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Tags black holes , electric universe , Leonard Abrams , relativity , Stephen Crothers

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Old 13th March 2012, 04:31 AM   #41
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So, Mr. Crothers is an all around tard then.
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Old 13th March 2012, 08:33 AM   #42
sol invictus
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Originally Posted by Vorpal View Post
I don't think the Ricci scalar is a particularly natural generalization of Gaussian curvature.
Really? The Gaussian curvature of a 2D manifold is the Ricci scalar of that manifold, at least up to some numerical factor of order 1.

Quote:
It's defined as the product of principal curvatures of a submanifold, and so in general not proportional to the Ricci scalar.
Gaussian curvature - at least in every definition I've ever heard - is defined for a 2D manifold (which can be a submanifold if you like). The Ricci scalar on the other hand is defined for any dimension, and it coincides with the Gaussian curvature in 2D. It's also the most important scalar curvature in higher dimensions, in a certain relevant technical sense. So....?
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Old 13th March 2012, 08:36 AM   #43
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Originally Posted by tensordyne View Post
So, Mr. Crothers is an all around tard then.
I suspect he's an intelligent person, at least in the narrow sense that he would score relatively highly on an IQ test. The problem is that some people get obsessed with certain topics to the point that they cannot think rationally about them, because the pain of being wrong about something they've invested so much time and effort in causes extreme cognitive dissonance.

It seems to be a common phenomenon, especially on the internet (which allows that natural tendency to grow unchecked, since there are few social consequences).
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Old 13th March 2012, 08:37 AM   #44
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Originally Posted by tensordyne View Post
So, Mr. Crothers is an all around tard then.
To quote Zwicky*, a spherical bastard, perhaps? Why? Because no matter what angle you look at him at, he's still a bastard!

* well, that's how I remember it; maybe it's an urban myth ...
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Old 13th March 2012, 03:31 PM   #45
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Originally Posted by sol invictus View Post
Really? The Gaussian curvature of a 2D manifold is the Ricci scalar of that manifold, at least up to some numerical factor of order 1.
Yep. Perhaps I don't understand in what way it's natural, but a generalization based on a single match doesn't seem particularly impressive.

Originally Posted by sol invictus View Post
Gaussian curvature - at least in every definition I've ever heard - is defined for a 2D manifold (which can be a submanifold if you like). The Ricci scalar on the other hand is defined for any dimension, and it coincides with the Gaussian curvature in 2D.
The most common definition is applicable to 2-surfaces in E³, with mean and Gaussian curvature being the sum and product of the principal curvatures, respectively, up to a constant. This has a very obvious generalization to n-surfaces in En+1 via the trace and determinant of the shape operator, and from there any submanifold of codimension 1 anywhere. This directly applies the original definition in terms of the extrinsic principal curvatures to higher dimensions.

Originally Posted by sol invictus View Post
It's also the most important scalar curvature in higher dimensions, in a certain relevant technical sense. So....?
It is indeed. So there is no problem in considering the Ricci scalar important in its own right without making analogies to the Gaussian curvature except as a purely coincidental match 2-manifolds.
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Old 14th March 2012, 08:28 AM   #46
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Originally Posted by W.D.Clinger View Post
Ziggurat answered your non-mathematical (scientific) question.

The trouble you're having with the mathematical argument is likely to be my fault.

