"General Relativity Contradicts Itself"

[Cap'n Refsmmat]

I opened this week's New Scientist and was in for a bit of a shock when I saw a full-page ad title "No Black Holes (General Relativity Contradicts Itself)". The clincher:

 

Then GR violates the relativity principle as stated above, thereby violating its own postulate, the equivalence principle.[...] A theory that contradicts its own postulate is invalid.

 

Surprise!

 

You can read the full text of the ad here (we may leave a comment to let the author know we're discussing his ad). I'm naturally a tad skeptical (the argument doesn't make sense to me), but I thought I'd open this up to a typical SFN free-for-all.

 

What do you think? Another crackpot?

[swansont]

Yeah. I've read something similar but can't find it.

 

I'm not a GR person, but I see two immediate problems with the post, besides some awkward wording: a ball that has some radius is inconsistent with "an infinitesimally small (in spacetime) freely falling frame." You can only have infinitesimal objects in such a frame.

 

I also don't see how you get two objects at rest with respect to each other in one frame moving in opposite directions when you move to another frame. If the issue is that the ball can't possibly be moving anywhere but toward the black hole in any frame, one has to wonder how the particle came to be at the event horizon and with a radial outward velocity sufficient to escape, but not having been at r-dr the instant before, which would be inside the event horizon, or not undergoing an acceleration to change its direction, meaning it's not in an inertial frame.

 

Invalid premises necessarily lead to invalid conclusions.

[heiwos]

Yes, almost certainly a crackpot. Still it's a good exercise...

 

I'm not a GR person, but I see two immediate problems with the post, besides some awkward wording: a ball that has some radius is inconsistent with "an infinitesimally small (in spacetime) freely falling frame." You can only have infinitesimal objects in such a frame.

An infinitesimally small frame is an arbitrarily small, but not point-sized, frame. A "ball that has some radius" can fit in that. An infinitesimal object is not point-sized, right?

 

I also don't see how you get two objects at rest with respect to each other in one frame moving in opposite directions when you move to another frame.

What two objects are at rest with respect to each other in the frame falling into the black hole? I don't see it. What frames are you referring to? X and Y?

 

If the issue is that the ball can't possibly be moving anywhere but toward the black hole in any frame, one has to wonder how the particle came to be at the event horizon and with a radial outward velocity sufficient to escape, but not having been at r-dr the instant before, which would be inside the event horizon, or not undergoing an acceleration to change its direction, meaning it's not in an inertial frame.

Nothing in the blog (I haven't seen the ad) says that the particle was ever at the horizon, or below it. It needn't have been. As long as it's possible in principle in GR for an escaping particle to be above the horizon in the frame, which it is, there's nothing amiss. The thought experiment need not show where the particle came from.

 

Invalid premises necessarily lead to invalid conclusions.

I don't see where there's an invalid premise. There surely is one though, or something else wrong with it, for thousands of real physicists over decades would not have missed some simple problem in GR. (Or at least the odds of that are close to nil.) Obviously it's not written by a real physicist or else it'd be in a peer-reviewed journal, and not be some math-less blog post. There's a proof somewhere that GR is self-consistent I think.

[ajb]

I have come across similar claims before, such as rotating black-holes can't exist etc.

 

For what I can gather, papers published in the ArXiV on the subject usually based on some interpretation or "result" that is not quite right.

 

General relativity does indeed predict it's own downfall in the hight gravity limit viz singularities. But this is nothing "special " about GR, classical mechanics predicts it's own downfall when you apply it to atomic structure and classical thermal physics breaks down when applying it to black-bodies. It is a good sign as it means there is plenty of work to do.

[heiwos]

For what I can gather, papers published in the ArXiV on the subject usually based on some interpretation or "result" that is not quite right.

Surely that's the case here. But what is it?

 

General relativity does indeed predict it's own downfall in the hight gravity limit viz singularities.

That's true, but let's be clear that the blog claims that GR contradicts itself about black holes, which GR is heretofore thought to predict validly, unlike singularities, where the theory has long been known to break down. In the extremely unlikely event the blog is right, the idea of black holes should be exiled to the dust bin of history. If it violated its own equivalence principle, the theory might be invalid (i.e. make incorrect predictions, if only slightly) even in weak gravity. It would be a major advance of physics, or a body blow, depending on your perspective.

 

I notice the author doesn't accept comments on his/her blog. Isn't that a sign of crackpotdom, not listening to what's wrong with an idea?

[ajb]

I have not read the blog carefully and don't intend to (too busy).

 

You are right in making the distinction between black-holes (i.e. event horizons) and curvature singularities. They are not the same thing. They are of course related and closely intertwined if cosmic censorship is indeed true.

 

What is possibly the case here is that this distinction has not been made and confusion has arisen. In particular, is there some confusion about coordinates singularities and real singularities?

