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A Flaw of General Relativity, a New Metric and Cosmological Implications
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Zanket
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Joined: 08 Jul 2006
Posts: 21

PostPosted: Fri Jul 21, 2006 7:29 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Quote:
The clock postulate describes how a _single_ clock behaves under
acceleration (i.e. it remains in synch with an instantaneously comoving
and collocated inertial clock, but in general that holds for only an
infinitesimal duration for each inertial clock and one needs a succession
of such inertial frames). It says nothing at all about how to synchronize
_multiple_ clocks, which is the issue I addressed in the measurement
technique I described.

Taylor and Wheeler address this issue in their book "Exploring Black Holes",
pg. 3-16. The situation in that section is the same as in my section 2. They
say: "A stone falling radially from rest at infinity [toward a black hole]
has speed dr_shell / dt_shell as measured by observers on shells [at each
altitude] through which the stone plunges". They don't mention your
measurement technique.



They have "eq. [23]" (see definitions in my paper): dt_shell = sqrt(1 - (R /
r)) * dt



A reader asks:



"... Let a firecracker explode at each shell as the stone passes. Clocks on
these different shells "run at different rates" according to that very
equation [23]. How can you possibly combine readings from these two
different-rate clocks to meter the shell time the stone takes between the
two flash emissions?"



Taylor and Wheeler reply:



"... When we measure velocity, however, we employ calculus in the
conventional sense of a limiting process, with dr and dt and dr_shell and
dt_shell all tending to zero. Then the firecrackers go off right next to
each other; the two clocks are-in the limit-on the same shell, so they run
at the same rate at this limit."



Quote:
For the case at hand, any non-infinitesimal distance matters, and a system
at rest relative to the black hole having a finite separation of clocks is
not a MCIF.



As noted above, the separation is zero in the limit. So your measurement
technique isn't needed.


Quote:
But the particle can be the measurer.

That is plain and simply not true. The measurement of an object's speed
must be relative to a system of coordinates, and the particle itself
cannot do that, it requires assistants at rest in the coordinate system
having clocks synchronized in the coordinate system and rulers of the
coordinate system.

Given the above, it should now be intuitively clear that the particle can be
the measurer.



Within the particle's frame your requirements can be met. The separation
between "assistants at rest in the coordinate system" can be zero in the
limit, so the particle can be infinitesimally small. The particle measures
the velocity of a shell observer as it passes by.
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Tom Roberts
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Joined: 24 Mar 2005
Posts: 1399

PostPosted: Fri Jul 21, 2006 4:54 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
From the link: "General relativity is built on a
foundation that includes the clock postulate." That would explain why Taylor
and Wheeler do not mention your measurement technique for the same scenario.

The clock postulate describes how a _single_ clock behaves under
acceleration (i.e. it remains in synch with an instantaneously comoving
and collocated inertial clock, but in general that holds for only an
infinitesimal duration for each inertial clock and one needs a
succession of such inertial frames). It says nothing at all about how to
synchronize _multiple_ clocks, which is the issue I addressed in the
measurement technique I described.


Quote:
The postulate directly contradicts you, showing that no such measurement
technique is required.

Not true. See above.

Quote:
"It says that our measurements of distance and time
are unaffected by any pseudo forces we feel, so that they are identical to
those of our MCIF." What caveats refute that?

Look up what they mean by "MCIF" and you'll see that it does NOT include
clocks in an accelerated system separated by a distance large enough to
matter (i.e. introduce errors larger than the measurement resolution).
For the case at hand, any non-infinitesimal distance matters, and a
system at rest relative to the black hole having a finite separation of
clocks is not a MCIF.

For instance, synchronize the clocks, and then make measurements on a
series of identically infalling test particles -- the symmetry of the
situation would lead one to expect those identically falling particles
will have identical speeds. But in fact the measured speeds will NOT be
the same for the different particles; they will be measured to be going
successively slower. This is simply due to the fact that the clocks in
such a frame do not remain synchronized (in _any_ frame of interest).


Quote:
But the
particle can be the measurer.

That is plain and simply not true. The measurement of an object's speed
must be relative to a system of coordinates, and the particle itself
cannot do that, it requires assistants at rest in the coordinate system
having clocks synchronized in the coordinate system and rulers of the
coordinate system.


Tom Roberts
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Dirk Van de moortel
science forum Guru


Joined: 01 May 2005
Posts: 3019

PostPosted: Thu Jul 20, 2006 10:38 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

"Zanket" <zanket@gmail.com> wrote in message news:LpHvg.427883$Fs1.98535@bgtnsc05-news.ops.worldnet.att.net...
Quote:
Shocking

Sorry, it was not meant to be shocking.

