## Sunday, March 06, 2005 ... /////

### KITP: Gross as actor, Feynman inventing Hawking radiation

As many of you, I am receiving hundreds of nonsensical e-mails from not terribly reliable sources but this one is pretty interesting because it authentically describes the atmosphere in Santa Barbara which hosts Science, Theater, Audience, Reader, an activity attempting to combine physics and literature:

• I am driving back to San Francisco from Santa Barbara in a few minutes but I want to get this down while it's fresh in my mind. I just had breakfast with Alan Lightman, a delightful Southern intellectual, and equally delightful Marcia Bartusiak (both from MIT). We were discussing Phil Morrison, Bethe, Salpeter - old days at Cornell. It got around to Hawking and what he will be remembered for. Then Alan Lightman, author of "Einstein's Dreams" told us the following "narrative" which was a big theme at Kavli meeting hosted by David Gross, who actually is a GOOD ACTOR. He did a scene as Feynman in QED - good job.

It is not hard to imagine as an actor - won't they put the video of this Feynmanian scene on-line? ;-) Note that Alan Alda is among the previous actors who were playing the role of Feynman, and therefore David Gross is in a good company even though Alda received the Nobel prize neither for the strong interaction nor for liquid nitrogen. OK, now the "narrative":
• In 1972 before Hawking came out with the Hawking radiation formula. Feynman was meeting with Kip Thorne's grad students, Bill Press, Saul Teukolsky & Lightman. They discussed a recent calculation of shining light on a rotating black hole and getting more energy out then in at expense of decreasing rotational energy of the hole. They all went back to Lightman's office. Feynman said: "Hey this is like stimulated emission. So he went to black board and did a A & B coefficient model and then when angular momentum J of the black hole J -> 0 there was still "A" spontaneous emission and it was the later Hawking formula!
Well, let me admit that I don't quite understand how the formulae from stimulated emission are useful for deriving the "Hawking formula", whatever it is. It could be interesting to try to reconstruct Feynman's blackboard.
• A maid erased the board that night before Lightman and the others realized they should have written down what Feynman wrote. Not even Feynman thought it was important enough to write a paper about apparently.
Well, the idea that Feynman derived Hawking's results before Hawking certainly sounds entertaining, but the details so far don't seem to be completely solid. Well, let me admit that my source is closely associated with extraterrestrial civilizations. He "shared a woman with Feynman" (different years) and an extraordinary photograph of Feynman with not-too-dressed women may be found in his book. Bizarre. ;-)

Finally, not all participants of the KITP activity enjoy these exhilirating stories about Feynman. Some of them - well, at least one of them - want to figure out how to prevent young physicists from hero-worshipping the politically incorrect and narrow physicist whose name was Richard Feynman, and convince them to hero-worship "broad intellectuals" and "better human beings", especially those who never "denigrate other fields".

#### snail feedback (45) :

Speaking of physicist actors who just won the nobel prize, David Politzer had a small role in Fat Man and Little Boy. He even has an entry in the IMDB. Just an interesting little tidbit, you can all go back to arguing about Feynman...

Hi Matthew,

yes, I know about this Politzer's role. Are you sure that the quality could compete with David Gross? ;-)

Having an entry is a great thing ;-), but it does not yet make one a great actor - by which I definitely don't claim anything about the particular case.

All the best
Lubos

I have seen QED (not with David Gross, though!;) and liked it a lot.

An interesting comment by Einstein on being a good physicist and a good man that I found here.

Einstein had a good friend, Michele Besso, with whom he discussed a lot of the ideas of the theory of relativity. But Besso never managed to achieve anything on his own. And late in their lives, Besso's wife asked Einstein, why was it that in spite of all his talent, her husband had never managed to achieve anything in science. Because he's a good man!'' exclaimed Einstein. That's it, that's exactly it, you have to be a fanatic, and that plays havoc with your life, and the lives of those around you.

yes, I know about this Politzer's role. Are you sure that the quality could compete with David Gross?
Well, Politzer had a speaking role in a major hollywood picture. They don't normally give those to slouches. Then again, in my opinion at least, Fat Man and Little Boy was a really bad film :) And QED is a stage play, so it's hard to compare. We'll have to put it down as one of those "unanswerable" questions.

You seem to be very sophisticated art-lovers. Among these physics plays, I have only seen Copenhagen - a pretty good piece.

