# (Alpha) General relativity is self-inconsistent v2

Discussion in 'Physics & Math' started by zanket, Jun 3, 2007.

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1. ### RJBeeryNatural PhilosopherValued Senior Member

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AlphaNumeric: I *still* read that as saying that universal special relativity only exists in the absence of gravity fields. The accuracy of the SR calculations, along with its effective area of symmetry, is dependent upon the curvature in the region. In other words, SR applies everywhere only if spacetime is "flat", otherwise we must consider it an approximation whose error is dependent upon the local curvature fields. Close?

BenTheMan, it appears that my "common misinterpretation" that matter never actually crosses the event horizon is not completely without merit...

USA Today reported on research done at Case Western Reserve which suggests something along the same lines. While it appears that their motivation was to reconcile the apparent loss of information associated with matter falling through the horizon, this interpretation also handles my personal objections and eliminates my confusion.

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5. ### PeteIt's not rocket surgeryRegistered Senior Member

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Hi RJ,
First - a disclaimer. I'm not an expert. I'm a business graduate who likes to splash in the shallows of physics like a day-tripper's kid at the beach. So, what I say could be wrong.

A key is in Alpha's note that SR is a local theory. You can use it for local spacetime, but not necessarily for far-removed spacetime. In practice, "local" for SR means "the nearby spacetime that is close enough to flat".

Compare this with Euclidean geometry on the Earth's surface - On Earth's curved surface, 2D Euclidean geometry is a local theory. It works OK in some local region (eg 40 km East then 30 km North makes 50km at 53° East of North), but not for larger regions (4000km East then 3000km North does not make 5000km at 53° East of North).

What that means in this particular context is that if a massive thing goes past you at high speed, then you can use SR to determine its kinetic energy from its speed relative to you as it passes by (ie when it is local to you). So something passing by with speed approaching c would have arbitrarily large energy.

But, if you measure the speed of that same thing when it is in a different place from you (non-local), SR might not be able to tell you the thing's kinetic energy from that measured speed, because the curvature of space-time might alter the relationship.

In particular:
As some object approaches and crosses the horizon of a black hole, its speed relative to a distant observer will approach and exceed c. But, since there is significant spacetime curvature between the observer and the object, we can't use SR to tell us what the object's energy is.

Beyond that, I can't help you - I very quickly get lost when I try to follow how to use GR quantitatively, so I don't know how to determine what the energy of an object crossing the horizon actually is in a distant observer's reference frame.

Last edited: Mar 13, 2009

7. ### PeteIt's not rocket surgeryRegistered Senior Member

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That's right, but be careful what conclusions you draw from it.

8. ### RJBeeryNatural PhilosopherValued Senior Member

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Ahh I think I'm close, thanks so much.

9. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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One should be very careful to draw the distinction between asking questions and making claims.

10. ### RJBeeryNatural PhilosopherValued Senior Member

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BenTheMan: So it's your position that my claim
is "bullshit" even though I have consequently provided evidence to support my perspective? Or is it simply "bullshit" that someone without a Physics degree could possibly have any intuitive insight that would be meaningful in real world Physics? Isn't that the true source of our conflict? You and others are offended that I have the gall to think critically without putting in the life commitment that you have?

11. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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RJB---

1.) I have started this conversation in an Alpha thread, which is my fault. Such conversations should not be taking place here. Respond, or don't...I don't care. I probably won't read it.

2.)
Quoting things like New Scientist will not help your cause, as they mainly write about crackpot stories. You can find all kinds of news stories to support all kinds of idiotic claims. There ARE physicists who believe black holes don't exist. There are also people who believe that the earth exists on the back of a giant turtle. The fact that some people believe such things doesn't make such beliefs legitimate.

3.)
You confidently state that "black holes can't form", even though you have no bones about flaunting your layman status. Problem solved.

Asking questions is encouraged. I've tried to model this forum as a place where people can come and ask questions. Throwing open the doors of the hall and confidently stating that 70 years of science should be overthrown because of your brilliant'' idea is strongly discouraged. Ask Farsight, or Reiku/saxion/gluon, or (...)

We understand many things about black holes, including (more or less) everything that happens at the horizon, where these thought experiments are taking place.