Dirk Vdm
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Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Thu Jul 20, 2006 8:46 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Shocking
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Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Thu Jul 20, 2006 8:46 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Quote:
See http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html: "[The
postulate] ...


Quote:
That statement is not Gospel, and it omits important caveats that apply
here. <shrug



Yes, the statement is not gospel, because theories are not gospel. But you
argue against GR. From the link: "General relativity is built on a
foundation that includes the clock postulate." That would explain why Taylor
and Wheeler do not mention your measurement technique for the same scenario.
The postulate directly contradicts you, showing that no such measurement
technique is required. "It says that our measurements of distance and time
are unaffected by any pseudo forces we feel, so that they are identical to
those of our MCIF." What caveats refute that?



And tell me, given that the postulate "has been verified experimentally up
to extraordinarily high accelerations", how would you go about proving your
claim? That is, how would you prove that the noninertial observer's
measurement is bogus, when experiments show it always equal to the
measurement in the MCIF? (Of course if you could prove your claim, GR would
be invalidated. <shrug>)



Your argument is also a red herring. You assume that the particle's velocity
is measured by noninertial observers (those at fixed altitudes). But the
particle can be the measurer. A measurement requires no action on the part
of the measured.
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Tom Roberts
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Joined: 24 Mar 2005
Posts: 1399

PostPosted: Wed Jul 19, 2006 4:09 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
Tom Roberts wrote:
Go back and re-read where I described it. One can hold the frame at rest
relative to the black hole, and release it just as the infalling particle
reaches it; its clocks must be preset so they will be synchronized in the
locally inertial frame immediately after release, and the measurement must
be made immediately after release (or the measurement is not done at rest
relative to the black hole). The key point is the synchronization of the
clocks used to measure the infalling particle's speed.

I think this measurement technique is unnecessary. For one, we on Earth
measure free-fall velocity without using that technique, and those
measurements are not meaningless.

But we on earth do not live in such high-field situations! In general,
the _ONLY_ velocity measurements that are reasonable and understandable
are those relative to a locally-inertial frame. _ALL_ others are bogus,
the only question is: "How bogus?", and that depends on the curvature of
the manifold and how non-inertial the coordinates actually are. For our
everyday lives, assuming the earth's surface is an inertial frame with a
gravitational force is quite adequate. But for tests of GR it is not.

IOW: in physics an important question is always: what are the errors?
What you propose does not introduce unacceptable errors in our everyday
lives, but in analyzing a black hole it does.


Quote:
See
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html: "[The
postulate] tells us that noninertial objects only age and contract by the
same gamma factor as that of their MCIF [momentarily comoving inertial
frame]. So, any measurements we make in a noninertial frame that use clocks
and rods, will be identical to measurements made in our MCIF."

That statement is not Gospel, and it omits important caveats that apply
here. <shrug>


Tom Roberts
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Dirk Van de moortel
science forum Guru


Joined: 01 May 2005
Posts: 3019

PostPosted: Tue Jul 18, 2006 6:39 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

"Zanket" <zanket@gmail.com> wrote in message news:FG8vg.145353$mF2.127585@bgtnsc04-news.ops.worldnet.att.net...

Quote:
You also seem to have a very severe problem with the simple
concept of asymptotes.

How so?

More or less like one of these
http://www.apa.org/journals/features/psp7761121.pdf
http://www.apa.org/journals/features/psp7761121.pdf
http://www.behavenet.com/capsules/disorders/narcissisticpd.htm
http://www.udel.edu/bkirby/asperger/aswhatisit.html
http://www.users.dircon.co.uk/~cns/

I'll assume that there really wasn't a problem that you could identify.

That is what autistic imbeciles usually assume when confronted
with their condition. It is normal. We see it happen al the time
on this forum. You are no exception:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ZanketHobby.html
Check your soul mates.

Dirk Vdm
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Dirk Van de moortel
science forum Guru


Joined: 01 May 2005
Posts: 3019

PostPosted: Tue Jul 18, 2006 6:38 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

"Zanket" <zanket@gmail.com> wrote in message news:AD8vg.145342$mF2.41682@bgtnsc04-news.ops.worldnet.att.net...
Quote:
... you also seem to
have a very severe problem with the simple concept of limits.



I agree that I misused "limit". I changed it to "asymptote".


Apart from formally dragging a sloppily worded statement (*),
true everywhere in a uniform (linear) gravitational field, over into a
spherically symmetric and highly non-uniform field, in which the
statement only happens to be true for a well defined limit-set of
locations, ...



A non-uniform field is everywhere uniform locally. The particle always falls within a uniform field, itself within a larger
non-uniform field. So when the particle's velocity approaches an asymptote of c in a uniform field, it automatically does that in
a non-uniform field as well. There's no way around that.



