http://news.yahoo.com/spy-chief-nominated-romanias-premier-182955470.html
Spy chief nominated as Romania's new premier
Spy chief nominated as Romania's new premier
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Yep. RC is getting it, sol is wobbling, ben's got nothing, and Clinger has shown himself to be an ineffectual windbag who pretends he's dealt with the argument by posing homework questions.
I didn't cut anything out, my sleight-of-hand retort was in response to your ad-hominem suggestion that I'd tried to hide something.
I didn't miss it. What we're talking about here is a frozen star. It isn't a singularity at all. There are no infinities, it's merely a c=0.
It's as much a singularity as a sphere of ice is a singularity to a fish frozen into it.
Sol deserved the little lecture. Move on.
As above.
I replied to it in detail, see post #88, it was simple stuff concerning maps.
That's got nothing to do with it. A bullet drops the same amount in a second as a dropped ball.
Electromagnetic fields exist. Remember what Minkowski said: "Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis...". It's one field and two forces. Sounds to be as if we need to have a separate discussion about electromagnetism. One for another day.
Your simple proof was wrong. When 2M/r = 1 at r = 2M you've got a division by zero in [latex]\[ \frac{dt}{d\tau} = \frac{e}{1-2M/r} \][/latex]. That's an undefined result, an infinity. But you just sail on past it. The finite proper time demands an infinite coordinate time, so it hasn't happened yet, and it never ever will.
And even a blind man can see the problem with it.
Ditto.
Reality Check
Penultimate Amazing
RC has always got it, sol has always been solid, ben got that you have nothing to support your position and Clinger has shown himself to be a competent mathematician.
Farsight is continuing to show his inability to learn physics or mathematics.
Farsight has shown that he cannot even do homework assignments
!Good stuff. I'll check the crossover point re a discussion on another thread.sol invictus said:
Come on man, think. Nobody can see anything when the speed of light is zero. And it is a real property of that location: you know this from those parallel-mirror light clocks I keep showing you. And because a photon doesn't slow down like a cannonball whilst moving vertically up out of a gravitational field. We don't see photons travelling at some slower speed because they've been emitted by a giant star. In similar vein a photon emitted vertically from the event horizon isn't going to lose all its speed and obligingly fall back down. It isn't going to curve back down either, because it was emitted vertically. The black hole is black and the photon doesn't get out because its initial speed is zero.
Edited to add:
It's no catch at all, merely cheap wordplay and obfuscation because the guy has no counter-argument. And if you want me to talk about the pole-in-the-barn paradox, it'll be my pleasure.
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dafydd
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Wonderful news! Way to go for the spooks!
This is going to be fun.
The stock answer is no, but this misses the crucial point: she hasn't crossed the event horizon yet. Even if she fell into the black hole a billion years ago, she hasn't crossed the event horizon yet. As we speak she's at the event horizon, frozen along with her light pulse, and she isn't noticing anything. She is in the same situation as a person who has been accelerated to the speed of light, her biological processes have stopped. We all know we can't actually accelerate our victim to the speed of light, I say it's because we're made of the darn stuff whilst you doubtless say it's because it would take infinite energy, but set that aside. Just go with the flow and assume we can. The person travelling at c is subject to infinite time dilation. For light to enter her eyes orthogonal to the direction of travel, light would have to be travelling faster than light. It can't happen. Light can't move in her frame, and nor can electromagnetic or biological processes. So it's not a case of she doesn't notice anything unusual, it's a case of she doesn't see or think.
See above.
Whoa. Let's have your observer open a porthole as she falls into the black hole. She's looking back at the universe. What does she see just as she reaches the event horizon?
You still don't get this sol, and it's important: time doesn't move. Things move. Things like light. Can you see time moving? No. Can you see light moving? Yes. It isn't time that stops at the event horizon. It's light. And remember electron spin and diffraction, and annihilation. Everything stops.