 

I don't see any calculations in the blog so I am not sure we can say what is going wrong. We would need to see a full paper on the subject.

[heiwos]

I don't see why the blog would need to make an explicit distinction between the horizon of the black hole and its singularity at the center. They are two different parts of a black hole, just like a car windshield is different than a car muffler. There'd be no confusion. In my books, the coordinate singularity is just a historical footnote, from the time when it was mistakenly thought that a horizon was a real singularity.

 

I also don't see why calculations should be necessary. Any form of logic will do in a proof. If I present a theory to you that says "I postulate such-and-such, and the postulate is false", you don't need to do any calculations to determine that the theory is invalid; the rules of logic are all that you need. As far as the calculations that show that GR predicts black holes, including that all objects below a horizon must fall (calculations that the logic in the blog depends on), that's been done in spades elsewhere. I wouldn't expect the blog to have to repeat that.

 

All that said, I'd really like to know what's wrong with this blog!

[Zephir]

What do you think? Another crackpot?

The problem is, the black hole concept is poorly defined. If we define the black holes as a pinpoint singularity surrounded by event horizon, we can always propose models, which will violate such definition apparently.

[heiwos]

Example please.

[ajb]

Zephir is right on this one. Black-holes and singularities are not so straight forward to define in general relativity. We have two options to consider. Either we consider space-times that are known to have what we think of as black-holes etc. or we can try to formulate more general mathematical statements and classifications.

It is this second approach that is much more difficult to define black-holes andsingularities. I am not an expert on this, you need to read Wald's book on general relativity. But from what I can gather, the standard approach is to remove the singular point so that you still have a well defined pseudo-Riemannian manifold. The singularity is seen as geodesic incompleteness (roughly, geodesic "fall off" the space-time).

 

Now about the lack of calculations. Unless he can present a formal mathematical statement and show it to be untrue or present some calculation that clearly gives an "unphysical" answer it is hard to say what they have done. General relativity is a mathematical theory so all sensible questions must be formulated mathematically.

[heiwos]

Black holes have a straightforward definition that is commonly used: a structure delimited by a horizon. The horizon has a straightforward definition: a surface that nothing--not even light--can pass outward through.

 

I see nothing about black holes in GR that is so murky that the blog cannot make its case with certainty. The blog's case is made at the horizon and above, and not at the central singularity. GR makes solid predictions everywhere but the singularity.

 

General relativity is a mathematical theory so all sensible questions must be formulated mathematically.

By that logic you cannot even make the statement you just made, because it's not made mathematically.

 

GR can be discussed, and even invalidated, without math. The blog is based on predictions of GR, like its prediction that all objects below a horizon must fall. Those predictions can be determined using math, which they have been in numerous other texts (so no need to repeat). Then those predictions in their written form can be compared against other predictions of GR, or its postulates in written form, to determine if there's any contradiction. Thorne makes that clear in his quote in the blog.

 

The problem with the blog must be identifiable by at least one statement in it that is wrong. If black holes are so ill-defined that the blog cannot even attempt to use their predicted features in an argument, then all the books I see about black holes are worthless fiction too. I don't buy that.

[Nentuaby]

If I may shift the topic a bit, does anybody have any information at all on the identity of this person? Buying a full page ad and filling it with two columns of text clipped from an anonymous blog which contains nothing else at all except the full text of the article... (And may I note, the ad is inconsistently clipped so as to make most of the footnote references useless... Not professional work even for the genre.)

 

Clearly, this is anomalous behavior. Certainly it's not how science is conducted. It's not even how crackpottery is conducted, on the whole- usually there's a name with a self-granted title attached to it... Call me a phillistine, or just say I prefer psychology to physics, but I'm really more interested in who this fellow is and what could possibly be driving him than the esoteric contents of the article.

[ajb]

The truth is unless a clear mathematical statement and some kind of calculation is presented, the general relativity community will not "believe" any arguments. Physics does not always follow our intuition and as we are discussing modern theoretical physics calculations are unavoidable. I think using just "words" can get you so far, but at the end of the day theoretical physics uses mathematics as it's fundamental language.

 

And my statement was about general relativity and not in general relativity. So there is no contradiction.

[pioneer]

I presented this in another topic but seems appropriate to this discussion. There is an aspect of classical gravity that GR can't explain. If I was to lift a bolder, on the surface of the earth, and place a block of foam under it, the foam will flatten. There will be a physical compression of the atomic spacing in the foam due to weight=>gravity. But the change in local GR space-time is too small to account for this. GR is missing something. If we return to the black hole, the GR contribution seems perfect. But this additional classical feature of gravity may also be contributing something.