... in your first (uniform field) situation the sloppy phrase
"approaching a limit of c"
only refers to
"objects at infinity" ...



I don't know why you think it refers to objects at infinity, when I say it's a directly measured velocity.


When you do that, you might immediately notice that you can cut
your article short and perhaps find another hobby.



I can keep the hobby now that I've changed "limit" to "asymptote".


(*) One example of sloppiness is the phrase:
"... approaches a limit of c."



It may be sloppy, but I think the meaning is clear. I see plenty of other web sites doing the same.



I think the meaning is still clear after correcting "limit" to "asymptote". I also see plenty of other web sites using the
shorthand "approaches an asymptote of <value>".

Welcome.
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ZanketHobby.html
You fit right in:
http://www.apa.org/journals/features/psp7761121.pdf
http://www.apa.org/journals/features/psp7761121.pdf
http://www.behavenet.com/capsules/disorders/narcissisticpd.htm
http://www.udel.edu/bkirby/asperger/aswhatisit.html
http://www.users.dircon.co.uk/~cns/
And, yes, by all means, you can and most certainly will keep
the hobby.

Dirk Vdm
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Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Tue Jul 18, 2006 5:15 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

I'll assume that there really wasn't a problem that you could identify.
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Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Tue Jul 18, 2006 5:12 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Quote:
... you also seem to
have a very severe problem with the simple concept of limits.



I agree that I misused "limit". I changed it to "asymptote".


Quote:
Apart from formally dragging a sloppily worded statement (*),
true everywhere in a uniform (linear) gravitational field, over into a
spherically symmetric and highly non-uniform field, in which the
statement only happens to be true for a well defined limit-set of
locations, ...



A non-uniform field is everywhere uniform locally. The particle always falls
within a uniform field, itself within a larger non-uniform field. So when
the particle's velocity approaches an asymptote of c in a uniform field, it
automatically does that in a non-uniform field as well. There's no way
around that.



Quote:
... in your first (uniform field) situation the sloppy phrase
"approaching a limit of c"
only refers to
"objects at infinity" ...



I don't know why you think it refers to objects at infinity, when I say it's
a directly measured velocity.


Quote:
When you do that, you might immediately notice that you can cut
your article short and perhaps find another hobby.



I can keep the hobby now that I've changed "limit" to "asymptote".


Quote:
(*) One example of sloppiness is the phrase:
"... approaches a limit of c."



It may be sloppy, but I think the meaning is clear. I see plenty of other
web sites doing the same.



I think the meaning is still clear after correcting "limit" to "asymptote".
I also see plenty of other web sites using the shorthand "approaches an
asymptote of <value>".
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Dirk Van de moortel
science forum Guru


Joined: 01 May 2005
Posts: 3019

PostPosted: Tue Jul 18, 2006 4:58 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

"Zanket" <zanket@gmail.com> wrote in message news:ne8vg.145270$mF2.97974@bgtnsc04-news.ops.worldnet.att.net...
Quote:
You also seem to have a very severe problem with the simple
concept of asymptotes.

How so?

More or less like one of these
http://www.apa.org/journals/features/psp7761121.pdf
http://www.apa.org/journals/features/psp7761121.pdf
http://www.behavenet.com/capsules/disorders/narcissisticpd.htm
http://www.udel.edu/bkirby/asperger/aswhatisit.html
http://www.users.dircon.co.uk/~cns/

Dirk Vdm
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Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Tue Jul 18, 2006 4:45 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Quote:
You also seem to have a very severe problem with the simple
concept of asymptotes.

How so?
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Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Tue Jul 18, 2006 4:36 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Quote:
You _still_ don't know what a limit is. Any quantity that "approaches a
limit of infinity" must achieve a value greater than any finite value,
such as c.



OK, I rephrase: It would reach c, were it not for the interpretation that
all objects at and below an event horizon must fall.

Quote:
Go back and re-read where I described it. One can hold the frame at rest
relative to the black hole, and release it just as the infalling particle
reaches it; its clocks must be preset so they will be synchronized in the
locally inertial frame immediately after release, and the measurement must
be made immediately after release (or the measurement is not done at rest
relative to the black hole). The key point is the synchronization of the
clocks used to measure the infalling particle's speed.



I think this measurement technique is unnecessary. For one, we on Earth
measure free-fall velocity without using that technique, and those
measurements are not meaningless. The most you could say is that they are
inaccurate. For another, Taylor and Wheeler do not mention that measuring
technique for the same scenario, in their book Exploring Black Holes. Also
the experimental confirmation of the clock postulate shows that this
technique is unnecessary. See
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html: "[The
postulate] tells us that noninertial objects only age and contract by the
same gamma factor as that of their MCIF [momentarily comoving inertial
frame]. So, any measurements we make in a noninertial frame that use clocks
and rods, will be identical to measurements made in our MCIF."



