Find me a quote.
I don't think there is one either in the popular literature or his published articles.

Find me a quote.
I don't think there is one either in the popular literature or his published articles.
I am not really certain what you mean by this. A large part of Hawking's publications explicitly deal with black holes  I doubt very much that he would have wasted so much of his career if he didn't think black holes existed.
As for quotes, you can just use the HawkingPenrose singularity theorems, if you like :
http://arxiv.org/pdf/hepth/9409195v1.pdf
The basic idea is that once certain conditions hold, spacetime necessarily becomes geodesically incomplete, i.e. there will be black holes. Quote page 22 :
Thus there must be a region of spacetime from which it is not possible to escape to infinity. This region is said to be a black hole.
Thanks for the reference, but it's a long discourse. A search didn't reveal to me any declarative statements on existence.
I have a copy of Black Holes and Baby Universes. In this book he leaves black hole existence as a hypothetical. However, it is so well disguised, as such, that a casual reading would leave a different impression.
A old Penrose paper didn't help, even though it something of an introductory article.
Both authors jumped the issue of horizon formation but become involved in all the particulars after the fact.
I quote from your OP title "Hawking Claimed Black Holes Exist, Right?
"
I've done a bit of research. I'm fairly certain there is no single peer reviewed paper with a theory on black hole formation. You know, stuff with equations and logical support.
The ball was sort of dropped. It was found, classically, that collapse from of arbitrary distributions of matter would asymtotically converge to a spherically symmetrical solution. Then they got stuck and couldn't get the damned matter to form a black hole.
After a time, as this mornfull state persisted, Hawking found all kinds of fun and interesting fun stuff you could do to lift the mood. And now we can all play with these peculiar toys.
The lack of a theory, being shrouded in the ancient history of more than 50 years ago, has not destroyed the fun. The ball is still lost in high grass.
I'm sorry Markus, but a paper that talks about characteristics built upon an initial presumption is not a sufficiently scientific resolution.
You will find a very indepth discussion, with appropriate mathematics and theoretical support, in Misner/Thorne/Wheeler, as well as in Wald, Schutz, Weinberg, Novikov and Zeldovich. In fact, most standard textbooks on the subject of General Relativity will show in detail how the interior Schwarzschild metric will automatically yield a gravitational collapse once the TolmanOppenheimerVolkoff limit is exceeded. I am therefore not certain what it actually is you are looking for and don't seem to be able to find.
Hawking doesn't contest these purely classical results, rather, what he does is examine what happens if we start to account for quantum effects  which is something GR as a classical theory cannot do.
I am not sure where you are getting this from, but it is quite simply not true. For example, if the initial matter distribution has overall net angular momentum, then the resultant black hole after collapse is not spherically symmetric.It was found, classically, that collapse from of arbitrary distributions of matter would asymtotically converge to a spherically symmetrical solution.
I am not sure what you mean by this. However, don't forget that the Einstein equations do not possess a general solution, so any solution for a specific scenario requires us to fix boundary conditions and symmetries, in the form of an ansatz for the metric. Even numerical solutions require boundary conditions  this is just a mathematical feature of this type of tensor equation.I'm sorry Markus, but a paper that talks about characteristics built upon an initial presumption is not a sufficiently scientific resolution.
Useful Idiot: Hawking was recently castigated for saying black holes do not exist. Matt Strassler tried to defend him in a blog, but note the comment by Peter Woit. He points out that Hawking explicitly said "there are no black holes", and concurs with those who have suggested that this was a deliberate hook, a media soundbite, purposefully inserted to generate hype.
The thing is, we have clear evidence that there are some very small very massive very black things out there. So black holes exist, whatever Hawking says. You may have heard me advocating the "frozen star" black hole interpretation, which is mentioned in this article. That's still a black hole, and in fact is even more of a hole than the prevalent interpretation that features a pointsingularity in the middle.
I am not blaming you Farsight, but this recurring misconception really bugs me, because Hawking never implied that black holes as objects do not exist, he merely questions the existence of event horizons. That is not really the same thing. Here is the relevant excerpt as well as the link to the original paper in question :Hawking was recently castigated for saying black holes do not exist.
http://arxiv.org/pdf/1401.5761v1.pdfThe absence of event horizons mean that there are no black holes  in the sense of regimes
from which light can't escape to infinity. There are however apparent horizons which persist
for a period of time. This suggests that black holes should be redefned as metastable bound
states of the gravitational field.
This is a classic and sad example of shoddy popsci journalism, by means of taking sentence fragments out of context. The paper as a whole paints an entirely different picture; in fact he goes on to explicitly say that
...which is the metric applicable to the exterior of a black hole with nonvanishing angular momentum. The upshot is this : Hawking's hypothesis ( and that is all it is at the moment ) questions the commonly understood structure of black holes, but not their existence as astrophysical objects. I would urge everyone to read his ( very short ) paper linked above to better understand what he was really trying to say.The no hair theorems imply that in a gravitational collapse the space outside the event
horizon will approach the metric of a Kerr solution
The allegation is that it wasn't just shoddy journalism, but Hawking seeking to "go direct to the media" and hype a nonpeerreviewed paper via a deliberatelyplanted soundbite. Hawking has been accused of this sort of thing before, see this physicsworld article:
"This morning there was lots of talk about science on BBC Radio 4′s Today programme – but I think it left many British scientists cringing under their duvets.
Stephen Hawking was on the show explaining why Mtheory – an 11dimensional structure that underlies and unifies various string theories – is our best bet for understanding the origin of the universe.
Hawking explained that Mtheory allows the existence of a “multiverse” of different universes, each with different values of the physical constants. We exist in our universe not by the grace of God, according to Hawking, but simply because the physics in this particular universe is just right for stars, planets and humans to form.
There is just one tiny problem with all this – there is currently little experimental evidence to back up Mtheory. In other words, a leading scientist is making a sweeping public statement on the existence of God based on his faith in an unsubstantiated theory..."
Well, I can't speak for others, but when I read the paper the meaning is clear to me, and it isn't that black holes don't exist. Likewise his other publications  no where does he say that physics excludes the possibility of a god, he only states that it is his opinion that no god is needed to explain the universe we see around us. These are very different things.
I suppose people will always read exactly what they want to read. That seems to be human nature; I'm guilty of that too sometimes.
It's hard to know what to think about this sort of thing Markus.
I would however say that in my experience "science is a battle of ideas". There are individuals and interest groups out there trying to promote their hypothesis at the expense of the competition. If they are successful, it becomes "the mainstream". For example Hawking radiation is mainstream. Even though there's no actual evidence to support it, and the given explanation is problematic. One for another day, and another thread.
Yes, that's right, and by and large that is a healthy state of affairs.
Yes, one can probably consider it mainstream at this point, but I agree with you that it is somewhat problematic. Granted, the case for its existence is a good and strong one, yet as I have mentioned previously on several occasions, I have certain lingering doubts about QFT in general and QFT/CST ( in curved spacetime ) in particular. I might very well be wrong though, I don't know, it's just a gut feeling at this stage.For example Hawking radiation is mainstream.
Hawking radiation will be very difficult to experimentally detect; but it might be possible to search for another QFT/CST effect  Unruh radiation. It's not directly related to Hawking radiation, but its detection would at least lend some support to QFT/CST as a model.
Have you read The Strangest Man by Graham Farmelo? It's about Dirac. On page 53 it's talking about 1923. It says this: "At that time, Cunningham and Eddington were streets ahead of the majority of their Cambridge colleagues, who dismissed Einstein's work, ignored it, or denied its significance".Originally Posted by Markus Hanke
It's a whole subject in its own right. We should perhaps discuss it properly sometime.Originally Posted by Markus Hanke
IMHO there's a big issue concerning electromagnetic geometry and spatial curvature as opposed to spacetime curvature. Again it's something to discuss separately.Originally Posted by Markus Hanke
I'm not sure Markus. I think people confuse vacuum fluctuations with virtual particles. That's another one that deserves its own thread.Originally Posted by Markus Hanke
So much to talk about!
The form of the two equations of covariant electromagnetism is independent of the number of dimensions, and independent of the chosen coordinate system. At the same time, the metric enters into this through the Hodge dual as well as covariant derivatives, so I don't really see how there could possibly be any issue.
Of course you don't. Nor does the wider physics community. If they could, there wouldn't be any issue.
See this thread started by Essenar. It isn't a great example because he's only a layman. But he said space is warped in a gravitational field. It isn't. See the bottom of this Baez article where you can read this:
"Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial".
However if you search the internet on things like strong curvature regime, you will appreciate that many physicists are not aware of this distinction. And the $64,000 dollar question is this: "If space isn't curved in a gravitational field, when is it?
Yes, it is indeed crucial.
I disagree. Spatial curvature gives you tidal forces, whereas curvature along the timelike direction gives you what we ordinarily perceive as gravity. I think that is pretty basic, and I can't imagine any qualified physicist somehow not being aware of this.you will appreciate that many physicists are not aware of this distinction.
In the presence of sources of energymomentum, it is both time and space that is curved, i.e. you get both gravitational time dilation as well as tidal forces. It should also be noted that you can't really separate time and space in the context of GR.If space isn't curved in a gravitational field, when is it?
The answer doesn't elude me. Infinite gravitational time dilation at the event horizon means it takes forever for a quantum fluctuation to occur. So it never ever does.
Originally Posted by KJWLet's have a separate thread on this.Originally Posted by Markus Hanke
event horizons fluctuate
That is true only for an external observer, but not for someone who is in the same reference frame as the pairproduced particles. For him the fluctuation is real, and happens with a nonzero probability and in finite time, in disagreement to the external observer. That's not the answer, it's the very issue.Infinite gravitational time dilation at the event horizon means it takes forever for a quantum fluctuation to occur. So it never ever does.
