Kruskal-Szekeres extension: counter-examples

Page 2 - Seeking answers about space? Join the Space community: the premier source of space exploration, innovation, and astronomy news, chronicling (and celebrating) humanity's ongoing expansion across the final frontier.
Status
Not open for further replies.
M

michaelmozina

Guest
ramparts":1ijg5f94 said:
Michael, bear in mind (I think you were saying something along these lines) that our willingness to engage amicably with NBH scales downward with each standoffish comment, each insinuation that there's a conspiracy of astrophysicists, and each time he refuses to engage in the same civil dialogue with which we try to engage him. Personally, I began this thread from a bit of a lower starting point because I'd already tried this with NBH a couple of months ago in another thread. After all the insults, insinuations, and three-post manifestos, when it came down to it, I asked him one question, several times, which was crucial to his argument, and he disappeared from the thread before he responded to it. So to be honest, I'm only expecting so much of a civil or productive dialogue.

I do hear you ramparts. I for one very much appreciate your attempt to be specific about your criticisms, and your focus on the science aspects of the debate. If you have the link to your previous discussion I'd be more than happy to read through that link as I get time. Things are finally calming down a bit at work so I should have some additional reading time on my hands. :)

I have had a lot of personal experience at presenting 'non standard' ideas to astronomers. I know what it feels like to be on his side of the aisle and I have some empathy for his position. :) I am personally skeptical of the "infinite density" concept related to 'black holes', more from the perspective of nuclear chemistry (Pauli exclusion principle) rather than a mathematical objection. Until reading his work, I'd not come across a mathematical objection to the idea that seemed to hold water and survived even my own limited skeptical review of the material. This authors presentations have been quite different in that respect. I must say his arguments "seem" (from my limited perspective) to be correct, at least I didn't see an obvious error. I for one would very much like to see you two move forward in the conversation if possible so that I can get a better understanding of where your differences lie. I'm learning a lot just by reading along. :) I appreciate your efforts and his.
 
R

ramparts

Guest
michaelmozina":1yjzhqs2 said:
I do hear you ramparts. I for one very much appreciate your attempt to be specific about your criticisms, and your focus on the science aspects of the debate. If you have the link to your previous discussion I'd be more than happy to read through that link as I get time. Things are finally calming down a bit at work so I should have some additional reading time on my hands. :)

The madness begins here, although I'm replying to a post of NBH's that's probably a couple of pages back. My last reply to him, after which he disappeared, is here.

I have had a lot of personal experience at presenting 'non standard' ideas to astronomers. I know what it feels like to be on his side of the aisle and I have some empathy for his position. :) I am personally skeptical of the "infinite density" concept related to 'black holes', more from the perspective of nuclear chemistry (Pauli exclusion principle) rather than a mathematical objection. Until reading his work, I'd not come across a mathematical objection to the idea that seemed to hold water and survived even my own limited skeptical review of the material. This authors presentations have been quite different in that respect. I must say his arguments "seem" (from my limited perspective) to be correct, at least I didn't see an obvious error. I for one would very much like to see you two move forward in the conversation if possible so that I can get a better understanding of where your differences lie. I'm learning a lot just by reading along. :) I appreciate your efforts and his.

"Non-standard" ideas get presented by scientists all the time, some very crazy ideas indeed, and get a perfectly fair hearing (even if they're treated with a healthy dose of skepticism). In fact, some of these crazy ideas end up being true, and get absorbed into the common wisdom. What is expected in return of the people presenting crazy ideas? They need to be experts - this doesn't necessarily mean having a Ph.D. (or being a grad student) but in practice it usually does - an Einstein, working from a patent office with no formal education, is all but impossible today. They need to put their ideas through the "proper" channels - instead of publishing in "alternate" journals (which you may edit) or posting online, or e-mailing scientists out of the blue as many cranks do, publish in an actual journal, and submit your work to the rigors of peer review. If the idea holds water, it will be fine. And finally, of course, civility is not only required, it is expected, and I shouldn't even have to list it. Using quotation marks around every other term in your paper and referring to "astrophysical magicians" does not meet that condition.

Now, it's pretty clear to me NBH is not an expert in GR, given some of the misunderstandings in our conversations, and the fact that instead of responding with science (see the thread I just linked to) he'd more often than not respond with miscellaneous quotes from textbooks - and honestly, if you're not extremely well-versed in a subject, how on Earth do you plan to overturn its results?

Most scientists certainly agree that the infinite densities of black holes are troubling. However, black holes as they exist in GR don't require infinite densities - they predict them, but then, GR isn't a theory of particle physics, so it's going to be missing detail on the smallest scales, and those details will be crucial. The important prediction of GR is that there can be a body from which light doesn't escape (an object which lies entirely within its Schwarzschild radius), and that doesn't require an infinite density. There is a good amount of hope that when the correct quantum theory of gravity is found (that is, a theory of gravity which does take into account how particles behave), it will have some way of preventing infinite densities - or at least, of explaining how the singularity works. Right now, contrary to popular belief, physics actually says nothing about the nature of the singularity. (Also: the Pauli exclusion principle is important, but it's not the main reason to be troubled by the infinite densities, as the exclusion principle only holds for fermions, or half-spin particles. Bosons, or whole-spin particles, aren't troubled by Pauli's rules ;) )

Finally, it's not at all surprising that someone who isn't well-versed in the language of GR is convinced by Crothers' papers. You can convince someone of more or less anything if they don't know all that much about the subject. This is the reason it's disingenuous to post groundbreaking theories on fora like SDC, where most people are laymen who are just trying to learn about the universe (Michael, I realize that doesn't quite apply to you). If someone presented me with an argument in biochemistry, about RNA, that's completely out of whack, how am I supposed to know how to refute it? If it has some jargon, some math (in the case of physics), and doesn't say anything overtly ridiculous, it will sound perfectly plausible to the untrained eye.
 
