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Jan Bielawski
science forum Guru

Joined: 08 May 2005
Posts: 388

Posted: Fri Jul 14, 2006 3:08 am    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

LEJ Brouwer wrote:
 Quote: Bilge wrote: LEJ Brouwer: Tom Roberts wrote: No physical anything happens. Merely the labels of coordinates get shuffled. As I said before, if you are going to 'merely' shuffle the labels of the coordinates, then you would have to 'merely' shuffle them in the Einstein field equations too - which means that what you are now solving are not the Einstein field equations. Don't be ridiculous. The metric has one timelike and three spacelike coordinates. For a spacelike metric, -+++, the entry with the - sign is timelike, regardless of what label you give it. Good grief. I despair for humanity. If dy/dx = x is solved by y = x^2 / 2 + c, and then I changed the x into a z wrote, y = z^2 / 2 + c, would I not have to change the original problem to dy/dz = z for the new solution to be valid? What is so ridiculous about that?

You missed the point. As I said earlier - you need to get the new
edition of Spivak, take a year off from posting nonsense on Usenet, and
study the basics.

 Quote: The proof is in the papers I reference in post #1, and I have also outlined the proof in another post. WHY DON'T YOU TRY READING IT???

They are no "proofs", just incompetent ramblings. It's not my fault
that I cannot prove to you that you are wrong as any such proof
requires by definition that you have already understood the errors
you've made.

--
Jan Bielawski
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 4:01 am    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

JanPB wrote:
 Quote: LEJ Brouwer wrote: Good grief. I despair for humanity. If dy/dx = x is solved by y = x^2 / 2 + c, and then I changed the x into a z wrote, y = z^2 / 2 + c, would I not have to change the original problem to dy/dz = z for the new solution to be valid? What is so ridiculous about that? You missed the point. As I said earlier - you need to get the new edition of Spivak, take a year off from posting nonsense on Usenet, and study the basics.

I do not feel any great urge to revise elementary differential geometry
simply because you cannot be bothered to check a simple proof.

 Quote: The proof is in the papers I reference in post #1, and I have also outlined the proof in another post. WHY DON'T YOU TRY READING IT??? They are no "proofs", just incompetent ramblings. It's not my fault that I cannot prove to you that you are wrong as any such proof requires by definition that you have already understood the errors you've made.

Yet you know mention no specifics of mathematical errors in these
"incompetent ramblings".

 Quote: -- Jan Bielawski

- Sabbir.
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 4:17 am    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

Tom Roberts wrote:
 Quote: LEJ Brouwer wrote: As I said before, if you are going to 'merely' shuffle the labels of the coordinates, then you would have to 'merely' shuffle them in the Einstein field equations too - which means that what you are now solving are not the Einstein field equations. This is not true. Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. It does not matter how you label the individual coordinates, except that it can be confusing if you re-use a given label for different coordinates, such as is done in the two sets of Schw. coordinates.

I must admit I haven't check whether the field equation is invariant. I
would be surprised if it was, though it is not impossible. HOWEVER, if
the r in the field equation is spacelike - how can the r in the
solution be timelike? (And similarly for t). And even if this seems
fine to you, this argument is still a red herring and does not remove
the constraint r>2m.

 Quote: What you still don't seem to realise is that r<2m does not physically exist, Hmmm. We are discussing the Schwarzschild solution of the Einstein field equation, not any real, physical system. This is all _theoretical_, and the manifold in the region r<2M is every bit as much a manifold as that in r>2M. So is the entire "second half" of the Kruskal extension.

Well, it's usually associated with the gravitational field outside a
spherical mass distribution (and typically a point mass). Even if you
disagree that this is a physical system, 2M is still a constant of
integration, and the condition r>2M arises from the _mathematical_ fact
that one cannot have a negative radial distance from the origin.

 Quote: so there is only ONE valid set of coordinates, i.e. r>2m. That is just plain wrong.

My, what a powerfully convincing argument.

 Quote: pointed this out at the start of the thread (in fact this is the whole point of bringing the matter up), and I even went through the proof of it in another post. Your "proof" assumed that it is possible to escape from any point in the manifold. This assumption is not valid for the Schwarzschild spacetime. shrug

What do you mean by 'escape' here? The proof involves measuring the
radial distance of any point from the origin and ensuring that this is
not negative.

