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Author Topic: Can a infalling object travel an infinite distance in finite time? Black holes..  (Read 3229 times)

Offline yor_on

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I would have like to have place for 'frames of reference' in the Caption too, but it was impossible, and the Q above is what leads to my Q below. The idea behind the first Q is that as you come near a Black Holes EV (Event Horizon) you will find all 'frames' getting 'compressed' meaning that trying to touch the EV with a steel rod will break the tip into smithereens, as it gets more and more compressed when closing to that mythical EV.

Also, the different 'frames of reference' created for a far observer, versus a near observer free-falling towards a BH, will make it impossible for them to agree on what they see, and where that Event-horizon will be. Read The Event Horizon for a fuller description of how the different frames will express itself.

The main thing here is that for the far observer observing it will take the near observer an infinite time to reach that EV as he falls, which (hopefully) makes the caption above to become sensible :) as if it take him a infinite time according to the far observer, then you as easily can exchange that time to 'infinite distance' at the speed of ?? whatever number you like..

After all Distance is made by 'velocity x time = Distance' right? Not speed x time as you can have a light corn bounce between mirrors, well, there it will come out the same, but if it was a ping-pong ball it would lose some time at every bounce and so diffuse the answer, I think?

Any which way, you now have it in a nutshell, a black one too, very difficult to locate..

==


As i understands it's all about 'frames of reference'. For the far observer the infalling observer never will touch the event horizon, for the infalling observer it will seem as if he too never will touch the event-horizon, although he possibly can arrive at the center of the singularity. That one is slightly weird to me :)

"Observers who fall into the hole are moving with respect to the  distant observer and so perceive the horizon as being in a different  location, seeming to recede in front of them so that they never contact  it. Increasing tidal forces (and eventual impact with the hole's gravitational singularity) are the only locally noticeable effects"

This might help us to see some light in the tunnel.

"It has been ninety years since Schwarzschild presented the first exact solution to the field equations of general relativity (Schwarzschild 1916). Representing the spacetime curvature outside of a spherical mass distribution, the existence of singularities in the solution led to several confusing problems. Importantly, the coordinate time is seen to diverge as an object falling in this spacetime approaches the Schwarzschild radius (r = 2m, in units where G = c = 1 and where m is the mass of the black hole), with the conclusion that the entire history of the Universe can pass before anything actually falls to this radius.

Paradoxically, the proper time as experienced by the falling object is finite through r = 2m and the faller reaches r = 0 in finite time. A reformulation of the Schwarzschild solution in free-falling coordinates revealed the Schwarzschild radius to be an event horizon, a boundary which can only be crossed from r > 2m, but not from r < 2m, leading to notion of complete gravitational collapse and the formation of black holes (Painlev´e 1921). However, even with these advances, the singular state of the Schwarzschild solution at r = 2m led even the most famous relativist to suggest that black holes cannot form (Einstein 1939).

The resolution was ultimately provided by Finkelstein (1958) who derived a coordinate transformation of the Schwarzschild solution which made it finite at r = 2m; this was, however, a rediscovery of the earlier work by Eddington (1924) who apparently did not realize its significance 2. With this transformation the true nature of the Schwarzschild radius was revealed, acting as a one-way membrane between the Universe and inner region of the black hole.

As discussed in many texts, the transformation to Eddington-Finkelstein coordinates clearly reveals the ultimate fate of an infalling observer. Now crossing the event horizon in a finite coordinate time, the future light cones for all massive explorers are tilted over such that there is no way back and the future ultimately lies at the central singularity. But after crossing the horizon, how long does the intrepid explorer have until this happens, and what can they do to maximize their survival time? For a free-falling path, the calculation of the proper time experienced by the explorer is a question found in graduate texts (e.g. see problem 12-14 in Hartle 2003) and it is straightforward to show that the maximum time that can be experienced below the event horizon is  = m (1)

For a stellar mass black hole, this will be a fraction of a second, but for a supermassive black hole, this may be hours. As will be shown later, this maximum time applies to a faller who drops from rest at the event horizon and any one who starts falling from above the event horizon and free falls into the hole will experience less proper time on the journey from the event horizon to the singularity.