Y

yevaud

Guest
michaelmozina":2gyc8q5r said:
In fairness to yevuad and this forum in general, space.com seems to be one of the more "open" and "fairly" moderated forums on the net. I don't know how you got under yevaud's skin, but it's not easy to do.

Not so much "under my skin," per se, but after a few dozen (or more) posts, each insinuating that people just don't know, aren't capable of, clearly haven't studied, people are out to get, etc., I must do my job here. Crothers has been vetted. Debate whether this vetting was proper and rigorous, yes; spend a great deal of time going on about vast, dark conspiracies, sorry, no.

And to NBH: this is not the first thread in which you've gone on at length about conspiracies, and how all other scientists are clearly lying/misrepresenting/incapable of understanding, and for THAT I have very limited patience indeed. We have been down this road before here, and none of us, I think, have any patience to do so again.

'Nuff said.
 
D

drwayne

Guest
Let me make a point that flows from my earlier recitation on the degree process.

It is hard for anyone, even a highly trained scientist, working in or close to his/her field to enter
a process at the very end and judge the validity of it. That is why you have an advisor and a
committee involved in the process for a Ph.D.

The validity of an idea does not often come from one Eureka! moment, but rather from a long series of
steps and tests, wrong and right turns. A paper can not capture this type of process, only involvement
in the process can give the full perspective.

Even Einstein, when he was working outside academia, had people with whom he was corresponding,
bouncing ideas off, in some senses a defacto committee.

Wayne
 
M

Molodei

Guest
Maybe it is strange but I feel where are the black holes and where are the planets with life. All your examples are submit and explain it. We have an equel technology of detecting the life on planets, with equipment and without it. Greate. Thank you.
 
X

xXTheOneRavenXx

Guest
Re: Turning the other cheek....

michaelmozina":13yfa5jg said:
I have a suggestion for you NBH.

I personally have a great deal of sympathy for, and a great deal of interest in your argument. I would suggest that you attempt to simply ignore the "emotional landmines" that are being placed before you by others. I know from experience that it is very hard to be on the receiving end of some of the personal (and IMO unfair) criticisms, and become "reactive" to that type of argument. A tit-for-tat response never seems to work very well in my experience, and believe me I've tried it. :)

In fairness to yevuad and this forum in general, space.com seems to be one of the more "open" and "fairly" moderated forums on the net. I don't know how you got under yevaud's skin, but it's not easy to do. I've managed that feat myself, but it wasn't easy. :) In my experience, your best bet is to politely ask him (and everyone else) to find the specific error in the work and ignore all the rest of the commentary. In my experience, he (they) will refocus his attention on the material.

Ramparts seems (from my vantage point) to be attempting to 'communicate" with you at the level of math, physics and science, but there's currently a lot of unnecessary posturing going on. I'm very interested in seeing that conversation develop, and I think it's in your best interest to develop it without reacting to the unnecessary stuff.

I know from experience that non mainstream ideas don't go over well with astronomers in general, but in my experience this particular astronomy forum is one of the few "honest" bastions of science in cyberspace. I think it's worth your time and effort and a little tongue biting on your part to see this conversation through, and to keep it as professional as is humanly possible given the circumstances.

There are some really good people here that will listen to a logical, rational and emotionless argument. If however you let the colorful commentary distract you, IMO it will work to your disadvantage. I know it's tough. I know it doesn't feel fair. I know it's not actually 100% fair, but hey, life isn't fair. It's still in your best interest to let the little stuff roll off your back and to keep everyone pointed back at finding the error in the material. Sooner or later things will calm down and things will go smoother. If you are emotionally reactive however, it probably won't go well.

Just my two cents...

It's not that I don't mind a good debate, or see new idea's arise michaelmozina. However it has been NBH's responses (speaking for myself mind you) quite negative to say the least. As I mentioned on numerous ocassions, the mathematics are far above my understanding... so I do research and review the citings done on Crother's work by those who do have the background knowledge necessary to decipher it. So far PIP (Progress In Physics) is the only site I have come across that favors Crother's work. This makes me very skeptical that the papers by Crother's has any validity because Crother's himself was on that review panel. When I presented this, and the negative citations of several professionals in the field including Hooft, Bruhn and others this really sets off NBH. I have also posted calculations others have utilized to point out why Crother's is wrong. Below is a site I have visited which clearly points out in laymans terms & mathematically Crother's misconceptions. Please excuse my lack of knowledge of the mathematics. However I'm just adding the below as per your earlier request to see mathematically where Crother's went wrong.

http://www.mathematik.tu-darmstadt.de/~bruhn/CrothersViews.html":13yfa5jg said:
Discussion of S. Crothers' Views on Black Hole Analysis in GRT
Gerhard W. Bruhn, Darmstadt University of Technology
06.03.2008

see also the

Open letter to Dr. D. Rabounski, Editor-in-Chief of the Journal PROGRESS IN PHYSICS *)
Quotations from Crothers' papers are displayed in black. Equation labels of type (n) refer to Crothers' papers.



