Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: flr on 09/04/2013 06:01:58
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In the following link
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html)
they are explaining the trip toward a black hole (BH) as seen by a far observer and by the traveler.
This is what they are saying:
Quote from the link: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html
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A more physical sense in which it might be said that things take forever to fall in is provided by looking at the paths of emerging light rays. The event horizon is what, in relativity parlance, is called a "lightlike surface"; light rays can remain there. For an ideal Schwarzschild hole ... the horizon lasts forever, so the light can stay there without escaping. (If you wonder how this is reconciled with the fact that light has to travel at the constant speed c—well, the horizon is traveling at c! Relative speeds in GR are also only unambiguously defined locally, and if you're at the event horizon you are necessarily falling in; it comes at you at the speed of light.)
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What do they want to say that "well, the horizon is traveling at c!" ?
Is some sort of "space drag?"
Also, I agree with their statement that "if you're at the event horizon you are necessarily falling in; it comes at you at the speed of light.", which means that at event horizon my local speed is c (is that so?).
However, why far away observer don't see me falling into BH at c?
Light from me (image of me) on event horizon gets out at c meaning that at event horizon I see the 'local' photon going away at c. However, something is dragging back toward BH the photon at speed c such that the far away observer see the photon staying on event horizon?
What exactly is keeping the photon from escaping for the far away observer?
Is something happening near BH to the local space-time similar like space-drag effect ?
But how could be space 'falling' into BH?
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Not at the event horizon, and not anywhere as I think those days :) The speed is translated into room (locally) as you pass that event horizon, in my eyes. It's a consequence of us not having singular dimensions, glued together, instead having a four dimensional reality in where all dimensions adapt to a constant 'c'. Or if we use degrees of freedom then what we have is defined through four, one temporal, the others three ways to define matter, and space. If you use that then there is nothing saying that there can't exist more degrees although undefinable from our measurements.
As for why you won't see him move, that one is tricky. Think of the red shift as something leaves a 'gravity well', If you are outside that well it should to you look as he disappear as the red shift becomes near infinite. Another thing to consider is how frames of reference treat the arrow when we compare relative our own ruler and clock. That he will be frozen at the event horizon, to you, are related to 'your local time' relative what time you find the event horizon to present measuring.
so, is it real?
Yes, it must be real, for you. But not to the observer falling in, he will see other effects instead, still finding himself to move as usual though, with his clock and ruler as always as they are joined to a same frame of reference, 'at rest' with each other.
As for the space moving faster than light? I'm not sure, it's one way to describe it, but 'space' is in that motto consisting of 'nothing' and all 'energy' you expect it to contain is indeterministic, not really 'there' on that very small scale, so there is in theory nothing stopping a 'space' from 'moving' FTL. But if we imagine something of restmass moving in a geodesic in that space space won't 'grab hold' of it, as some river. 'Space' or a vacuum, is truly weird.
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Ahh, at the speed of light :)
Well, that is relative you, and you can't move any faster.
Or rather, you can't move at 'c', so just before 'c' he must mean.
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There is one thing more with that picture though. If you imagine yourself free falling towards a event horizon, it doesn't matter if we define it as moving, or you, as long as we are discussing uniform motion. If we now define the speed to close to 'c' it means that from the infalling observers perspective the rest of the universe would speed up, possibly even go to its entropic 'death of equality/heat bath' before you ever reach that singularity's center, maybe even at the event horizon.
And from the eye of a (immortal) far observer you would then hang there, at the event horizon, for eternity. I don't subscribe to you moving at 'c' there, as that by implication must mean that no matter ever, will pass the event horizon from the universes perspective, assuming the universe dies before it. The other position you can take is to assume that a black hole then will continue to exist and you will fall in a 'normal matter' (ignoring tidal forces) never exceeding 'c' inside that new 'room' the black hole will adapt too, relative you. And that is also a weird thought :)
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Baez uses light cones defining time, I don't, I use the same arrow at all times, unvarying, of a same amount locally. That mean that wherever you go your local clock and ruler will be the same. But it allow a universe to exist, and speed up, relative you, even though the information about that universe might be distorted. As far as I know light will still be found to come at you at 'c' at the event horizon, presuming that you can't be at that speed yourself, but it must be redshifted relative you as both you, and the light coming from the outside, are '(co)moving' relative the singularities center.
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If we now define the speed to close to 'c' it means that from the infalling observers perspective the rest of the universe would speed up, possibly even go to its entropic 'death of equality/heat bath' before you ever reach that singularity's center, maybe even at the event horizon.
