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Mathematician Claims Black Holes Are the Result of Bad Math!
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by mgmirkin | September 7, 2008 at 10:32 pm
2917 views | 47 Recommendations | 45 comments
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Much as science hates to have its apple cart upset, mathematician Stephen J. Crothers seems to be spoiling to do just that! He claims that the equations used to justify the existence of "black holes" are themselves either incorrect or inapplicable, thus meaningless and in error...
Needless to say, his assertions rub astronomers and astrophysicists the wrong way. However, if his assertions are accurate, then a large chunk of current astronomy is predicated upon a false concept.
Crothers claims to have mathematically (and rigorously) demonstrated that the math behind black holes has been incorrectly applied and in some cases incorrectly attributed (IE, the wrong scientists given credit for particular valid or invalid mathematical contributions).
To briefly summarize some of Crothers' claims regarding the history of black hole theory:
The so-called "Schwarzschild" solution is not due to Karl Schwarzschild at all. The experts have either not read Schwarzschild's 1916 memoir or have otherwise ignored it
... The so-called "Schwarzschild" solution is due to David Hilbert, itself a corruption of a solution first derived by Johannes Droste in May 1916, whose paper has also been buried or ignored at the convenience of the experts
... It appears that the experts have not read Hilbert either
... Hilbert's mistake spawned the black hole and the community of theoretical physicists continues to elaborate on this falsehood, with a hostile shouting down of any and all voices challenging them. Schwarzschild's solution has no black hole, and neither does Droste's solution. Schwarzschild's paper is a piece of flawless mathematical physics, but Hilbert's is a poor show
... Marcel Brillouin's 1923 paper, in English, in which he gives another valid solution
... also simply and dramatically demonstrates that the black hole is nonsense. Brillouin's paper has also been ignored.
Crothers provides links to the original papers of the various authors he claims got it right (Schwarzchild, Droste & Brillouin) and those he claim got it wrong (Hilbert). He also reserves a few ascerbic observations for many of the so-called "experts."
The experts are always quick to conveniently brand anyone who questions the black hole as a crackpot. Unfortunately for the experts that does not alter the facts. The experts must also include Schwarzschild himself as a crank since his paper invalidates the black hole outright, as does Brillouin's, and Droste's. They must also label Einstein a crackpot, because Einstein always rejected the idea of the black hole, claiming in his research papers and other writings that it is not physical, and that singularities in the field nullify the theory of General Relativity.
Crothers speaks in no uncertain terms. His assertions that astronomers / astrophysicists got the math wrong are also relatively to the point, though a bit overly technical...
First, the fundamental black hole (a so-called "Schwarzschild" black hole) is allegedly obtained from a solution for Ric = Rij = 0 (subscripts i,j = 0,1,2,3), which is a spacetime that, by definition, contains no matter. So the alleged black hole can interact with nothing because its associated spacetime is empty by definition - it precludes the presence of any matter by virtue of Ric = 0. So there is no matter outside the black hole by initial hypothesis.
The argument goes that by setting Einstein's energy-momentum tensor to zero it can be shown that the Ricci scalar invarinat is zero and will also set the Ricci curvature tensor to zero.
The problem is that the energy-momentum tensor describes the matter causing Einstein's alleged "curvature of spacetime." Setting it to zero basically means removing all matter / mass from the associated spacetime (our spacetime)! In essence Ric=0 (the Ricci curvature tensor set to zero), from which the mathematical notion of black holes were derived, describes an empty universe!
Our universe is NOT empty. This appears to be a fundamental flaw in the mathematical / physical reasoning behind black holes... Assuming Crothers' understanding of the associated math and its physical implications is correct.
Crothers goes on to expose what he considers to be several other fundamental flaws in black hole theory.
... the alleged radius of the event horizon, the [so-called] "Schwarzschild radius", is not a distance in the spacetime manifold, let alone a radial distance. The astrophysical scientists have asserted this in ignorance of even elementary differential geometry!
...it is not the geodesic radial distance from the centre of spherical symmetry of the spatial section.
...it is in fact the inverse square root of the Gaussian curvature of any spherically symmetric geodesic surface in the spatial section of the spacetime manifold ... the radius of Gaussian curvature thereof.
In essence what Crothers highlights is that the "Schwarzchild radius" is not a physical radius of a sphere in 3D space. It is the radius of Gaussian curvature, a completely different mathematical entity than scientists obliviously claim it to be (according to Crothers).
Wikipedia defines "radius of curvature" thus:
Radius of curvature is a term characterizing the measure of how curved, or bent, a given curve or surface is.
This is considerably different from the typical "radius" of a sphere.
In essence, it seems Crothers is implying that astronomers and astrophysicists do not understand differential geometry and have misused one type of radius in place of another, and thus created a more-or-less fictional entity: the black hole.