Abstract
In the last years since 2005 S. Crothers has published a series of papers in the Journal PROGRESS IN PHYSICS*) (see [3]) which deal with the alleged fact that black holes are not compatible with General Relativity. Crothers views stem from certain dubious ideas on spacetime manifolds, especially in the case of Hilbert/Schwarzschild metrics: His idea is that instead of the 2-sphere of the event horizon there is merely one single central point. It will be shown below that this assumption would lead to a curious world where Crothers' ''central point'' can be approximated in sense of distance by 2-spheres Sr of radius r > α. Hence the event horizon cannot be a single point. − Concerning the two validity regions of the Schwarzschild metric in contrast to Crothers' claims the fact is recalled that both validity regions of the Schwarzschild metric can be covered by introduction of the Eddington-Finkelstein coordinates.

*) NB.: The journal ''PROGRESS IN PHYSICS'' should not be mixed up with the prestigious and much older IOP-journal ''Reports on Progress in Physics''.




1. Crothers' basic views
Crothers bases his objection of Schwarzschild black holes on two statements: Concerning the Schwarzschild metric (2.1) below he asserts in the Introduction of [1]:

When the required mathematical rigour is applied it is revealed that
1) ro =α denotes a point, not a 2-sphere, and that
2) 0 < r < α is undefined on the Hilbert metric.




2. Objections to claim 1)
This assertion cannot be true: We consider the Schwarzschild/Hilbert metric

(2.1) ds² = − (1 − α/r) dt² + (1 − α/r)−1 dr² + r²(dθ² + sin²θ dφ²)

in the spacetime that is accessible for a physical observer, i.e. for r > α: Here the metric (2.1) defines submanifolds Sr for each pair of fixed values of t and r, the metric of which follows from (2.1) to be

(2.2) ds² = r² (dθ² + sin²θ dφ²) .

Hence Sr is a 2-sphere with radius r. The set Sα of singularities of the Schwarzschild/Hilbert metric has the metric

(2.3) ds² = α² (dθ² + sin²θ dφ²).

and hence is a 2-sphere as well.

The distance between Sr and Sα is given by Crothers' ''proper radius'' (cf [1, eq. (14)] with C(r)= r²)

(2.4) Rp(r) = [r(r−α)]½ + α ln |(r½+(r−α)½) α−½|

measurable in radial direction between arbitrary associated points of the concentric spheres. Since Rp(r) is continuous at r=α the distance between Sr and Sα tends to 0 for r → α:

(2.5) limr → α Rp(r) = Rp(α) = 0 .

Therefore, the set Sα of the metric singularities can be approximated with respect to the distance Rp(r) by concentric 2-spheres of radius r > α: Thus,

Sα cannot be a single point.


See also Section 4.




3. Objections to claim 2)
This claim is not true: As will be recalled here the region r > α, accessible for human observers, can be extended to the region r > 0 by the introduction of simple coordinates well-known as Eddington-Finkelstein coordinates (cf.[4, p.184]). The additional part of the world - usually called ''black hole'' is not directly explorable by human observers. We can only try to extrapolate the rules that have been found in the accessible part of the world.

The special structure of the Schwarzschild metric (2.1) allows a simple extension from the obvervable region r > α to the region r > 0 crossing the former boundary r = α.

Before doing so it is advantageous to simplify the notation by an obvious transformation: By applying the substitution r/α → r we can simplify the Schwarzschild metric (2.1) to

(3.1) ds² = − (1 − 1/r) dt² + (1 − 1/r)−1 dr² + r²(dθ² + sin²θ dφ²)

i.e. in case α>0 we are allowed to assume α=1 without loss of generality.

Now we rewrite eq. (3.1) to

(3.2) ds² = (1 − 1/r) [ −dt² + ( r dr/r−1)²] + r²(dθ² + sin²θ dφ²) .

Instead of t we introduce a new variable v by

(3.3) v = t + r + ln |r−1| ,

hence r dr/r−1 = dv − dt and

(3.4) ds² = − (1 − 1/r) dv² + dv dr + dr dv + r²(dθ² + sin²θ dφ²) ,

which metric form is free from singularities in the region {(v,r) | 0 < r < ∞, v ÎR}.

The singularities of the Schwarzschild metric (1.1) at r=α=1 are spurious merely, i.e. no singularities of spacetime.
Remark Equ. (3.3) is valid for r < 1 as well, which generally yields dv = dt + dr + dr/r−1. Inserting this in eq. (3.4) leads back to eq. (3.1) as the reader will check immediately. Therefore we have the result:

The metric (3.4) is an extension of each of the two validity regions of the Schwarzschild metric (3.1) to the other one.
This result can be applied to again calculate the induced metric on the sphere Sα to obtain eq. (2.3) again (with α=1).