I've watched the thought-provoking physics movie "What the bleep do we know". It questions the materialistic orientation of most scientists and exposes the long withheld secret that quantum mechanics is inconsistent with the dominant paradigm of reductionistic materialism.

Is it true Briane Greene is a trained actor and has appeared in plays and films, or has at least had cameos? If so which ones? There was a Cambridge physicist who also appeared in plays and some films, John Taylor I think was his name but I am not sure.
Steve

Yes! Brian Greene played a lot when he was young. Also, in 2000 he appeared in the movie "Frequency".

Hi Lubos,

Maybe the apparent grudge against Feynman finds its roots in his quite destructive behavior toward his students.

The following from the biography of Schwinger, Climbing the Mountain, p. 604, by Mehra & Milton, illustrates that more prominent people than the one alluded to in your blog held something against the way Feynman was.

========

Steven Weinberg offered some opinions as to why Schwinger was so much more effective than Feynman in educating graduate students. Like Max Born, 'when you read the list of [Schwinger's] students you realize what an impact he had. Some of them were his students because they went to Harvard, but a lot of them went after him individually.' 'Feynman even to a greater extent than Julian was unwilling to take on the ordinary burdens of academic life. Feynman was even more of an obvious genius than Julian; with Julian it's obvious he's an intellectual, with Feynman he comes across as a longshoreman, and then you find out that he's doing this very exciting and very inspired work, and the incongruity makes him seem even more of an awesome personality.' Feynman, along with Murray Gell-Mann, projected an overpowering aura at Caltech, so much so that some people had to leave. 'Schwinger didn't have that much of an aura.' 'Julian had a strong sense of duty,' manifested, for example, in the care which he took toward his courses, and in his taking on graduate students; while Feynman 'didn't take duty that seriously,' and only took on those tasks which appealed to him.

========

Umm, I am no cosmologist, but it is possible to see how this analogy works. Consider that the Black hole is in a pure quantum state, described by its rotational quantum number and other variables, then the light entering + black hole is a "dressed" quantum state and a change in energy is associated with a corresponding change in rotational quantum number of the Black hole - this is qualitatively what happens with stimulated emission. Of course, things like "black hole wavefunction " etc have conceptual questions associated with them, but it is possibly not neccesary to accept them in entirety, and instead pretend that the rotational spectrum of the black hole is quantised which would be sufficient to calculate changes in energy of radiation.
v.

Hi Lubos,

It is fairly well-known fact that Zeldovich also came up with an idea of "Hawking" radiation" as a stimulated emmision, as documented in Kip Thorn's article on Zeldovich.

Cheers,

"Copenhagen - a pretty good piece".

Yes, it was a decent piece.

Hmm according my postlude at hep-th/9905021, it was playing at the Duchess theater in May 1999. At that time I was more impressed that now. I believe I put a newpaper note for the play in the IAMP meeting at 2000, so it seems that the play got at least a whole year of stage.

John (J.G.) Taylor did indeed undergo a theatrical training. This is evident in his presentational style: he projects his voice like a thespian of the old school. Whether he is also a member of the Magic Circle is not known; he has at times shown a disconcerting interest in spoon bending and the paranormal.

Robert

One of my proffessors when I was an undergrad was in one of Feynmans celebrated classes in caltech that later became those great books.

Feynman was a horrible teacher, and an incredible narrator. He told us the story that one day, a student lifted his hand up.

Feynman irately stopped his discourse, and took the students question. He then snapped and said 'if you had been paying any damn attention you'd know the answer yourself'. It then became clear to everyone that questions were not allowed. Most of the students also struggled with the material as it was presented, the teaching of physics alla Feynman never really made it past that stage. Feynmans books are relegated to backup material (and great backup at that).

Btw im a hero worshiper of Feynman, but he was a tad arrogant =)

The blackhole concept is troublesome in that the event horizen is a "fake" singularity, not a real singularity, in the sense that it depends on the reference frame of the observer.

If a traveler enters a blackhole, he would see nothing unusual when he passes through the "event horizen". Because the event horizen the traveler sees is located further insider than the one some one at infinite distance sees.

Therefore, some one in the vicinity of the event horizen (the one observed by some one far away) would NOT think he is in the vicinity of event horizen, but still far from it, so he would be able to see both the events one meter below the "event horizen", and one meter above it.