Crothers has also previously challenged physicists to review his rigorous papers on the history of "black hole" theory and those refuting black holes mathematically.
This issue bears further attention and review by the astrophysical community (as opposed to unscientific summary dismissal of an unpopular idea). Even if the attention is a mathematical disproof of Crothers' work, at least it would be in the realm of good science. Point, counter-point.
If, however, Crothers' work is upheld, and black holes are essentially "mathematical nonsense," astronomers will have a long hard road ahead of them, if their favorite hobby-horse is found to be defunct. What, then must be called upon to explain various observations in space that have heretofore been dressed up to fit the mold of "black holes?" Interesting times ahead!
See also:
The Black Hole Catastrophe
A Fractal Distribution of Matter in the Universe May Topple the Big Bang. If So, What's Next?
An Argument for the Consideration of Electrodynamics in Cosmology
Big Bang vs. Plasma Cosmology: Competing Approaches to Understanding the Universe
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Most RecentMost Recommended Comments (45)
at 00:18 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
Bad maths is one thing, but having to rewrite the book on a verified phenomenon is something else entirely. 'Interesting times ahead', indeed!
at 00:44 on September 8th, 2008
If Crothers is right, perhaps "verified" should be put in "quotation fingers"?
I'd agree that having to rewrite the book sounds bad. However, the book has already been constantly rewritten as observations more or less failed to live up to expectations. Black holes were supposed to "gobble all and give nothing back," and yet they seem to spit up in the form of polar jets that nobody's been able to satisfactorily explain, etc. etc. New observations seem to constantly bring unexpected new things to light. It's the unexpected part that's a bit worrisome, scientifically, as predictive power is what scientists usually strive for as the gold standard. That there are so many unexpected "surprises" seems to indicate that maybe they don't understand the beasts as well as they think. If Crothers is right, then the fact that the math has been wrong might explain a few things. What to replace black holes with might be a sticky proposition. I mean, we definitely see SOMETHING out there. The question then becomes "if not black holes, then what?"
Regards,
~Michael Gmirkin
at 01:23 on September 8th, 2008
fair point - "verified" it is. I know they're currently scrutinising SgrA* and I could have sworn that Hawkings Radiation had been confirmed.
at 07:00 on September 8th, 2008
If I recall correctly, Hawking radiation is supposedly something where a pair of particles are "somehow" created, one on each side of the event horizon and one of them falls into the black hole, but the other somehow magically makes an escape... If I'm recalling it correctly, I'm not sure how they can claim to have "verified" something that minute? But I'm sure it would be an interesting read, even if only as a fairy story for the kids. *wink* *tongue planted a little bit in cheek...*
~Michael
at 09:07 on September 8th, 2008
As I recall, it's something to do with pixies living in the quantum vacuum, when a matter/antimatter pair pop into 'existence' (Boson Pixies, I'd assume) and one of them gets cruelly devoured by the Singularity Monster, before the matter/antimatter pair can annihilate themselves. I have a vague recollection of someone losing a bet to Hawking over that one.
(and, if we're talking fairy stories, did you hear about that devout Atheist who saw The Big Bang in a slice of toast)
at 10:39 on September 8th, 2008
I'm still not entirely convinced about Hawking radiation, of course. I mean, if we're talking just outside the "event horizon," then we're asymptotically approaching a point where supposedly not even light can escape its pull. How does one half of the pair get enough energy to escape while the other doesn't? How far would the "escaping" particle get before it suddenly realized there was a black hole there and fell back in as it massively decelerated then started accelerating toward the black hole? I mean, it doesn't get to go skipping on its merry way in ignorance of the black hole's gravity, does it...? Or does it just get a "get out of jail free," "pass go," "collect $200" card from the Community Chest? ;o) I've just always wondered that, since hearing about Hawking radiation...
at 00:51 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
If black holes are the result of bad math, I must have made a bunch of black holes in my life.
at 01:11 on September 8th, 2008
If bad math leads to black holes, I'm sure that a few term papers have been swallowed up in college math classes over the years. Err, wait, no, those met with paper shredders, not black holes. ;)
Regards,
~Michael
at 05:07 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
at 05:18 on September 8th, 2008
mgmirkin, I like this story. it challenges all the theories, then again we can only theorize from this earth perspective, however living in an infinite universe.. anything is possible including the existence of compressed time and matter portals..somewhere out there ; )
Thanks for sharing this. it's good stuff Michael!
at 06:49 on September 8th, 2008
Well, it more-pr-less challenges ONE theory. But that theory, if taken down, may take a number of other theories with it. Considering mythical "black holes" are now assumed by astronomers to reside in the heart of just about every galaxy out there. If the "black hole" proves to be a fictional entity, then what must they be replaced with? MECOs? Plasmoids of massive dimensions? Something "else" entirely?