 

There appears to be a simple GR fix, that allows GR to accommodate this. But it require a fundamental change from space-time contraction to space-time expansion. Although GR is caused by mass, only space-time is directly being affected. To explain this, we start with a 3-D mass that is contained in a coordinate system from (0,0,0) to (1,1,1). If we only expand space-time to (2,2,2) but leave the mass contained by (1,1,1) the mass is now more compressed relative to the expanded coordinate system. The coordinate system goes further into space-time like gravity does. From our reference we see the mass appear to attract and get squished by gravity.

 

If we contract space-time to (0.5,0.5,0.5) with the classical mass still at (1,1,1) now the mass has expanded relative to the coordinate system. This is what is described by SR, but not GR. In SR one sees themselves or their mass appearing to extend further into space in their reference. There is no squishing affecting going on where we compress physically like the foam. We appear to become more inflated within space-time.

 

To test the space-time expansion assumption for GR, one would expect that time will speed up since the time scale will also expand. In the center of stars the average event is nuclear which are the fastest. The gravitational work generates heat, which allows everything to speed up. We don't get a time dilation affect within the largest stars, slowing their average nuke burn relative to small stars. Their burn time speeds up even more, in the opposite direction of time dilation. They have more time expansion so more changes of state happen per sec.

[D H]

I presented this in another topic but seems appropriate to this discussion. There is an aspect of classical gravity that GR can't explain. If I was to lift a bolder, on the surface of the earth, and place a block of foam under it, the foam will flatten. There will be a physical compression of the atomic spacing in the foam due to weight=>gravity. But the change in local GR space-time is too small to account for this. GR is missing something.

 

Since extraordinary claims require extraordinary evidence, you will need to back this statement up with math. What you are saying is that GR cannot explain how a simple scale or accelerometer works.

[Tom Mattson]

I opened this week's New Scientist and was in for a bit of a shock when I saw a full-page ad title "No Black Holes (General Relativity Contradicts Itself)". The clincher:

 

 

 

Surprise!

 

You can read the full text of the ad here (we may leave a comment to let the author know we're discussing his ad). I'm naturally a tad skeptical (the argument doesn't make sense to me), but I thought I'd open this up to a typical SFN free-for-all.

 

What do you think? Another crackpot?

 

Smells like Zanket to me.

[heiwos]

The truth is unless a clear mathematical statement and some kind of calculation is presented, the general relativity community will not "believe" any arguments.

I totally buy that! At the same time, it's absolutely ridiculous. It's like, Thorne could write his laymen's book about black holes, and the proofreader could say "wait a sec, you've got an obvious contradiction here in these two paragraphs", and Thorne would say, "you got the math to back that claim up?"

 

Another way to look at it, it would be silly that relativity can be discussed at length in these forums, largely with words, but if someone poses some supposed paradox, math suddenly becomes required to present the paradox. I think a worded paradox is fine, and there's a solution (that shows a problem with this blog) that can also be put into words.

 

While I can certainly agree that this crackpot's notion is lost on the "general relativity community," even if it's right, I'm still very curious what's wrong with it. It'll drive me crazy if I don't know! The blog seems to make it undeniable that an object anywhere below the horizon cannot possibly have the same velocity as an escaping particle, with respect to a frame falling through a horizon. If so, there's no way (it seems) that that frame can be equivalent to some other frame, like one in intergalactic space, in which case GR contradicts its own equivalence principle. Location doesn't constrain velocity in the intergalactic frame.

 

I'm as curious as anything as to why this hasn't been raised as a paradox before. At least I haven't seen it before. It's as good as any of the others about relativity that I've seen. I'd love to see the solution.

[heiwos]

I've been defending the blog on another site, to try to see what's wrong with it. After much discussion and thought, it seems that there is nothing wrong with it. GR does contradict itself. The more you think about it, the more obvious it becomes. I feel privileged to be maybe just one of two people in the world who knows that, and knows that black holes are just a mistake. The best the supposed GR expert on the other site could come up with is that--surprise!--black holes are white holes too, so that what's said in all those books about black holes (namely, that anything inside the horizon of a black hole must keep falling all the way to r=0) is not true after all. Funny how GR can be saved only by showing that perhaps its most well-known prediction is not really a prediction of it.

 

But black holes may be believed indefinitely into the future, if only because the crackpot author didn't add the math required to appease those with a math bias. I don't see why he/she couldn't have just thrown some math in there, rather than just reference it, to support GR's prediction that anything below a horizon keeps falling. Dumb!

 

Serious question: is there anything to prevent someone from adding the math and taking the credit? If so, I might go for it. From what I've read, papers often just need to have the right look & feel (i.e. math and graphs and $10 words where $1 words will do), and an author from academia, to get published. The content doesn't really matter, since they aren't really reviewed anyway (e.g. to explain the Bogdonav (sp?) Affair). Is that right? Or maybe it's the opposite in this case, that any paper that shows that GR has a problem would be blocked from publication, since there is so much riding on GR now? Like the Chandra X-ray telescope that looks for black holes. Are there any well-known but still open-minded journals out there? Anyone know someone who'd wanna be the academic contributor?