Therefore, he will be able to relay information from inside the event horizen, to outside the event horizen. Hence the notion that someone "outside" the blackhole could not see information "inside" blackhole is broken. Such notion would have to be broken because there is not an absolute and definite definition where the event horizen is, it depends on observers. What one observer considered "inside" may be considered as "outside" by another observer at closer distance.

Actually if you consider a photon travelling from an arbitrarily close distance from the center of the blackhole. It can travel an arbitrarily long distance outward, and lose a considerable percentage of its energy. But the percentage of energy lose can never really reach 100%, just approach 100%. So ultimately, the photon can still reach any distance, and carry information from its origin to the observer at distance.

Has any one considered this paradox?

Quantoken

> The blackhole concept is troublesome

Indeed it is.

Maybe you want to consult the available literature before you make your statements and postings.

Wolfgang said:
"Maybe you want to consult the available literature before you make your statements and postings"

I did exactly that already. It is NOT like I just heard of blackhole yesterday and I have not read any literature.

The problem is none of the literatures directly address the paradox I raised. In fact all known literatures contradict each other. Some say the event horizen is not a real sigularity and there is nothing unusual around the event horizen. Some say it is an absolute boundary that no thing can go from below to above.

You can't have both sayings. The event horizen either is a real sigularity, or is not a real sigularity. You get completely contradicting conclusions from existing literatures. So there need to be some clarification.

Imagine you follow one photon all the way from some where way below the event horizen, and going outward, you certainly would see the photon's energy reduced as it go outward. But there does not seem to be anything that will prevent the photon from travelling to infinity, albert at reduced energy level and frequency. That conconsion certainly contradict with another observer who stayed far away all the time.

How do you reconcile this two observers, one stay with the photon and another stayed at a distance?

Quantoken.

Quantoken,

you need to read a textbook which explains Kruskal diagrams or Penrose diagrams.
(e.g. "Gravitation" by Misner, Thorne, Wheeler)

Then draw the situation you describe as such a diagram and you will discover how your paradox disappears.

Best,
Wolfgang

Wolf gang:

I do not buy \$200 textbooks just for the sake of internet discussion. Please reference something that one can access freely on the internet.

If you are familiar with the argument, then you should be able to directly quote them here to dispute the paradox I raised here. If all you can say is "read book A" and "read book B", then the discussion is not addressing any question and not going any where.

Dear Quantoken,

the most valuable part of your posting is "Wolf gang" - I never realized that this may be the origin of the name. ;-)

Your argument that you can write nonsense because the textbooks are expensive is cute. Let me try to give you a free argument.

You're incorrect imagining what a horizon is. You should learn and remember that the event horizon is a light-like hypersurface. Locally you can imagine that it is a plane - for example the horizontal plane z=0 - which moves in the transverse direction (for example up) by the speed of light.

If something is below the horizon, i.e. under the ground, it will never be able to propagate its information above the horizon (to the skies) simply because the information would have to travel faster than light.

Otherwise your comment that in the standard picture, the observer can't say whether she's already under the horizon, is absolutely correct.

Best
Lubos

As a start, please answer a straight fordward question with a definite yes or no: Is event horizon a true singularity, or just an artifician one? Do not give me an answer like "read book A or B". Just say yes or no.

Second, if envent horizon is a false singularity, why it prevents things from going across the event horizon? Or some observer see things going through event horizon, and some others don't?

Third, how do you reconcile different observations by different observers, some can crossing event horizon never happens, some say it happens?

Quantoken

No, the event horizon is not a physical singularity. The curvature invariants don't diverge, for example.

The horizon can only look like a singularity in some (natural) coordinates, so therefore it is the so-called coordinate singularity.

There is a genuine singularity in the center of the black hole - but this is a very different place from the horizon.

The position of the horizon is a completely objective place in spacetime that all observers agree upon. It can be crossed by an infalling observer - this is what we mean by the observer falling into a black hole - but it can only be crossed in one direction. You can't return simply because the horizon seems to be "moving away" by the speed of light, and you can't catch up with it.

When we say that it "never happens" that the observer crossed the horizon from the viewpoint of the external observer, it just means that the time coordinate of the external observer does not cover "all possible times".