Regards,
~Michael Gmirkin
at 06:18 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
at 06:19 on September 8th, 2008
wow, lots of SPAM appearing all over NP in comments.
at 06:26 on September 8th, 2008
(Spam comments have now been deleted.)
at 06:44 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
Although I am no specialist I have felt for some time that physics has been hopelessly obfuscated - for whatever reason, either deliberatly or by accident ...
All that the current quantum models have ever really been good for is designing nuclear weapons ... imagine that ?
Anyway, a good read, even if way over my head ...
at 06:56 on September 8th, 2008
Yeah, it's still a little bit over my head, though I've tried to simplify a couple of the issues into layman's terms.
IE, the "Schwarzchild radius" isn't the physical measure of the distance from the center of a sphere to its outer edge. Rather it's the "radius of curvature" which is some part of telling how curved or distorted a surface is. Yet it's commonly referred to as a physical radius of a black hole['s event horizon?]... Also, the Ric=0 bit apparently means that, by hypothesis, the solution is only good for a universe in which there is no matter / mass (thus it would be inapplicable or irrelevant / meaningless to our universe).
Those seems to be a few of the major flaws, though others are also discussed by Crothers in several of his articles / papers...
Regards,
~Michael Gmirkin
at 07:11 on September 8th, 2008
The technicalities of modern quantum field theory are overwhelming for all but the rarest of mathematical prodigies, and not having anything like these gifts myself, my own impressions and observations are necessarily more like those of the 'artisan craftsman' ...
I fall back to something Tesla once said about the curvature of space - paraphrasing, of course, 'Space, being space has no properties at all. It's impossible for space to have curvature!'
That enigmatic statement on it's own, the product of the mind of a remarkable prodigy like Tesla would have no special significance for me at all if it were not for the following information which comes from very ancient Indian texts -
'Space is that which exists without obstruction' ...
That's all they say about it! Very similar indeed to what Tesla himself had to say, don't you think ?
at 09:37 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
Great piece - I enjoyed the read!
at 10:33 on September 8th, 2008
Thanks! :) Glad it was enjoyable. Hopefully it all made sense? I know that the original explanation were intended for more academic readers. I think I understood what he was saying and received some private guidance from some peers online. But, again, not being a mathematician, I'm probably not qualified to fully understand or evaluate the maths involved. So, I'm just relying on what others have mentioned in discussion of what he's talking about.
Regards,
~Michael Gmirkin
at 11:17 on September 8th, 2008
Long ago I read a very good book titled "Bye Bye Big Bang, Hello Reality" that does a stellar (forgive the pun) job of pointing out many aspects of the singularity sham, from big bang to black holes. It is time that people work hard to find people with the clout or exposure to really push this shame into the limelight. Tax dollars are being sucked down these fantasy black holes faster than the speed of light. The people spending this money keep their heads in the sand becaue it pays not to look for the problems in current dogma and hurts to speak out. So let's do an end run and stop trying to appeal to those profiting from the lies and mistakes and work really hard at appealing to those of us footing the bill. There must be many watchdog committees around this country. Let's dig them up and start campaigning for them to become active in demanding accountability. Demand these guys prove there is good cause for what they are doing in light of the known inconsistancies. How about it gang? What's the point in being "newsy" if we don't really get the word out?
at 18:24 on September 10th, 2008
I agree wholheartedly - but would need someone with great dedication to first take up the cause.
at 15:38 on September 8th, 2008
mgmirkin, I like this story. It's good stuff.
Keep it comin' Michael. ...it's electrifying!
at 18:48 on September 8th, 2008
Stephen Crothers is exactly right!
There are NO BLACK HOLES.
Only 3,000 different types of atoms account for all visible matter in the universe.
Mass/energy relationships (E = mc^2) in those 3000 data points reveal repulsive forces between neutrons that:
1. Prevent the collapse of neutron stars into Black Holes;
2. Produce solar luminosity, solar neutrinos, and the solar wind; and
3. Power other stars and the cosmos.
REFERENCES:
1. O. Manuel, C. Bolon, A. Katragada and M. Insall, "Attraction and repulsion of nucleons: Sources of stellar energy", J. Fusion Energy 19 (2001) 93-98.
2. O. Manuel, Cynthia Bolon and Max Zhong, "Nuclear systematics: III. The source of solar luminosity", J. Radioanal. Nucl.Chem. 252 (2002) 3-7.
3. O. Manuel, E. Miller, and A. Katragada, "Neutron repulsion confirmed as energy source", J. Fusion Energy 20 (2003) 197-201.