From No Way Back: Maximizing survival time below the Schwarzschild event horizon.   

And there we will find the proper math too.

As for the gravity, as i understands it, what will kill are 'tidal forces', like the frame dragging of a spinning BH, all depending on what type of BH one falls into. A free fall is just following the geodesics of SpaceTime and as such 'weightless', no matter where you fall. The same as a uniform motion inside a 'black box' will seem equivalent to all other uniform motions, no matter their velocity as compared to a common frame of reference or 'origin', as I understands it that is :)

But the closer one comes to the EV the more accentuated the different 'frames of reference' will be, and the more compressed they should become. But before passing any EV the tidal forces will tear apart all particles in your body, the directions depending on the tidal forces vectors. Ouch, it seems as if i was wrong there saying that you will be killed by tidal forces before the EV. It depends on the size apparently.

" For a supermassive black hole, such as those found at a galaxy's center, this point lies within the event horizon, so an astronaut may cross the event horizon without noticing any squashing and pulling (although it's only a matter of time, because once inside an event horizon, falling towards the center is inevitable). For small black holes whose Schwarzschild radius is much closer to the singularity, the tidal forces would kill even before the astronaut reaches the event horizon For example, for a black hole of 10 Sun masses and the above-mentioned rope at 1000 km distance, the tensile force halfway the rope is 325 N. It will break at a distance of 320 km, well outside the Schwarzschild radius of 30 km. For a black hole of 10,000 Sun masses it will break at a distance of 3200 km, well inside the Schwarzschild radius of 30,000 km. "

Spaghettification 

Anyway: Here's my question.

This is quite a headache for me, wondering how to differ one of those frames from another, I mean, a cubic mm of 'normal matter' on Earth, how many different 'frames' does it contain? it have quarks, electrons, atoms etc, all having their own mass, spins and gravity, shouldn't they too represent different 'frames of reference'? As well as a cubic mm of the event horizon (ahem:) or a black hole would do?

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« Last Edit: 10/09/2010 18:27:20 by yor_on »


 

Offline CPT ArkAngel

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As soon as something takes spacetime it is surely made of many frames of reference.

What i understand of the Holographic principle is that everything going through the event horizon is stored as kind of (analog to) holographic information at the event horizon, thus, keeping the conservation of information intact (no information is lost inside the black hole, entropy is not reduced). I always thought that if you want to accelerate something at the speed of light or beyond, you have to change it into light. What if there is no spacetime beyond the event horizon and everything crossing it is transformed into light, making a kind of holographic image on it. This could produce an image at the singularity point that is interacting physically with the Universe...
« Last Edit: 10/09/2010 04:57:05 by CPT ArkAngel »
 

Offline yor_on

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Conservation of information CPT :) I've read about the holographic principle even though it been some time since last. What interests me as much as frames, and how you define those, is the idea building information. We see it in a lot of theories but it's a very slippery thing to me. I have no real problem with the idea of SpaceTime being a self contained 'bubble' conserving whatever it is we have here, well i have in a way. We also have 'Virtuality' intruding from 'nowhere' as well as 'vacuum energy'. But the principle seems to hold in that they exist without infusing or stealing energy from our 'real reality' aka SpaceTime, possibly? There is of course the idea of inflation intruding where space is expected to grow, the question here is if we can call a growing SpaceTime for 'self contained'? And that question have nothing to do with the fact that the amount of energy may be constant per distance, or rather , it has. If we trust to distance as a true measure of a quantity then a bigger SpaceTime will need more 'vacuum energy' to keep itself constant. And such a universe may be in 'equilibrium' but it seems hard to call it 'self contained' or 'closed'?