 Quote: Tom Roberts

- Sabbir.
N:dlzc D:aol T:com (dlzc)
science forum Guru

Joined: 25 Mar 2005
Posts: 2835

Posted: Fri Jul 14, 2006 4:41 am    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

Dear LEJ Brouwer:

"LEJ Brouwer" <intuitionist1@yahoo.com> wrote in message
news:1152850629.183256.303340@s13g2000cwa.googlegroups.com...
 Quote: Tom Roberts wrote: LEJ Brouwer wrote: As I said before, if you are going to 'merely' shuffle the labels of the coordinates, then you would have to 'merely' shuffle them in the Einstein field equations too - which means that what you are now solving are not the Einstein field equations. This is not true. Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. It does not matter how you label the individual coordinates, except that it can be confusing if you re-use a given label for different coordinates, such as is done in the two sets of Schw. coordinates. I must admit I haven't check whether the field equation is invariant. I would be surprised if it was, though it is not impossible. HOWEVER, if the r in the field equation is spacelike

* outside the horizon *

 Quote: - how can the r in the solution be timelike?

* inside the horizon *

That is the problem with the choice of "simple" coordinates.
Choose Kruskal coordinates and there is no such problem.
Consider what you are straining at is equivalent to using the LT
to evaluate something for the range 0 <= v <= oo, noting that
gamma blows up at c, and beyond c things become imaginary.

 Quote: (And similarly for t). And even if this seems fine to you,

It is just a mathematical *map*, using a certain type of *ruler*,
not some fundamental desciption of "reality".

 Quote: this argument is still a red herring

No, it is your fundamental misunderstanding, and until you can
see past this, you will coninue to be frustrated. I ought to
know, as I am still struggling with this too.

 Quote: and does not remove the constraint r>2m.

Or what happens to gamma when v -> c.

Maybe I'm helping, maybe I'm not...

David A. Smith
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 9:45 am    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

N:dlzc D:aol T:com (dlzc) wrote:
 Quote: Dear LEJ Brouwer: "LEJ Brouwer" wrote in message news:1152850629.183256.303340@s13g2000cwa.googlegroups.com... I must admit I haven't check whether the field equation is invariant. I would be surprised if it was, though it is not impossible. HOWEVER, if the r in the field equation is spacelike * outside the horizon * - how can the r in the solution be timelike? * inside the horizon *

Actually, I meant it as I said it - in the Einstein field equation, r
is spacelike and t is timelike. It is not possible therefore for r to
be timelike in the solution to the Einstein field equation, which means
that only the exterior solution is correct, and that the interior
solution is wrong.

 Quote: That is the problem with the choice of "simple" coordinates. Choose Kruskal coordinates and there is no such problem. Consider what you are straining at is equivalent to using the LT to evaluate something for the range 0 <= v <= oo, noting that gamma blows up at c, and beyond c things become imaginary.

Even the Kruskal coordinates has problems - in this case two quadrants
of the solution (i.e. those corresponding to r<2m) are invalid - the
change in coordinates cannot change that. I don't understand your
analogy with the Lorentz transformation.

 Quote: (And similarly for t). And even if this seems fine to you, It is just a mathematical *map*, using a certain type of *ruler*, not some fundamental desciption of "reality".

I disagree - the radial distance is a function of r, and the radius
must be nonnegative, so this constrains the possible range of the
parameter.

 Quote: this argument is still a red herring No, it is your fundamental misunderstanding, and until you can see past this, you will coninue to be frustrated. I ought to know, as I am still struggling with this too.

The only thing that frustrates me is that people have become
conditioned not to recognise the blindingly obvious if it jars with
their preconceptions. I am not surprised that you are struggling with
it, as the standard picture is simply inconsistent.

 Quote: and does not remove the constraint r>2m. Or what happens to gamma when v -> c. Maybe I'm helping, maybe I'm not... David A. Smith

I don't know, but I appreciate the effort.