Where above? It isn't hot at all. Heat is an emergent property of motion. Motion is time-dilated out of existence. And I'm off to bed.
The speed of light isn't actually zero. There is a particular frame in which a particular ratio of coordinates equates to zero. That ratio is observer-dependent, and except in special contexts it doesn't actually represent the speed of light.
Nope. You keep analyzing that clock from the frame of special observers---one inertial observer in flat space, another maximally-accelerating observer near the horizon---and ignoring others. I have no idea why you think this is a good idea, or why you think that these observers get "the right answer" while my falling observer is somehow wrong.
Remember, Farsight, real GR can handle any observer, and can give consistent answers no matter what observer is chosen. The actual laws of GR include your rope-observer and his infinite blueshift, and your outside-observer and his nothing-has-fallen-in-yet redshift ... and it does so without contradicting, or ignoring, or devalueing, the experiences of my falling-straight-in observer ... the one who, according to a calculation you have failed to criticize or notice or debunk in any way, goes through the horizon in a finite proper time and can do local speed-of-light measurements all the way down.
Not "yet" according to a clock at rest. She crosses the horizon in a finite time according to her own clock (and many other possible moving clocks).
Dammit, Farsight, this is an explicit solution of GR. It's in Misner Thorne and Wheeler with all of the coordinates, algebra, etc. laid out. I gave you the exact equation of motion---what do you think I did, made that up by throwing darts at a keyboard? Is there an error in the MTW derivation? Did they make a bad starting assumption?
She's moving very fast. Remember that collection of photons that your rope-observer thought was blueshifted like crazy? The infalling observer is nearly co-moving with those photons, and that motion "undoes" the blueshift. If she looks back, she sees an ordinary view of the Universe. Photons from behind enter her porthole with nonzero (but unremarkable, nonsingular) redshifts or blueshifts and with no special history/time compression. If she looks forward, she can see objects a finite distance in front of her; such objects are necessarily co-falling with her, having entered the black hole before she did. In front of those objects, she sees a rapidly-shrinking-as-she-falls-towards-it event horizon that she's doomed to keep approaching. This "Schwarzchild surface" has all of the properties of an event horizon---she sees things redshift as they approach it---except that she's doomed to continue approaching it.
Nope, you're wrong. An observer falling through the horizon has an ordinary experience of space, time, motion, and light. Neither light nor time stop at the event horizon. You're wrong to think it does. You were tricked into thinking this by over-relying on a particular set of clocks.
ETA: http://casa.colorado.edu/~ajsh/singularity.html
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Farsight is using strictly circular reasoning.
F: "Everything stops at the event horizon."
S: "Here is an explicit GR solution showing something not-stopping at the event horizon."
F: "That solution can't be true, because everything stops at the event horizon."
sol invictus
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So you agree that she experiences nothing at all unusual. She's sitting there looking at her light clock, and it's behaving exactly as it always did, she feels no forces, none of the other instruments inside her sealed lab read anything. For her, the moment when she arrives at the horizon (or let's say when she arrives at 0.0000000000000000000000000000000000001 mm outside it) is just a perfectly normal moment, after a finite number of light-clock-bounces.
But according to you we have to cut time off right at that perfectly ordinary, unremarkable moment. You can't ask what comes after that moment. You can't ask what bizarre law of physics could stop time right then, with nothing unusual happening, in a vacuum region of space.
You can't ask any of those questions, because you won't let yourself. You refuse to use any system of coordinates other than the Schwarzschild coordinates. And that (arbitrary and unjustified) choice prevents you from asking or answering any such question, because those coordinates only cover part of the spacetime.
No. She experiences what she'd experience if she was moving at c. She experiences nothing.
That moment hasn't come yet. Let's you and me wait a billion years, and that moment still hasn't come yet. It never comes. She's sitting there in front of her light clock, but light isn't moving in the clock, it isn't moving towards her eyes, and electromagnetic processes aren't moving in her instruments and in her brain.