4. Somewhat elementary differential geometry
We shall determine here a subset of the event horizon to show again that it cannot be only one central point:

The metric of an equatorial section θ = π/2 through an Euclidean space parametrized by spherical polar coordinates (r, θ, φ)

(4.1) ds² = dr² + r² (dθ² + sin²θ dφ²) Þ ds² = dr² + r² dφ² .

yields a plane with polar coordinates (r, φ), while θ = π/2.

A similar equatorial section for the Schwarzschild metric at constant time variable t yields the metric

(4.2) ds² = (1 − α/r)−1 dr² + r² dφ²

which is no longer plane, i.e. no longer representable in a plane, say z=0. However, instead of the plane z=0 we can define a surface z = z(r,φ) over a plane with polar coordinates (r,φ). Due to the spherical symmetry z cannot depend on φ, hence we have to consider a rotational surface z = z(r): The metric of this surface is given by

(4.3) ds² = (1 + zr²) dr² + r² dφ² .

Comparison with the metric (4.2) yields zr = (α/r−α)½ , hence

(4.4) z(r) = 2 [α(r−α)]½ .

This is a rotational surface generated by rotating the parabola z = 2 [α(r−α)]½ around the z-axis, see the figure of that surface (cf. [6] Flamm's paraboloid) .

We see that z = 0 for r = α is the (red marked) boundary of the accessible world, where z > 0.

The boundary (subset of the event horizon) is not a single point.


The boundary (subset of the event horizon) is not a single point.
5. Further comments on Crothers' paper [1]
Let us compare the metric usually attributed to Schwarzschild

ds*² = (1 − α/r*) dt² − (1 − α/r*)−1 dr*² − r*² (dθ² + sin²θ dφ²) (6)

with Crothers' "new" metric:

ds² = (C½−α/C½) dt² − (C½/C½−α) C'²/4Cdr² − C (dθ² + sin²θ dφ²) (7)

This metric has a certain blemish: the differential dr can be removed, such that the variable r is completely substituted by the new variable C using C'dr = dC, hence

(5.1) ds² = (C½−α/C½) dt² − (C½/C½−α) 1/4CdC² − C (dθ² + sin²θ dφ²)

What Crothers did not mention in his papers [1] and [2]:
Both metrics, defined by the eqs.(6) and (7)/(5.1) are equivalent, i.e. the associated manifolds are identical, merely represented by different coordinates (t,r*,θ,φ) and (t,C,θ,φ) repectively, associated by the coordinate transform
(5.2) C = C(r*) = r*² and r* = r*(C) = C½.

So normally there is no reason for considering other than the STANDARD form (6) of the Schwarzschild metric. Other equivalent forms may be of historical interest merely. Crothers' question of correct naming of the different versions of equivalent metrics has become obsolete nowadays. For more see Section 6.

From the coefficients goo of the metrics (7) and (6) respectively it can be seen directly that the metric (7) becomes singular at C½ = α, while the metric (6) becomes singular at r* = α.

Crothers defines a value ro by the equation C(ro) = α². From C(r*) = r*² we obtain ro = α: While the metric (7) is singular at C = C(ro) = α² the equivalent metric (6) has its corresponding singularity at r = ro = α.

Crothers is interested in a radial coordinate with an evident geometrical meaning. Therefore he introduces a new variable, a "proper radius" Rp by radial integration of the line element ds of (7) (dt=0, dθ=0, dφ=0) starting from the singularity, which after some calculations yields

Rp(C) = [C½ (C½−α)]½ + α ln |(C¼+(C½−α)½) α−½| (14)

The same result would have been attained by radial integration of the line element ds* of (6) starting at its singularity r* = α:

(5.3) Rp*(r*) = [r*(r*−α)]½ + α ln |(r*½+(r*−α)½) α−½|

where r* = C½. We then have Rp*(r*) = Rp(r*²).

Conclusion The use of the metric (7)/(5.1) instead of the technically simpler Schwarzschild metric (6) is an unnecessary complication which cannot yield new results exceeding those attained by use of the Schwarzschild metric.



6. Some comments on Crothers' paper [2]
Crothers' problems with the analysis of GRT are mainly caused by his misconceptions concerning the role of coordinates. In his paper [2] we read:

The black hole, which arises solely from an incorrect analysis of the Hilbert solution, is based upon a misunderstanding of the significance of the coordinate radius r. This quantity is neither a coordinate nor a radius in the gravitational field and cannot of itself be used directly to determine features of the field from its metric. The appropriate quantities on the metric for the gravitational field are the proper radius and the curvature radius, both of which are functions of r. The variable r is actually a Euclidean parameter which is mapped to non-Euclidean quantities describing the gravitational field, namely, the proper radius and the curvature radius.