Best wishes,

Sabbir.
Sue...
science forum Guru

Joined: 08 May 2005
Posts: 2684

Posted: Fri Jul 14, 2006 11:46 am    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

LEJ Brouwer wrote:
 Quote: N:dlzc D:aol T:com (dlzc) wrote: Dear LEJ Brouwer: "LEJ Brouwer" wrote in message news:1152850629.183256.303340@s13g2000cwa.googlegroups.com... I must admit I haven't check whether the field equation is invariant. I would be surprised if it was, though it is not impossible. HOWEVER, if the r in the field equation is spacelike * outside the horizon * - how can the r in the solution be timelike? * inside the horizon * Actually, I meant it as I said it - in the Einstein field equation, r is spacelike and t is timelike. It is not possible therefore for r to be timelike in the solution to the Einstein field equation, which means that only the exterior solution is correct, and that the interior solution is wrong. That is the problem with the choice of "simple" coordinates. Choose Kruskal coordinates and there is no such problem. Consider what you are straining at is equivalent to using the LT to evaluate something for the range 0 <= v <= oo, noting that gamma blows up at c, and beyond c things become imaginary. Even the Kruskal coordinates has problems - in this case two quadrants of the solution (i.e. those corresponding to r<2m) are invalid - the change in coordinates cannot change that. I don't understand your analogy with the Lorentz transformation.

I understand why he makes the analogy but I consider it faulty.
Let's examine the real physical phenomena that gives us a
basis to interchange a spatial and temporal axis. It is not
railroading or philosophy about a rigid grid that god hung the
planets on.

<< Note that the time-dependent solutions, (509) and (510),
are the same as the steady-state solutions, (504) and (505),
apart from the weird way in which time appears in the former.
According to Eqs. (509) and (510), if we want to work out the
potentials at position and time then we have to perform
integrals of the charge density and current density over all
space (just like in the steady-state situation). However, when
we calculate the contribution of charges and currents at position
to these integrals we do not use the values at time , instead
we use the values at some earlier time >>
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html

The freedom we take to resolve this little nearfield issue
with an imaginary time doesn't give us carte' blanche with
anything we can rotate into the Lorenz gauge and demonstrate
a principle of invariance. It only shows that an operation is
Lorenz invariant without any consideration what other absurdities
are created or masked.

The most obvious of which is operating on neutral far-field
objects as though they were charged nearfield objects.

At some point SR's basis of retarded potential has to
be distinguished from GR's notions of mass and
energy density equivalenece.

When I look at something based on the Schawrtzchild solution,
I automatically assume an error because I know a change in
energy was expressed as a change in time. Pound-Sinder
is the perfect example.

Sue...

 Quote: (And similarly for t). And even if this seems fine to you, It is just a mathematical *map*, using a certain type of *ruler*, not some fundamental desciption of "reality". I disagree - the radial distance is a function of r, and the radius must be nonnegative, so this constrains the possible range of the parameter. this argument is still a red herring No, it is your fundamental misunderstanding, and until you can see past this, you will coninue to be frustrated. I ought to know, as I am still struggling with this too. The only thing that frustrates me is that people have become conditioned not to recognise the blindingly obvious if it jars with their preconceptions. I am not surprised that you are struggling with it, as the standard picture is simply inconsistent. and does not remove the constraint r>2m. Or what happens to gamma when v -> c. Maybe I'm helping, maybe I'm not... David A. Smith I don't know, but I appreciate the effort. Best wishes, Sabbir.
Daryl McCullough
science forum Guru

Joined: 24 Mar 2005
Posts: 1167

Posted: Fri Jul 14, 2006 5:03 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

LEJ Brouwer says...

 Quote: Actually, I meant it as I said it - in the Einstein field equation, r is spacelike and t is timelike. It is not possible therefore for r to be timelike in the solution to the Einstein field equation, which means that only the exterior solution is correct, and that the interior solution is wrong.

Back up here. The Einstein field equations don't say anything about
"r" and "t". They don't say anything about which basis vectors are
spacelike and which are timelike. What they say is that

G_uv = k T_uv

where G_uv is a tensor formed from second derivatives of
the metric tensor g_uv, and T_uv is the stress-energy tensor,
and k is a constant related to Newton's constant G (there
might be a factor of pi or something).