Never the less, it's 'information' people love to refer to as the smallest 'bits' 'pixels' 'qbits' etc of our SpaceTime, an almost mythical property that. And I still haven't seen what it really is. the problem, for me, is the idea of that no information can be 'lost'. We live in a non-linear universe, a universe with many answers to one question as observed at  the quantum level. We use 'cut offs' to get away from that fact and then we test those cut offs against what we think is reality, the closest match to what we expect in form of other experiments etc will decide those 'cut offs', and so we have walked around the disconcerting fact that the universe seems to have a slightly different approach to 'science' than what we humans have. So the universe I expect to be of a fractal nature, 'self-like' in many ways, dolls inside dolls inside dolls :)


And if that is true there will be hidden constants to it, that we only can see when repeatedly observing some strange 'coincidence' what we in Sweden call 'nature constants'. but this 'information idea' seems to treat the universe as a closed system when it comes to the answers, with a 'finite amount of answers' as implied by the idea that it is 'closed'. Open ended systems are undefinable in their amounts as I see it, even though we might be able to arrange them in some order, as we do with 'smaller and larger infinities' mathematically. There is also the question of the uncertainty principle adding a undefinability to our observations. Consider thoughts, would you call that information? If you do, and I'm sure I will call it that in any way :) What are retrievable there? The electrochemical activity? Is that the thoughts, naah, send electricity through the brain and you will see an awful lot of electrochemical activity, none of them related to thoughts. But thoughts are what created this idea of information, nothing less.

So I find the idea questionable to say the least. Then again, if you by information mean all 'states' of a universe, whatever those 'states' may be defined as, and defined they need to be before any real discussion is possible, also including what they expect thoughts to be, and then think of time as a movie that we can play backwards. Then we theoretically can say that all is included and that this is what we mean by 'information'. Even though the definition is totally meaningless in that it doesn't define anything more than two things, a 'closed universe' and time as a property that we for this question can play backwards. But the real mistake here is what I see as information and what this definition call information. In a non-linear universe 'paths' bifurcates meaning that they break open into sudden splits, they are unpredictable on the 'individual plane' and impossible to back track after enough iterations been made. That is the universe and that is information lost.

We can't just expect to play the universe back and so expect us to find the same amount of answers, well, we would see the bifurcations made, so in that sense we could say that we saw all that was there, but as they are 'individually unpredictable' we would find when 'restarting the movie' that the universe this time would choose slightly different paths than the time before, at least that's my expectation. And that's where those so called 'nature constants' seems to step in to bring order, somehow they form a larger pattern when found, and being constant they will be the same for both 'movies', that means that this pattern won't change, even though the 'individual approaches' and bifurcations will be different this second time we play the movie 'the universe and all' :)

And that's my kind of universe, love-able and mysterious, steered by patterns but leaving a lot of room for individual approaches and 'free will'. You will see a similar pattern in statistics, the weather, most anything you keep a record of for a longer time, and one might notice that if looked on this way it's not only us humans that seems to have a 'free will' individually, the whole universe share that approach to reality more or less, as the bifurcations are unpredictable even though the overall patterns won't be.

It's a very weird idea, information, and as I see it very hard to define. More like a fad to me than anything really defined, and considering Hawking radiation most needed to be defined, as we there discuss a singularity with no defined center and an unknowable 'interior' Terra incognito and 'here there might be thygers' :) and I think 'states' is a better name for it too. Information means something useful to me, but the 'states' of this universe and what 'real' information we write on that melting ice-cube can never be retrieved by us, once melted. The uncertainty principle alone guarantees that, as well as our inability to encompass a whole universe in retrieving the same, furthermore we always brings in new 'noise' into any 'system' we observe, even though it might be possible in some situations to use what's called 'weak' observations, avoiding to observe the system directly, and instead just look at the interactions made with systems 'beside' it to guess what happened. Although I sincerely doubt that ever will work with our written answer to the riddle of the 'universe and all' on that ice-cube. And by the way, the answer is, as we all know, 42..