It's the same issue for distinguishing between the original "frozen star" black hole interpretation and the contemporary "point singularity" interpretation. See the formation and growth of black holes on mathspages. The gedanken observer at the event horizon is said to see everything happening normally "in his frame". But IMHO he's like the gedanken observer who is travelling through space at the speed of light. Gravitational time dilation is infinite. He doesn't see anything. Ever.
So they say. But how can something fluctuate where gravitational time dilation is infinite?Originally Posted by pikepobedy
As pointed out, this is true only for an external observer  spacetime is smooth and regular at the event horizon, so nothing physical is infinite there. Remember what we have said before  everyone is right, but only in his own frame of reference !Gravitational time dilation is infinite. He doesn't see anything. Ever.
Because the infinity is only a coordinate artefact for external observers, it is not physical for the local reference frame where the fluctuation happens. It's "real" only for the external observer. That is very easy to show, and I believe I did that once or twice before, but I am happy to do it again if you like.So they say. But how can something fluctuate where gravitational time dilation is infinite?
Existence is a finicky thing.
To an observer outside the event horizon, we want to know if something is causally connected. This is the state of us humans on planet earth. So in terms of us as observers, existence, for us, is something that is observable. The same state of affairs for any observer in any state of motion outside the event horizon.
The issue of 'existence' depends upon its definition. Whether you are comfortable to say that something exists if it can interact in finite time or transfinite time. Transfinite elements are nothing new to relativity physics; infinitesimals and transfinites are the elements of general relativity. So they should not be discounted off hand.
The single mechanism to establish causal interaction with a black hole would be by Hawking radiation that results from gravitational gradient. But highly collapsed matter laying outside the event horizon would also obtain a similar gravitational gradient. Evidence of Hawking radiation is insufficient.
Evidence of closein stars about the galactic center is also insufficient for the same reason. Ablation of mater withing a region short of the even horizon would obtain the same measurements. The wackedout astronomers are befouled of reasoned thinking. Anyone can look at the crap they publish on arXives. They've transcended the boundaries of science into the occult. They dont give a **** so long as they have something tintilating to published such that fools will be impressed with their intelligence. Parasites.
Lastly is the matter of Hawking radiation. This is not tunneling. This involves particles transiting spatially over transfinite distances in finite time. This is not physics. This is Hawking's pretend world.
MODERATOR NOTE : I don't want to see this type of language on this forum. No swear words or obscenities please. Thank you.They dont give a fuck if they have something tintilating to publish.
That's what people generally say.Originally Posted by Markus Hanke
OK, let's talk about this. But first of all we need to talk about time. We need to get that right before we can move on to spacetime and gravity and black holes. Here's a thread: time travel is a fantasy. It's fairly straightforward. There isn't much to object to. But when you accept it you find yourself on a ratchet. Let's see how we get on.
To be honest, I fail to see the relevance of this to the matter at hand. I do not believe that time travel as it is commonly understood is physically possible, but this is a different topic. Also, for the purpose of this thread we will keep the discussion in the context of GR only.That's what people generally say.
OK, let's talk about this. But first of all we need to talk about time. We need to get that right before we can move on to spacetime and gravity and black holes. Here's a thread: time travel is a fantasy. It's fairly straightforward. There isn't much to object to. But when you accept it you find yourself on a ratchet. Let's see how we get on.
As for whether it is possible or not to fall through an event horizon, one must first understand what a singularity actually is in the context of GR. Simply put, a gravitational singularity is defined as a region of spacetime past which geodesics cannot be extended; this concept is called "geodesic incompleteness". To test whether or not the event horizon of a black hole fulfils this definition, the textbook approach is normally one of these :
1. Examine the invariants of the Riemann curvature tensor, to see whether they are well defined at the region in question
2. Choose different sets of coordinates and test how those behave at the region in question
Number (1) is the simplest and most elegant, because it is entirely independent of the choice of coordinates; the most straightforward of the ( several ) curvature invariants is the Kretschmann scalar, which, in Schwarzschild spacetime, evaluates to
If you plug the Schwarzschild radius into this, you will find that this scalar remains finite and well defined. The same holds true for all other invariants, such as the Euler scalar and the Chern scalar  they all remain regular at the event horizon, indicating that spacetime there is not in fact singular. This is further compounded by pursuing avenue (2) and explicitly choosing different coordinates  such as EddingtonFinkelstein, KruskalSzekeres or Novikov comoving coordinates. All of these are perfectly regular and smooth at the event horizon, once again demonstrating that time dilation is not infinite there.
Personally I would go along yet another route, and examine the geodesic structure of spacetime itself. Suppose we define a section of a freefall geodesic that is located entirely outside the event horizon; then we do the same for a section that is located entirely inside the event horizon. Finally, we examine whether it is possible to match and join these geodesic segments so that the resulting curve is everywhere smooth, continuous and differentiable. Without going into the maths, the answer is of course yes  hence the event horizon is not a region past which geodesics cannot be extended, so it is not a singularity, and hence gravitational time dilation is not infinite there. The event horizon is just that  an event horizon, i.e. a causality boundary.
Having said all that, we must nonetheless remember what we have stated earlier  no external observer will ever see anything reach the event horizon, or the horizon itself form for that matter. For him, that is physical fact, so the infinite time dilation is physically real for such an observer. However, if we consider another observer who freely falls into the black hole, this is no longer true  he finds that he reaches the event horizon in finite wristwatch time, crosses it, and meets whatever lies beyond. Again, this is physical fact for him, and the infinite coordinate time dilation has no meaning for him. Here is where we encounter one of the cornerstones of GR  all observers are right, but only in their own frames.
When it comes to Hawking radiation this is precisely the difficulty  both the external observer as well as the infalling observer crossing the horizon are correct in what they measure and determine, yet they disagree, so there seems to be a contradiction. So what is the resolution ? I think the first thing we have to realise here is that a black hole which radiates and evaporates over time CANNOT be a Schwarzschild black hole, which is by definition completely static  an evaporating black hole is of course not static, so analysing this situation in terms of the Schwarzschild metric is bound to fail. I am not surprised that we get a contradiction. Secondly, we must remember what QFT/CST teaches us  the number of particles in a region of curved spacetime is not well defined, and, more importantly, is an observerdependent quantity. An external observer far away and an infalling observer may disagree on the vacuum ground state, and hence on the number of particles to be found in a given region. That's a natural consequence of the theory.
I am sure there are more subtleties involved in QFT/CST that I am not aware of, but the above indicates already that our thinking in terms of Schwarzschild spacetime won't get us very far here. I'm also curious as to what KJW's insights into the above are...?
Me too.
I've read everything you've said above. And the thing is this Markus: that contradiction tells you that something is wrong. But you can't find it. Because it's implicit in your textbook approach. You have to go back to the beginning and play detective to find it. Please read the time travel essay and give some comment upon it, then accept the simple conclusion I offer, which is that clocks don't literally measure "the flow of time". You cannot open up a clock to see time flowing through it. After that we then move on to the next thing. I am confident that you will find the exercise most rewarding. And that you will understand why it is utterly relevant.
There's nothing alternative about it. It's all plainvanilla stuff, to do with how to spot a nonreal solution. But if you'd like to look at the details of the physics and tell us how the particle that fell into the black hole must have had a negative energy, I'm all ears.
I would formulate it differently  the contradiction tells us that we are approaching this issue in an incorrect way.that contradiction tells you that something is wrong.
By far the biggest problem I see is that treating an evaporating black hole as a Schwarzschild black hole is definitely wrong; this might be a good approximation in the first stages of its lifespan, but most certainly not for later stages. I suggest the full analysis has to be done using either VaidyaBonner spacetime, or Kinnersley spacetime; both of these are sufficiently different from the Schwarzschild solution that our naive comparison of external and internal observer is no longer valid. Furthermore, one would need to consider what happens to quantum fields in such spacetimes  a very nontrivial question, and I don't know if such an analysis has been done yet.
Maybe I am missing something, but the link itself seems to give the answer to this.But if you'd like to look at the details of the physics and tell us how the particle that fell into the black hole must have had a negative energy, I'm all ears.
There are no negativeenergy particles Markus. The "given" explanation doesn't stand up.
Definitely.Originally Posted by Markus Hanke
I beg to differ. IMHO they aren't getting to the heart of the problem. To do that you have to look afresh at plainvanilla curved spacetime. And before you do that you have to look at time. That's where it starts. Only then are we approaching the issue in the correct way. Note that two out of three authors of MTW do/did believe that time travel is physically possible. Like I said, it's all to do with recognising a nonreal solution.Originally Posted by Markus Hanke
Actually it does, because we are dealing with a curved spacetime, so energy is an observerdependent quantity; remember that the sum total of the energy originates from the gravitational field, which is by definition negative. To be perfectly honest I fail to see any issue at all, because energy is nowhere created from nothing  if an external observer sees a particle originate from a black hole, that black hole in its entirety has just lost energy, so whatever stays behind and drops into the event horizon is accounted for as "negative". That particle itself will observe the exact opposite, again because the "accounting" for this process is observerdependent. In both cases, the energy needed to create the pair in the first place comes from the gravitational field, so the black hole shrinks.
Btw, I think the thermal ( Hawking ) radiation is observable only by stationary external observers, i.e. by observers whose 4acceleration is not zero. A freely falling observer experiences zero 4acceleration, so they won't see any Unruh radiation field, and hence can't measure any Hawking radiation. This whole thing is highly observerdependent in the first place. I am really curious as to how the Unruh temperature law looks like in Vaidyalike spacetimes, but can't find any papers on the subject.