It's like the "paradox" due to Zenon - Achilles and the turtle. Let me simplify it. Achilles moves by constant velocity, but we describe his motion as follows: he first moves by 1 meter, then by 1/2 meter, then by 1/4 meter, 1/8 meter, and so on. You repeat this step N times where N can even be infinite, and Achilles still moved by less then 2 meters. It's only because the variable N is not a good one to describe the whole life of Achilles - N becomes infinitely dense near the mark "2 meters". Other people who use better variables than N know very well that Achilles is able to move by more than 2 meters.

In the black hole case, the time measured by the external observers are analogous to N, and only cover a part of Achilles' life. But the life continues even after infinite values of N - if one uses a different time coordinate, e.g. one measured by Achilles' watches, you will see that the life continues even after he crosses the horizon.

Lubos said:
"Locally you can imagine that it is a plane - for example the horizontal plane z=0 - which moves. in the transverse direction (for example up) by the speed of light."

Why would the event horizon MOVE, if the blackhole is a static one, not expanding? Are you suggesting that if one goes outward from below the event horizon, he will find the event horizon expanding outward at light speed so he can never catch up with it. And once the observer stop moving outward, instantly the event horizon also stops moving outward instantly?

I am not sure if such a "ghostly" event horizon which follows every move of the observer is what the theory of GR describes.

It's certainly an amusement to spell Wolfgang as "wolf gang", so probably I will keep doing the same for fun. But no I do not think the name resulted from the English name of "wolf" and "gang" :-) At least it's not an English name. Just as my name quantoken is not a swedish name :-)

Quantoken

"Why would the event horizon MOVE, if the blackhole is a static one..."

The black hole is a manifestly static solution in the Schwarzschild coordinates. Unfortunately, these are exactly the coordinates that become singular near the horizon, and they give you a wrong intuition how physics looks like near the horizon.

If you want to see that physics near the horizon is smooth and not catastrophic - much like the flat space - you can use other coordinates which are kind of "freely falling" (in freely falling frames, you're gonna see physics like in flat space). For the freely falling observer, physics will NOT be static, and the horizon, whose position is fixed in the static coordinates, will be receding by the speed of light.

Once again - there are different coordinates. One of them make it clear that the solution is static, but they are bad and singular for the description of the near horizon physics. The other coordinates are smooth for this physics near horizon, but the geometry is not t-independent in these coordinates.

Quanto,

Anyone of these books should be able to be gotten from the library of your local community, or college libraries.

Geons, Blackholes & Quantum Foam, by John Archibald Wheeler, with Kenneth Ford, page 236, para 2.

"This hypothetical entity, a gravitating body made up entirely of electromagnetic fields. I call geon(g for the gravity, e for electromagnetism," and on as the word root for"particle"). There is no evidence for geons in nature and later was able to show that they are unstable-they would quickly self-destruct if they were ever to form. Nevertheless it is tempting to think that nature has a way of exercising all the possibilties open to it. Perhaps geons had a transitory exitance early in history of the universe. Perhaps(as some students and I speculate much more recently), they provide an intermediate stage in the creation of the blackholes."This was the first indication to me, that what string theory was doing, was what was on the mind of John Wheeler in regards to the quote. What is a GEon?

When you follow the history, to Kip Thorne, the student of Wheeler you can see how this history has arrived at a interesting crossroads today, with the subject of string theory and what the graviton represents.

At the same time this model apprehension is taking place, we were learning something about gravitational wave production and the roads leading to our current technologies in LIGO.

Studing Webber and the Aluminum bars will greatly advance the world that Dvali, Nima and others are seeing here in dimensional relationships?

This has been a wonderful journey for me.

So what do you propose an observer feel falling into a blackhole will see, according to HIS free falling reference frame?

He would see the center of blackhole at a distance R away from him. Would you say he will see this R reducing, instead of increasing. In any case that's what "falling" means logically, right? If R increases, he is not falling, but leaving.

So the distance from this observer to the center of the black hole will have to be a bounded value.

Now what do you suppose the horizon he sees will be like. Are you saying he will see a event horizon quickly receeding at light speed, so he could never catch? Well, of the distance to the center is bounded, and the event horizon is receeding (shrinking) towards the center. Then within a finite time it will hit the center and from that point on, the observer no longer sees a blackhole!!!

How would you explain that paradox?

Does the observer see himself crossing the event horizon, based on his own coordinates, in either direction he travels?

Quantoken

Dear Q.,

I assume that you want to understand how to resolve the apparent paradoxon and not just create some noise.