How do you get r is spacelike and t is timelike from that?

--
Daryl McCullough
Ithaca, NY
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Fri Jul 14, 2006 8:47 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

LEJ Brouwer wrote:
 Quote: Tom Roberts wrote: Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. I must admit I haven't check whether the field equation is invariant.

It is trivial. <shrug>

 Quote: I would be surprised if it was, though it is not impossible.

Then you sure don't know much about this at all. This is a trivial
consequence of the arbitrariness of coordinates and the tensor nature of
the field equation. <shrug>

 Quote: HOWEVER, if the r in the field equation is spacelike - how can the r in the solution be timelike? (And similarly for t).

Your question does not make sense, because of the nature of the field
equation.

Whether or not a given coordinate is timelike or spacelike depends on
the metric components, and one is solving the field equation for those
components. So it is not possible to say "the r in the field equation is
spacelike" until you have solved the field equation and _looked_ at the
g_rr metric component. For the Schwarzschild manifold, using the usual
Schw. coordinates, r is spacelike in the region r>2M and is timelike in
the region r<2M, and the coordinate singularity at r=2M makes it
impossible to answer for that value. Yes, this is a PUN on the symbol
"r" -- there are _TWO_ disjoint coordinate systems here, using the same
symbols _WITH_DIFFERENT_MEANINGS_. Sloppy mathematicians (aka many
physicists) do not always make such things clear, and indeed until 1960
or so this was not known by anybody; today is 2006 and you have no
excuse for your ignorance. <shrug>

 Quote: And even if this seems fine to you, this argument is still a red herring and does not remove the constraint r>2m.

You remain adamantly confused. You need to _study_. <shrug>

 Quote: the condition r>2M arises from the _mathematical_ fact that one cannot have a negative radial distance from the origin.

The Schw. r coordinate is most definitely _NOT_ "radial distance from
the origin". And your _ASSUMPTION_ that there is a "radial distance from
the origin" is _FALSE_ in the Schwarzschild manifold. Indeed, the locus
r=0 is deleted from the manifold and there is no "origin" (and that
locus is NOT a point). One could imagine substituting the limit point(s)
of incoming timelike paths from r=2M to the limit r->0, but there is no
definite value for such paths and that "distance" can have any positive
value (for different paths).

You seem to think that the Schwarzschild manifold is "just like we
perceive outside the earth (neglecting the air, etc.)". This is just
plain not so. You need to learn that this is NON-Euclidean geometry.
Indeed, this manifold is not anywhere close to Euclidean near and inside
its event horizon. The only way to understand the geometry is to study
the metric.

Tom Roberts
dda1
science forum Guru

Joined: 06 Feb 2006
Posts: 762

 Posted: Fri Jul 14, 2006 9:25 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 9:44 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

Daryl McCullough wrote:
 Quote: LEJ Brouwer says... Actually, I meant it as I said it - in the Einstein field equation, r is spacelike and t is timelike. It is not possible therefore for r to be timelike in the solution to the Einstein field equation, which means that only the exterior solution is correct, and that the interior solution is wrong. Back up here. The Einstein field equations don't say anything about "r" and "t". They don't say anything about which basis vectors are spacelike and which are timelike. What they say is that G_uv = k T_uv where G_uv is a tensor formed from second derivatives of the metric tensor g_uv, and T_uv is the stress-energy tensor, and k is a constant related to Newton's constant G (there might be a factor of pi or something). How do you get r is spacelike and t is timelike from that? -- Daryl McCullough Ithaca, NY

Hi, I think the semantics are getting a little mixed up here. I am not
claiming that r is spacelike *because* of the Einstein field equation -
I am simply stating the *fact* that r is spacelike in the Einstein
field equation - and indeed in any other equation in which r is a
radial parameter. The radial direction is spacelike by definition and
the temporal direction is timelike by definition. That's all there is
to it. The fact that the radial direction is timelike in the interior
Schwarzschild solution is further evidence that this solution is not a
valid one.

- Sabbir.
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 10:02 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

Tom Roberts wrote:
 Quote: LEJ Brouwer wrote: Tom Roberts wrote: Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. I must admit I haven't check whether the field equation is invariant. It is trivial.