4.)
I can assure you, this is not the case. I and others are offended because you think critically, make a mistake, and then refuse to admit that you're wrong, even when shown the proper logic, or told the correct answer by someone who HAS put in a life commitment to answering these questions.

12. ### RJBeeryNatural PhilosopherValued Senior Member

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1. If you hadn't made the "bullshit" comment I wouldn't have responded so rudely.

2. Three of the links I provided were a summary of the paper submitted to and accepted by Physical Review D. The fourth was a link to the actual paper. I was surprised at the prevalence of references to this particular paper which you were apparently unaware of when you made the comment that this concept was a "common misinterpretation".

3. I'm pretty sure I didn't say "confidently that black holes can't form". I said that matter never making across the horizon was a resolution to the problems I had with understanding black holes (while at the same time admitting my lack of knowledge in this area). Then some posters said I don't know enough to even identify problems. Then I pointed out that this very solution not only solves my issues but it also resolves the "loss of information" paradox, and that this POV is seen as a fresh new alternative to the concept of how black holes behave.

If you would've said something like "yes it's possible that matter never makes it across the event horizon but due to your lack of formal education the reason for this is probably much deeper than the reason that you suspect it is," I would have accepted that comment. But the fact is that it was YOU and GUEST432 and ALPHANUMERIC that appeared to be claiming with authority either directly or indirectly that this interpretation was completely FALSE.

4. I invoke the Alpha Rule that requires you to defend your statements. Please provide examples of the following:

Last edited: Mar 13, 2009
13. ### Guest254Valued Senior Member

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A black hole is a certain type of solution to Einstein's field equations. You claimed (or believed, or felt, or wanted) that there is some sort of paradox (which there isn't), which is resolved if matter cannot cross the event horizon. Please offer us some science. Please outline a detailed review of the simplest case (Schwarzschild) indicating why a test particle can never, ever penetrate the event horizon. This will involve detailed calculation, obviously. The GR I know has no problems in dealing with in falling test particles in a neighbourhood of the event horizon (for example see Kruskal, 1960), so these calculations will be routine. I want to see the armchair physicist do some physics.

If, however, your claims are baseless, then I see a problem with your conformity to these "alpha rules". I have no problem with people making grand claims, as long as they can show something to back them up with. In this case, I'd like to see some physics.

14. ### zanketHumanValued Senior Member

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Fair warning, I don’t have a lot of time to devote to this old thread. My argument has improved since the OP. (I’ve got it down to the point where the direct objections typically contradict multiple reputable references.) I’ll summarize before responding to any leftover relevant replies.

First, on math: unnecessary. Reams of texts on GR, including sprinkled all over the internet, show its predictions in plain language suitable for laymen. When those predictions clearly contradict one another, that is a problem with those texts at least. I am satisfied that dozens of smart physicists (like Thorne and Taylor and Wheeler) did not all just happen to make the same mistakes. I am satisfied that the true problem lies with GR itself. Your conclusions may differ; that’s fine, we don’t have to agree.

The equivalence principle, in Einstein’s own words, implies in no uncertain terms that the laws of physics are the same in all inertial frames, including those in our real, gravity-endowed universe. This can be true even though a tidal force is always present in our real frames/labs. An inertial frame must meet Thorne’s definition in the OP; i.e. be small enough that the tidal force in the frame is negligible, so that the result of the SR experiment conducted in the frame can agree with the predictions of SR to all the significant digits for the experiment. This is how SR is experimentally confirmed to numerous significant digits in our real labs. As I mentioned to RJBerry above, a speck of dust in a galaxy far, far away from us can throw off any of our SR experiments at some precision. That doesn’t mean that I can’t use the equivalence principle to show a contradiction of GR. The tidal force just needs to be properly accounted for.

In principle, to how many significant digits can an experiment of SR agree with the predictions of SR in a given-sized inertial frame falling through the horizon of a black hole? The answer is that it depends on the mass of the black hole: the larger its mass, the more the significant digits. (The horizon is at r = 2M, so the larger the mass, the greater the circumference of the black hole.) There need not be any spaghettification at the horizon. A given lab falling through the horizon of a black hole, even one larger than a cruise ship, could be a better lab for testing SR (i.e. have a weaker tidal force throughout it) than any lab in which humans have tested SR to date—whether the lab is better depends on the black hole’s mass.