If this is indeed the case I suggest you consider what I already told you:

1) there is no paradoxon here (trust me on this)
I understand exactly why you are confused, but this does not mean there is a paradoxon here.

2) I told you that the easiest way to understand this is to draw the corresponding Kruskal diagram.
But you will have to spend the effort to learn what a Kruskal (or Penrose diagram) is. As you see textual explanations do not get you very far.

3) If buying a book is too expensive for you, then search for cheaper or free alternatives. But I will not do this for you.

The main reason you are confused is because your everyday concepts like "seeing", "approaching" etc. are not well defined enough. Again you will need to learn more ...

By the way, I bought MTW when I was 16 and without regular income.
It was definitely worth the expense.

But you have of course the choice to hang around on various blogs and continue to post nonsense.

Best,
The Wolf

Bekenstein BoundConsider any physical system, made of anything at all- let us call it, The Thing. We require only that The Thing can be enclosed within a finite boundary, which we shall call the Screen(Figure39). We would like to know as much as possible about The Thing. But we cannot touch it directly-we are restrictied to making measurements of it on The Screen. We may send any kind of radiation we like through The Screen, and record what ever changes result The Screen. The Bekenstein bound says that there is a general limit to how many yes/no questions we can answer about The Thing by making observations through The Screen that surrounds it. The number must be less then one quarter the area of The Screen, in Planck units. What if we ask more questions? The principle tells us that either of two things must happen. Either the area of the screen will increase, as a result of doing an experiment that ask questions beyond the limit; or the experiments we do that go beyond the limit will erase or invalidate, the answers to some of the previous questions. At no time can we know more about The thing than the limit, imposed by the area of the Screen.Page 171 and 172 0f, Three Roads to Quantum Gravity by Lee Smolin

Dear the wolf of a gang:

I am interested in finding the truth, not making noises. But my way of finding truth is through logic and reasoning, not through brainwash and religious convertion.

My income allows me to buy any book I want, if I really want. But that's not the issue. You are still refusing to answer me with straight answers but simply ask me to buy books. You can not buy all the books, if you do, it still boils down to have to answer logical paradoxes using logic reasoning. You fail to provide any.

If some one comes to me and tell me "convert to buddhism and all your puzzles will be answered", I would have considered it a better offer than what you have here.

But I am still only interested in discussions which contain logic and reasoning.

Quantoken

Plato:

I have the "Three road" book. And Bekenstein Bound is one of my favorite topic and one of the basises of my GUITAR. But's it's unrelated to current discussion.

Let me put it in this way. Let many observers line up from a location within the event horizon, to a location far away. All of them are NOT moving.

Of course, to the observers near event horizon, based on their own reference frames, they do not see anything un-usual at all. So it's quite possible for these observerd to RELAY information from one to another. This way, information that the remote observer thought came from some where inside the horizon would have successfully REALYED to him, therefore break the conventional notion.

What prevents the observers from being able to relay information this way? Where does the relay chain break and how it is broken?

Quantoken

I must add a very important note. It is still hard for me to believe that Lee Smolin wrote something that could imply that *he* was the author of the conjecture. Lee Smolin has nothing to do with the discovery of the holographic principle and I hope that he always refers to the real authors properly - and it was just you who did not read carefully enough. The holographic conjecture, based on the Bekenstein's bounds and the
Bekenstein-Hawking entropy of the black hole, has been first proposed by Gerard 't Hooft and discussed in more detail by Lenny Susskind:
To me I would want to see how Daniel Kabat sees? In order to do this you needed a model that would help you see.

Would we debate who thought about it first or rather the importance Holographically we are introduced to the suject of quantum gravity?

This comment has been removed by a blog administrator.

There is some confusion in the old literature about the singular nature of the Schwarzchild solution. Books and papers written before the 1960s often refer to the "Schwarzchild singularity" of the Schwarzchild metric at r=2GM. This a misnomer since there is of course no actual physical singularity at r=2GM. It is a "coordinate singularity". For a while physicists were confused about the difference. To check for a true physical singularity you compute the Kretchmann scalar
R^(abcd)R_{abcd) which diverges or blows up at the singularity at r=0.

The details of the Schwarzchild solution were not understood until Kruskal and Szerkes found a maximally analytical extension using hyperbolic coordinates. It is quite a simple and beautiful result. The extension contains 2 asymptotically flat regions and
2 singularities. The usual Schwarzchild coordinate patch covers only half of the analytical extension.