Crothers expects a geometrical meaning always being attached to a coordinate. He insinuates that the coordinate r, known from spherical polar coordinates as radial distance from the center, should maintain its meaning when appearing in another context, e.g. as the parameter r of the Schwarzschild metric. In [2, Sect.2] we read about an isotropic generalization of the Minkowski line element:

ds² = A(r)dt² − B(r)dr² − C(r) (dθ² + sin²θ dφ²) , (2a)
A,B,C >0 ,

where A,B,C are analytic functions. I emphatically remark that the geometric relations between the components of the metric tensor of (2a) are precisely the same as those of (1). The standard analysis writes (2a) as,

ds² = A(r)dt² − B(r)dr² − r² (dθ² + sin²θ dφ²) , (2b)

and claims it the most general, which is incorrect. The form of C(r) cannot be pre-empted ...

This renaming method is somewhat lax but often used in mathematics, though it could be misunderstood if taken literally: The setting C := r² means that a new meaning is assigned to the variable r. Since r already occurs in eq.(2a), it would be better to use a new symbol, say r*, not r, for the new variable: r*² := C(r). As a consequence the terms A(r)dt² and B(r)dr² must be rewritten as functions of the new variable r* by introducing new cofficients A*(r*):=A(r) and B*(r*):=B(r)(dr/dr*)². This yields

ds² = A*(r*)dt² − B*(r*)dr*² − r*² (dθ² + sin²θ dφ²) , (2b*)

Then, all *s are removed to obtain

ds² = A(r)dt² − B(r)dr² − r² (dθ² + sin²θ dφ²) , (2b)

To repeat it: The terms A, B, r in (2a) and (2b) respectively have different meanings, here precisely specified. However, the rewriting (2a) as (2b) is perfectly justified herewith.

Without loss of generality the coefficient C(r) in eq. (2a) can be assumed as C(r)=r².

References
[1] S. Crothers, On the General Solution to Einstein's Vacuum Field and its Implications for Relativistic Degeneracy. , PROGRESS IN PHYSICS Vol. 1 , April 2005
http://www.ptep-online.com/index_files/ ... -01-09.PDF

[2] S. Crothers, On the Geometry of the General Solution for the Vacuum Field of the Point-Mass, , PROGRESS IN PHYSICS Vol. 2 , July 2005
http://www.ptep-online.com/index_files/ ... -02-01.PDF

[3] S. Crothers, The Published Papers of Stephen J. Crothers,
http://www.geocities.com/theometria/papers.html

[4] S.M. Carroll, Lecture Notes on General Relativity, http://xxx.lanl.gov/pdf/gr-qc/9712019

[5] N.N. , Eddington-Finkelstein coordinates, http://en.wikipedia.org/wiki/Eddington- ... oordinates

[6] N.N. , Schwarzschild metric, http://en.wikipedia.org/wiki/Schwarzsch ... paraboloid

[7] A.J.S. Hamilton, More about the Schwarzschild Geometry, http://casa.colorado.edu/~ajsh/schwp.html

[8] N.N. , Gullstrand-Painlevé Coordinates, http://en.wikipedia.org/wiki/Gullstrand ... oordinates
 
M

michaelmozina

Guest
Re: Turning the other cheek....

xXTheOneRavenXx":24w1wxjn said:
http://www.mathematik.tu-darmstadt.de/~bruhn/CrothersViews.html

I appreciate you bringing me up to speed on previous conversations. Obviously I have some reading to do, but I appreciate the link, and ramparts link to the prior thread.
 
X

xXTheOneRavenXx

Guest
Your welcome. I also apologize for the lengthy post. Whenever we have this same old conversation, I do my best to research the information. Personally I can't imagine and infinite density, however everywhere I look the BH theories seem to hold water with every site, except PIP. So I can't help but highly question Crother's work, and BH's constant rant about how there are all these conspiracies out there. It is really frustrating at times. It's not that I disrespect BH for his efforts, or personally telling Crother's he's wrong. However everything I have read and understood point to him being wrong, and missing something that hasn't been missed by everyone else in the field. That's why this time I included the links and the math explaining why Crother's is apparently proven mathematically wrong. I can't double check the work myself, however the author of the above post depicts in his writings that's it's wrong. Am I correct in assuming his math is correct? I just think it would be beneficial if BH took this arguement up the necessary channels. If the results were in his favor I would merely give him my congrates. I just don't see him doing that for whatever reasons he has.
 
M

michaelmozina

Guest
xXTheOneRavenXx":17yycmgq said:
Your welcome. I also apologize for the lengthy post. Whenever we have this same old conversation, I do my best to research the information. Personally I can't imagine and infinite density, however everywhere I look the BH theories seem to hold water with every site, except PIP.

I suppose its the "infinite density' aspect that just doesn't sit right with me.

So I can't help but highly question Crother's work, and BH's constant rant about how there are all these conspiracies out there.

I think it's important that you question Crother's work and ramparts certainly seemed to try to do that from what I could see. I think I may owe Yevaud an appology after reading that thread. I definitely have a much better "understanding" of his frustration at least. There seems to be a lot of unnecessary "huffing and puffing" going on in that thread.

As someone that isn't exactly 'mainstream' in their thinking, I don't believe that it is so much a 'conspiracy' as a "bias". The mainstream has a particular "way of thinking" and they do tend to get uptight when those core beliefs are questioned. In this case IMO there is a legitimate *physical* reason for questioning the notion of infinite density (from QM), but I had not seen a mathematical objection until coming across Crother's work. Frankly after reading that entire thread, it is abundantly clear to me that I'm not qualified to keep up with the subtleties of the conversation.