4. O. Manuel, Michael Mozina, Hilton Ratcliffe, "On the cosmic nuclear cycle and the similarity of nuclei and stars," J. Fusion Energy 25 (2006) 107-114 (arxiv.org/abs/nucl-th/0511051)
at 22:03 on September 8th, 2008
mgmirkin, I like this story. It's good stuff. But what happens now? Will Crothers be conveniently ignored by astrophyscisists/astronomical community.
at 08:53 on September 9th, 2008
It's worked so far, why stop now? ;o)
Kidding mostly... And yet, kind of not. It's sad that ideas get quashed because they're unpopular rather than science allowing for open discussion on a point-counterpoint basis. If an idea is good it will be replicated and verified. If it is bad, it will be refuted in subsequent papers. That's how science works (supposedly). Not by quashing papers before science has had a chance to work (IE, evaluate the paper on its merits, and then respond yea or nay with subsequent papers).
Regards,
~Michael Gmirkin
at 05:26 on September 10th, 2008
mgmirkin, I like this story. It's good stuff.
at 15:41 on September 15th, 2008
The article about black holes is confusing. It seems you are a victim of pure mathematics. Black holes are a fact. there is no discussion. If mathematic theories can not follow, means Interdisciplinary capacity missing. All modern network scientists learned that. If you start with gravity as result of the deformation of the 4 dimensional space time continuum you are close to event thinking. The cern scientists I interviewed in switzerland about black holes from the LHC have a simple start up solution. They say if you believe universe has only 3 dimensions you come to the conclusion the LHC is not producing mini black holes. If you believe in more dimensions ..up to 11 you will have black holes generated by the big bang machine. Black holes in the universe Eating just up collapsing stars emitting energy mc²=E. What abstract the energy or matter has minus or plus is not of primary interest. The revolution in physics started with quantum leap of electrons Balman Brecket series etc. Why not exploiting quantum leaps into negative matter/energy and back . the next challenge.
at 16:59 on September 15th, 2008
Huh? Please rephrase in English... I didn't catch but about 3 words of that (figuratively speaking).
The article was not about black holes, per se. It was about the notion that the math underlying them may be faulty.
I'm not sure how you feel I've been victimized by math. I don't feel victimized. I think that math is a perfectly good tool, when used properly by those trained in its intricacies. I think it sometimes gives us too much of a sense or confidence, where none should exist. Especially if it has been abused in a way that "sounds good" but says something silly or inapplicable. Or worse, writing science fiction in the language of math...
Was it really your intention to state that there should be no discussion in science? Especially on topics as fundamental as the proper use of mathematics in science or whether our current theories are predicated upon faulty premises?
The article is NOT about the Large Hadron Collider, nor speculating whether it will or won't create miniature black holes (my money is on "it won't").
The universe does not care what you or I believe about how many dimensions it has. It has as many as it has. No more, no less. So, the quote or paraphrasing from the alleged CERN scientist seems to be either obfuscating or disingenuous about not admitting that science still really doesn't understand as much about the universe and its workings as scientists lead us to believe (if they're not confident in something as basic as how many dimensions we live in, or are actually physically possible).
The last few sentences didn't make much sense to me, personally. Care to comment further?
at 07:59 on September 17th, 2008
Hi, mgmirkin , thanks for answer. Why confusing public with terms "black hole" at LHC experiment times? Well I always felt victimized by math, it was me too stupid to discuss about an epsilon environment, when I could go instead for a nice student party. All great scientists envisioned the idea by intuition, look at the creator of AC transmission Nikola Tesla,Niagara falls power station . He saw It then he made it. Later come some bean counters to explain it by rules or math. The revolutionary developments have to do with precision engineering.. The cern scientists in Europe work in team like they created Internet. You are a lonsome rider. Thanks for riding on the black hole wave, your statement "there should be no discussion in science, hm...
at 08:59 on September 17th, 2008
Hmm, well, it wasn't intended as a commentary on LHC. By me at the least. Though , I know some people have claimed everything from black holes to various exotic particles will be created by LHC, some of which may lead to armageddon (or more likely NOT)...
But, the timing was more-or-less coincidental, I think. IE, Crothers wrote in response to a submitted journal paper about "black holes," not in response to anything with respect to LHC. So, aside from the anecdotal speculation that LHC might produce mini-"black holes," the one has little to do with the other.
With respect to my statement about "discussion in science," I believe there should be discussion in science, or else what is the point of science? Without discussion, science would wither and die. I was merely referring back to your statement "Black holes are a fact. There is no discussion." in questioning whether you, in fact, believe there should be no discussion/questioning in science? IE, should we simply accept edicts from on high? Or are we allowed to question them, review them, and in some cases bend or break them (if they're faulty)?
I'm not quite so "lonesome" a rider as you might think. A number of other scientists and interesting folk also question the scientific orthodoxy.
But, in any event, it's been good chatting!
Regards,
~Michael Gmirkin