Much earlier (1935) Einstein and Rosen wrote a paper on the "Einstein-Rosen bridge". They were looking for a geometric description of a particle within GR in terms of a space of two identical sheets, with the particle being the bridge or "Schwarzchild wormhole" connecting these. However, their own coordinate system (Einstein-Rosen coordinates) is incomplete and discards the region [0,2GM] containing the curvature singularity. Basically they glued the two regions together to make a sort of wormhole (the ER bridge) with the region containing the true singularity cut out. Their coordinates are indentical to only a part of the maximally extended Schwarzchild geometry found by Kruskal. The ER coordinates are basically bad coordinates at the horizon. As I said, people were confused about this for quite a while. Anyway, you need to read ANY basic GR text for the details of the Kruskal coordinates and the nice Kruskal diagram. It is not hard.

Also, when dealing with objects falling over horizons you have to distinguish between comoving coordinates and proper coordinates. An unfortunate astronaut can pass through an event horizon and not notice, since he is using comoving coordinates. (For a massive hole the horizon is quite flat with negligable tidal forces.) Quite soon though he will start to feel himself being torn apart as the tidal forces grow and he gets nearer the singularity. However, an observer far from the hole ,where the metric is asymptically flat or Minkowskian, using proper coordinates sees him "frozen" there at r=2GM like a fly in a spider's web. It's a redshift effect. There is no paradox.
Best
Steve

Dear Quantoken,

Your numerous typos are really quite entertaining. In particular, I wish to insinuate that -- not so much the singularity -- it is you who is an "ARTIFICIAN".

Despite the fact that you are good for some serious laughter in my office, I do not want you to misunderstand my remark as encouragement. In fact, I hope you are pretty discouraged. ;))

Best wishes,
Christian

Christian:

It's ridiculous for you to pick on my typos since obviously you do NOT have much to say other than my typos! Granted I am not an office secretary and I am not a good typer, so WHAT? Is that a big deal? If all internet discussions have the strict typesetting requirements like ARXIV articles, then the internet discussion will just be boring and un-interesting.

Focusing on others' typos is just too low on your part, Christian!

Quantoken

Steve:
The same physics should be observed regardless what coordinate system you want to use. So you need to reconcile different conclusions drawn from different coordinate systems.

The remote observer sees the astronaut "freezing" at the event horizon, while the astronaut himself does not see anything unusual in his surroundings, because they are making their observations from different reference frames. That's fine.

But the problem is the falling astronaut is capable of relaying his observation (he is able to "see" like say one meter inside the event horizon) and other information, to the remote observer.

So the remote observer is capable of obtaining information, indirectly through relay, and find out all the goings going on both inside and outside the event horizon, despite of the fact that he only sees a freezed astronaut as directly observation.

How do you reconcile his direct observation and indirectly obtained information, which contradicts each other. It is as if you witness some one dead and then you receive a phone call from the dead people. Either what you see (direct observation) is untrue, or what you hear (indirect information relay from near horizon) is un-true. What you see and what you hear is incompatible.

Quantoken

I think Quantoken is asking why the poor astronaut who doesn't notice anything funny at the event horizon in his comoving coordinates cannot relay information back. That is, imagine the poor bloke, continuously sending messages to the Houston space center, and imperceptible to him, suddenly his messages will no longer reach Houston. Where is the discontinuity that causes this to happen?

Quantoken, the best layman's explanation of this I've seen is that of a rowboat caught in rapids. To the person in the rowboat comoving with the water, it is not obvious that there is a point of no return. However, at some point the water is flowing so fast that he cannot make any headway rowing upstream. There is no physical discontinuity that marks the spot.

Arun:

Your rowboat analog is a very good one. But I guess the person unable to row upstream is analog to the astronaut unable to excape from a blackhole.

One the same analogy, the problem of relayed information can be represented by a chain of rwoboats, each at close distance to each other. For the unfortunately person who can not row up-stream, since there is no unusual geometry in his vicinity observed from his comove coordinate, he can well hop onto the next rowboatd following in, and then jump to next one. If he keep hopping this way he can escape to the bank even if he can not save his boat.

What's wrong with that? What's wrong of relaying information the same way from inside the horizon to outside?