It is really frustrating at times. It's not that I disrespect BH for his efforts, or personally telling Crother's he's wrong. However everything I have read and understood point to him being wrong, and missing something that hasn't been missed by everyone else in the field.

Sure, but pretty much everyone with a new idea or a "beef" with current theory, or even a preference for a different cosmology theory, tends to be in disagreement with the mainstream, and "sees" something that most others seemed to have missed. I can see how that sounds "fishy' from the mainstream perspective, but from my vantage point the mainstream has indeed missed some important things, and has a long history of revising it's theories based on things they originally missed.

In this particular case however, I'm not sure. In the case of ambiguity, it's easy to 'trust the experts', but it seems like the number of suitable "experts" that can critique work at this level is somewhat limited.

That's why this time I included the links and the math explaining why Crother's is apparently proven mathematically wrong. I can't double check the work myself, however the author of the above post depicts in his writings that's it's wrong. Am I correct in assuming his math is correct?

It looks correct to me, but I would like to hear Crother's response. Sometimes mathematical arguments contain physical errors, or physical assumptions that are invalid. In this specific case I do not believe that I am capable of picking out such errors.
 
S

SpeedFreek

Guest
noblackhole has not returned to this thread in three weeks now.. I hope he can return from beyond the event horizon! ;)

One thing that has been niggling at me about this thread... is it a mere coincidence that Crothers has come out with a paper about the Kruskal-Szekeres extension, after my suggestion in the previous No Black Holes thread?

SpeedFreek":2rz0yvia said:
You need to change your coordinatization to use something like the Kruskal–Szekeres extension in order to understand what happens with the coordinate singularity at the Schwarzschild radius in the context of the in-falling observer.

Of course, I don't believe for a minute that an eminent scientist like Crothers would take a suggestion from little-ol me, so I can only assume this was the inevitable next step in his crusade...

:|
 
M

michaelmozina

Guest
ramparts":w8zhoydz said:
Michael, bear in mind (I think you were saying something along these lines) that our willingness to engage amicably with NBH scales downward with each standoffish comment, each insinuation that there's a conspiracy of astrophysicists, and each time he refuses to engage in the same civil dialogue with which we try to engage him.

Having read the thread that you suggested I understand and sympathize with your frustration. The "astrophysical magicians" comment got old pretty quickly even to me after awhile. :) You have the patience of a saint my friend.

FYI I want to thank you (and NBH and Gerhard W. Bruhn from Raven's link) for giving me quite an education on some of the more subtle aspects of GR theory. It's clear to me that I'm in over my head on the subtleties of some of the core of these arguments, but I enjoyed the discussion (mainly because I wasn't involved in it.). :)

One thing you said in this thread still haunts me however:

As for it not being Schwarzschild's solution, who cares? Maybe it was, maybe it wasn't. Sometimes things do get named for people who didn't discover them - in fact, that's very common in physics. But the solution exists, a derivation of it is very easy to find in any standard GR textbook, and saying "that's not what Schwarzschild said!" is certainly not a scientific argument against the solution.

Is it relevant that Einstein rejected BH (infinite density) theory or relevant that Schwartzchild specifically avoided a singularity in his work? Maybe you're right about it not being relevant, but one can't help but wonder. It is their work after all that is being used to support the idea in the first place, so one would have to believe that their opinions on this topic have merit. One also wonders if the use of their names in conjunction with the idea isn't an attempt by the mainstream to give the idea a false sense of scientific legitimacy that it otherwise does not deserve in the minds of the individuals who wrote the original formulas. It's not clear to me from reading this material that it matters, but then one can't help but wonder.
 
M

michaelmozina

Guest
SpeedFreek":lolocm3j said:
noblackhole has not returned to this thread in three weeks now.. I hope he can return from beyond the event horizon! ;)

One thing that has been niggling at me about this thread... is it a mere coincidence that Crothers has come out with a paper about the Kruskal-Szekeres extension, after my suggestion in the previous No Black Holes thread?

SpeedFreek":lolocm3j said:
You need to change your coordinatization to use something like the Kruskal–Szekeres extension in order to understand what happens with the coordinate singularity at the Schwarzschild radius in the context of the in-falling observer.

Of course, I don't believe for a minute that an eminent scientist like Crothers would take a suggestion from little-ol me, so I can only assume this was the inevitable next step in his crusade...

:|

From an amateur's perspective it's impressive to me that he *can* switch coordinate systems freely and still make his points. From my perspective, it does tend to strengthen his arguments so it was a great suggestion! :)
 
S

SpeedFreek

Guest
michaelmozina":m2b9nbe1 said:
From an amateur's perspective it's impressive to me that he *can* switch coordinate systems freely and still make his points. From my perspective, it does tend to strengthen his arguments so it was a great suggestion! :)

Of course he can switch coordinate systems, it is a feature of general relativity, but if you carry the same misconceptions across different coordinate systems, your conclusions are still misconceived.

:)
 
M

michaelmozina

Guest
noblackhole":2zycx70c said:
The astrophysical magicians' standard method for conjuring up the black hole is the Kruskal-Szekeres "coordinates". This very recent paper makes a mockery of those "coordinates" by counter examples:

http://www.ptep-online.com/index_files/2010/PP-20-01.PDF

The black hole is history.