Yes they do. The issue arises because Schwarzschild spacetime is built on the very premises that the central object is static and stationary; obviously, a radiating body does not fulfil that criterium, so the Schwarzschild metric isn't the correct solution to describe it. Having said that, I am no expert on either the VaidyaBonnet nor the Kinnersley solution, so I don't know what exactly they have to say to the original question. I do know however that both of these account for the changes in mass of the BH, and the associated changes in geometry. These solutions are vastly more difficult to treat and visualise, because they contain offdiagonal terms in the metric.IMHO they aren't getting to the heart of the problem.
If that is their personal opinion, then I would disagree with them, but with the stipulation that my very disagreement is a personal opinion too. I don't think anyone can give a definitive answer as to whether time travel ( as we usually think of it ) is physically possible.Note that two out of three authors of MTW do/did believe that time travel is physically possible.
It isn't negative, Markus. It's positive. "The energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". That's on page 185 of the Doc30 Foundation of the General Theory of Relativity.Originally Posted by Markus Hanke
There's issues everywhere you turn. Gravitational field energy is positive but people say it's negative and then they talk about invariant mass regardless of the mass deficit. Yes, conservation of energy applies, but it applies to mass+Kinetic energy, and to massless photons too. People say a downward 511keV photon gains energy and is blueshifted, even though when you direct it into a black hole, the black hole mass only increases by 511keV.Originally Posted by Markus Hanke
The moot word is "if". Hawking radiation remains a conjecture. Let's say the particle is a photon. How does light escape a black hole? Put your gedanken hat on and imagine you're standing on the surface of a massive body shining a laser torch straight up. It doesn't curve round, it doesn't slow down, it doesn't fall down. Now make the body more massive. And repeat.Originally Posted by Markus Hanke
But there are no negativeenergy particles. Have you ever seen one? Or heard of any? I haven't.Originally Posted by Markus Hanke
If the energy comes from the gravitational field it comes from space. It comes from vacuum energy and the black hole is a spaceeater. It grows.Originally Posted by Markus Hanke
I agree with you about the freelyfalling observer being unable to measure any Hawking radiation. But I would take that a stage further. The bottom line is this: gravitational time dilation is real, and quantum fluctuations are not immune to it.Originally Posted by Markus Hanke
I am confident that there is a way to understand all this such that it is rocksolid simple with no contradictions. But again, you have to start with time, then move on to curved spacetime and take it one step at a time.Originally Posted by Markus Hanke
I'm confident that I can, from first principles, in a fashion that's in line with Einstein and the evidence, that nobody can counter. It all starts with opening up a clock and asking yourself what do I see?Originally Posted by Markus Hanke
Yes, Farsight, that is exactly what I can't see any issue with this. Suppose you are stationary very far from the black hole, and a particle passes you by that was just emitted from the black hole via the Hawking mechanism. You determine the energy to be positive, as you would with any other particle as well. Now, because the energy of the gravitational field is in no way different than any other type of energy ( see your link ), and pair production doesn't create energy ( it only converts it into another form ), the infalling particle that never reaches you is necessarily accounted for as negative.
Or to put it quite simply  the black hole emits a particle, and looses the precise amount of energy associated with that particle, because the energy needed to create that particle came from its own gravitational field. It works like any other emitter. It's a matter of "accounting", just like the difference between coordinate and proper measurements; that doesn't mean the infalling particle somehow has negative mass, it means only that globally energy is emitted, as determined by the external observer (!). Of course, the infalling particle itself disagrees, but then that is exactly what we expect.
Same as any other body with enough momentum. The Hawking mechanism takes place just outside the horizon boundary.How does light escape a black hole?
Not here on Earth, there aren't. From the point of view of an external observer ( not locally where the particle itself is though !! ) however, this is exactly what happens.But there are no negativeenergy particles.
Agreed.Hawking radiation remains a conjecture.
In the Schwarzschild metric, it is the constant parameter "M" that signifies the total massenergy of the entire spacetime. Hawking radiation will mean that M reduces over time ( which is why the Schwarzschild metric is not the correct metric to use here ), so the black hole would shrink.If the energy comes from the gravitational field it comes from space. It comes from vacuum energy and the black hole is a spaceeater. It grows
That is true, it is indeed real. It is just important to keep in mind the distinction between gravitationally dilated coordinate time ( which is observer and coordinate dependent ), and the effect of curvature on the length of world lines ( i.e. proper time ), which depends on neither observer nor coordinate system used. The coordinate time becomes infinitely dilated at the event horizon; world lines of particles are also effected, but they are not infinitely stretched. It is in fact possible to extend a world line smoothly and continuously through the event horizon.The bottom line is this: gravitational time dilation is real, and quantum fluctuations are not immune to it.
Remember what we said before  everyone is right, even if they disagree on things, and no one is "more right" than anyone else. It is GR's job to ensure that the proper global relations between such observers are in place. This is relatively straightforward in the classical case, but obviously not so much in the quantum world.
You see the same as you would if you cut open a ruler. I am not sure what you expect; clocks are not time. Rulers are not space. They are just instruments, and they are freely interchangeable. You can measure separation between events in spacetime with a ruler and get a result in meters, or you can measure it with a clock and get a result in seconds, or you can use both and get the speed of light in m/s. Either way, the physical separation never changes.It all starts with opening up a clock and asking yourself what do I see?
Markus, you've missed the important point: there are no negativeenergy particles. They don't exist! They are a figment of somebody's imagination. A nonreal solution!Originally Posted by Markus Hanke
It's a matter of physics! Show me a negative energy particle!Originally Posted by Markus Hanke
If a particle is emitted, energy is emitted, and the black holes mass reduces. But there still aren't any negative energy particles.Originally Posted by Markus Hanke
No it doesn't. An ascending body slows down then falls back down. Light doesn't do that. This is one of those crucial little things you have to think through to resolve those contradictions.Originally Posted by Markus Hanke
No it isn't. There are no negativeenergy particles, full stop.Originally Posted by Markus Hanke
If the pair production that is said to drive Hawking radiation occurs above the event horizon, both particles could fall into the hole. Energy has then been added to the black hole. And note that pair production creates electrons and positrons, not photons. And that virtual particles are "field quanta". They aren't shortlived real particles popping in and out of existence like magic. And virtual particles are not the same as vacuum fluctuations. It just gets worse and worse. The contrast with GR is marked.Originally Posted by Markus Hanke
Pause for thought there. World lines are abstract things in the static thing called spacetime. They do not exist in the space that particles move through.Originally Posted by Markus Hanke
The elephant is not in two places at once. There are no contradictions. There are no paradoxes. They aren't all right. Trust me on that Markus. I'll demonstrate it to you to your absolute satisfaction, just bear with me.Originally Posted by Markus Hanke
No you don't. You see something moving. It might be a pendulum. Or a quartz crystal. Or cogs. And if you could see them, the hyperfine spinflips which emit microwaves. There's always something moving inside a clock. And it isn't some river of time. A clock is not some cosmic gasmeter thing which literally measures the flow or passage of time. This is probably the most important thing you can appreciate when it comes to clearing up those blackhole general relativity contradictions. It all starts with this.Originally Posted by Markus Hanke
Sure. Because it's determined by the motion of light. You use it to define your second and your metre. A light year is a distance. But you could define your year from it.Originally Posted by Markus Hanke
I'm afraid you missed my points too ( which once again comes down to local vs global )  perhaps we should let this particular issue rest for the moment, because I must admit that I don't have a really good idea how else/better to explain my thoughts on this. Perhaps I can come back to it later on, if I can think of a good way to visualise it.
I am not sure what you mean by this. All freely falling objects trace out geodesics, that includes both massive objects as well as light. In the case of massive bodies these are timelike geodesics, for light they are null geodesics. The equations of motion are the same, though.No it doesn't. An ascending body slows down then falls back down. Light doesn't do that. This is one of those crucial little things you have to think through to resolve those contradictions.
Correct.World lines are abstract things in the static thing called spacetime.
World lines in spacetime correspond to a succession of points in space at a succession of instances in time. This is just a different perspective  consider a donut. You look at it sideways, it's just a solid piece of dough with chocolate on it. Look at it topdown, it's a torus with a hole in the middle. Same donut in both cases. Same universe in both cases.They do not exist in the space that particles move through.
No. It takes energy to produce the particles in the first place, which came from the BH's gravitational field. If both fall in, the net effect is exactly zero. No energy is ever created or destroyed anywhere.Energy has then been added to the black hole.
Hawking radiation is not GR, which is a purely classical theory. It is a prediction by QFT/CST.The contrast with GR is marked.
In both instances you see a lattice structure of atoms, no more and no less.No you don't. You see something moving. It might be a pendulum. Or a quartz crystal. Or cogs.
If an observer physically sees or measures something and reports back on it, then he is right. But I agree, there are no physical contradictions, ever. GR ensures that.There are no contradictions. There are no paradoxes. They aren't all right.
I think it is very interesting how different our outlooks on the universe are. You seem to be pursuing the search for some absolute "truth", whereas to me reality is an inherently subjective concept. To me, there is no problem in observers disagreeing without there being a contradiction; to me, everyone has their own reality, the search is not for the truth, but rather for concepts on which everyone can agree. Yes, these concepts are abstractions, but then that makes perfect sense to me since there isn't anything absolute that is somehow more physical than something else.
You cut open a clock, and find cogs and mechanisms; I cut open a clock and find only atoms arranged in some way.
You cut open a ruler, and find solid wood/metal/plastic; I cut open a ruler and once again find only atoms arranged in some way.
The arrangements differ, but the fundamental particles they are made up of do not.
Likewise, neither clocks nor rulers are space or time to me; they are just measuring devices made up of fundamental particles, and there is no fundamental difference between them.