Well, maybe all the signs just happen to cancel - frankly I don't
really

 Quote: I would be surprised if it was, though it is not impossible. Then you sure don't know much about this at all. This is a trivial consequence of the arbitrariness of coordinates and the tensor nature of the field equation.

No, it's because working out curvature components etc is usually pretty
boring and time-consuming and I see no reason to do so when the outcome
will not affect the present discussion in any way.

 Quote: HOWEVER, if the r in the field equation is spacelike - how can the r in the solution be timelike? (And similarly for t). Your question does not make sense, because of the nature of the field equation.

I really don't know what you are talking about.

 Quote: Whether or not a given coordinate is timelike or spacelike depends on the metric components, and one is solving the field equation for those components. So it is not possible to say "the r in the field equation is spacelike" until you have solved the field equation and _looked_ at the g_rr metric component.

Ignoring for a moment the fact that this entire thread of reasoning is
a separate argument from the one which I began to explain why r<2m is
physically invalid, your statement is completely wrong. If I have to
solve an equation for x where x is subject to some constraint, then the
solution had better satisfy that constraint. As I said elsewhere, the
radial direction is spacelike by definition.

 Quote: For the Schwarzschild manifold, using the usual Schw. coordinates, r is spacelike in the region r>2M and is timelike in the region r<2M, and the coordinate singularity at r=2M makes it impossible to answer for that value. Yes, this is a PUN on the symbol "r" -- there are _TWO_ disjoint coordinate systems here, using the same symbols _WITH_DIFFERENT_MEANINGS_. Sloppy mathematicians (aka many physicists) do not always make such things clear, and indeed until 1960 or so this was not known by anybody; today is 2006 and you have no excuse for your ignorance.

I am sorry, but you are very very confused. This is probably not your
fault, as the textbooks must say the same things to have even the
semblence of consistency. If r had a single 'meaning' in the equation
to be solved, how can it have two different 'meanings' in the solution?
<shrug>

 Quote: And even if this seems fine to you, this argument is still a red herring and does not remove the constraint r>2m. You remain adamantly confused. You need to _study_.

<shrug>

 Quote: the condition r>2M arises from the _mathematical_ fact that one cannot have a negative radial distance from the origin. The Schw. r coordinate is most definitely _NOT_ "radial distance from the origin".

Ah, so you finally figured that out did you? Well done. Slow, but
you're getting there...

 Quote: And your _ASSUMPTION_ that there is a "radial distance from the origin" is _FALSE_ in the Schwarzschild manifold. Indeed, the locus r=0 is deleted from the manifold and there is no "origin" (and that locus is NOT a point).

Ah, you had me fooled for a moment - you haven't figured it out at all,
have you? r is just a parameter. r=0 need not be the origin. In the
Schwarzschild solution, the origin is at r=2m. r=0 does not exist -
because r<2m does not exist - that is why the interior solution does
not exist. I suggest you go back to the start of the thread and try
again. <shrug>

 Quote: One could imagine substituting the limit point(s) of incoming timelike paths from r=2M to the limit r->0, but there is no definite value for such paths and that "distance" can have any positive value (for different paths). You seem to think that the Schwarzschild manifold is "just like we perceive outside the earth (neglecting the air, etc.)". This is just plain not so. You need to learn that this is NON-Euclidean geometry. Indeed, this manifold is not anywhere close to Euclidean near and inside its event horizon. The only way to understand the geometry is to study the metric.

Umm, I think you will find that I was the one that pointed out that
this point is non-Euclidean - which is why the radial distance and the
area do not satisfy the usual relationship. So there is little point in
lecturing me about it when you are the one that has clearly
misunderstood what is going on. Can I suggest that you review your
differential geometry? <shrug>

 Quote: Tom Roberts

I am sorry Tom, but you are totally clueless <shrug>.
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 10:05 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

dda1 wrote:
 Quote: snipped. Why is that you Pakis never admit to error? Is it your religion? You afraid that you loose face? Well, you already lost a lot of face by continuing to post, you have been exposed as a fraud by several of us already. Why do you think that you can't publish your stuff in any peer reviewed journal? Eh?