But then it appears that me (the traveler) and the far away observer are in some kind of agreement.
The far away observer needs to wait till the entropic 'heat death' of the universe to see me 'very very close' to event horizon, but then myself I agree with the far away observer that so much time passed in his local frame (10^500 years let's say) that his (far away) universe must be by now fairly close to entropic death.
The only disagreement then is that while I experienced locally (near BH) just (say) 50 heartbeats, the far away observer experienced as many as 10^500 heartbeats (and his universe is almost 'entropic dust'). And as I understand, it is possible that while I experience locally 50 heartbeats, somebody else somewhere experiences (locally) 10^500 heartbeats , because that means for time to be relative.
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But then: When the faraway observer has 10^500 heartbeats (in its local frame), I only experienced (say) 50 heartbeats in my local frame and I am still running toward event horizon. So, I have not reached event horizon yet when the local clock of far away observer is 10^500 and, correspondingly, my local clock is 50.
Then the question is: There is nothing right now inside the event horizon of BH from both our our perspective (too little time passed here) and traveler perspective (his local time keep slowing down but he still have to reach those 50 local heartbeats and he must right now after (say) 10 billion years in our frame, still be fairly far from event horizon.
So there is nothing inside BH, right now, instead, it is just matter rushing toward event horizon. Is that so?
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That's the big question :)
Either there is no debris that can reach the singularity under the universes existence, at least until the 'heat death'. That might then mean that there is no new black holes, only those created at some origin, or possibly that you can get a new black hole, as that is a compression of mass, but you can't feed it?
Or they get feed.
It's also a question if they even pass the event horizon, I guess? Because well past that they can be defined as belonging to the black hole, wherever they are.
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And no, time is only 'relative' in a comparison between frames of reference. If you use heartbeats to define a life span, then you will have the same amount of heartbeats, wherever you go, and no matter how fast it seems to be to you, locally measuring a speed relative ? fixed stars maybe?
Your local time is not relative, it's a fixed amount, relative your local clock (and ruler)
The question there though, is at what scale this 'fixed amount' plays. If we use NIST then they have found frames of reference at centimeters (gravitational time dilation). Myself I would like to define it at Planck scale. But the discrepancies are so small locally that they are not noticeable, normally experienced that is. And then you have one more definition to consider, the one where you are defined as being 'at rest' with something else. Macroscopically we could say that you are 'at rest' with Earth, everyone sharing a same arrow of time, which would be a very good description macroscopically although questionable from NIST point of view (and mine).
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@youron
What I meant to say is this:
I am near BH, and I start the clock, I count my local time, and then stop it after 50 heartbeats (in my local time).
During the amount of time I am experiencing 50 heartbeats near BH, it should be that the far away observer experienced 10^500 heartbeats.
Am I getting this right?
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As far as I get it you should be. Not counting heartbeats, you have to remember that this is no different from a gravitational time dilation though. And that NIST have shown existing, differentiated just by centimeters, on Earth too. Time is to me a very local phenomena, and a constant relative both heartbeats and frames of reference, locally measured. You can see the last most easily, imagining someone joining the exact same frame of reference as you. They will then perceive their ruler and clock to be the exact same as yours, or, ignoring that, you and they will have the exact same description of the rest of the universe.
Remember that idea of how all photons should be able to be superimposed upon each other? If we could do the same with matter all observer dependencies would disappear. It's all about comparing frames of reference to each other. That's also why so many believe 'time' and its arrow to be a illusion. But they seem to forget contractions :) And you can easily replace the arrow with 'c' if you like, 'splitting' light to Planck scale. That is where light take one Planck step in one Planck time. Under that it becomes meaningless to describe (as far as I know).
Using that you can see the universe two ways, either with light propagating or using light as a ultimate clock, lightening up a reality. and that last one is the one I like most I'm afraid. A very weird idea, with me being partial to such. But then we also will have left all main-stream definitions for a very theoretical one, simplifying some of the things I find hardest to understand, although becoming a universe where most of our definitions, from motion to distances becomes? The easiest definition is to describe light as propagating I guess, especially as we find it to have sources (Suns) and sinks (mass). With a Sun being a little of both I better add.
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That's the big question :)
Either there is no debris that can reach the singularity under the universes existence, at least until the 'heat death'. That might then mean that there is no new black holes, only those created at some origin, or possibly that you can get a new black hole, as that is a compression of mass, but you can't feed it?