Those finite number of light bounces takes an infinite coordinate time to occur. They never happen.
Not so. The moment never comes. The supposed time after that moment is time after the end of time. Come on sol, look at the lefthand chart on post 135. The chopped-off top goes up to infinity. There's no getting past it.
Stop talking about stopping time. make the leap to stopping light, and then there's nothing bizarre about it at all. Think back to the optical clocks losing synchronisation at different elevations, simplified to parallel-mirror light clocks.
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One light beam is going slower than the other, and c = √(1/ε0μ0). The vacuum impedance of space Z0 = √(μ0/ε0) is increasing. Increase it so that it totally impedes the motion of light, and you stop light. Then nothing moves and clocks don't tick. Waves can't propagate through space any more. It's that simple.
I don't fight shy of asking questions. I examined my own convictions long ago, and I work hard not to have any. Show me some scientific evidence that disproves something I say, and I will readily put my hands up, hang my head in shame, and say Sorry, I was wrong. I've done it before and I'll do it again. But that's what it takes, not some wan accusation concerning psychology.
Not so. I challenge the use of neverneverland coordinates in cloud-cuckoo land. What we have here is an inverted version of Zeno's paradox: It takes an arrow one second to move half the distance between it and the target, and the arrow doesn't know it's slowing down. It never hits the target. The arrow's finite proper time is a fairytale.
Spacetime isn't something real, sol. Space is real, that black stuff between the stars. The thing that sustains waves and fields. Motion through it is real. Spacetime is a mathematical space in which there is no motion. You don't move through it. And when light doesn't move at the event horizon, all worldlines go straight up. Come on sol, we're nearly there with this. Examine your own psychology. You can't elucidate a clear explanation of why I'm wrong. Why not? Because I'm not. And I'm not some "my theory" guy pushing some damn fool hypothesis, this is just frozen-star stuff that you've never thought through. Think it through for yourself. Ask yourself whether the time really flows and whether the speed of light is really constant, and what gravitational time dilation really is. Don't stay locked in a position whereby you can't ask any of those questions, because you won't let yourself.
Och, I hope you find this thread stimulating.
There are no frames ben. They don't exist. A reference frame isn't something you can point to up in the sky. Your observations and your measurements are affected by your motion, and by the thing we call gravitational potential, that's all.
It's a good idea because frames aren't real whilst gravitational potential is. Light clocks tick slower when you're lower, and so do you. That's what actually happens, and light doesn't escape from a black hole. Now come on, address this:
And it is a real property of that location: you know this from those parallel-mirror light clocks I keep showing you. And because a photon doesn't slow down like a cannonball whilst moving vertically up out of a gravitational field. We don't see photons travelling at some slower speed because they've been emitted by a giant star. In similar vein a photon emitted vertically from the event horizon isn't going to lose all its speed and obligingly fall back down. It isn't going to curve back down either, because it was emitted vertically. The black hole is black and the photon doesn't get out because its initial speed is zero.
The issue isn't whether it's real GR, ben, but whether the solution is real.
Don't give me laws, give me scientific evidence and logic. It's the law just won't do.
Point it out or repeat it and I'll knock it down like the rest of them.
But in an infinite time according to my clock and your clock, and ET's clock. So she never crosses the horizon.ben m said:
And MTW is wrong. That's what this whole discussion is about. Your good book is wrong. Look at that lefthand chart and the chopped off infinity. A clock going infinitely slow along with an observer observing infinitely slow doesn't get you past the end of time. Hop skippity jump!ben m said:
Yes!ben m said:
Gotta go.
Yes, there are coordinate systems in which she never gets there. The coordinate system where you and I are sitting still watching our clocks? That's one of them. Einstein's GR includes that.
Hey, whoa! That's a different clock, in a different location, moving at a different speed. Why did you take results from your clock and decide that they would be true on this one? You forgot to do the transformation.
... according to some clocks, and not others. Why don't you use GR to do this frame transformation? Is GR wrong?