Suppose an experiment of SR is being conducted in the International Space Station, when the ISS (while maintaining its orbit around the Earth) falls through the horizon of a black hole so massive that no instrument in the ISS or yet created by mankind is capable of registering the slightly increased tidal force. Is the experiment invalidated? No, it isn’t, according to equivalence principle. The experiment can continue just fine, and is still valid to a certain number of significant digits. Even as the Earth crosses the black hole’s horizon, the Earth stays in orbit around the Sun, the Moon stays in orbit around the Earth, and nobody need notice anything out of the ordinary, even visually. The spaghettification could be delayed until a billion Earth years later.

If the predictions of GR can be used to show by example that the laws of physics among inertial frames must radically differ, that would be the death of the theory, because GR would then contradict itself (namely, its equivalence principle).

Such an example exists. The tidal force is ruled out as the culprit, because the tidal force in the anomalous frame can be weaker (or stronger, it doesn’t matter) than the tidal force in the “ordinary” frame. In my post to RJBerry above I noted that a law of physics that GR demands in X (an inertial frame falling through the horizon of a black hole) does not apply in an inertial frame that is wholly above the horizon (perhaps orbiting some neutron star such that the tidal force in this frame is stronger than the tidal force in X). In an inertial frame that is wholly above the horizon, even one in which the tidal force is stronger than in X, a free test particle located anywhere in the frame can in principle have the same velocity (limited to some number of significant digits) with respect to the frame as that of any other possible (in principle) free test particle in the frame. That’s a law of physics that does not apply in X, according to GR. In X, a free test particle located below the horizon cannot (even in principle) have the same velocity (to any number of significant digits) with respect to X as that of a free test particle that is above the horizon and escaping to infinity. The particle that is below the horizon must be falling toward the central singularity, according to GR, whereas the escaping particle is rising away from the black hole. GR allows the particle that is above the horizon to escape, with a velocity relative to X that must be less than c as locally measured (or else GR has a different major problem).

I noted above that X need not be arbitrarily small; it could be as large as a cruise ship with my case re GR’s self-inconsistency still made. However, you are free to imagine that X is an arbitrarily small, nonzero-sized frame.

A common objection claims that the escape velocity throughout X must be c, so that no particle in X can be escaping the black hole. I think people glom onto this one when they can’t see any other way to save GR. The horizon (where by definition the escape velocity is c) is a specific altitude that is reached by X as it falls. Then it is logically impossible to preclude X from—when it falls a bit further—covering a region in which a free test particle can either escape (from the upper part) or not escape (from the lower part).

Once people realize that it’s impossible to show that the escape velocity throughout a nonzero-sized X is c, they tend to revert to trying to prove that X must be point-sized. So let me note again that our experiments that have confirmed SR are perfectly valid despite taking place in real (nonzero-sized) labs, because each experiment confirmed SR to only a certain precision (number of significant digits) that was not so fine as to allow the numerical result to be affected by the tidal force in the lab. Which is to say the tidal force in the lab was negligible for the purposes of the experiment. In the self-contradiction of GR shown above, the tidal force is eliminated as a culprit, so the self-contradiction has nothing to do with the size of X per se.

The standby objection is to harp on the lack of math above. So let me emphasize that the law of non-contradiction, a law of logic that trumps anything GR has to say, applies equally well to both worded and mathematical statements. GR texts translate GR’s math into worded predictions. The OP includes the equivalence principle in Einstein’s own words. While you can validly say that I have not shown a self-inconsistency of GR mathematically, claims that I cannot show a self-contradiction without using math, at least a self-contradiction of GR texts, have no merit.

15. ### zanketHumanValued Senior Member

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Who are you referring to? I made no such claim. Would help if you quoted.

16. ### Guest254Valued Senior Member

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I'm referring to RJBeery.

However, in your direction: I believe it's been made clear to you why your conclusions are wrong, but it doesn't seem like you want to listen. Don't take my word for it though: submit your work to a decent theoretical physics journal and let us know how you get on.

17. ### zanketHumanValued Senior Member

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That's the oldest non-argument in the book.