For what it's worth NBH, I highlighted some examples of "loaded emotional language" from your opening post. I do not believe that these types of comments are helping your case on a public forum. FYI, I'm probably the last person in the world to complain about the use of ridicule or shock value in posts (because I've definitely done it myself), but IMO it's not really helping your argument. In fact, from the perspective of a layman on the topic in question, it actually detracts from what seems to be pretty solid set of mathematical and physical arguments.

From reading the various papers and responses, it is clear to me that I simply do not have the conceptual understanding or background necessary to fully appreciate your arguments or to evaluate them fairly. If I can't do that, even with some basic grasp of GR, it seems highly unlikely to me that most folks around here are going to fully appreciate your arguments. What they will "understand" is how "calmly" and "professionally" you can present your case.

Your responses from the other thread were often filled with useful information, and they were highly informative. Occasionally they are arguably *too* informative in the sense that you're typically arguing a number of different points simultaneously rather than trying to "hammer home" a single specific point. If there is something I might suggest to help your case with folks like me that are open to your ideas, I would encourage you to "pick your battles" very clearly and pick the specific issue or issues that you believe have the most merit. The papers seem more "on target" in that regard and they have a better "feel" about them as a result. I would love to see you respond to the key points raised on the the website by Gerhard W. Bruhn by the way.

http://www.mathematik.tu-darmstadt.de/~ ... Views.html
 
M

michaelmozina

Guest
SpeedFreek":28hfyg03 said:
michaelmozina":28hfyg03 said:
From an amateur's perspective it's impressive to me that he *can* switch coordinate systems freely and still make his points. From my perspective, it does tend to strengthen his arguments so it was a great suggestion! :)

Of course he can switch coordinate systems, it is a feature of general relativity, but if you carry the same misconceptions across different coordinate systems, your conclusions are still misconceived.

:)

It's been quite awhile since I've needed to switch coordinate systems, but typically if I screwed something up in one system, it didn't tend to work out so well in the other coordinate system. I suppose that you're right that misconceptions can be carried from one system to another, but usually that's not how it went down for me. Usually if I blew it big time in one coordinate system, or couldn't solve the problem in one system, the reason became very apparent in the other coordinate system.
 
S

SpeedFreek

Guest
michaelmozina":2r54ld65 said:
Usually if I blew it big time in one coordinate system, or couldn't solve the problem in one system, the reason became very apparent in the other coordinate system.

But what if there is no problem with either coordinatization, except for an argument about the "real meaning" of one of the equations?

This is from the paper in the OP:

The Kruskal-Szekeres “coordinates” are said to “extend” the so-called “Schwarzschild solution”, to remove an alleged “coordinate singularity” at the event horizon of a black hole at r = 2m, leaving an infinitely dense point-mass singularity at “the origin” r = 0. However, the assumption that the point at the centre of spherical symmetry of the “Schwarzschild solution” is at “the origin” r = 0 is erroneous, and so the Kruskal-Szekeres “extension” is invalid; demonstrated herein by simple counter-examples.

Personally, I don't have a problem with the assumption that, if a star undergoes gravitational collapse, then the centre of the star can be considered to be the origin point r = 0, as viewed from the outside. I don't see why Crothers seems to have such a big problem with it.

;)
 
S

Saiph

Guest
especially since more modern and sophisticated BH models don't use that assumption IRRC...
 
M

michaelmozina

Guest
SpeedFreek":1yp8g23m said:
michaelmozina":1yp8g23m said:
Usually if I blew it big time in one coordinate system, or couldn't solve the problem in one system, the reason became very apparent in the other coordinate system.

But what if there is no problem with either coordinatization, except for an argument about the "real meaning" of one of the equations?

I hear you. In fact that "real meaning' of the key equations seem to be at the core of Crother's argument. That particular line of reasoning seems to require a far better understanding of the equations than I personally possess. That tends to be somewhat frustrating because it is very hard to tell from a layman's perspective whether that sort of argument has merit. It might have merit, but then again unless one really comprehends the subtle aspects of these equations it's impossible to tell. I find that most of the "meaning of the equation' statements simply go flying about a foot and a half over my head. :)
 
S

Saiph

Guest
you're not alone there micheal. Following the math, or trying to, makes my head hurt.

That's one of the reasons I don't mind people discussing the credentials of the 'experts' involved here. As the paper isn't presented to us to provide observations, and the OP hasn't explained the math (or used it) we have to address the less reliable explainations of the findings and assumptions.

And even then it gets really hard. So you look at the author and figure out if they're credible.

And Crother has enough red flags that while I won't completely dismiss the ideas themselves...I'd have to see them from a better source before I put any real weight behind them.

Same goes for other theories I read too. String theory, for example, is way beyond me. The only reason I lend it any credence is the preponderance of respectable scientists that support it. And even then, they acknowledge that we can't know how valid it is yet, not for some time to come, due to the nature of any experiment that could confirm it.
 