The steps of that argument go as follows:
  1. The Painlevé-Gullstrand metric is equal to the familiar Schwarzschild metric outside the event horizon.
    That's exercise 25 in the "Black holes" thread. Given exercise 24, the proof of exercise 25 is just a trivial calculation using high school algebra.
  2. The r, θ, and φ coordinates of the Painlevé-Gullstrand metric are identical to the r, θ, and φ coordinates of the Schwarzschild metric (by exercise 25).
  3. The Painlevé-Gullstrand metric satisfies Einstein's field equations for empty space.
    (I didn't prove that, because the proof is both tedious and uncontroversial. Even Crothers agrees that the familiar Schwarzschild metric satisfies Einstein's field equations for empty space. Combined with exercise 25, that implies that the Painlevé-Gullstrand metric satisfies Einstein's field equations outside the event horizon. The coefficients of the metric are analytic in the coordinates, so the Painlevé-Gullstrand metric must satisfy the field equations at the event horizon as well. That's all we need for the following steps.)
  4. According to general relativity, light follows null geodesics.
  5. For null geodesics, ds=0.
  6. For radial geodesics, which are directed entirely toward or entirely away from the center of spherical symmetry, the conventional spherical coordinates θ (elevation) and φ (azimuth) don't change.
  7. For radial geodesics, therefore, dθ=dφ=0.
  8. At the event horizon, r=2m so β=1.
  9. Substituting ds=dθ=dφ=0 and β=1 into the Painlevé-Gullstrand metric, we find that null radial geodesics at the event horizon satisfy
    <br />
\[<br />
0 = dr (dr + 2 d \tau)<br />
\end{align*}<br />
\]<br />
  10. That means one of the two factors must be zero.
  11. That means dr=0 or dr=-2dτ.
  12. That means dr/dτ=0 or dr/dτ= - 2.
  13. That means the world line for inwardly directed radial light has coordinate velocity dr/dτ= - 2 at the event horizon. (The radial coordinate for inwardly directly radial light at the event horizon is decreasing as the time coordinate τ advances into the future.)
  14. That means the world line for outwardly directed light has coordinate velocity dr/dτ=0 at the event horizon. (The radial coordinate for outwardly directly radial light at the event horizon isn't changing.)
  15. That means a photon that's emitted radially outward at the event horizon never escapes beyond the event horizon. It stays forever at the event horizon.
  16. That also means a photon that's emitted radially inward at the event horizon proceeds rapidly toward the central singularity, contra Crothers and Farsight.
If you don't understand how one of those steps follows from preceding steps, or you don't understand how one of those steps is derived, please let me know which steps require elaboration.
The "fault" is mine. That's very helpful, thanks.
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Old 1st March 2015, 03:18 PM   #47
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Originally Posted by tensordyne View Post
I am glad that S. Crothers is being discussed here. I have corresponded with him a bit on email and read over his whole website pretty thoroughly. I have to admit that I agree with him that black-holes should not be considered a good prediction of General Relativity, but I have different reasons then he does for thinking this.

I would love to discuss in another thread perhaps why I think this is so, but for now it seems more worthwhile to go over what I make out to be the main claims of Crothers and why I either agree or disagree with those claims.

1. He challenges the legitimacy of the stress-energy pseudo-tensor.

I think his analysis is in error on this point as he sets up various straw-man arguments. This is kind of technical so I will leave out the messy details unless anyone is interested about discussing it.

2. He challenges the legitimacy of using multiple bodies in GR as there are no known solutions or existence theorems on such solutions.

This is very bad logic. The problem is he is not thinking like a physicist here. A test mass in motion in a gravitational field is very well described in GR using the geodesic equation. Two masses and good predictions, no big deal.

His complaint about using the Schw. Sol. for the geometry exterior to two masses in orbit about each other is also off because of his peculiar aversion to using approximations when talking about physics (which is very annoying btw).

3. He claims that the r in the Schwarzschild solution is the curvature of radius.

Agreed. Calculated it myself and it is. How much emphasis you put into the significance of this fact is up for debate I suppose though.

4. Complaint about Ric=0. His complaint is that since there is no mass or energy where Ric=0 is solved, how can one then find a solution to such a situation that includes mass.

This kind of gets into territory of why I think black-holes are not a good physics prediction of GR, so let me shy away from that for now and just state the following.

It has been proven very conclusively that exterior to a spherically symmetric mass all solutions of the metric are equivalent to Schw.'s sol. What is the name of that damn theorem? Oh well, forgot.

My point is, assertions about the stress-energy tensor being zero in one region and yet having curvature in that same region being a problem are false. There is no problem because the source for the field would then be in another region giving the curvature. Let me stop there.

5. He challenges whether Astronomers have detected BH's or not because the test of a BH behaving as per current understanding is not whether there is a certain amount of energy-density in a given region (that does not test the predictions about BH's as per current consensus understanding), but tests of things like whether there is an event horizon or singularity (or singularities perhaps more realistically speaking?). Further, it is a complaint of his that both the event horizon and any singularities are unfalsifiable.

I agree with the complaint that just because a region has such and such a density of energy does not show that there is a BH there acting in the way that BH's are supposed to act according to current consensus. The problem is that energy density in some region is not the same as observing a singularity or event horizon (or perhaps other putative aspect of BH's). This is true.

I do agree that singularities are unfalsifiable, but I think that event horizons in principle constitute a falsifiable prediction. The aspect of light not being able to escape would probably be unfalsifiable, but it is asymptotically falsifiable to show that closer and closer to such a horizon things get smeared out as it were.
That would be Birkhoff’s theorem: “any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric.” Source: Wikipedia
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Old 1st March 2015, 05:54 PM   #48
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"On Certain Conceptual Anomalies in Einstein’s Theory of Relativity"
By Stephen J. Crothers, January 2008
(Sorry, can't post link to the article; new member -- use Google)
Originally Posted by Stephen J. Crothers
4 Misconception: that Ricci = 0 is admissible

Ruv=0 is inconsistent with the physical foundations of General Relativity as adduced by Einstein in that it violates Einstein’s Principle of Equivalence, and so writing Ruv=0 is erroneous in the first place.