Regardless, anyone who insists on using that technique can assume that it is
applied. My paper isn't wrong just because it doesn't mention it. It's good
enough to say the "velocity as directly measured at each altitude".


Quote:
Just using Schw. coordinates to measure a coordinate speed is useless --
there are no limits on such a coordinate speed.

The analysis in section 2 is wholly above an event horizon, where there is a
limit on such a coordinate speed.


Quote:
If an event horizon can be shown to be inconsistent within GR, then its
existence would be in doubt.

Yes. But you have not done so. <shrug

Not that you have shown. <shrug>



Thanks for pointing out that I misused "limit". But your issue went away
when I corrected it to "asymptote".


Quote:
I have since looked briefly at the article by Crothers that you quote. He
makes the same mistakes you do:



I don't recall quoting Crothers.


Quote:
But that manifold can be uniquely extended into the region r<2M, and out
to another exterior. All claims that this region "does not exist" or "is a
point" are just plain wrong. The interior is _DIFFERENT_, not "non
existent". <shrug



You contradict yourself. All such claims cannot be wrong if its existence
can be in doubt, as you agreed it can.
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Dirk Van de moortel
science forum Guru


Joined: 01 May 2005
Posts: 3019

PostPosted: Sun Jul 16, 2006 6:48 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

"Zanket" <zanket@gmail.com> wrote in message news:KMtug.137595$mF2.99686@bgtnsc04-news.ops.worldnet.att.net...
Quote:
Apparently you do not know what a limit is. It is very simple: ...

[snip]

Quote:
I changed the misusage of "limit" in the paper to "asymptote". The conclusions remained the same.

You also seem to have a very severe problem with the simple
concept of asymptotes.

Dirk Vdm
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Tom Roberts
science forum Guru


Joined: 24 Mar 2005
Posts: 1399

PostPosted: Sun Jul 16, 2006 6:25 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
Tom Roberts wrote:
This is GR, and relative to any locally inertial frame, no timelike object
can exceed the speed c. Period. Your "infinity" up there is just plain
wrong. You _REALLY_ need to learn the basics.

I didn't say it reaches >= c. I said it approaches a limit of infinity.

You _still_ don't know what a limit is. Any quantity that "approaches a
limit of infinity" must achieve a value greater than any finite value,
such as c.


Quote:
How can a locally inertial frame be at rest relative to a black hole, when
an inertial frame is by definition in free fall?

Go back and re-read where I described it. One can hold the frame at rest
relative to the black hole, and release it just as the infalling
particle reaches it; its clocks must be preset so they will be
synchronized in the locally inertial frame immediately after release,
and the measurement must be made immediately after release (or the
measurement is not done at rest relative to the black hole). The key
point is the synchronization of the clocks used to measure the infalling
particle's speed.

Just using Schw. coordinates to measure a coordinate speed is useless --
there are no limits on such a coordinate speed.


Quote:
If an event horizon can be shown to be inconsistent within GR, then its
existence would be in doubt.

Yes. But you have not done so. <shrug>


I have since looked briefly at the article by Crothers that you quote.
He makes the same mistakes you do:
a) confusing coordinates on the manifold with the manifold itself
b) making assumptions and expecting the math to conform to them
c) fantasizing about a new geometrical concept: a point with
nonzero area

He provides nothing new in deriving the exterior Schwarzschild metric.
His insistence on his Ansatz (eq 1,2,3) is ill founded. Yes, the
external manifold obeys it, and yes the interior does not. What he did
not do is consider whether or not the external manifold he found can be
extended inside the horizon, he merely asserts it cannot. As is well
known, this exterior manifold can indeed be extended into the interior,
and then to a second exterior. <shrug>

In short: the Schwarzschild spacetime does not conform to his Ansatz
everywhere, just in the exterior region. His (and your) blind adherence
to the assumptions of that Ansatz is hopeless. The interior of the Schw.
spacetime is not static. Just as you cannot reasonably expect the
universe to obey your personal wishes and dreams, so too you cannot
expect mathematics to do so. <shrug>

So yes, if one requires a manifold that is static and spherically
symmetric, the exterior Schwarzschild manifold is the only solution.
This is well know (see Birkhoff's theorem). But that manifold can be
uniquely extended into the region r<2M, and out to another exterior. All
claims that this region "does not exist" or "is a point" are just plain
wrong. The interior is _DIFFERENT_, not "non existent". <shrug>


Tom Roberts
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