This thought exercise has been very revealing to me because this concept had never really crossed my mind before. It seems quite possible to me that, according to both observational perspectives, our traveler to the black hole has not yet reached the singularity. However, the event horizon is only the point of no return, not the point of exaggerated acceleration. Only when the traveler gets close enough to the singularity will his velocity become enough to exaggerate the time dilation differential between both observers to cause the effect your speaking of. Even so, according to the locally removed observer, his image will still appear to remain at the event horizon.
It's also a question if they even pass the event horizon, I guess? Because well past that they can be defined as belonging to the black hole, wherever they are.
It is however quite possible for the traveler to pass the event horizon in accordance with his own observational perspective. This is true because, in the case of super massive black holes, it would be quite possible for the traveler to penetrate the event horizon without even realizing it. Only when the approach to the singularity becomes close enough for gravity to accelerate him to a significant fraction of c, will time begin to slow down for him and speed up for the locally removed observer. Black holes of this mass would need to be, however, very massive indeed. Nevertheless, the possibility still remains.
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Some time ago, when I was trying to sort out my thoughts about infinity, I got to thinking about this topic. As is my wont, I wrote everything down. I'll try extracting some bits from my notes, which might be relevant here. I would certainly appreciate some comments.
The general theory of relativity predicts a time dilatation in a gravitational field, so that, relative to an observer outside of the field, clocks go more slowly, as do other processes such as atomic activity and the physical ageing process. The stronger the gravitational field in any place, the more extreme will be the time dilatation. Schwarzschild reasoned that if the total mass of a black hole is thought of as being concentrated at the very centre, as it would seem to be, then at a finite distance from that centre the geometry of space-time would change drastically from that to which we are accustomed. This distance became known as the Schwarzschild radius, and a sphere of that radius around the central singularity is referred to as an “event horizon”. Science fiction has popularised the concept of the event horizon to the extent that most people are aware that it marks the point of no return, not only for any unwary space traveller who might cross it, but also for anything else, including light, that finds itself inside the sphere. What is less widely realised is that the curvature of spacetime in the region of the event horizon is so extreme that it gives rise to a phenomenon so strange that it seems to defy all logical reasoning. To an outside observer any object approaching the Schwarzschild radius appears to take an infinite time to penetrate the event horizon. If that object were an astronaut armed with a clock, her observation would be that she passed through the event horizon in a finite period of time, nor would she be aware of any abnormalities of time as she did so. The reason for this is that her clock would deviate from that of an observer outside, and at a constant distance from, the event horizon, so grossly that the same event that, observed from the outside, took an eternity, would occur within a finite time within the frame of reference of the free-falling astronaut. Obviously, the two observers are seeing the same event – a unique and immutable spacetime event – yet their interpretations of the time taken for that event to play out could hardly be more different. For the outside observer the other figure is “frozen” for ever at the point of passing through the event horizon; while the falling observer records her uninterrupted passage through the event horizon, without a suspicion of a brief delay, much less an infinite hold-up. It would seem, therefore, that the concept of infinity might be as elusive as the concepts of absolute motion, or absolute rest, and we are left wondering if any of these concepts can form a meaningful part of our observable Universe. What we must not lose sight of, though, is that it is our perception of infinity, not necessarily infinity itself, that is relative.
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It is worth spending a little more time thinking about the situation in which an astronaut is observed falling through an event horizon. Above, I described this as a unique and immutable spacetime event; so, how can something that is unique and immutable appear to be so different in different frames of reference? Of course, any apparent dichotomy is illusory because each spacetime event is unique only in the frame of reference of each observer. nowhere is there any change to a spacetime event, nor does a single event occur in a different guise in any single frame of reference.