Coincidently, that Ruv=0 is inadmissible was realised independently and at about the same time as the Author, by M.W. Evans, via a different line of thought — by using ECE theory.
Well, there you have it; proof positive -- small minds do think alike.

Last edited by Slings and Arrows; 1st March 2015 at 06:02 PM.
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Old 21st June 2015, 09:43 PM   #49
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The forum's software no longer renders LaTeX correctly, making this thread's equations unreadable. I have therefore translated my contributions to this thread into HTML hosted at another site.
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Old 21st June 2015, 10:25 PM   #50
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Originally Posted by W.D.Clinger View Post
The forum's software no longer renders LaTeX correctly, making this thread's equations unreadable. I have therefore translated my contributions to this thread into HTML hosted at another site.

Excellent! Thank you for your time and effort, it is greatly appreciated. I have been anxiously waiting for months, hoping you would update the thread with readable equations. Many thanks!
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Old 22nd June 2015, 08:07 AM   #51
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Originally Posted by W.D.Clinger View Post
The forum's software no longer renders LaTeX correctly, making this thread's equations unreadable. I have therefore translated my contributions to this thread into HTML hosted at another site.

I have been reviewing the equations, and it looks like you mistakenly repeated the same equation twice; probably just linked to the wrong graphical image:

Leonard S. Abrams
http://www.cesura17.net/~will/Epheme...hers/isf8.html
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Old 22nd June 2015, 08:39 AM   #52
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Now fixed. Thank you for spotting this.
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Old 22nd June 2015, 12:01 PM   #53
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Originally Posted by W.D.Clinger View Post
The forum's software no longer renders LaTeX correctly, making this thread's equations unreadable. I have therefore translated my contributions to this thread into HTML hosted at another site.
Fantastic, this is one of my favourite threads on this forum! I very much enjoy your straightforward and understandable, yet rigorous explanations. Thank you.
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Old 22nd June 2015, 01:21 PM   #54
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Originally Posted by sol invictus View Post
I suspect he's an intelligent person, at least in the narrow sense that he would score relatively highly on an IQ test. The problem is that some people get obsessed with certain topics to the point that they cannot think rationally about them, because the pain of being wrong about something they've invested so much time and effort in causes extreme cognitive dissonance.

It seems to be a common phenomenon, especially on the internet (which allows that natural tendency to grow unchecked, since there are few social consequences).
I'd add that the internet also allows people like Crothers to recruit acolytes and find fellow travellers, forming an echo chamber that tends to further reinforce the belief that their "theories" are right.
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Old 23rd June 2015, 10:22 AM   #55
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My favorite Crothers quote:

Quote:
The cosmic microwave background (CMB) is not cosmic in origin, it is produced by the Earth’s oceans.
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Old 23rd June 2015, 11:30 AM   #56
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Originally Posted by Perpetual Student View Post
My favorite Crothers quote:

Quote:
The cosmic microwave background (CMB) is not cosmic in origin, it is produced by the Earth’s oceans.
That's not Crother's idea, though, he's just repeating what he heard from Robitaille.

They're birds of a feather, of course. In the same way that Crothers' crackpottery involves reading 100-year-old Schwarzschild papers and thinking he's the only one to have checked the math on basic GR. Robitaille's crackpottery involves reading 150-year-old Kirchhoff papers and thinking he's the only one to have done the logic on basic thermodynamics. Crothers thinks his "correct" Schwarzschild reading justifies his rejection of black holes, Robitaille thinks his "correct" reading of Kirchhoff lets him reinterpret Cosmic Microwave Background data as some sort of misidentified Earth background noise.
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Old 23rd June 2015, 11:34 AM   #57
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Originally Posted by Perpetual Student View Post
My favorite Crothers quote:
Maybe he's never heard of WMAP... or more likely he's ignored it.
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Old 23rd June 2015, 12:58 PM   #58
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Originally Posted by Perpetual Student View Post
My favorite Crothers quote:
That seems either profoundly dickish or flatly insane.
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Old 23rd June 2015, 01:25 PM   #59
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Originally Posted by theprestige View Post
That seems either profoundly dickish or flatly insane.
This is a profoundly false dichotomy!
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Old 23rd June 2015, 03:07 PM   #60
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Originally Posted by BazBear View Post
Maybe he's never heard of WMAP... or more likely he's ignored it.
Well, what Robitaille does is:

a) Complain about how blackbody radiation only occurs in solid-state cavities
b) "Therefore" it's impossible that COBE saw blackbody radiation from deep space
c) Since space is infinite, filling it with blackbody radiation ("COBE detected something with huge signal to noise!") requires an infinite power source infinitely far away (or something?)
d) Makes more sense to look for a close-up solid state. Probably the Earth!
e) <gibberish about the COBE and WMAP receiver capabilities>
f) <gibberish about COBE and WMAP data analysis>
g) <gibberish about the true physics of blackbody radiation>
h) Therefore cosmology is wrong! When do I get my Nobel? Or at least my Telesio prize?