Sorry, Farsight, Einstein appears to disagree with you. I have a spacetime that Einstein says is valid, a coordinate system in that metric that Einstein's math says is valid, and an equation of motion following Einstein's prescription. Which part is the "fairytale"?
When else does Einstein's math go so far wrong? How did, e.g., Hulse and Taylor predict the pulsar spindown rate? They used Einstein's math, straight out of the box, without doing a separate, nonmathematical "fairytale check" using the Farsight ask-a-distant-observer-and-don't-transform method?
sol invictus
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I didn't ask about the moment she crosses the horizon. I asked about the moment just before (say, 1 microsecond as measured by her clock), which does take place even in the coordinates you insist on.
You've agreed that our intrepid explorer will live up to that moment, and moreover will notice nothing whatsoever unusual. Not only will she not notice anything unusual, she won't be able to measure anything unusual, no matter how precise an experiment she does (again, apart from tidal forces - but even those don't necessarily tell her she's crossed a horizon). For her, up until that moment all clocks are ticking as usual, she's getting hungry at the usual rate, she can play tennis or a game of billiards as usual. She can even open a porthole and look outside at the stars behind her - for a large black hole she'll see nothing unusual, just some displacement of their location due to lensing.
So here we have this experimenter, living normally, noticing nothing - and yet, according to you, at some random instant that she cannot possibly determine by any experiment, time just..... stops. One can't ask about any moment afterwards. You even assert that there is no moment afterwards. According to you, time literally comes to an end, with no warning and no physical mechanism.
That's a totally absurd position on its face. (And let me point out again that it's also manifestly wrong, because any location in space is on the horizon in some set of coordinates.)
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Daylightstar
Philosopher
W.D.Clinger
Philosopher
some homework problems for Farsight, epilogue 2
The homework problems I posted in Part 1 (see also this correction), Part 2, and Part 3 covered the basic definition of a spacetime manifold, Schwarzschild charts, and Lemaître charts. The relationship between Schwarzschild and Lemaître coordinates was first described in
What we now know as Lemaître coordinates were introduced in section 11 of that paper. From its introduction:
Section 11 begins by stating the Schwarzschild metric in Schwarzschild coordinates and referring to the singularity at r=2M. Then:
In other words, the singularity is a mere coordinate singularity, akin to the coordinate singularities that occur at the poles of apolar spherical coordinate system. Lemaître then derives what we now call Lemaître coordinates and states the metric in those coordinates. Having proved the equivalent of my exercises 20 and 21, Lemaître concludes section 11 as follows:
Farsight's arguments are based upon his own personal misinterpretation of that "fictitious singularity" as a genuine singularity.
Farsight's like the guy who's got his atlas open to a chart that shows only the 48 contiguous states, and is using that chart to deny the existence of Hawaii and Alaska. When we tell him the next page contains a chart of all 50 states plus Mexico and Canada, he refuses to look.
I am not making this up:
Because Farsight literally does not understand the most basic facts about spacetime manifolds, he is not qualified to judge whether MTW and other textbooks are right or wrong. He could learn something about relativity if he tried, but that might take a day or so of effort (or much longer if he has to learn calculus first). It's much easier for him to dismiss erudition out of hand, just because erudition and knowledge lead to conclusions that don't agree with his uninformed prejudices.
My exercises didn't do Farsight any good because he didn't do them. The exercises helped me, though, because I had never before used Lemaître coordinates.
Exercises 20 and 21 don't just tell you what's wrong with Farsight's argument: They show you. If you're proficient in high school algebra and differential calculus, you should be able to work through all of the exercises (except exercise 8) in a few hours. Those exercises won't make you into an expert on general relativity, but they'll give you a head start on Farsight.
The homework problems I posted in Part 1 (see also this correction), Part 2, and Part 3 covered the basic definition of a spacetime manifold, Schwarzschild charts, and Lemaître charts. The relationship between Schwarzschild and Lemaître coordinates was first described in
Georges Lemaître. L'Univers en expansion. Annales de la Société scientifique de Bruxelles A 53, 51 (1933).