X

xXTheOneRavenXx

Guest
I guess that's my *beef* with Crother's work, is that it is a review board that he personally sits on that gives credit to the work while others dismiss it as being incorrect. I think you would agree with me siaf & michael that if another review board of scientists with a meritable background were to give this work a positive review, there would be a lot less critizism against it. Certainly we would still expect many questions to be asked by the astronomical community, however I believe that the arguements Crother's makes would be more open to acceptance.
 
R

ramparts

Guest
michaelmozina":3jy5i1j5 said:
One thing you said in this thread still haunts me however:

As for it not being Schwarzschild's solution, who cares? Maybe it was, maybe it wasn't. Sometimes things do get named for people who didn't discover them - in fact, that's very common in physics. But the solution exists, a derivation of it is very easy to find in any standard GR textbook, and saying "that's not what Schwarzschild said!" is certainly not a scientific argument against the solution.

Is it relevant that Einstein rejected BH (infinite density) theory or relevant that Schwartzchild specifically avoided a singularity in his work? Maybe you're right about it not being relevant, but one can't help but wonder. It is their work after all that is being used to support the idea in the first place, so one would have to believe that their opinions on this topic have merit. One also wonders if the use of their names in conjunction with the idea isn't an attempt by the mainstream to give the idea a false sense of scientific legitimacy that it otherwise does not deserve in the minds of the individuals who wrote the original formulas. It's not clear to me from reading this material that it matters, but then one can't help but wonder.

By most accounts, a typical relativist today, even one far less brilliant than Einstein, understands GR, on the whole, a lot better than Einstein ever did. We simply know a lot more know than we did in his day.

Once a scientific idea is out there, we give the inventor credit (usually :lol:), but we don't really give them a special place in its further development. It is an open idea, out for the world to do with as they please. So if I were to come up with a new theory, my opinions on it would be no more valid on their own than the opinions of anyone else who studies it.

That said, I have no idea what Einstein's personal opinions on black holes were, so this may all be a moot point.
 
R

ramparts

Guest
michaelmozina":265xq36r said:
It's been quite awhile since I've needed to switch coordinate systems, but typically if I screwed something up in one system, it didn't tend to work out so well in the other coordinate system. I suppose that you're right that misconceptions can be carried from one system to another, but usually that's not how it went down for me. Usually if I blew it big time in one coordinate system, or couldn't solve the problem in one system, the reason became very apparent in the other coordinate system.

Physics is the same in all coordinate systems - the reason we'd switch between them is that the math can be more or less tractable in different coordinate systems. Some coordinate systems also break down at certain points - this is true of the Schwarzschild system, just as its true of the latitute/longitude system we use to describe the Earth's surface (what's the latitude/longitude at the North Pole?).
 
R

ramparts

Guest
michaelmozina":1oa00fvl said:
SpeedFreek":1oa00fvl said:
michaelmozina":1oa00fvl said:
Usually if I blew it big time in one coordinate system, or couldn't solve the problem in one system, the reason became very apparent in the other coordinate system.

But what if there is no problem with either coordinatization, except for an argument about the "real meaning" of one of the equations?

I hear you. In fact that "real meaning' of the key equations seem to be at the core of Crother's argument. That particular line of reasoning seems to require a far better understanding of the equations than I personally possess. That tends to be somewhat frustrating because it is very hard to tell from a layman's perspective whether that sort of argument has merit. It might have merit, but then again unless one really comprehends the subtle aspects of these equations it's impossible to tell. I find that most of the "meaning of the equation' statements simply go flying about a foot and a half over my head. :)

If I were in your position with regards to GR (which I was until quite recently), I would use a simple heuristic: who's more likely to be right, the last century's worth of scientists, or some guy on the internet who says they all made the same simple math mistake? ;)
 
R

ramparts

Guest
xXTheOneRavenXx":ohz8ds50 said:
I guess that's my *beef* with Crother's work, is that it is a review board that he personally sits on that gives credit to the work while others dismiss it as being incorrect. I think you would agree with me siaf & michael that if another review board of scientists with a meritable background were to give this work a positive review, there would be a lot less critizism against it. Certainly we would still expect many questions to be asked by the astronomical community, however I believe that the arguements Crother's makes would be more open to acceptance.

Yeah; I once spent an hour or so reading the correspondences with established physicists he put up on his website. It's incredible how he lets us see how every single scientist he ever talks to tells him he's wrong. As I see it, it's like this:

Crothers: "You and every single physicist since 1916 made a simple math mistake."
Physicists: "You made a simple math mistake."

Again, even if I were unable to understand more fully the mistakes he makes, I'd see the probabilites pretty clearly there ;)
 
N

noblackhole

Guest
Interesting: Herr Prof. Dr. Gerhard Bruhn's scribblings against Crothers are presented here, but Crothers' response to the silly professor is not. Crothers made mince meat of Herr Bruhn long ago. Bruhn even admitted Crothers mathemaitcs is correct but refused to giveup the precious black hole. Here is Crothers' response to Bruhn, amongst a few others:

http://www.sjcrothers.plasmaresources.com/BHLetters.html

The black hole is dead - it was still born.

Crothers' counter examples to the Kruskal-Szekeres "coordinates" are absolute. The K-S "coordinates" are nonsense.
 
Status
Not open for further replies.