Just as much as GR is a mathematical model to represent the universe, so is our very own consciousness and mind, too  you perceive and model the world very differently than I do. To give another slightly less trivial example  I am a synesthetic, and amongst other things I associate colors with words and certain symbols. For instance, the integral sign in mathematics feels dark blue to me, and a very specific tone of dark blue at that. For you, that doesn't make any sense  in your description of reality, this color would presumably be entirely absent so far as the integral sign is concerned, whereas for me it is a natural part of it. Clearly there is a contradiction  for me all integrals are blue, whereas you don't have that concept at all. Am I any more right than you are ? No, we are both right, but each of us only in our own frames of reference. There is no contradiction.
Now imagine what kind of gravity model a bat would come up with. Or a dolphin. Or an elephant. Or a jellyfish. They will all agree that stones fall down, but they might come up with entirely different models as to why that is so, according to how they perceive the universe.
Sorry, this isn't really on topic, but I find it fascinating
It's interesting all right. Leaving aside the Hawking radiation for a moment, yes we do have very different outlooks. Yes, I search for objective truth. I don't accept that reality is subjective. It might seem like it is, but there are no contradictions, and there are no paradoxes. Yes, two observers can see things different, but there is a deeper reality that they can both understand. I don't have any issue is searching for concepts on which everyone can agree, but would take it further and say we do physics because we are curious, We seek to understand. We seek the truth, not just concepts.
As for synaesthesia, I know I see blue. But I know that it's a quale, in my head, and what's really there is some light with some frequency. Some regular cyclical motion. It's a strange thing is motion. Remember me saying you can perform repeated Compton scattering to entirely convert an electromagnetic wave into the motion of electrons? Or you could perform pair production with that photon to convert it into an electron? (And a positron of course, but forget that). Because the point is this: the electron is made of the thing that became the motion of electrons. The electron isn't really fundamental because you can make it, and it's made of kinetic energy. Unlike you I don't see energy as a mere property of a thing, I see it as the fundamental thing from which other things are made. I cut open a clock, I see motion. You cut open a clock, you see particles. But I cut open a particle, and I see motion. The mass of a body is a measure of its energycontent and all that.
The dolphin and the elephant might have different models. But if they're smart they'll know that if those models contradict one another there's something wrong somewhere, and they need to get their heads together.
Let's come back to Hawking radiation. I'd like to focus on what I said was a crucial point:
Those geodesics are abstract mathematical things. Look at the Wikipedia article and note that it says a freely moving or falling particle always moves along a geodesic. But a geodesic is in static spacetime. There is no moving along it. Later on the article refers to the equations of motion. That motion is through space. Not spacetime. The particle doesn't really trace out a geodesic. Instead the geodesic maps its motion. And the map is not the territory, de dah de dah.Originally Posted by Markus Hanke
Let's try to focus on the motion through space. You throw a brick straight up: it slows down then it falls back down. Then you point your laser straight up and turn it on briefly to emit one photon. What happens to that photon? Does it curve round? No. Does it slow down? No. Does it fall back down? No. Now make the planet more massive, and iterate. There is no point where the force of gravity curves the photon round or slows it down or makes it fall back down. So when you take it to the limit and iterate all the way to a black hole, why can't the light get out?
The answer Markus, is most revealing.
It is a beginning lesson for those who study GR to generate functions that continuously map the real numbers to a geodesic. One can also consider a continuous map from the proper time of an object to the geodesic.
So it is essentially false to say one cannot move along a geodesic.
As long as one graphs a physical system, one could mistakenly say that the physical system is static because there exists a graph that presents it (or part of it) statically. That would be a gross example of mistaking the map for the territory. It would be a worse mistake to use this mistake to reject a model because it can be used to create graphs.
In order to do this properly, one has to create a system of coordinates; this requires a proper understanding of spacetime.Let's try to focus on the motion through space.
The important point is that spacetime models space at all times, so there's no motion through it. IMHO it's important to bear this in mind. If you find yourself talking about light curving because it moves through the curved spacetime around the Sun, your description is flawed. That might not sound like a big deal, but I'm confident it's the key to resolving those GR contradictions Markus was referring to.Originally Posted by KJW
An inference from what? The distant observer hasn't observed any Hawking radiation yet either. The thing is KJW, is that once you resolve those GR contradictions, you're left with big problems for Hawking radiation. That might sound novel, but take a look at Sean Carroll's blog. He's talking about the early universe rather than a black hole, but note this: "in a new paper we’ve come to a surprising conclusion: cosmologists have been getting it wrong for decades now. In an expanding universe that has nothing in it but vacuum energy, there simply aren’t any quantum fluctuations at all".Originally Posted by KJW
Spacetime is a fourdimensional manifold. While timelike directions are distinguished from spacelike directions, the timelike directions are not unique. What one observer regards as a purely temporal direction may be a combination of a temporal direction and a spatial direction to another observer. In other words, the separate notions of space and time must be unified to a single notion (spacetime) so that all inertial observers are equivalent regardless of their relative velocities.
My reply was in response to your argument that there are no negative mass particles (falling into the blackhole). It was not an argument in favour of Hawking radiation, so whether or not Hawking radiation is observed is irrelevant to my reply which is merely that the absence of negative mass particles is not an obstacle to Hawking radiation
I already pointed out a problem I had with Hawking radiation. But one can't so readily dismiss the mathematics that led to the hypotheses of Unruh radiation and Hawking radiation. Also, the quantum nature of Unruh radiation and Hawking radiation prevents one from only considering GR which is a purely classical theory.
PhysBang: it isn't a nonsequitur. There are parallels between black hole physics and the physics of the early universe.
I'm sure we've all read Minkowski's Space and Time, and we're all familiar with Minkowski spacetime where we draw worldliness and lightcones. But the fact remains that those observers move through space rather than spacetime, and it's their different states of motion that affects their measurements of space and time  which they measured using the motion of light. And the only actual directions are spatial directions. It doesn't matter how you move through space, you cannot "move in a different time direction". You cannot move such that you end up in the middle of next week, or last week. Time travel is a fantasy.Originally Posted by KJW
Noted.Originally Posted by KJW
It's not dismissing the mathematics, it's flagging up the issues.Originally Posted by KJW
True. But GR is one of the best tested theories we have. Initial confirmation came in 1919, only 3 years in and there was a war on. Meanwhile Unruh radiation and Hawking radiation remain hypothetical after 40 years.Originally Posted by KJW
Farsight, there were too many points made in the last couple of posts to address individually, so I'd just like to remark a couple of things :
1. You are correct, spacetime and everything in it are static. It models everything everywhere at all times; this is fully understood, and is one of the great strength of GR, not a shortcoming of some kind. Your posts read as if you are under the impression that we are somehow confused about this, but I can assure you that isn't the case. Your point about the Wiki article is well made though, because "moving along a geodesic in spacetime" isn't technically correct. The geodesic itself is the test particle, nothing moves here.
2. Hawking radiation is not a GR prediction, nor can it be accurately modelled by GR, since it is a purely classical theory. I believe I have pointed that out on several occasions. Hawking radiation is an attempt to apply concepts of quantum field theory to curved spacetimes; a highly nontrivial undertaking, and not suitable to point out perceived "issues" with GR, because it goes far beyond the confines of the classical model.
3. I agree with you that the notion of time travel will likely remain in the domain of science fiction. I do, however, retain enough of an open mind on the issue to understand that I may well be wrong on this in the end.
4. There are no physical contradictions anywhere in nature. GR as a model is internally selfconsistent, and does not produce physical paradoxes. If it did, it would be useless as a predictive model. The trick is to understand that local observers disagreeing on certain things while agreeing on others does not constitute a paradox, because GR explains to us their global relation in a curved spacetime. For example, an external observer determining infinite time dilation at the event horizon, and a freely falling observer crossing that horizon without noticing anything special is not a contradiction or a paradox; it's a natural consequence of the geometry of curved spacetime. This global geometry ( as opposed to coordinate measurements performed on it ) is selfconsistent and free of any contradictions everywhere outside the singularity.
5. I agree that both Unruh radiation and Hawking radiation have not been experimentally verified; they are hypothetical concepts. But then so is all of QFT in curved spacetimes. If it turns out that there is an actual, physical contradiction between GR and QFT/CST that cannot be reconciled, then my bet would currently be on QFT/CST having an issue; it seems to me that GR is too well tested and verified to have any fatal flaws.
6. I don't think it is possible to formulate covariant laws of physics ( i.e. laws that take the same form for all observers ) without using the concept of spacetime.
There are parallels. Google on universe "inside out black hole" and you see various articles. And see the time travel thread where EinsteinRosen bridges came up: "...the collapse reaches a bounce and forms a regular EinsteinRosen bridge (wormhole) with a new, growing universe on the other side of the event horizon"...
I don't favour point singularities or wormholes or white holes myself. I don't think there's a new growing universe on the other side of the event horizon. But I do acknowledge that there are parallels between black hole physics and the physics of the early universe.
This would only be true in EinsteinCartan gravity, so it is just a hypothesis.
There are also important differences. The vacuum region around black holes is Ricci flat, but Weyl curvature is nonvanishing. In the early universe the opposite is true  the Ricci tensor would be nonzero, but the contributions by the Weyl tensor would be negligible or absent. The geometry external to gravitational singularities and cosmological singularities just isn't the same, despite the superficial similarities.But I do acknowledge that there are parallels between black hole physics and the physics of the early universe.
Very informative comments. We have theoretical predictions and experiments trying to compare the theoretical predictions with actual measurements of the natural phenomena predicted. Hawking radiation: Visiting a Laboratory frame near the event horizon isn't going to happen so 'smart' physicists came up with an 'analog' experiment which can be conducted in our local proper lab frame here on the surface of the earth. This is the experiment William Unruh was involved with to detect and measure a classical analogue of Hawking radiation.