But he has heard of WMAP and doesn't *ignore* it per se. He just gets himself good and confused until he's convinced he's predicted that WMAP will pick up a huge Earth background and mistake it for a CMB monopole.

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Old 23rd June 2015, 03:19 PM   #61
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Some of the <gibberish about ...> ben m glides over is, um, curious/funny.

For example, it seems to include things like (my glosses) "water is everywhere", "water does crazy/strange/whatever things in the WMAP microwave bands", "THEREFORE WMAP detected water", "what's the biggest source of water? The Earth's oceans!", "THEREFORE WMAP detected microwave emission from the Earth's oceans! (it cannot have come from anywhere else)".
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Old 23rd June 2015, 03:19 PM   #62
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Originally Posted by ben m View Post
Well, what Robitaille does is:
...
But he has heard of WMAP and doesn't *ignore* it per se. He just gets himself good and confused until he's convinced he's predicted that WMAP will pick up a huge Earth background and mistake it for a CMB monopole.
ignoring the fact that COBE and WMAP data are consistent and COBE was in earth orbit and WMAP at L2.
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Old 23rd June 2015, 04:40 PM   #63
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Originally Posted by hecd2 View Post
ignoring the fact that COBE and WMAP data are consistent and COBE was in earth orbit and WMAP at L2.
Not "ignoring" precisely. Robitaille mentions that WMAP was at L2, then subsumes it into the miasma of gibberish as though of course a satellite at L2 would be swamped by Earth radiation! He also seems aware that COBE and WMAP are reported to be consistent, but of course <insert data analysis fever swamp> that's what they WOULD say.
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Old 25th June 2015, 11:09 PM   #64
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Originally Posted by W.D.Clinger View Post
Stephen J Crothers has published 17 articles in Progress of Physics. One of those papers was co-authored by Jeremy Dunning-Davies, who edited an issue of The Open Astronomy Journal that's being discussed in the thread that asks "How did crackpot Electric Universe papers get published in a peer-reviewed journal?" Crothers was sole author of the other 16 papers.

Today I'm going to discuss the very first of those papers:
Stephen J Crothers. On the general solution to Einstein's vacuum field and its implications for relativistic degeneracy. Progress in Physics April 2005, Volume 1, pages 68-73. http://www.ptep-online.com/index_fil...5/PP-01-09.PDF
That paper contains four technical sections, plus a dedication to Leonard S Abrams and an epilogue that explains how Crothers became interested in general relativity through the Adams paper I discussed previously. The first two technical sections basically repeat what Adams wrote, adding only some snark and a sloppy reformulation (that I believe to be incorrect) of one relatively unimportant formula.

In section 3, Crothers strikes out on his own. Here's what remains of the first half of section 3 after snark, redundancy, and irrelevancy have been excised:

-----------> See the LaTeX enable equations: Here

Several things:

According to (23), at r=r0, g00 = 0. Equation (23) says nothing about Φ.

If g00 = 0, then equation (21) says Φ = 1, not ½.

I think Crothers got Φ = ½ by using his "weak far field" approximation under the assumption that C(r0)=(2m)2, but that weak field approximation is obviously the wrong formula to use for calculations in the strong field at r=r0. (Crothers takes that value of the radial coordinate r to be the location of the point mass, when it's actually the event horizon, but that doesn't matter here: it's a strong field either way).

The correct calculation of Φ = 1 appears to refute the main point Crothers is trying to make here. (I'm not entirely sure what point Crothers is trying to make here. Perhaps a physicist could explain it to me. Crothers couldn't.)

Finally, g00 is coordinate-dependent. (That's an observation, not a criticism, because the gravitational potential has to be coordinate-dependent.) Crothers thinks he's stuffed all of that coordinate-dependence into C(r), but that's true only for coordinate systems that satisfy a number of assumptions. Crothers made some of those assumptions explicit, but quite a few others are implicit. One of those assumptions is that the coordinates take advantage of spherical symmetry so he can ignore all but the time and radial coordinates; that's fine. Another assumption is that the metric is static. That rules out all coordinate systems that cover the event horizon and its spatial interior.

So I don't even believe equation (21) can be true in general.

Crothers made a very simple math error. The gravitational potential 'Φ' is equal to 1; yet Crothers erroneously computed a value of 1/2.

Crothers mathematics is just plain wrong!

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