Ahem. and. For your information :)

Phiewww :)
==

Too long huh :)

 

==

« Last Edit: 10/09/2010 11:14:16 by yor_on »
 

Offline Farsight

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...Anyway: Here's my question. This is quite a headache for me, wondering how to differ one of those frames from another, I mean, a cubic mm of 'normal matter' on Earth, how many different 'frames' does it contain? it have quarks, electrons, atoms etc, all having their own mass, spins and gravity, shouldn't they too represent different 'frames of reference'? As well as a cubic mm of the event horizon (ahem:) or a black hole would do?
None. A reference frame is an abstraction, not something that actually exists. It's an artefact of measurement. In special relativity it's associated with your motion, wherein you measure time and distance differently when you move fast. This is then related to general relativity via the principle of equivalence, such that standing on the surface of the earth is like accelerating through space.

I can cure your headache. You know where you quoted this:

Importantly, the coordinate time is seen to diverge as an object falling in this spacetime approaches the Schwarzschild radius (r = 2m, in units where G = c = 1 and where m is the mass of the black hole), with the conclusion that the entire history of the Universe can pass before anything actually falls to this radius.

Stop and think for a minute about what this really means in the real world. It's obvious once you see it: it never ever happens. That's why this is wrong:

Paradoxically, the proper time as experienced by the falling object is finite through r = 2m and the faller reaches r = 0 in finite time.

As the infalling observer gets closer to the event horizon his proper time is increasingly time dilated. At the event horizon this time dilation is infinite. So that finite proper time is being measured using a stopped clock! All processes are similarly stopped. Hence: 

However, even with these advances, the singular state of the Schwarzschild solution at r = 2m led even the most famous relativist to suggest that black holes cannot form (Einstein 1939).

That's Einstein backing me up. Note however that black holes still can still form, but singularities at the centre can't. Now take a look at this:

The resolution was ultimately provided by Finkelstein (1958) who derived a coordinate transformation of the Schwarzschild solution which made it finite at r = 2m... As discussed in many texts, the transformation to Eddington-Finkelstein coordinates clearly reveals the ultimate fate of an infalling observer.

The major text here is Misner/Thorne/Wheeler's "Gravitation". It's wrong, because the coordinate transformation is a mathematical trick that pretends that the stopped clock isn't stopped. Sadly people take this as bona-fide relativity, so going against Einstein. The correct understanding is offered by the Weinberg field interpretation. Have a read of The Formation and Growth of Black Holes to see mention of this. The author does side with the MTW interpretation which is a pity. But the point of me linking to the article is to demonstrate that what you usually hear about black holes is only one interpretation of GR, rather than what GR actually says.

 

Offline yor_on

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You can't have read the paper? The link didn't work, as i found out just now, checking it after reading your conclusions. Which bothers me quite a bit, although I have fixed it now :) It's quoted verbatim from "No Way Back: Maximizing survival time below the Schwarzschild event horizon." above Farsight, as I also stated in that other post. Please read it before first though, then you can always correct the authors and tell them where they did go wrong. I'm sure they will take notice, and even thank you, if you now would be correct in your conclusions. You can find them at the School of Physics at the University of Sydney. Geraint F. Lewis and Juliana Kwan.

As for the rest? Well, we seem to differ in our view of the importance of those frames of reference. I find those frames to be more than just abstractions, they are closer to reality than anything we had before them, and as such I wonder where it 'ends' :) Where the limits are, if there even is any for what can become a 'frame of reference'. We use them regularly to describe reality macroscopically, but it seems to me that they should be just as relevant microscopically? But it is a matter of definition of course, I don't feel I have the full understanding of them, maybe you feel you have? But read the paper first, and then you can explain where their math is wrong, to your hearts desire.
===

You wrote "As the infalling observer gets closer to the event horizon his proper time is increasingly time dilated. At the event horizon this time dilation is infinite. So that finite proper time is being measured using a stopped clock! All processes are similarly stopped. Hence: "

Well, that's one view, but as far as I understand 'frames of reference' your wristwatch will 'tick' as usual when compared against the rate of your heartbeats, no matter (excuse the pun) where you are. If infalling towards the EV, or being here on Earth. To assume otherwise means that you disallow both Edington and Finkelstein. Also, the time dilation can only be proved versus a common origin as in the twin experiment where you know before that they were identical twins, even though it is valid for all other frames too naturally. And that we already have tested, and found to be correct. For example, GPS systems have to be adjusted for different frames of reference. And as for Einstein doubting it. He didn't protest because he thought of any 'clocks stopping' as you seem to assume.

"Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius... In 1939 he published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein's argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse.

But it is well understood today (and was understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined. Nevertheless, the extent to which the models of black holes in classical general relativity correspond to physical reality remains unclear, and in particular the implications of the central singularity implicit in these models are still not understood. Efforts to conclusively prove the existence of event horizons have still not been successful, and most scientists acknowledge that no such proof is even possible. "

To expect a frame of reference existing in SpaceTime where 'times arrow' won't 'tick/move' is interesting but, as I expect it to be, wrong. You have to differ between the frames of reference. That the far observer sees the infalling observer 'hover', unmoving above the event horizon, is a direct result of two 'frames of reference' not agreeing on time, nor distance.
==

We have to assume that times arrow exists inside a event horizon too. To do otherwise should mean that matter would have no time-like direction after meeting the event horizon, and if so I expect the matter unlikely to pass the EV, even though that clock still was ticking to your heartbeats, all the way down to it. That seems, to me, to indicate that the singularity would be hidden inside a surface of matter, resting on the Event Horizon, which I deem highly improbable.
« Last Edit: 10/09/2010 21:37:31 by yor_on »
 

Offline Farsight

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You can't have read the paper? The link didn't work, as I found out just now, checking it after reading your conclusions. Which bothers me quite a bit, although I have fixed it now :) It's quoted verbatim from "No Way Back: Maximizing survival time below the Schwarzschild event horizon." above Farsight, as I also stated in that other post. Please read it before first though, then you can always correct the authors and tell them where they did go wrong. I'm sure they will take notice, and even thank you, if you now would be correct in your conclusions. You can find them at the School of Physics at the University of Sydney. Geraint F. Lewis and Juliana Kwan.
I'll do that. Meanwhile, what would you rather do, believe the evidence and the logic and Einstein, or some professor? 

As for the rest? Well, we seem to differ in our view of the importance of those frames of reference. I find those frames to be more than just abstractions, they are closer to reality than anything we had before them...
Lead me out into the back garden, point up to the clear night sky, and show me a reference frame. When you can't, you'll perhaps understand that a reference frame really is an artefact of measurement.

You wrote "As the infalling observer gets closer to the event horizon his proper time is increasingly time dilated. At the event horizon this time dilation is infinite. So that finite proper time is being measured using a stopped clock! All processes are similarly stopped. Hence: " Well, that's one view, but as far as I understand 'frames of reference' your wristwatch will 'tick' as usual when compared against the rate of your heartbeats, no matter (excuse the pun) where you are. If infalling towards the EV, or being here on Earth. To assume otherwise means that you disallow both Eddington and Finkelstein.
Yes, that's the size of it. In reality your wristwatch has stopped, and your heart has stopped too, forever. The next tick and the next beat only happen after the end of time. Or in other words, never. It's like you're in a film that has slowed down and slowed down until eventually it's stopped. Only you've kidded yourself that the film is still rolling. It isn't.
 
Also, the time dilation can only be proved versus a common origin as in the twin experiment where you know before that they were identical twins, even though it is valid for all other frames too naturally. And that we already have tested, and found to be correct. For example, GPS systems have to be adjusted for different frames of reference. And as for Einstein doubting it. He didn't protest because he thought of any 'clocks stopping' as you seem to assume.
He did. Einstein knew about the "operational definition" of time, and that clocks clock up motion. When he wrote general relativity he gave the equations of motion, and he knew about the coordinate speed of light going to zero. That means no more motion, and everybody in the universe at large agrees on this.   

"Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius... In 1939 he published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein's argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse.
Don't quote me some anonymous author saying Einstein was "inconclusive" on this. He was wrong about some things, but not this. Because the coordinate speed of light at the event horizon is zero, and Einstein knew it.