Classical aspects of Hawking radiation verified in analogue gravity experiment [+ links to the teams papers]
Hydrodynamic simulation of black hole evaporation process
Quantum Gravity Laboratory
William G. Unruh
Has Hawking radiation been measured?
[1401.6612] Has Hawking radiation been measured? [26 January 2014]
Trippy stuff.
Last edited by brucep; 05172014 at 06:30 PM.
It is. Despite all previous comments I wouldn't really want to put any money on the existence of Hawking radiation either, though. Hawking's calculations and arguments are all sound, but what I am not so sure about is their very foundation, i.e. QFT in curved spacetimes. But this is just my personal opinion, which I am not able to back up. It's a gut feeling more than anything.Trippy stuff.
It might be just a gut feeling now Markus, but I think it will be more than that at a future date.
They aren't the same, hence my reference to "inside out". But there are parallels. See Hawking on the Big Bang and Black Holes. Hawking even refers to quantum fluctuations re black holes and the early universe.Originally Posted by Markus Hanke
You aren't, but google on move through spacetime. Many people are. Follow some of the links, you see Brian Cox, Sean Carroll, and when you dig further, Kip Thorne.Originally Posted by Markus Hanke
Thanks.Originally Posted by Markus Hanke
Maybe there's been some misunderstand there. Hawking radiation doesn't point out issues with GR. It's the other way around.Originally Posted by Markus Hanke
You aren't.Originally Posted by Markus Hanke
GR doesn't produce paradoxes, but misunderstanding does. Check out the elephant and the black hole. Like I said previously, if there's a contradiction, if there's a paradox, something is wrong somewhere, and you have to go back over everything and play detective looking for it.Originally Posted by Markus Hanke
Agreed. Especially since there is one mother of a fatal flaw in QFT/CST.Originally Posted by Markus Hanke
I don't think it's an issue myself. If a lightbeam moves from A to B through space you talk about distance. If the lightbeam moves back and forth inside some clock you talk about time. Then you talk about spacetime, and the model works.Originally Posted by Markus Hanke
I think people are just careless and don't always use the correct terminology. I often say "the flow of time", or "time flies today", or "time goes slow"; but these are just artefacts of language.
This might well be true, but then again, since we don't have a black hole close by, it's hard to say for sure. I think there is still much work to be done in the whole area.Hawking radiation doesn't point out issues with GR. It's the other way around.
That's true. I suppose the white elephant in the room is not so much Hawking radiation, but the "vacuum catastrophe" ( which is not directly related to GR as such ); something, somewhere, isn't right.Like I said previously, if there's a contradiction, if there's a paradox, something is wrong somewhere, and you have to go back over everything and play detective looking for it.
Me too. But I think that this is the source of those contradictions we were talking about.Originally Posted by Markus Hanke
I think it's already been done myself.Originally Posted by Markus Hanke
There are other things that aren't right. Once they click they seem so simple and obvious you wonder why anybody could have ever got them wrong.Originally Posted by Markus Hanke
For example, take gravitational blueshift. A descending photon is blueshifted, right? It increases its frequency, right? And E=hf so the energy increases too, right? Wrong. Gravity is not a force in the Newtonian sense. You add energy to a brick when you lift it up, gravity doesn't add energy when the brick falls down. It merely converts potential energy into kinetic energy. Drop a 1kg brick into a black hole. The black hole mass increases by 1kg. Conservation of energy applies. It's the same for a 511keV photon: the black hole mass increases by 511keV/c². The photon isn't blueshifted. It doesn't increase its frequency. It doesn't increase its energy. It only appears to do so because when you descend, you change. You and your clocks are subject to gravitational time dilation, and you are subject to the mass deficit.
Another one of course is why doesn't the light get out of a black hole? When you can answer this one, you can resolve those contradictions. Totally.
How so ? QFTs in curved spacetimes is not a finished product, but an area of active and ongoing research.
Remember the donut. Look at it sideways, and you see a solid piece of dough. Now change your perspective, and look topdown : the central hole appears. Was the hole created, or the donut changed ? Did you change yourself ? No  all that has changed is the relationship between you and the donut. I think this is pretty well understood, and relativity works much the same way.The photon isn't blueshifted. It doesn't increase its frequency. It doesn't increase its energy. It only appears to do so because when you descend, you change.
General relativity "works". The gravitational time dilation means fluctuations take forever and thus never happen. That's it. End of story.Originally Posted by Markus Hank
It doesn't, Markus. I must insist on this. Remember the mass deficit. That descending 511keV photon doesn't gain any energy at all. The black hole mass increases by 511keV/c², not a zillion megatonnes. You know this. You know about conservation of energy. And you know about that mass deficit. So you know that when you go lower and measure photon blueshift, the photon appears to have gained energy. But it hasn't. Instead you've lost it. You and your clocks are now going slower. Did you change? Yes.Originally Posted by Markus Hanke
I was referring to QFT/CST in general rather than to Hawking radiation in particular. Quantum fields could be anywhere in a curved spacetime, not just smack bang on an event horizon. Also, as pointed out earlier, you need to distinguish between coordinate measurements of some external observer, and proper measurements within any given frame; in a curved spacetime, these generally don't coincide.
Btw, even for an external observer the time dilation becomes infinite only exactly on the horizon, and nothing can "escape" from there anyway; any fluctuations slightly above the horizon would still happen, even for a far away observer.
The other complication is that due to the HUP even the horizon itself is not precisely localisable.
Isn't this pretty much what I was trying to point out  you are only looking at the donut from a different perspective, the donut itself hasn't changed. Only the relationship to the observer has.So you know that when you go lower and measure photon blueshift, the photon appears to have gained energy. But it hasn't.
I am not certain that we mean the same thing by "mass deficit" in the context of GR. What I mean by this term is the phenomenon that when particulates of matter clump together to form a larger mass, some of their total energy will be lost through gravitational radiation in the process. There is an upper limit to how much "deficit" one can obtain from this, and it can be explicitly calculated :
Phys. Rev. D 13, 2736 (1976)  Gravitational mass defect in general relativity
Reading through your comments, it doesn't seem that this is what you are referring to. Can you clarify ?
Groan. I just lost my post. Start again:
That's what they say. I guess what I'm saying is when you focus on those contradictions and resolve some of those GR "non real solution" issues, you come to appreciate that there's more wrong with Hawking radiation than you first thought. Let's come back to it after we've talked about those contradictions.Originally Posted by Markus Hanke
No. There is no donut. There's you and a photon. When you measure some variance either it changed or you changed. And it didn't. So you did. Or there's you and an electron. When you don't measure some variance either neither of you changed or you both did. Only you know that you did, so you know that it did.Originally Posted by Markus Hanke
Yes, that's it. The simple example is the Earth and a brick. Then you say the Earth is so much bigger than the brick that you ignore the motion of the Earth. The brick falls down at 11km/s, its kinetic energy is radiated away, and its mass is reduced.Originally Posted by Markus Hanke
I can't see that paper, but I agree there's a limit. This has an important implication. It's a gamechanger.Originally Posted by Markus Hanke
I hope the above is clear enough. Now drop a 511keV electron into a black hole. There is a limit to how much of its massenergy can be converted into kinetic energy. See Freidwardt Winterberg's firewall paper: http://www.znaturforsch.com/aa/v56a/56a0889.pdf . I wouldn't say I agree with all of it. But I agree with the sense of it. We have gammaraybursters for a reason.Originally Posted by Markus Hanke
The difference between coordinate and proper measurements at different places in a gravitational field is not a contradiction; it's just a natural consequence of the presence of curvature.
I must reiterate again that Hawking radiation is not something that is predicted by GR at all  it is an attempt to incorporate quantum effects into classical gravitation.
The donut was just an example to illustrate a concept.No. There is no donut.
I am not sure if I follow you. At the point of measurement both the observer and the photon are in the same frame of reference, i.e. at the same place, so they are both subjected to the same amount of gravitational time dilation wrt a faraway reference point. That seems trivial to me.When you don't measure some variance either neither of you changed or you both did.
Actually, it's not quite that simple. Consistently defining the notion of "kinetic energy" isn't possible in curved spacetimes; you can define the total energy at infinity, but you can't consistently split it into a kinetic and a potential part, at least not in general spacetimes, so saying that "kinetic energy is radiated away" is misleading. It is better to say that after Earth and brick have collided and become one body, the total mass of the new body is slight less than the sum Earth+brick.The brick falls down at 11km/s, its kinetic energy is radiated away, and its mass is reduced.
The contradictions involve things like the elephant that goes to the end of time and back and is in two places at once.Originally Posted by Markus Hanke
No probs.Originally Posted by Markus Hanke
You know how the theory of relativity is really the theory of invariance? Well, sometimes things appear to be invariant because of a "covariance". You change along with your ruler and the thing you're measuring. So it looks like something hasn't changed. Even though it has. And the inverse is true. Sometimes something looks like its changed when it hasn't, and instead you have. We end up with people talking about photon blueshift and electron invariant mass. When actually the descending photon didn't gain any energy but the electron did lose mass.Originally Posted by Markus Hanke
You can say that, but don't forget p=mv and KE=½mv². Momentum is shared equally between the Earth and the brick, but the brick has the lion's share of the kinetic energy. The Earth's motion towards the brick is not detectable. The brick's 11km/s is. So we focus on the brick. The rest mass of the brick in free space is greater than the mass of the selfsame brick sitting cold and motionless on the surface of the Earth. The difference amounts to 11km/s worth of kinetic energy. The kinetic energy of the falling brick came from the brick. The kinetic energy of a falling electron comes from that electron. It started off with 511keV. You cannot keep taking energy out of it without consequence. Hence Winterberg's firewall.Originally Posted by Markus Hanke
The "Susskind Elephant" is once again an attempt to apply quantum physics to curved spacetimes; just like Hawking radiation on its own, it demonstrates the difficulties in unifying these two disciplines. It does not demonstrate a contradiction in classical GR as a model, if that is what you meant.