If this interpretation of the effects of spacetime distortion is correct, it must mean that any body, any fragment of cosmic debris, that has ever (in its own frame of reference) fallen through an event horizon into, for example, a black hole, must, in the frame of reference of any outside observer who stops to look, be still stuck at the event horizon. The entire accretion history of a black hole since the formation of its event horizon should be visible to any observer whose technology allows him or her to manoeuvre into the right position. Of course, an observer will see these things by virtue of the light reflecting from them, but because the objects will not have crossed the event horizon, in the observer’s frame of reference, this should not be a problem. Perhaps there is a problem, though, because strange as this duality of time might seem, it is even stranger to realise that, outside the frame of reference of the distant observer, all this material is not there, because it has long since plunged down the ever steepening gravity well into the depths of the black hole. Let us assume that the astronaut passed through the event horizon (in her frame of reference) ten years earlier; and that the distant observer is five light years away. Five years ago, would there have been any light reflecting off the space suit of the astronaut such that the distant observer would be able to see her? Could it be that we, confined as we seem to be within our three dimensions of space and one, strictly linear, dimension of time, are here being given a glimpse of eternity? If eternity is an infinite "now", then there is, indeed, no problem, other than one of interpretation. We will return to this thought later, but we have other things to consider first. One of these things is an alternative way of looking at the problem of the seemingly everlasting accretion sphere of the black hole. Perhaps what popular science books tend to present as a problem is, in reality, nothing more than a recurrence of Zeno’s paradox. If we consider the situation from the point of view of the outside observer as an example of asymptotic decay, in which the infalling object is not simply stuck for ever in the same state, but is gradually vanishing, with its progress being recorded by an asymptotic curve, then, in theory, it would never actually vanish, but in reality, like Zeno’s arrow, it would come to a conclusion. In other words, it would vanish. This seems to be the simplest explanation, and the simplest may well be the best.
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This seems to be the simplest explanation, and the simplest may well be the best.
Excellent pair of posts Bill, and these thought exercises brings another peculiar question to mind:
If both the in falling astronaut and the distant observer are living in the same universe, and we can presume so, the supposed end of all things will surely occur for them both. But the visitor to the black hole will, in his frame of reference, experience it much earlier than the distant observer. Nevertheless, the end will come on a cosmic level at the same time.
Can we therefore conclude that from beginning to end, speaking about the universe that is, our cosmos can be both instant and very prolonged. What does this say about time? And depending on where one finds themselves, has the future already been framed for us and we that, so to speak, take our time are only living each frame one frame at a time while another can experience them all at once?
Aahhhhhh the mystery of it all!!!
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As we are moving into the realms of philosophy, also adding that it, after all, is a Friday with all what that imply :)
What is it that tells you that anything happen?
Light (radiation).
And what is so peculiar about this light?
It's a constant.
Radiation is the force and information carriers defining a universe. And in my mind also the definer of a arrow.
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Interesting comments, Ethos; brings to mind the "Omega Point theory". This quote from Paul Davies seems relevant, and links to yor_on's comment about light. He is describing a hypothetical situation in the closing seconds of the contracting Universe in which a (presumably disembodied) intelligence still remains.
“Whatever the speed of thought, the speed of light remains unchanged, and light can travel at most a distance of one light-second per second. Because the speed of light defines the limiting speed at which any Physical effect may propagate, it follows that no communication can take place between regions of the universe more than one light-second apart during the final second. (This is another example of an event horizon, not so much like that which prevents information from escaping from a black hole, but more like that which prevents information from reaching us from beyond the sort of information horizon which we discussed elsewhere.) As the end approaches, so the size of communicable regions and the number of particles they contain shrink towards zero. For a system to process information, all parts of the system need to communicate. Clearly, the finite speed of light acts to restrict the size of any “brain” that may exist as the end approaches, and this in turn could limit the number of distinct states – hence thoughts – such a brain could have.
To evade this restriction, it is necessary for the final stages of cosmic collapse to deviate from uniformity – and in fact this eventuality is very probable. Extensive mathematical investigations of gravitational collapse suggest that as the universe implodes, the rate of collapse will vary in different directions. Curiously, it is not simply a matter of the universe shrinking faster in one direction than another. What happens is that oscillations set in, so that the direction of most rapid collapse keeps changing. In effect, the universe wobbles its way towards extinction in cycles of ever-increasing violence and complexity.
Barrow and Tipler conjecture that these complicated oscillations cause the event horizon to disappear first in this direction then in that, enabling all regions of space to keep in touch. Any superbrain would need to be quick-witted and switch communications from one direction to another as the oscillations brought more rapid collapse in one direction and then another. If the being can keep pace, the oscillations could themselves provide the necessary energy to drive the thought processes. Furthermore, in simple mathematical models there appears to be an infinite number of oscillations in the finite duration terminating in the big crunch. This provides for an infinite amount of information processing, hence, by hypothesis, an infinite subjective time for the superbeing. Thus the mental world may never end, even though the physical world comes to an abrupt cessation at the big crunch.”
BTW, the book is in the loft, but I can get the title if anyone is interested.
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Interesting thought Bill. Haven't seen that one before.