I haven't been able to locate that paper online, and I don't read French anyway, but I found this English translation yesterday:Georges Lemaître. The expanding universe. (Translated by M A H MacCallum.) General Relativity and Gravitation, volume 29, number 5, 1997, pages 641-680. DOI: 10.1023/A:1018855621348. Online at http://www.springerlink.com/content/k52l15p7g086mqu5/
What we now know as Lemaître coordinates were introduced in section 11 of that paper. From its introduction:
Lemaître said:
Section 11 begins by stating the Schwarzschild metric in Schwarzschild coordinates and referring to the singularity at r=2M. Then:
Lemaître said:
In other words, the singularity is a mere coordinate singularity, akin to the coordinate singularities that occur at the poles of a
Lemaître said:
Farsight's arguments are based upon his own personal misinterpretation of that "fictitious singularity" as a genuine singularity.
Farsight's like the guy who's got his atlas open to a chart that shows only the 48 contiguous states, and is using that chart to deny the existence of Hawaii and Alaska. When we tell him the next page contains a chart of all 50 states plus Mexico and Canada, he refuses to look.
I am not making this up:
Farsight hasn't done his homework. As shown in exercises 20 and 21, that division by zero occurs only when the metric is expressed in Schwarzschild coordinates. When exactly the same metric is expressed in Lemaître coordinates, there is no division by zero at the event horizon.
Farsight hasn't done his homework, so he's using the wrong coordinate system here. As shown in exercise 23, Schwarzschild coordinates describe the situation as observed by an observer at infinity (or by an observer who's undergoing an outward acceleration that exactly counteracts the gravitational attraction of the black hole). As shown in exercise 22, Lemaître coordinates describe the situation as observed by the unfortunate woman who's free-falling into the black hole.
Farsight hasn't done his homework. As shown in exercises 20 and 21, the spacetime manifold extends beyond the open set on which Schwarzschild coordinates are defined. Had Farsight done his homework, he'd know Lemaître coordinates are finite and perfectly smooth at the event horizon, where Schwarzschild coordinates blow up because of a mere coordinate singularity.
Farsight hasn't done his homework. Had he worked through the exercises, he'd know Lemaître coordinates describe exactly the same spacetime manifold whose outer portion is described by the Schwarzschild coordinates. He'd also know that Lemaître coordinates cover more of that manifold because they don't suffer from the coordinate singularity that limits Schwarzschild charts to the submanifold that lies outside the event horizon. Lemaître charts provide a perfectly smooth description that goes all the way down to the physical singularity at the heart of the black hole.
Farsight hasn't done his homework. He flat-out refused to work through a simple set of exercises that would have taught him a few basic facts about general relativity and the spacetime manifold surrounding a black hole.
Because Farsight literally does not understand the most basic facts about spacetime manifolds, he is not qualified to judge whether MTW and other textbooks are right or wrong. He could learn something about relativity if he tried, but that might take a day or so of effort (or much longer if he has to learn calculus first). It's much easier for him to dismiss erudition out of hand, just because erudition and knowledge lead to conclusions that don't agree with his uninformed prejudices.
My exercises didn't do Farsight any good because he didn't do them. The exercises helped me, though, because I had never before used Lemaître coordinates.
Exercises 20 and 21 don't just tell you what's wrong with Farsight's argument: They show you. If you're proficient in high school algebra and differential calculus, you should be able to work through all of the exercises (except exercise 8) in a few hours. Those exercises won't make you into an expert on general relativity, but they'll give you a head start on Farsight.
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W.D. Clinger, my hat's off to you; your three "homework" posts were very educational. To me, anyway. My MTW coursework is in the increasingly-distant past, and your posts remind me of things I *used* to be able to solve and prove.