Yes, that was exactly my point. It's just a change in observer relations, not in the physics, so there is no physical contradiction. That is also what I was trying to demonstrate with the donut  nothing changes in the physics of that deliciously sweet object, the central hole emerges only through a change in perspective. There are no real contradictions so long as we stay in the purely classical model of GR.Well, sometimes things appear to be invariant because of a "covariance".
I don't think it demonstates a problem in GR at all. Instead I think it demonstrates a massive problem in the prevalent understanding of black holes.Originally Posted by Markus Hanke
I agree. And then some.Originally Posted by Markus Hanke
I disagree. There isn't really an issue of "understanding" in the context of GR; you just apply the relevant maths and see what happens. The problem is that the Schwarzschild metric is not the appropriate maths to use in this scenario, because if you allow anything to fall into a black hole, it ceases to be Schwarzschild, pretty much be definition.
You need to remember what the exterior Schwarzschild metric is based on  a static, stationary, spherically symmetric metric without any charge or angular momentum. If you send an elephant hurtling into your black hole, the whole setup is no longer stationary and spherically symmetric, so the Schwarzschild solution is not the right one to use.
The problems comes when "what happens" can't actually happen. It's that difference between mathematically valid and physically valid, because of those boundary conditions. We'll get on to that once we've talked through that speed of light and then kicked gravity around. I promise you'll say ooooh wince when you see what I mean.
We all know how a falling brick falls faster and faster and faster. We all know how the ice skater spins faster when she pulls her arms in. We tend to think of a black hole in similar terms. We shouldn't. Think on this:Originally Posted by Markus Hanke
You know how I've been pushing you to tell me why the light doesn't get out? You're standing on a massive body shining your laser straight up. The light doesn't curve round, it doesn't fall down, and it doesn't slow down. Instead it speeds up.
I already know what you mean, and I do wish things were so simple in curved spacetimes  but they aren't. Time doesn't "stop" locally at the event horizon just because a distant observer determines that to be so using his equally distant method of assigning labels to events.
"Faster" as measured by whom ?We all know how a falling brick falls faster and faster and faster.
Because below the event horizon the radial coordinate becomes timelike in character, so nothing can go back out simply because nothing can move into the past. That's the whole point in having an event horizon  it's a causality boundary.You know how I've been pushing you to tell me why the light doesn't get out?
Lights are null geodesics, which, in the presence of massive bodies, are very much different in geometry than they would be without that body. Remember how you agreed with me that the concept of "spacetime" is a good model  this scenario is an excellent demonstration of that fact.The light doesn't curve round, it doesn't fall down, and it doesn't slow down. Instead it speeds up.
You've read the formation and growth of black holes, and you're aware of the two interpretations of GR. I think one of them is right and one of them is wrong. But not the same one as Wheeler. Or Kevin Brown. Or you. Or everybody else. Here's an excerpt:Originally Posted by Markus Hanke
"According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence".
The guy watching it fall down. He clocks it accelerating at 9.8m/s².Originally Posted by Markus Hanke
Only it isn't. The black hole still causes things to fall down. And your answer isn't convincing. It's a maths answer, and we want a physics answer to make sure we aren't dealing with a nonreal solution. And besides, we already know that things can't move into the past because they don't literally move into the future. You're standing on the surface of a gedanken body shining your laser torch straight up. The light doesn't curve round, it doesn't fall down, and it doesn't slow down. Instead it speeds up. I wave my magic wand and make the body smaller and more massive. The light still doesn't curve round, it still doesn't fall down, and it still doesn't slow down. Then we repeat ad infinitum until we find the light doesn't get out. Why not? Because the radial coordinate becomes timelike doesn't satisfy.Originally Posted by Markus Hanke
No problem. But remember that spacetime is static, and that the world line is an abstract thing in the model that represents motion through space. So when Wikipedia says "This last equation signifies that the particle is moving along a timelike geodesic; massless particles like the photon instead follow null geodesics" it's missing a trick.Originally Posted by Markus Hanke
Yes. The model works.Originally Posted by Markus Hanke
IMHO it works as far as the event horizon. Then that's it. There's nothing more to be said.Originally Posted by Markus Hanke
The problem with this is that it is a naïve interpretation of the Schwarzschild metric. The event horizon is the envelope of a family of lightcones. Thus, objects that are stationary at the event horizon are moving at the speed of light. Thus, a clock is "frozen" at the event horizon in precisely the same way that a clock moving at the speed of light is "frozen".
A worldline represents the set of events in spacetime at which a pointlike object exists.
You see, this is where we think differently, because in my mind there is no contradiction between the two, so the question of "right" or "wrong" never arises. They are both right, but only in their respective frames.
The distant observer sees the object gain speed for a while, but as the horizon is approached he will see it slow down.The guy watching it fall down.
No, it's very physical. Outside the horizon, the centre of the black hole is below you. Inside the horizon, it is in your future. These are physically very distinct scenarios.It's a maths answer
It represents more than that  it represents the entire history of the test particle, past present and future.and that the world line is an abstract thing in the model that represents motion through space
Both: no issue re the worldline.
Yes. This is the nub of it. This gets to the heart of the matter.Originally Posted by KJW
No. It can't fall through because it can't move faster than light.Originally Posted by Markus Hanke
Exactly. And it's a light clock.Originally Posted by KJW
I hope you will see that one is right and one is wrong.Originally Posted by Markus Hanke
That can't be true. Falling bodies fall faster and faster, not slower and slower. You can never see a falling body slow down. So you must see something else.Originally Posted by Markus Hanke
I will try to show you that the latter is not physical at all.Originally Posted by Markus Hanke
I mentioned already that the r and t coordinates change character ( and sign ) at the event horizon, so obviously the geometry of the interior region is such that you cannot just naively extend the same formulas for the exterior region to an infalling frame. The above conclusion is one that a distant observer somewhere outside the event horizon would reach, and for him that makes sense, because he never sees anything actually entering that region. However, it is not a valid conclusion for a freefall frame, nor is it a valid conclusion for an observer actually located behind the horizon, for whom there are no longer any stationary shells.
As I tried to point out on many occasions, there is no physical contradiction between coordinate measurements and proper measurements, so it is not a case of one being "wrong" and one being "right". They are both valid descriptions, but from different angles. I recall you have already agreed that GR is a fully covariant model, so no system of coordinates (=observer ) can be any more "right" than another one. In terms of standard long/lat coordinates, the North Pole is a coordinate singularity, yet many an intrepid explorer has walked across it quite comfortably !I hope you will see that one is right and one is wrong.
It gains coordinate speed initially, but the ratio dr/dt obviously varies along the infall path; at a certain "turnaround" point no further increase happens, and as the object keeps approaching the horizon, the distant observer will measure it to become slower and slower; at the event horizon, the coordinate speed would be exactly zero. Look at this animation :That can't be true. Falling bodies fall faster and faster, not slower and slower.
HubbleSite: Black Holes: Gravity's Relentless Pull interactive: Encyclopedia
Notice how the freely falling clock first gains coordinate speed, then stagnates, then starts to slow down ( all in terms of coordinate speed ). If you wish we can put some maths around this, to make it clearer.
The fundamental issue with this is that all we have to tell us about a particle's infall trajectory below the event horizon are the mathematics of the Schwarzschild geometry. There is no empirical data, nor will there ever be, so there isn't any way for you to show that these mathematics are unphysical. You can certainly speculate on this, and I have already conceded that in the absence of a model of quantum gravity the exterior metric might not be a good model for the interior region, but that is far cry from being able to just declare proper measurements in a freely falling frame to be unphysical.I will try to show you that the latter is not physical at all.
There's your contradiction again Markus. Let's come back to it.Originally Posted by Markus Hanke
This is no North Pole! I can see you walk across that North Pole!Originally Posted by Markus Hanke
I liked that animation. But I'd say there's a important distinction between the clock going slower and slower and the falling speed going slower and slower.Originally Posted by Markus Hanke
Not yet. This is where Winterberg's firewall comes in.Originally Posted by Markus Hanke
Noted. I need to say something about gravity before we proceed with this. Time for that new thread.Originally Posted by Markus Hanke
That's precisely my point. The long/lat coordinate system is singular at the north and south poles, yet you can walk across it without any issue. The same is true for the event horizon of a black hole  Schwarzschild coordinates become singular there ( hence all quantities derived from those coordinates  such as time dilation  diverge ), yet you can fall through it no problem.
There is no contradiction.
Yes. The former is a coordinate measurement, the latter a proper measurement. Again, there is no contradiction in this  it is just a different way to label the same events.But I'd say there's a important distinction between the clock going slower and slower and the falling speed going slower and slower.
You missed the obvious point. I'm the distant observer. I can see you cross the North Pole. But I can't see you cross the event horizon. They are very different. You might think you can see yourself cross the event horizon. But you started falling a billion years ago, and here's the $64,000 dollar question: have you seen yourself cross it yet? The answer is no. And it's always no.Originally Posted by Markus Hanke
There is a horrible problem here Markus. Horrible. One that makes all talk of crossing the horizon rather academic. Remember what I said in the gravity thread: in essence the reducing speed of light is transformed into the downward motion of the electron. If you drop a brick at elevation A, its falling speed at the lower elevation B relates to the difference in the coordinate speed of light at the two locations. And it's falling into a black hole. Think about it.Originally Posted by Markus Hanke
Farsight, I think you know very well that I was making an analogy to explain the nature of coordinate singularities; I was doing this to avoid the rather more complicated mathematics in (3+1)dimensional spacetime, which I know are not your strength.I'm the distant observer. I can see you cross the North Pole.
