
> parameters.  Is it possible, in principle, to measure this,
> for an observer inside?

Measuring its magnitude is surely not possible, as an observer inside cannot 
possibly observe the whole thing. An observer outside cannot see the whole 
thing, either, but can make global measurements that can determine its total 
angular momentum. An observer inside cannot make such global measurements.

So let's consider the simpler question: can an observer inside determine whether 
the black hole is rotating at all? And in which direction around what axis? The 
black hole must be very massive (= very large) for this to make sense, so the 
observer has time to make observations.

The usual standard for "no rotation" is a locally inertial frame, and any 
observer in freefall is at rest in one. How can such an observer observe the 
black hole "itself"? (to check if it is rotating wrt her locally inertial 
frame). The answer, of course, is that she cannot, because the black hole 
"itself" has no substance to observe.

But a key aspect of a Kerr black hole (i.e. one with nonzero angular momentum) 
is that inside its horizon the locally inertial frames are rotating relative to 
distant locally-inertial frames. Assuming there are distant stars and galaxies 
in the universe being discussed, the observer inside the black hole can see the 
blue-shifted light from these distant objects. And she can observe the rotation 
of her locally-inertial frame relative to these light rays. Yes, the null 
geodesics they follow will pick up some of the rotation, but not all of it, and 
I'm pretty sure she could determine the axis and direction of that rotation, 
which necessarily corresponds to the overall rotation of the black hole.


> Similarly for the entire universe - does it make sense
> to speak of 'universal rotation', and possible to
> measure this?  Or at least observe a non-zero rotation?

It does make sense to consider an overall rotation of the entire universe. It is 
challenging, however, to construct the corresponding boundary conditions "at 
infinity", and they seem rather unphysical. For a compact universe (i.e. one 
with no boundary and thus no need for boundary conditions), I don't think there 
can be an overall rotation that is consistent with any possible topology. I'm 
not sure about a universe that is compact spatially but not temporally.

The Kerr manifold is a universe with an overall rotation. It is quite 
complex.... It is not compact.


Tom Roberts

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#376152

On February 10, tjrob137 wrote:
>> A black hole has angular momentum as one of its characteristic
>> parameters.  Is it possible, in principle, to measure this,
>> for an observer inside?
>
> Measuring its magnitude is surely not possible, as an observer
> inside cannot possibly observe the whole thing.
>
> So let's consider the simpler question: can an observer inside
> determine whether the black hole is rotating at all? And in which
> direction around what axis?  The black hole must be very massive
> (= very large) for this to make sense, so the observer has time
> to make observations.
>
> The usual standard for "no rotation" is a locally inertial frame,
> and any observer in freefall is at rest in one. How can such an
> observer observe the black hole "itself"? (to check if it is rotating
> wrt her locally inertial frame). The answer, of course, is that she
> cannot, because the black hole "itself" has no substance to observe.
But if no such substance, it raises the question of what
exactly is rotating, besides space itself, which is a
'thing', in GR, and so should be observable.  Perhaps
'frame dragging' comes ino play (although I barely
understand that bit), which was recently onserved by
a Stanford team.
As another point, there appears to be a pardox here.
Free fall is supposedly an inertial frame, hence not
rotating, according to SR.  But the infalling obserever
must be rotating with the black hole, as he falls toward
the center.  Therefore this should be observable, as
rotation is absolute.
That is, the observer must 'spiral' as he falls, if
that makes sense, given the weird geometry inside.
> But a key aspect of a Kerr black hole (i.e. one with nonzero angular
> momentum) is that inside its horizon the locally inertial frames
> are rotating relative to distant locally-inertial frames. Assuming
> there are distant stars and galaxies in the universe being discussed,
> the observer inside the black hole can see the
> blue-shifted light from these distant objects. And she can observe the rotation
> of her locally-inertial frame relative to these light rays. Yes, the null
> geodesics they follow will pick up some of the rotation, but not all of it, and
> I'm pretty sure she could determine the axis and direction of that rotation,
> which necessarily corresponds to the overall rotation of the black hole.
>
>
> > Similarly for the entire universe - does it make sense
> > to speak of 'universal rotation', and possible to
> > measure this?  Or at least observe a non-zero rotation?
>
> It does make sense to consider an overall rotation of the entire 
> universe. It is challenging, however, to construct the 
> corresponding boundary conditions "at infinity", and they seem 
> rather unphysical. 