As for Farsight, I think Upton Sinclair said the right thing. "It is difficult to get a man to understand something, when hissalary ego depends upon his not understanding it."
As for Farsight, I think Upton Sinclair said the right thing. "It is difficult to get a man to understand something, when his
We sit here watching our clocks and looking through our telescopes, and we adopt the thing we call a coordinate system for our measurements. I've just been out for a cigarette, and I looked up at the night sky. I saw stars. They exist. The space between them exists too, and we're sure enough that black holes exist too. But coordinate systems don't. Here we are 13.7 billion years after what appears to be the beginning of the universe, at 18:22 GMT on 11th February 2012, and she hasn't got there yet. Let's call her Alice. There is no situation or coordinate system in which she has got there yet.
Whoa yourself. You said She crosses the horizon in a finite time according to her own clock, in post #156. I merely said She's sitting there in front of her light clock, so don't clutch at straws suggesting I forgot something. It doesn't matter what coordinate system you use, and regardless of transformations from one to another, you can't make Alice's collision event happen yet and not happen yet.
No, but some of the things people ascribe to GR are.
The point singularity in the middle of the black hole. It's always in the future.
It doesn't. The interpretation of the maths goes wrong when people sweep an infinity under the carpet. Now where's that expression of yours?
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Sure I can. I've done it. It's an ordinary, boring disagreement-between-observers, of the sort that happens all the time in SR and GR. One observer thinks a quantity has diverged, another doesn't. As Sol has emphasized, you can find observers who have such disagreements even in flat spacetime.
OK.
Agreed. But as she approaches the event horizon, she's subject to increasing gravitational time dilation. Her awareness is slowing down, and she doesn't notice it. She doesn't notice anything unusual as she stops noticing everything.
There's some issues with this, but let's come back to it another time.
I told you that the motion of light ceases due to total vacuum impedance in post #159. Please don't try to suggest that I'm advancing wild hypotheses without scientific support. For your convenience I'll reiterate what I said:
Stop talking about stopping time. Make the leap to stopping light. There's nothing bizarre or mysterious. Think back to the optical clocks losing synchronisation at different elevations, simplified to parallel-mirror light clocks.
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One light beam is going slower than the other, and c = √(1/ε0μ0). The vacuum impedance of space Z0 = √(μ0/ε0) is increasing. Increase it so that it totally impedes the motion of light, and you stop light. Then nothing moves and clocks don't tick. Waves can't propagate through space any more. It's that simple.
It isn't manifestly wrong. Those coordinate systems are abstract mathematical artefacts. Black holes exist, space exists, light exists, gravitational fields exist. All these things are manifest. Coordinate systems are not.
sol invictus
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That's precisely what you are doing.
That's exactly the point. Coordinate systems are human conventions, they have no bearing on reality. You can choose any coordinates you like - and it's only in the coordinate system you insist on always using that light slows down or time stops at the horizon. In an infinite number of other coordinate systems, all equally as valid as yours, nothing unusual happens at the horizon.
What's with the eleastic? See this article re gravitomagnetism.
I'm not, you are. I'm showing you the variable speed of light, you're refusing to look, preferring instead to wallow in mathematical abstraction and erudition and to believe that for a stopped observer a stopped clock carries on ticking. And please, spare me your not-qualified to judge pomposity. You have no counter-argument, and it shows.[W.D.Clinger said:
Look in the mirror, ben. You have no counterargument, remember?
It's pretty clear that he does, and I don't understand why you quote that bit rather than addressing it.
Daylightstar
Philosopher
No, your 'elastic response'.
I did not ask you to again post a link to a story which does not detail your 'elastic response' with respect to space ('that black stuff between the stars') sustaining/holding/supporting waves and fields.
I asked you to detail your 'elastic response', your claimed 'method' for space ('that black stuff between the stars') to sustain/hold/support waves and fields.
If you'd be so kind, please do so now.