Of course not, because the infinite time dilation is real for you as an external observer. The North Pole singularity is also real for the captain of a boat or plane starting off somewhere else, because no matter what course he plots to go over it, the trajectory he determines in terms of long/lat coordinates will never be smooth and continuous there. However, in both cases, when you physically go there, you will find the surface of the earth to be smooth and regular, just as you find spacetime to be smooth and regular at the horizon. The issue is one of coordinate mapping, not physical features.But I can't see you cross the event horizon.
This is true, but it is true only for an external observer watching the brick fall. It is not true for the brick in his own frame. This is why I keep telling you that everyone is right, but only in their own frames; this is just a different way to state the principle of covariance, in that you are free to pick your frame of reference without affecting the physics, just as you are free to measure your commute to work in any which way you like without affecting the commute itself. You need to free your mind of the idea that there is anything special or inherently privileged about the rest frame of a distant observer  there isn't. What he determines is valid enough for him, but not necessarily for anyone else; this is why Schwarzschild coordinates are also called bookkeeper coordinates; it's just a convenient device to assign labels to events. And the same is true for any other observer  for example, the infalling observer cannot decide to just ignore the fact that the distant observer never sees him cross the horizon; he is not any more privileged than that external observer. Infinite time dilation from a faraway point of view is just as "real" as finite proper time from a rain frame point of view. The underlying reality here is the events that make up spacetime, not the way we label them; and what we find when we investigate the way these events are related to one another is that it is smooth, continuous, and quite regular even at the horizon.If you drop a brick at elevation A, its falling speed at the lower elevation B relates to the difference in the coordinate speed of light at the two locations.
Now mind you, all of this is based on a purely classical model of a classical spacetime; it might very well be the case that this picture changes radically once we start to consider the quantum structure of the vacuum itself. This remains to be seen  the above is just classical GR.
One key difference is that no matter what coordinates you use, the local temporal coordinates will compare in transfinite ratio. The brick will not breach the event horizon before the entire universe, bricks, atoms and protons, are ripped apart by ever increasing dark energy in finite time.
No. From the point of view of a faraway external observer ( Schwarzschild bookkeeper coordinates ), the brick will never reach the event horizon, never mind fall through it, as you say. This is real, but only for that faraway observer. On the other hand, for the brick itself in his freefall frame it takesOne key difference is that no matter what coordinates you use, the local temporal coordinates will compare in transfinite ratio.
to fall from rest very far away into the centre of the black hole ( GullstrandPainleve coordinates ). This time is finite and well defined, and also real, but only in the frame of falling brick. They are both right, but only in their own frames; the important bit to realise is that what becomes singular at the horizon are the Schwarzschild coordinates, not spacetime. This singularity can be removed by a simple coordinate transformation.
As for seeing the end of the universe  that obviously can't be the case, though it seems to be a persistent misconception. What you see at the horizon simply depends what light does before it gets to you there, and there isn't any way for light from distant future events to reach you, because even at the event horizon such events remain outside your light cone, so there is no causal connection. This is immediately clear if you draw your light cone on a KruskalSzekeres diagram. See here also for further info on this  it's a question that comes up again and again :
general relativity  Does someone falling into a black hole see the end of the universe?  Physics Stack Exchange
What happens to you if you fall into a black holes
So sorry to be so tardy Markus. I'm ashamed that I haven't responded in over a week. Utmost apologies.
The analogy failed. The mathematics is a weakness of sorts for you in that it gets in the way of the physics. You haven't crossed that event horizon yet, and you never ever will. Your vertical light beam doesn't get out because the speed of light where you are is zero. And it cannot go any lower, and you cannot exceed the speed of light.Originally Posted by Markus Hanke
But it is smooth and continuous. He sails right over that North Pole, he doesn't even notice it, but he can still see light reflecting off some lump of ice. However when you're at the event horizon, you don't. The speed of light is zero there. It takes forever for you to "see" some lump of ice, so you never ever do. You don't see everything as normal. You don't see anything. KruskalSzkeres coordinates won't change that. It's like putting a stopped observer in front of a stopped clock then claiming that he sees it ticking normally. He doesn't. He doesn't see anything. Ever.Originally Posted by Markus Hanke
That's what they say. I say it isn't true. Moreover I also say you meet a fiery end before you even get to the event horizon.Originally Posted by Markus Hanke
I have. And I've freed my mind from "picking my frame of reference". Seeing the big picture with all the frames isn't adopting a privileged frame.Originally Posted by Markus Hanke
That infinite time dilation is definitely real. What amazes me is that people who consider themselves to be relativists persuade themselves that it can be totally ignored. That it can be magicked away with a mere coordinate transformation. As if that can make a stopped clock tick.Originally Posted by Markus Hanke
Again that's what they say. But stop and think for a minute. Spacetime is an abstract mathematical model. Events are real occurences. And as you approach that event horizon, you experience fewer and fewer of them compared to what you previously experienced. You of course do not notice this. But nor do you notice when you fall asleep at night.Originally Posted by Markus Hanke
I don't think the quantum nature of light matters much. The h in E=hf sits well with the photon having a nonzero active gravitational mass. And for every action there is a reaction. I'll post something on this, but not today.Originally Posted by Markus Hanke
All analogies fail, which is why they are analogies. But regardless, I disagree with you on this  the analogy is very fitting in this case.
Exactly.But it is smooth and continuous. He sails right over that North Pole, he doesn't even notice it
I suppose then we have arrived at a point where we need to agree to disagree. It seems I can't convince you of what I am trying to explain, but neither have you presented anything that makes me question my understanding of the subject matter. I am not too proud to admit that at present I have no new arguments to present that haven't already been mentioned.I say it isn't true.
Yes, that is quite possible.Moreover I also say you meet a fiery end before you even get to the event horizon.
If your aim is to adopt a point of view that includes all frames, then why do say that the frame of the distant observer is physical, whereas the frame of infalling object is not ? This seems like a selfcontradiction to me. Remember that all observers experience the same geometry here ( in the sense that both the external as well as the infalling observer are part of the very same spacetime ), they just use different coordinate systems to describe it.Seeing the big picture with all the frames isn't adopting a privileged frame.
It cannot be totally ignored at all  that is why I specifically stated that infinite time dilation for the external observer is quite real, as you can read in my post. But then, so is the finite infall time for the observer in free fall.What amazes me is that people who consider themselves to be relativists persuade themselves that it can be totally ignored.
Everything considered my gut feeling tells me that you really haven't grasped what I was trying to explain to you all along  I put this down as a failure on my part, in that I wasn't able to get the point across. Like I said, at the moment I really don't know how else to explain it and make it clearer.
The clock never stops in its own frame, it's only the distant observer who determines it to be infinitely dilated. I could try now to go over the detailed explanation for this once again, but since I have done it several times already, I don't think it would do much good.As if that can make a stopped clock tick.
I don't know who "they" is, but when I look at the Einstein equations and their solutions, it all seems pretty selfevident to me. And I am not even a scientist nor expert in the field.Again that's what they say.
I never stop thinking. I don't know whether you are under the impression that I and others here merely regurgitate textbooks  but if you are I can tell you for a fact that you are mistaken. It is precisely the "thinking" part that has me interested in physics, as opposed to more "fact learning" based disciplines such as for example history, which doesn't interest me too much. Only because I happen to agree with what most textbooks tell us about GR doesn't mean I am not thinking; I think and test my understanding all the time, both online and offline. I am actually happy if someone shows me holes in my understanding or uncovers misconceptions that I might have, because it means that I can progress.But stop and think for a minute.
As for what you present, I understand perfectly well what it is you are trying to say. It's just that it is not in line with what GR is telling us, in the sense that the distant external observer cannot be any more or less physical than any other observer. It's very simple, really ( all quantum effects aside )  the infinite time dilation of the external observer is real and physical, and the finite infall time of the freefall observer is also real and physical. That's the whole point of GR.
I never mentioned light, I was speaking of the microscopic structure of the vacuum itself. And I don't agree that it doesn't matter, it's just that many aspects of the interplay between gravity and the vacuum structure just aren't understood yet.I don't think the quantum nature of light matters much.
OK noted. I think your stance will change once you appreciate the input from the other threads.Originally Posted by Markus Hanke
I guess it's a subtle distinction between all coordinate systems are equally valid and all real coordinate systems are equally valid.Originally Posted by Markus Hanke
Which brings us back to the contradiction that IMHO is readily resolved.Originally Posted by Markus Hanke
Don't think that. I understand all this. Au contraire, you you haven't grasped what I'm trying to explain!Originally Posted by Markus Hanke
It wouldn't. This is the core issue. A clock is either stopped, or it isn't. When it is, putting a stopped observer in front of it doesn't change anything.Originally Posted by Markus Hanke
Good stuff.Originally Posted by Markus Hanke
Only there's a contradiction, and we will continue to think until we have resolved it.Originally Posted by Markus Hanke
What structure? That's definitely one for another day.Originally Posted by Markus Hanke
Define "real coordinate system" as opposed to "coordinate system".I guess it's a subtle distinction between all coordinate systems are equally valid and all real coordinate systems are equally valid.
There is no contradiction, so there is nothing that needs resolving.Which brings us back to the contradiction that IMHO is readily resolved.