 

(Sorry if I sound critical of academia. I have to ask since I'm not an academic and it does seem like real science doesn't matter nowadays, most places I look. Like some sites, such as physicsforums, you can't even discuss a thing such as this. I asked to be deleted from that site, since not even being able to discuss a proposed problem with physics seems very against the spirit of scientific discovery & learning to me. I don't wanna even start down the road of getting a "real" paper written about this topic if it's already well known in the scientific community that all the major journals would block a paper that shows that GR has a problem.)

[swansont]

I don't wanna even start down the road of getting a "real" paper written about this topic if it's already well known in the scientific community that all the major journals would block a paper that shows that GR has a problem.)

 

Is that what "they" say?

 

———

 

One issue here is that a mathematically self-consistent can't have any contradictions. If you find one, it means you've done something wrong, not that the theory has problems. You show a problem with a theory by demonstrating that it doesn't describe nature, and that requires an actual experiment.

[heiwos]

Is that what "they" say?

I'm not suggesting that "they" say anything.

 

One issue here is that a mathematically self-consistent [theory] can't have any contradictions. If you find one, it means you've done something wrong, not that the theory has problems.

If you were right about that, and GR is mathematically self-consistent, then something must be wrong with the blog. But nobody seems to be able to show anything wrong with its argument, and its argument is relatively straightforward, so that there should be something obviously wrong with it if it was wrong. The way I see it, the blog just points out a contradiction that's in plain sight in most every text on GR, once you know where to look.

 

Your comment is along the lines of what I'd like to know. Will every major physics journal be so pre-convinced that GR is self-consistent, such that they will not even read any paper that purports to show otherwise? Is science that closed-minded? Seriously, I'd like to know. I'd like to work with an academic to convert the blog into a publishable paper. But if journal editors/reviewers today are too closed-minded, I'd be wasting my time even when the blog is right.

 

I can think of a few examples of ideas that are currently widely accepted that were initially rejected simply because scientists at the time were pre-convinced that the idea could not possibly be right. Of course it turns out that they were wrong for whatever reason.

 

GR's prediction that everything below the horizon of a black hole must fall is based on more than just math; it's also based on SR's postulate the nothing can be locally measured to move faster than the speed of light. That dependency on a postulate leaves room for GR to be mathematically self-consistent but be self-inconsistent as a whole.

 

For example, here's a mathematically self-consistent theory that obviously contradicts itself: SR plus the postulate that nothing can be locally measured to move faster than half of the speed of light. This proves you wrong that a "mathematically self-consistent [theory] can't have any contradictions".

 

You show a problem with a theory by demonstrating that it doesn't describe nature, and that requires an actual experiment.

You can also show a problem with a theory by showing that it contradicts itself. That's what the blog does.

[swansont]

Mathematical self-consistency can be tested separately. So you don't need "pre-convincing" of that — any treatise that shows a contradiction in a thought experiment is necessarily flawed. Finding the flaw is an intellectual exercise, and often a useful one. If you propose that 1+1 ≠ 2, and hand me ten pages of "proof," I know there's a flaw. I don't have to find it to reject your work.

 

You can construct a self-consistent theory with the postulate that the speed limit is c/2. It will look exactly like SR, because all you have to do is change c to c'. However, there will be no contradictions in any thought experiment. The falsification will occur when we find that photons actually travel at 2c', that time dilation deviates from the prediction and that we can routinely accelerate particles to speeds greater than c'. Physical experiments, because we require that our theories actually describe nature.

 

But a thought experiment that describes something contrary to what we expect to see means that the expectations are unphysical or the thought experiment is flawed.

[heiwos]

If you propose that 1+1 ≠ 2, and hand me ten pages of "proof," I know there's a flaw. I don't have to find it to reject your work.

Agreed. But the blog is a different animal than that.

 

You can construct a self-consistent theory with the postulate that the speed limit is c/2. It will look exactly like SR, because all you have to do is change c to c'. However, there will be no contradictions in any thought experiment.

My example was SR plus the postulate that the speed limit is c/2 (not SR changed so that the speed limit is c/2 rather than c). That would be a theory that is mathematically self-consistent but contradicts itself, because it predicts velocities > c/2. A mathematically self-consistent theory can still contradict its own postulates.

[swansont]

How is limiting speed to c/2 consistent with SR?

[heiwos]

I didn't say it was.

[swansont]

Then what's your point? The contradiction is in the lack of self-consistency. If the system isn't self-consistent it doesn't fit the criteria of the earlier discussion.