Oh, right, I forgot. Thanks for reminding me. I was distracted by the GR textbook on my desk, which contains such sentences as this:
Misner Thorne and Wheeler page 11 said:
I've got some niggling feeling that this is relevant, given that your argument revolves around something to do with v=0, and that when t=infinity it's true that 1/t=0, but ... well, I can't put my finger on it. Someone of my feeble intellect could never build that into something as high-falutin' as an actual counter-argument.
Maybe if I had the textbook on an actual counter. Would that help?
ctamblyn
Data Ghost
I seem to remember having this conversation once before, but I could be thinking of someone else. I think I remember you suggesting some time back that gravity could be described in terms of a sort of "refractive index" of space.
I hope one of the professionals here will correct me if I'm wrong, but if I understand this correctly your hypothesis implies that gravity could be described completely by a single scalar field. If so then your wrong to say "it's that simple", since AFAIK there are no successful scalar theories of gravity.
For example, Nordström (who knew what he was doing) tried to formulate such a theory back in 1913. It suffers with a number of problems:
- It predicts that light is not bent by gravitational fields (in contradiction to observation).
- It predicts that the perihelion of Mercury's orbit will lag by 7 arcseconds per year, instead of advancing by 43 (contradicting observation).
- It gets the Shapiro time delay prediction wrong (contradicting observation once more).
Since this matter is anything but "simple", perhaps you could actually show that your theory fares better than Nordström's when applied to these classical tests?
No I'm not. I'm advocating the "frozen star" concept that dates back to Oppenheimer as mentioned here: http://arxiv.org/abs/1003.1359 . The author of this paper says "matter can indeed fall across the event horizon within a finite time" but disagreeing with that really isn't some wild hypothesis. Come on sol, you do yourself a disservice by trying to portray it as so.
I'm not choosing any coordinate system, I'm pointing out the hard scientific evidence of optical clocks and giving a chain of logic saying the speed of light really does vary like Einstein said, and that light doesn't get out of that massive thing at the centre of the galaxy with stars swinging around it for a simple reason. You know full well that light going straight up from a black hole doesn't curve back down, just as light passing between two stars isn't curved. The light doesn't get out because it's stopped. You don't need a coordinate system to see the bleedin' obvious that leads you to this: parallel-mirror light clocks at different elevations lose synchronisation because the speed of light isn't constant. Not the coordinate speed of light isn't constant. You've got light moving between two mirrors, that's what's actually there, not the human convention of a non-inertial reference frame, and not time flowing. Just light, moving through the space between mirrors.
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Did you read the paper? It quotes Oppenheimer himself agreeing with us and disagreeing with you.
Yes, Farsight, it is a wild hypothesis to imagine that some parts of GR are correct except that this one particular coordinate-singularity is "real" and observer-independent. That's standard crackpot physics.
Would you like to reiterate his pretty clear counter-argument? Didn't think so.
I can't detail it without going into electromagnetic four-potential and displacement current and the nature of the photon, and that would take a long time. Please start a thread if you want me to talk about it it. But meanwhile have at displacement current on wiki and note the Maxwell quotes where elastic is mentioned:Daylightstar said:
"The author of this method of representation does not attempt to explain the origin of the observed forces by the effects due to these strains in the elastic solid, but makes use of the mathematical analogies of the two problems to assist the imagination in the study of both".
"These relations are independent of any theory about the mechanism of dielectrics; but when we find electromotive force producing electric displacement in a dielectric, and when we find the dielectric recovering from its state of electric displacement...we cannot help regarding the phenomena as those of an elastic body, yielding to a pressure and recovering its form when the pressure is removed."
Also see Einstein talking about the history of field theory in 1929. Here's a few snippets:
"People slowly accustomed themselves to the idea that the physical states of space itself were the final physical reality...
It is only natural that attempts were made to represent the material particles as structures in the field...
But the special theory of relativity showed that this causal correlation corresponds to an essential identity of the two types of field. In fact, the same condition of space, which in one coordinate system appears as a pure magnetic field, appears simultaneously in another coordinate system in relative motion as an electric field, and vice versa..."