I don't know - maybe it's because you don't like Pakis?
dda1
science forum Guru

Joined: 06 Feb 2006
Posts: 762

Posted: Fri Jul 14, 2006 10:09 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

LEJ Brouwer wrote:
 Quote: dda1 wrote: snipped. Why is that you Pakis never admit to error? Is it your religion? You afraid that you loose face? Well, you already lost a lot of face by continuing to post, you have been exposed as a fraud by several of us already. Why do you think that you can't publish your stuff in any peer reviewed journal? Eh? I don't know - maybe it's because you don't like Pakis?

This is why no peer reviewed journal would publish your stuff? This is
why you get kicked of moderated forums? Because we all don't like Pakis?
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Fri Jul 14, 2006 11:00 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

dda1 wrote:
 Quote: LEJ Brouwer wrote: dda1 wrote: snipped. Why is that you Pakis never admit to error? Is it your religion? You afraid that you loose face? Well, you already lost a lot of face by continuing to post, you have been exposed as a fraud by several of us already. Why do you think that you can't publish your stuff in any peer reviewed journal? Eh? I don't know - maybe it's because you don't like Pakis? :) This is why no peer reviewed journal would publish your stuff? This is why you get kicked of moderated forums? Because we all don't like Pakis?

Well, YOU certainly don't seem to like Pakis.

A major reason for my 'stuff' not being published could be that I tend
to question knowledge that has become 'established' when the
foundations of that knowledge are dubious. For example:

I claim that there is a luminiferous aether, when it has been
'established' that there isn't one.
I claim that quantum theory has a classical basis, when it has already
been 'established' that quantum theory is more fundamental than
classical mechanics.
I claim that classical black holes have been seriously misunderstood,
even though their nature has already been 'well established'.
I claim that classical electrodynamics is a direct consequence of
general relativity, which is just pretty hard to believe.
I claim that antigravity exists, even though it is generally taken for
granted that it does not.
I claim that general relativity is responsible for the existence of the
standard model gauge group, and that the elementary particles are
solitonic solutions of GR, when clearly such a claim is absurd.
I claim that string theory is a red herring, and a great sapper of
funding, resources and manpower, even though it is the only theory
currently considered to be a possible 'theory of everything'.
I claim that cold dark matter consists of neutrinos, which are
gravitational dipoles responsible for MOND, and which can be predicted
from first principles from GR, which is also pretty hard to believe.
I speculate that there was probably no 'big bang', but that it is more
likely that 'in the beginning' there was a 'big collapse'.
....and so on (I am sure you get the picture).
In general, I don't blindly assume that everything I am told or read in
books is correct, and am willing to question when things are not clear
or do not seem right.
And as it happens, yes, I was born in East Pakistan (now Bangladesh)
and am also a practising Muslim - I believe that there is no God but
Allah, and that the prophet Muhammad (may peace be upon him), is His
messenger, and I believe in all the prophets sent by Allah to guide
mankind, from the first prophet Adam (pbuh), all the way through to
Jesus (pbuh) and Muhammad (pbuh), who was the final prophet. Some
people might not like that.

And I think that's more than enough reason for establishment folk to
discard my work without looking at it. Don't you? Besides, my writing
style and my tendency to make imaginative extrapolations isn't
necessarily to everyone's liking. Not all my ideas turn out to be right
it's true, but I still think it's good to come up with bright new
ideas, and to always question the status quo, as that is ultimately
what leads to progress.

- Sabbir.
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Fri Jul 14, 2006 11:10 pm    Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?

LEJ Brouwer wrote:
 Quote: I am simply stating the *fact* that r is spacelike in the Einstein field equation - and indeed in any other equation in which r is a radial parameter.

Where does the symbol "r" obtain this magical power???

You _really_ need to learn the basics. Symbols have no power whatsoever,
they mean merely what we designate them to mean, and in the case of GR,
as I said before, we don't know whether a given corodinate is timelike
or spacelike until we solve the field equation and examint the relevant
metric components. <shrug>

 Quote: The radial direction is spacelike by definition

Your definition of words and symbols has no power over the mathematics.

Tom Roberts
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