We know the universe isn't infinite, though it may 
expand forever.

However, if it is rotating, there must be an 
axis of rotation, implying a preferred reference frame. 
Which could be seen by an observer in some higher dimension.

Like the expanding balloon membrane analogy - 
if the balloon is rotating, it occurs in the 
3rd spatial dimension.


> For a compact universe (i.e. one with no boundary and thus 
> no need for boundary conditions), I don't think there
> can be an overall rotation that is consistent with any possible 
> topology. 
> I'm not sure about a universe that is compact spatially but 
> not temporally.

?

> The Kerr manifold is a universe with an overall rotation. It is 
> quite complex.... It is not compact.

In math, compact means finite domain, so I'm not sure of your usage.

--
Rich

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#376191

On 2/13/16 2/13/16   12:34 AM, RichD wrote:
> On February 10, tjrob137 wrote:
>> The usual standard for "no rotation" is a locally inertial frame,
>> and any observer in freefall is at rest in one. How can such an
>> observer observe the black hole "itself"? (to check if it is rotating
>> wrt her locally inertial frame). The answer, of course, is that she
>> cannot, because the black hole "itself" has no substance to observe.
> But if no such substance, it raises the question of what
> exactly is rotating, besides space itself, which is a
> 'thing', in GR, and so should be observable.

No. You need to distinguish between world and model. GR is a MODEL of the world. 
Space is part of the MODEL, not the world, and is not at all a 'thing", and is 
not ITSELF "observable". Ditto for spacetime.

	But the structure of spacetime can be observed indirectly via
	its effect on the motions of objects (e.g. the geodesic paths
	followed by small freefalling objects).


> Perhaps
> 'frame dragging' comes ino play (although I barely
> understand that bit), which was recently onserved by
> a Stanford team.

Yes. A rotating black hole "drags nearby frames" vastly more than the earth.


> As another point, there appears to be a pardox here.

Only due to your misunderstandings.

> Free fall is supposedly an inertial frame, hence not
> rotating, according to SR.

And GR, locally.

> But the infalling obserever
> must be rotating with the black hole, as he falls toward
> the center.  Therefore this should be observable, as
> rotation is absolute.

But in GR rotation is not "absolute" in the sense you mean.

For any LOCAL observation, a locally inertial frame is the standard relative to 
which rotation can be measured. But for NON-local observations, there is no such 
standard. But one can, in some circumstances including this one, observe signals 
sent from a distant inertial frame and measure one's own inertial frame's 
rotation relative to the distant one.


> That is, the observer must 'spiral' as he falls, if
> that makes sense, given the weird geometry inside.

For a Kerr black hole this just so happens to be true, but your approach to it 
is wrong. Near the black hole's horizon, locally inertial frames rotate relative 
to distant (locally out there) inertial frames.


> We know the universe isn't infinite, though it may
> expand forever.

One must be more precise. We know the universe is not infinite in the past 
temporal direction. But we have no knowledge whether it is infinite or finite 
spatially, or in the future temporal direction.


> However, if it is rotating, there must be an
> axis of rotation, implying a preferred reference frame.
> Which could be seen by an observer in some higher dimension.

Perhaps. But WE are not such observers, so this is useless speculation outside 
of physics.

Moreover, there can be regions in which the rotation is different from that of 
other regions, so this "preferred frame" need not be universal or global (e.g. a 
universe containing multiple Kerr black holes orientated differently).


>> For a compact universe (i.e. one with no boundary and thus
>> no need for boundary conditions), I don't think there
>> can be an overall rotation that is consistent with any possible
>> topology.
>> I'm not sure about a universe that is compact spatially but
>> not temporally.
>
> ?
>
>> The Kerr manifold is a universe with an overall rotation. It is
>> quite complex.... It is not compact.
>
> In math, compact means finite domain, so I'm not sure of your usage.

I use it in the usual topological sense: a compact manifold is closed (i.e. 
contains all its limit points), and thus has no boundary. In the geometry of 
physics this implies that it has finite volume (though there are unphysical 
mathematical manifolds for which this is not true).


Tom Roberts

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