Or see LIGO where you can read this:
"When large masses move suddenly, some of this space-time curvature ripples outward, spreading in much the way ripples do the surface of an agitated pond".
Note that space isn't a substance, it isn't some elastic solid in the usual sense. But waves do propagate through it. We know that electromagnetic waves do, and we're confident that gravitational waves do too. And LIGO is intended to detect a transient length-change in the arms of the interferometer:
"The space-time ripples cause the distance measured by a light beam to change as the gravitational wave passes by".
If the distance changes, the thing that's waving is space. And the wave can only propagate if space somehow "kicks back" via some kind of elastic response.
sol invictus
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Of course it is. It disagrees with all established science, including the very same science you claim to be using to reach your conclusion.
Then you should be happy with a choice of coordinates in which the coordinate speed of light does nothing unusual at the horizon. But you're not, you refuse to accept that. Ergo, you're insisting on one specific coordinate system. That's precisely the contrary of the fundamental truth general relativity is based on - that choices of coordinates are meaningless and arbitrary.
You're such a GR novice that you don't even notice when you're using a coordinate system.
ctamblyn
Data Ghost
Um, the paper you linked to disagrees with you explicitly. From pp. 5-6:
Shuang-Nan Zhang said:
(Here, RH refers to the event horizon radius.)
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ctamblyn
Data Ghost
I wonder, which is the "privileged" coordinate system to use in the real world (i.e. the one that lacks spherical symmetry and may or may not be asymptotically flat, etc.)
Yes I did and no it doesn't, because it says this:
“An external observer [O hereafter] sees the star asymptotically shrinking to its gravitational radius [the radius of the event horizon of the BH of the same mass, RH = 2GM/c2 hereafter.].” This means that O will never witness the formation of an astrophysical BH. Given the finite age of the universe and the fact that all observers are necessarily external, the last conclusion of Ref. 1 seems to indicate that astrophysical BHs cannot be formed in the physical universe through gravitational collapse.
Yeah yeah, I give you the frozen star and it's some wild hypothesis? And now crackpot physics? Sheesh, come on, hurl some more abuse at me. Call me feather-spitting names, as much as you like. It only makes it even more patently obvious that you've got no counter-argument whatsoever. LOL.ben m said:
Is that all you're left with? That the frozen star disagrees with all established science? To hell with the light and the mirrors, to hell with my post #177, you're going to ignore the scientific evidence and start bleating about all established science. Sol, I am disappointed with you. I expected rather more. I expected a rational discussion, not evasion.
What part of I'm not choosing any coordinate system did you fail to understand? Coordinate systems don't exist, remember? Coordinate systems are human conventions, they have no bearing on reality. What's real is light moving through space. Or not moving through space.
I'm sorry sol, but there are no "fundamental truths", and the general relativity you've been taught is a corrupted version of the real thing. Einstein told you the speed of light varied, and the scientific evidence is right there under your nose. Get used to it.
Oh slings and arrows. I don't need a coordinate system to see two optical clocks losing synchronisation, I just look at the numbers. And I don't have to be the Brain of Britain to work out that the speed of light isn't constant, or come across Einstein telling everybody about it. Then when I hear people saying Einstein told us the speed of light is constant I can laugh and say, Ooh, lookie here, two racehorses running at the same speed:
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Um, I did say The author of this paper says "matter can indeed fall across the event horizon within a finite time" but disagreeing with that really isn't some wild hypothesis..
Yes, that's what we've all been saying. In the coordinate system of an external observer, objects arrive at the event horizon only when t=infinity. That's the easily-computed, well-known GR prediction for this quantity in this coordinate system. The statement that "stuff never falls in" is a statement about the experience of coordinate system O, not an invariant statement about spacetime.
And the paper explicitly points out a coordinate system, different than O, that sees stuff fall in. You have an astounding ability to ignore that.