18. ### Guest254Valued Senior Member

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Hey, you're obviously working on another level to me, so I think it best if you send your work to some experts and let them judge its merits. Submit your work to a decent theoretical physics journal, and let us know how you get on.

19. ### zanketHumanValued Senior Member

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That's the second-oldest non-argument in the book.

20. ### Guest254Valued Senior Member

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Why wont you send your work to a reputable journal?

21. ### AlphaNumericFully ionizedRegistered Senior Member

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No, I'm offended you think that without putting in some effort you think you can see further than everyone else on a topic you have read nothing about.

Every single person who has a degree in physics and above worked to get it. Some found the work easy but those people generally spend a lot of time reading and less time going "Huh!?". To do postgrad GR is hard. Not a person who has done it will say otherwise.

But yet you think you don't need to put in any effort to know or do more. If you'd read 'GR' by Wald, cover to cover in a day, put it down and said "It's all pretty straight forward" and then churned out say a 4 line proof to the Positive Energy Theorem, I'd be damn impressed. You've shown that with much less effort than it took me (or anyone else in history) you've grasped the topic. But you haven't. You haven't read any books and it's clear if you did, you'd struggle enormously with them.

Now I know people from both sides of the scale. I know people who effortlessly learnt what still bemuses me, in 1/10 the time I've been thinking about it. Quite a few of them are likely to remain permanent residents of Cambridge, UK. I also know a fair few who fail to grasp why linear equations admit linear combinations of solutions as solutions and it takes 30 minutes of my time to explain it to them. You're the latter and you believe yourself the former. If you were the former people like Ben r Guest or myself would notice, we have seen such people in our friends or our students. They are easy to spot. So its not a case of I'm offended that you can do this stuff with minimal effort compared to us, I'm offended you think you can do this stuff with absolutely zero effort and I'm willing to be you did less than stelllar in high school maths and physics, am I right?

You put in less effort than the brightest of the bright would need to understand GR and despite not being anywhere close to the mediocre of the mediocre, you think you're in a position of knowledge.

I have one or two students like you. They're a little more loud mouth, they put their hand up more to get me to read their 'brilliant method' than to get help and then they sail through to an unspectacular 15/25, or in the case of one prat 2/25 (best mark of the last month for him!).

So tell me, how did you do in high school maths and physics, out of interest?

22. ### AlphaNumericFully ionizedRegistered Senior Member

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Okay, you want an Alpha level response to why GR has SR as a symmetry?

Definition of Lorentz transforms : $\Lambda^{a}_{c}\eta_{ab}\Lambda^{b}_{d} = \eta_{cd}$

Required to prove : $g_{ab}\to g_{ab}$ under $\Lambda$ put at point in space-time.

Introduce new notation : a,b,c,d are curved space indices. $\mu,\nu,\sigma,\tau$ flat space indices.

Define vierbein as the transformation between flat and curved indices : $e^{\mu}_{a}$ thus defining $g_{ab} = e^{\mu}_{a}\eta_{\mu\nu}e^{\nu}_{b}$.

Lorentz transforms $\Lambda$ act only on flat space indices and so if we do a Lorentz transform $e^{\mu}_{a} \to \Lambda_{\sigma}^{\mu}e^{\sigma}_{a}$.

Effect on g : $g_{ab} = (\Lambda_{\sigma}^{\mu}e^{\sigma}_{a})\eta_{\mu\nu}(\Lambda_{\rho}^{\nu}e^{\rho}_{b}) = e^{\sigma}_{a}(\Lambda_{\sigma}^{\mu}\eta_{\mu\nu}\Lambda_{\rho}^{\nu})e^{\rho}_{b} = e^{\sigma}_{a}\eta_{\sigma\rho}e^{\rho}_{b} = g_{ab}$.

Therefore GR has Lorentz symmetry at any point in the space-time where $e^{\mu}_{a}$ is well defined. Shall I continue talking about vierbeins and allowing spinors to couple to space-time or shall I give you 3~6 years to go learn enough GR to understand what I just said?

23. ### zanketHumanValued Senior Member

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Even though it might be an apt example, noninertial acceleration, like that of a thrusting rocket, opens a big can of worms I don't care to get into.

My post #51 covers this. Note that a relative gravitational acceleration of two free test particles in different parts of a frame is the definition of the tidal force.