But it is well understood today (and was understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined. Nevertheless, the extent to which the models of black holes in classical general relativity correspond to physical reality remains unclear, and in particular the implications of the central singularity implicit in these models are still not understood. Efforts to conclusively prove the existence of event horizons have still not been successful, and most scientists acknowledge that no such proof is even possible.
That's fair enough about the central singularity, but not about the event horizon. 

To expect a frame of reference existing in SpaceTime where 'times arrow' won't 'tick/move' is interesting but, as I expect it to be, wrong. You have to differ between the frames of reference. That the far observer sees the infalling observer 'hover', unmoving above the event horizon, is a direct result of two 'frames of reference' not agreeing on time, nor distance.
A frame of reference doesn't actually exist as something that's out there. It's just an artefact that helps you describe how you see things when you're in a particular state of motion or in a particular gravitational environment. But when your clock doesn't tick, you don't see anything. You might think you do, but you don't. Because it isn't just a stopped clock you have to contend with. Your thoughts have stopped too, and so has light.   

We have to assume that times arrow exists inside a event horizon too. To do otherwise should mean that matter would have no time-like direction after meeting the event horizon, and if so I expect the matter unlikely to pass the EV, even though that clock still was ticking to your heartbeats, all the way down to it. That seems, to me, to indicate that the singularity would be hidden inside a surface of matter, resting on the Event Horizon, which I deem highly improbable.
The Scharzschild radius is where the singularity is. The singularity at r = rs is no illusion. The illusion is that stopped clocks magically keep on ticking when you adopt "another coordinate system" which does a hop skip and a jump over the end of time into a pseduoscience never-never land beyond the end of time. It never happens, yor-on. It hasn't happened yet, and it never ever will.
« Last Edit: 10/09/2010 23:26:05 by Farsight »
 

Offline yor_on

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Everything we say are abstractions. Nothing special with that, all languages are, from boolean logic to Swahili. And I want to understand those 'frames of reference' and how they are and can be used, simple as that. I was hoping for an discussion, not defending why, and also to see the concepts limits if possible. Our arguing about the clock stopping or not is just a discussion around how those frames should be interpreted, if you hadn't noticed. So, if you just want to argue the meaninglessness of my wondering Farsight, please take that discussion somewhere else.

Einstein didn't believe that a black hole could exist as he imagined that it, long before that, would be revolving at the speed of light. Which is an impossibility for matter to do, according to the the theory of relativity. Your clocks stopping, or mine ticking, both discuss a singularity Einstein didn't believe could form, you can easily check that on the net. Don't take any boring professers word for that :)

'Frames of reference' are quite complicated to me :) As they are the underlying concept explaining how motion, space and time fits together, and with that 'the sheer improbability of having changing references describing distances' And even if you don't find it mindblowing I still do, and I guess I will do so until I die. I have some references here if you, or anyone else is interested.

Let's start with Absolute and Relational Theories of Space and Motion Then read this Frames of reference  (2 pages)..
After that one can take a look here Space and Time: Inertial Frames

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This one ain't bad either, if you now read the first three, why not take a look here too for some nice graphics? Inertial reference frames.   

« Last Edit: 11/09/2010 20:43:12 by yor_on »
 

Offline Farsight

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There's nothing mindblowing about reference frames, yor on. From your second link:

An observational frame (such as an inertial frame or non-inertial frame of reference) is a physical concept related to state of motion.

A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations.


Try focussing on the special relativity case, then move to general relativity via the principle of equivalence. I'd avoid getting bogged down with absolute v relative if I were you, and maybe it would be better if you came back to black holes another time. 

 

Offline yor_on

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Ah well, this discussion is shot dead I think :)
But for those of you still curious, do read my references.
And don't get 'stuck on them' as Farsight likes to say. If you find it 'hard melted' just open another page and read. After a while that 'first one' will start to make sense too ( hopefully :)
 

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