Actually if some one near the horizon can manage to transmit information from one nanometer inside horizen, to just one nanometer outside, he would have successfully brought information from inside to outside already. Since he sees nothing unusualy from his own comoving coordinate, why can't he do that?

It's very troublesome that the event horizon is not a real one, but purely due to selection of coordinates, and then to also argue that such an unreal boundary really has the magic power to absolutely stop information or mass from crossing the boundary.

Quantoken

Q.,

in Arun's analogy the rowboats represent light and thus you cannot jump from one rowboat to the next since this would imply signals faster than light.

Unfortunately, your choice seems to be to stay on the level of analogies and blog comments.
So you will not understand the difference of local features vs. global properties (e.g. event horizons).
And that's ok with me; You do not have to understand or learn physics ...

Best,
Wolfgang

PS: This was my last post to this issue and I apologize to Lubos for using his space for this.

Wolf:

You still don't get it there is NO real singularity near the horizon. The geometry is just fine and there is no extreme spacetime curvature or anything like that, as far as the local observer is concerned. Actually the boater won't even notice the stream is moving if he only looks locally. So there is no reason why he can not jump to the next boat. If he really can't then he would have observed some oddity in his local geometry, which is impossible, because we already know there is nothing unusual in the geometry near the event horizon, to the local observer.

Quantoken

Just a friendly warning, but Arun was using the Eddington coordinate wheareas the others were using the Schwarzschild coordinates.

The Schwarzschild metric is unnecessarily complicated. Let's look at the Rindler coordinates instead.

In Cartesian coordinates, we have t and x with the metric

ds^2=-dt^2+dx^2

focus on the wedge x-t>0, x+t>0.

Choose the coordinates tau=arctanh(t/x) and r=sqrt(x^2-t^2).

Then, ds^2=-r^2 d tau^2 + dr^2

r=0 is the "event horizon".

Suppose a particle takes a path x=1. It would look like r=sech tau. It looks like the particle approaches the event horizon asymptotically in the past and in the future, but in reality, it only spent the amount of proper time 2 in the Rindler wedge.

Another thing the Kruskal coordinates should make people realise -- but they often don't -- is that a black hole has no "center" --- the singularity is *not* a point sitting waiting for you at the center of a ball. Failing to understand this leads to a lot of silliness, eg the papers of Samir Mathur about the insides of black holes.

Anonymous says:
"leads to a lot of silliness, eg the papers of Samir Mathur about the insides of black holes"

So just like I said, there are plenty of contradictions and diagreements between published literatures. So it's a problem far from being understood fully yet.

I do not know what "Samir Mathur" says and I am willing to believe anonymous is right and Samir is wrong. But to be fair, in any issue that's controversial, I must assume myself a neutral position and be ready to accept both possibilities.

I am trying to spend some more time thinking over this Schwatzchild metric. Nothing presented so far explains away my paradox where presumably information can be relayed locally, because the geometry seems to be nothing unusual locally.

People must realize the r and t in Schwatzchild metric may NOT be the actual distance and time. See this:

I quote:
"The quantity ds denotes the invariant spacetime interval, an absolute measure of the distance between two events in space and time, t is a `universal' time coordinate, r is the circumferential radius, defined so that the circumference of a sphere at radius r is 2 pi r, and do is an interval of spherical solid angle."

Clearly r is defined as "circumferential radius", where 2*PI*r would give the correct circumference. That definition of r may NOT mean it's the same r as "distance to the center".

We know in flat spacetime, we can say radial distance r times 2*PI equals the circumference. I do not know how you can use the same 2*PI factor, knowing full well we are NOT talking about flat spacetime in the vicinity of blackholes.

Another thing troublesome is we started by assuming light speed C is one. But now you look at how fast light travels next to the event horizon, it's much slower than one. Contradiction to our initial assumption.

Further troubling is when you ask the falling astronaut "what is your observed distance from the center of the blackhole". Based on available litenature when he approaches the event horizon he sees a seemly infinitesimal distance away from event horizon for the outside observer expanded to a huge huge distance for himself. So he would observe his distance to the center of blackhole become greater and greater as he "falls in". That notion completely contradict the logical meaning what "falls into something" means. Falling in must necessarily means a shrinking distance logically!!!

Something must be wrong with how we define local distance and time. Because we really don't know whether the ruler we used are shrinking, or the stuff around us are shrinking.

Quantoken