heiwos

It may be obvious to a reasonable person that the thought experiment is sufficiently rigorous. For example, a reasonable person doesn't need to see the thought experiment include the axiom x=x to be convinced that it's sufficiently rigorous.

That's not what I said. Asking for more rigor of the thought experiment is different than dismissing it due to an unspecified lack of rigor. Yet asking for more rigor becomes silly at some point, like demanding that all axioms be stated, even x=x, so asking for more rigor can be tantamount to conveniently finding a "problem" where no problem exists. That's obviously not good science, which explains why the apparent paradoxes that were resolved when more rigor was applied were not dismissed due to lack of rigor until that lack was found.

You didn't specify the axioms on which your point is based. "Rigor" has different meanings to different people. Some people may want a claim to specify all the axioms on which it depends, even ones like x=x, otherwise they'll dismiss the claim as being insufficiently rigorous. It can get silly. We see here that if lack of rigor is a problem, it can be pointed out as a mistake. So it wouldn't be good science to dismiss a thought experiment due to an unspecified lack of rigor.

Yes, the blog we've discussed elsewhere seems to do that. Yes, because "self-consistent" is synonymous with "doesn't contradict itself". True when the theory is self-consistent, otherwise false. I agree that the twin paradox doesn't show a problem with SR. This looks fine to me. A thought experiment that claims to show that a theory is self-inconsistent cannot be refuted by simply assuming that the theory is self-consistent and then making the tautology, "If the theory is self-consistent, it can't contradict itself." That’s just ignoring a challenge to the theory (it's not good science). If the thought experiment is invalid, then there must be a mistake in it that can be pointed out. For example, the twin paradox contains a mistake.

It's not my thought experiment. I'm just making a side point about thought experiments in general.

Thought experiments are not just predictions. They can make valid conclusions. Wikipedia has it right here:

The point is that you're wrong that a theory cannot contradict itself when it's mathematically self-consistent. Create a new theory by adding postulate to SR that says the speed limit is c/2. The new theory is mathematically self-consistent, yet contradicts itself (it's self-inconsistent as a whole). Because you're wrong on that, the blog is not shown to be refuted--as you suggest--simply because it concludes that GR contradicts itself. GR could be mathematically self-consistent but still contradict itself. The other way to tell that you are wrong is because the blog does show that GR contradicts itself, and does so simply. If the blog was wrong for any reason then it should be a simple matter to point to a statement in it and show why it's wrong. But even a supposed GR expert on another site could not do that. Every statement in the blog seems to be correct.

I didn't say it was.

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

I'm not suggesting that "they" say anything. 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 can also show a problem with a theory by showing that it contradicts itself. That's what the blog does.

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.)

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.

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. 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.

Example please.

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!