This is what I meant when I said I don't think you have really understood what I was trying to explain all along  my main aim in all of this is to point out that there is no contradiction here. Both observers are right in their frames, without there being a contradiction. And if there is no contradiction, there is nothing that needs resolving. That's the whole point of classical GR  to globally relate local frames, and to determine that relationship from given sources of energymomentum.Only there's a contradiction, and we will continue to think until we have resolved it.
The former is set up using the motion of light, which we use to define our second and our metre. The latter is one you think you would have if you were at a place where light doesn't move. Such as at the event horizon. But you don't. Because when light doesn't move all notions of space and time collapse. It's something like the gravastar "gravitational vacuum" which is "a void in the fabric of space and time". See this image. Where it's blue you've got some kind of real coordinate system. Where it's black you don't.
There is Markus. The outside observer reckons the infalling observer grinds to a halt. The story goes that the infalling observer doesn't notice anything unusual. What I'm saying is that he doesn't notice anything. Because he has ground to a halt.
Let's try to address this via a new thread. Like I've said previously, one starts with time, then moves on to the speed of light, then gravity, then hopefully one has a clearer idea about the nature of black holes.
PhysBang: I can do some of the maths. My understanding is something to do with me being an IT guy who has had to "get under the maths" when programming complex equations, and something to do with me reading the original works. Einstein said what he said.
I'm afraid that doesn't make any sense.The former is set up using the motion of light, which we use to define our second and our metre. The latter is one you think you would have if you were at a place where light doesn't move.
Correct, that is what he determines in his external frame of reference, using his own method of labelling events and measuring separations.The outside observer reckons the infalling observer grinds to a halt.
Also correct, it is what he determines in his infall frame, using his own method of labelling events and measuring separations. There is no contradiction  they are both right, but only in their own local frames.The story goes that the infalling observer doesn't notice anything unusual.
That means you are arbitrarily declaring a specific frame ( a faraway stationary observer ) to be physically privileged. That is manifestly in violation of the principle of relativity, which tells us that there are no preferred or privileged frames.What I'm saying is that he doesn't notice anything. Because he has ground to a halt.
Farsight, I'll be open and honest with you  there is only so many times one can go over the same things again and again. There is nothing to be gained by doing this, since we have already been through these, multiple times in fact. GR isn't about coordinate light speed in a privileged frame, it is about how local observers are globally related, and how that relationship arises from sources of energymomentum.Like I've said previously, one starts with time, then moves on to the speed of light, then gravity,
Yes, and what he said in his original 1915 publication is precisely this :Einstein said what he said.
in slightly unfamiliar but nonetheless mathematically accurate notation. The meaning of this is clear, and there is no "interpretative layer" to it.
It does once you "get" it. I put you at some gedanken location, and you use rods and clocks or the motion of light or anything else to define your coordinate system. No problem?
However when I put you at a location where gravitational time dilation is infinite, you haven't defined your coordinate system yet. And you never ever will. You never get to define your coordinate system.
Sorry to keep saying this: they can't both be right.
I don't see it that way. I think the principle is violated when people declare that a frame exists when it doesn't. Einstein would never have agreed with the idea of a black hole featuring a central point singularity.
But Einstein did say the speed of light varies with position. That's now been expunged from GR. As a result I think GR is the "Cinderella" of contemporary physics, and a lack of understanding of gravity is hampering scientific progress.
It just doesn't say anything about the nature of black holes. Here's an English translation by the way:
The Field Equations of Gravitation  Wikisource, the free online library
This all seems like a very complicated fantasy. The reason that Einstein, and others after him, gave for rejecting a preferred reference frame was that it palyed no role in any physical consequence. So far, Farsight, you reject the standard science of black holes on the basis ofmyour fantasy, but you give us no reason to accept your fantasy other then attempts to present theologicallike arguments about the word of Einstein. Where is the physical consequence of anything you say?
No problem whatsoever. This works everywhere and for all observers, including ones at the event horizon, including ones falling through it, including ones stationary far away. There is never any problem, that's what I was trying to explain.I put you at some gedanken location, and you use rods and clocks or the motion of light or anything else to define your coordinate system. No problem?
Gravitational time dilation is never infinite anywhere outside the hypothetical singularity. You seem to be either missing or ignoring this very important point. A faraway observer determines ( not measures ! ) time dilation to be infinite at the event horizon only because he is somewhere else. If you put him to where the horizon is, no infinities are to be found anywhere. The determination of there being infinite time dilation is solely due to the global relationship between frames that are far away and frames that are at the horizon, but it has not the physical significance that you are trying to attribute to it. In fact, a strong case can be made in that it has no physical significance whatsoever.However when I put you at a location where gravitational time dilation is infinite, you haven't defined your coordinate system yet.
Of course they can. Can you explain to me exactly why they cannot both be right ? They are both local frames, they are both subject to the same laws of physics, and neither one of them is privileged in any way. So where is the contradiction ? Remember that only because it mightn't make sense to you, or it is not obvious or common sense to you does not mean there is a physical contradiction here. It is precisely this  that there is no contradiction between these frames  that lies at the heart of what GR is.Sorry to keep saying this: they can't both be right.
Are you implying that freely falling frames of reference cannot exist ?I don't see it that way. I think the principle is violated when people declare that a frame exists when it doesn't.
We aren't talking about singularities at the moment, we are talking about how faraway stationary frames and freely falling frames are related. We have already established that the event horizon is not a physical singularity.Einstein would never have agreed with the idea of a black hole featuring a central point singularity.
Not at all. No one questions the notion of coordinate speed  what we question is its physical significance, since it can never be measured. It can only be calculated, and it is hence intrinsically a coordinate artefact. No experiment that you perform can ever physically measure coordinate speed, you can only ever measure proper speeds, and then do calculations. Surely you can see that.But Einstein did say the speed of light varies with position. That's now been expunged from GR.
It says everything there is to know about ( classical ! ) black holes, just as it says everything there is to know about any phenomenon of classical gravitation, with the notable exception of spinorbit coupling. The above is the law of physics that all observers agree on, regardless of their position and their state of relative motion  everything else follows from that.It just doesn't say anything about the nature of black holes.
That's the official story. I'm saying that once you appreciate time then the speed of light and how gravity works, you realise it's a fairy story. And why. Let me do the next thread and see if that helps.
The distant observer claims the infalling observer never crosses the event horizon. The infalling observer claims he does. They can't both be right.
No. You could be in a falling box, there's no issue with that. But now you've mentioned it, I will say that strictly speaking, no frame of reference actually exists. We can say that you exist and I exist and the black hole exists. But a reference frame is an abstract thing. It's little more than "a state of motion". Try replacing "in my frame of reference" with "in my state of motion". Then try to think about a situation where there is no motion.
Again, that's the official story.
No. When you appreciate time then the speed of light you appreciate that one optical clock 30cm lower than another is showing you the varying speed of light. It's an optical clock. It doesn't go slower when it's lower because time goes slower, it goes slower because light goes slower. You know the same applies to the parallelmirror light clock. Try taking this to the limit and putting the lower clock on the event horizon.
But it doesn't tell you why light curves or why the electron falls down. I'll do a new thread on black holes. It might be an idea if you reread what I said about gravity. Remember the idea with all this is that I give you stepbystep explanations that you can't fault, and the logic leads remorselessly to something we can agree on. Something that make you say whoa.
Edit: here's the new thread, I hope you like it. Or at least get something out of it:
http://www.thephysicsforum.com/speci...afterall.html
Last edited by Farsight; 06232014 at 09:22 PM.
Except that all over the internet, people show the faults. Again and again. And then you either ignore the faults, insult the people pointing out the faults, or move on in embarrassment to another part of the internet.
The main fault is that you have no physics: where is something that we can use to actually do something in the physical world?
Well, unless you can start to appreciate why there is no contradiction between these two, we will just continue to go in circles. There not being a contradiction between these is the very essence and heart of GR  so long as you don't understand this, you don't understand GR. Nothing to do with being "official" or not.The distant observer claims the infalling observer never crosses the event horizon. The infalling observer claims he does. They can't both be right.
Whether official or not  it's mathematical fact that the singularity at the EH is a coordinate singularity, not a physical one.Again, that's the official story.
Yes it does, or else it wouldn't be much good as a model for gravity...But it doesn't tell you why light curves or why the electron falls down.
Your logic is fundamentally flawed in that you don't appear to understand the crucial distinction between local and global in GR. This is why you keep thinking that there must be a contradiction between the faraway observer and the one in free fall, even though there clearly isn't. It seems to me you are thinking either that both are global viewpoints, or that the external observer alone is a global viewpoint, both of which are wrong. They are both purely local viewpoints  once you appreciate what this means, and how such local frames are related, you will immediately see that nothing at all needs "resolving", because there are no contradictions anywhere. That's really kind of the whole point of GR.Remember the idea with all this is that I give you stepbystep explanations that you can't fault, and the logic leads remorselessly to something we can agree on.
I will not accept those contradictions Markus. The infalling observer either stops at the event horizon or he doesn't. The elephant is either in one place or the other, not both. You might think these things are mathematical facts, but your justification is nonexistent. All you're saying "you don't understand GR". It just isn't enough.
PhysBang: then explain those faults.
Farsight, I don't think that the elephant is in two places at the same time in either frame of reference.
I wonder what an observer just inside the event horizon would claim? Or one just outside?
See Universe Review for one contradiction. See New Scientist for another. Both are unsatisfactory.
IMHO the observer just inside the event horizon doesn't claim anything, because he's "frozen" by infinite gravitational time dilation. The one just outside would say he sees the elephant slowing down and redshifting and freezing. But that's not accounting for Friedwardt Winterberg's firewall. I mentioned that on the new thread, but haven't gone into it yet.
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